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Engineering Applications of Artificial Intelligence 19 (2006) 721–730

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Neural management for heat and power cogeneration plants

Giovanni Cerri�, Sandra Borghetti, Coriolano Salvini

Department of Mechanical and Industrial Engineering, ROMA TRE University, Via della Vasca Navale 79, 00146 Roma, Italy

Received 20 May 2006; accepted 21 May 2006

Available online 28 August 2006

Abstract

This paper deals with the problem of finding the optimum load allocation on machines and apparatuses in complex Cogeneration Heat

and Power (CHP) plants. A methodology based on Neural Networks (NN) has been developed. A database has been populated by using

a real plant simulator.

Two kinds of plant neural models have been trained, the first consists in an Identification Neural Model (INM) that provides a

‘‘picture’’ of the actual plant status by using monitoring data as input; the second consists in an Optimum Load Allocation Neural Model

(OLANM) whose inputs are boundary conditions and outputs the Degrees of Freedom corresponding to the optimum operation set

points. To reduce the relevant computational effort required to populate the training databases a sequential chain of neural models has

been arranged. The methodology has been applied to a typical industrial cogeneration plant installed in Turin (Italy). Results are

presented and discussed.

r 2006 Elsevier Ltd. All rights reserved.

Keywords: CHP; Plant models; Optimisation; Diagnosis; Neural networks

1. Introduction

Cogeneration Heat and Power (CHP) Plants are used tofeed electric and thermal power (such as hot water, chilledwater and steam) contemporaneously for industrial anddomestic processes. They are usually equipped with parallelcomponents, such as heat engines (diesel engines or gasturbines) and steam turbines. Parallel fired steam gen-erators and waste heat recovery boilers (installed in theengine exhaust paths) supply steam at various pressure andtemperature levels.

One of the major management tasks of CHP operationsis related to the achievement of the optimum of aneconomic objective that can represent cost (to be mini-mized) or profit (to be maximised). The objective caninclude aspects related to energy savings, pollutant emis-sion reduction or particular goals to achieve benefits.

Optimum plant management can be related to twoproblems: (i) the optimum load allocation among plantparallel groups, and (ii) the production planning inter-

e front matter r 2006 Elsevier Ltd. All rights reserved.

gappai.2006.05.013

ing author. Tel.: +3906 55173251; fax: +39 06 5593732.

ess: cerri@uniroma3.it (G. Cerri).

preted as the sequence of a significant number of loadallocations resolved with a step-by-step numerical integra-tion along the time.Optimum management is a complex task especially when

thermal and electric loads can be allocated on several plantcomponents operating in parallel arrangements. In order toreach an effective result the actual statuses of machines andapparatuses have to be identified. Availability and effi-ciency (or other suitable indexes of performance) of eachcomponent can be evaluated from monitored data byintroducing functions or factors representing actual com-ponent statuses.The simulation of complex CHPs is a key task for

management purposes. Traditional simulators are based onapproximation formulas related to physical and chemicalaspects as well as empirical descriptions of complexphenomena. CHP plant simulators can be really accurate,they may contain the reality of machines and equipmentas well as status functions that represent the time-dependent behaviour related to the performance deteriora-tion due to fouling, erosion, corrosion etc. (Diakunchak,1992; Mathioudakis et al., 1999; Cerri et al., 2006). Suchsimulators are described by highly non-linear equations

ARTICLE IN PRESSG. Cerri et al. / Engineering Applications of Artificial Intelligence 19 (2006) 721–730722

and inequality functions and thus require iterative solu-tions relating to simultaneous and sequential methodolo-gies (Cerri, 1996).

The solution of the optimisation problem usuallyrequires a really long CPU time and memory occupancy.Thus if results have to be produced in real time or quasireal time to support plant operator decisions traditionalequation-based simulators are inapplicable. Neural Net-works (NN) calculation approach demonstrated to bereally useful in these types of applications leading to reallyshort CPU time and almost no memory occupancy.

Traditional physical, chemical and empirical-basedapproximation methodologies can be substituted by anumerical function approximation based on NNs. NNshave been successfully applied to a number of engineeringproblems, which are highly non-linear in nature. Forexample, in the field of plant control, Pham and Oh (1999)explored the approximation of the inverse dynamics ofunknown plants using recurrent back propagation NNs.The proposed scheme can be used for on-line adaptivecontrol of time-variant systems. In the field of powerproduction, DePold and Glass (1999) and Kobayashi andSimon (2001) investigated NN applications to Gas Turbineprognostics and diagnostics. NNs have been applied byBoccaletti et al. (1999) to accurately evaluate thermody-namic processes quantities avoiding iterations.

In order to assess the feasibility of NN approach inpower plant process evaluations Boccaletti et al. (2001)applied a ‘‘feed forward’’ technique with a back propaga-tion learning algorithm to set up the model of a GasTurbine equipped with a Heat Recovery Steam Generator(HRSG). Data from physical-empirical plant simulatorhave been used to train such neural model. The NNsimulator demonstrated to perform calculations in a reallyshort computing time with a high degree of accuracy.

In the field of combustion, Cerri et al. (2003) successfullyreplaced a traditional chemical kinetics model with adetailed chemistry neural model for methane/air combus-tion and integrated it in a finite volume ComputationalFluid Dynamics (CFD) code.

CHP plants are equipped with Distributed ControlSystem (DCS) that provides a relevant number ofmeasured data that could be used to train a neural model.However, the direct utilisation of plant-monitored quan-tities presents some drawbacks. Firstly, it has to be pointedout that the plant is not available for ‘‘ad hoc’’ measure-ments campaigns aimed at producing a data set coveringthe whole range of operation of the plant. Moreover, sinceplant performance depends heavily on ambient conditions,data should be collected on annual basis. As previouslystated, plant behaviour changes continuously due todeterioration performance occurring with time. Besides,relevant changes in plant behaviour can be observedat particular instants as a consequence of maintenanceinterventions (i.e. compressor washing). Thus measureddata collected in different times refer to virtuallydifferent plants, each of them characterised by a different

level of performance deterioration affecting machines andapparatuses.In order to overcome the previously stated difficulties

(inherent in the use of monitored data for trainingpurposes) physical-empirical simulators apt to reproducethe real plant behaviour in each operating condition havebeen set-up. In order to account for each actual plantstatus Actuality Functions (af) have been introduced in themodels. af coefficients referring to a certain operatingcondition are identified by using the correspondingmonitored data. By means of these simulators, perfor-mance plant maps have been produced and utilised to trainplant neural models. In the end the plant neural modelsreceive boundary conditions (load demands, ambientconditions, fuel prices etc.) and monitored data as inputand return the optimum load allocation as output.The set up of a neural model devoted to the optimum

load allocation of a complex system such as a CHP plantrequires the population of a Data Base of relevant size. Toreduce the needed computational effort, an approach basedon neural models of plant components used in a cascadearrangement is proposed and discussed.

2. CHP plant modelling

Modelling approach concepts are widely explained in(Cerri, 1991, 1996; Cerri et al., 1999, 2000, 2005; Boccalettiet al., 2000). To introduce the reader to such concepts asynthesis is here reported.A cogeneration plant may be seen as a pool of

cogenerative plant sections made of various componentsand apparatuses, which collaborate in the production ofelectric and thermal power. The external electrical andthermal networks can be seen as market reservoirs(i.e. electric and thermal power may be sold or bought).The plant model is based on a modular description in a

really broad sense. Each module can represent a singlecomponent or a group of them. The module library allowsan easy configuration of complex plants. Each modulecontains the physical-empirical component model thatmathematically can be expressed by a set of non-linearequations that represents the conservation of mass, energy,momentum, and entropy and includes constitutive andauxiliary equations. The last ones describe processes andphenomena occurring in the machines and apparatusesallowing the calculation of quantities related to sourceterms in the conservation equations. Other sections of thecomponent model contain functions and correlationsrelated to emissions, costs and control aspects.Models of compressors, combustion chambers, gas and

steam expanders, heat transfer devices, pumps, mixers,valves, connections, splitters, junctions, electric generators,electric grids, etc. have been developed. The above modelsare generic in nature and can be applied to commerciallyavailable and ad hoc-designed components.To fully establish the model of each component two

concepts have been introduced. The first one is the

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‘‘Reality’’, which identifies the deviation from a ‘‘standardexpected’’ situation defined by the model and the realsituation which can be observed on the real plantcomponent. To allow the model to reproduce the realcomponent behaviour in a reference situation suitableReality Functions (rf) are introduced. Usually, formachines and apparatuses, such situation refers to ‘‘Newand Clean’’ conditions (Cerri et al., 2005, 2006).

Reality functions are calculated by solving a minimisa-tion problem whose objective function is a Root MeanSquare Error (RMSE) evaluated by comparing measuredand calculated quantities. The former can be obtained bycarrying out ‘‘ad hoc’’ campaigns or at least collected atplant-acceptance tests.

During operations the component behaviour changescontinuously due to phenomena such as fouling, erosion,wear, etc. Therefore, the second concept introduced is the‘‘Status’’, here considered as the deviation of the realcomponent behaviour from ‘‘New and Clean’’ conditions.The actual plant status is taken into consideration byintroducing Actuality Functions (Cerri et al., 2005, 2006)which allow the model to reproduce the real behaviour ofany particular real present plant component with referenceto: (a) work exchange and heat transfer; (b) dissipativephenomena related to internal friction and couplingbetween fluid and surfaces; (c) effective flow functionmodifications. It is assumed that component performancedegradation corresponds to af less than one. af identifica-tion is carried out by using plant DCS-monitoredquantities.

As a result, the model of the generic kth component of aCHP plant can be expressed by a set of equations:

Fkðnk; dk; rfk; afk; xkÞ ¼ 0 (1)

and inequalities:

Dkðnk;dk; rfk; afk; xkÞX0, (2)

where nk represents the vector of Degrees of Freedom(DOFs) which specify the component operating point (i.e.the load allocated on the component itself), dk the vector ofboundary conditions (site conditions, prices of thermal andelectric power and costs of consumables), rfk and afk theabovementioned Reality and Actuality Functions. xk is thevector of relevant process and state quantities such aspressures, temperatures, mass flows, fluid compositions,mechanical stresses, electrical and thermal powers, etc.

The set of inequalities Dk expresses conditions establish-ing the feasibility domain of the solution.

The model of the whole plant is built by matching thecomponent models. The plant simulator is represented by aset of equations:

Fðn; d; x; rf; afÞ ¼ 0 (3)

and inequalities:

Dðn; d;x; rf; afÞX0, (4)

which relate plant quantities x to boundary conditions d,rf, actual plant statuses (af) and DOFs n.It has to be pointed out that when component models

are matched together to assemble the whole plant some ofthe component boundary conditions dk as well as someDOFs nk have to be treated as elements of plant unknownvariables vector x. For example, considering the compres-sor model alone, inlet pressure, temperature and fluidcomposition and exit pressure may be assumed asboundary conditions. If operations at variable rotationalspeed are allowed and inlet guide vanes (IGV) and otheradjustable stator vanes exist, DOFs specifying the loadallocated on the component are the rotational speed andthe settings of variable geometry rows. By assuming theabove quantities the model can be solved for xk (mass flow,exit temperature, pressures temperatures and fluid velo-cities along the gas path, etc). When the same compressor isconnected to other components to build the model of a gasturbine plant, the pressure at compressor exit and therotational speed are defined by thermo-fluid-dynamic andmechanical matching conditions with the other plantcomponents (combustion chamber and gas expander).Thus they have to be regarded as plant-dependent variableswhose values are determined after solving the plantsimulator.The equations set F contains the subsets Fk of each

component module and further conditions expressingmatching constraints which establish the correct couplingamong plant components.As a first step rf have to be identified to reproduce plant

‘‘New and Clean’’ behaviour. The adopted solutiontechniques are widely discussed in Cerri et al. (2005). Sincerf values do not change during plant operations they can beimplicitly included in the structure of the model itself.For plant optimum management purposes three kinds of

problems have to be solved: (1) the matching of the actualcomponents; (2) the identification of the status of eachcomponent; (3) the optimum load allocation.The solution methodology is general with respect to the

specific problem. According to the modular approachdescribed in Cerri (1996) the block diagram is shown inFig. 1. The approach consists in establishing an objectivefunction (Fob) and in solving the following problem:

Search z which :Minimise Fob Fðn; d;x; afÞ���

¼ 0;Dðn; d;x; afÞX0�, ð5Þ

z being the vector of unknown quantities. Fob and z

structures change depending on the kind of problem faced:

(1)

Matching problem: In this kind of problem DOFs areassumed (n ¼ n�), boundary conditions are known(d ¼ d�) as well as actuality functions (af ¼ af�).Unknowns are the plant quantities z ¼ x. Fob isrepresented by the plant unbalance:

D ¼ FTF (6)

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Variable attribution to modules

Initial guess z°

Module J Module NModule 2Module 1

Calculation of Fob

Min Fob ?

STOP

YES

NO New z

Fig. 1. Modular structure of plant model.

G. Cerri et al. / Engineering Applications of Artificial Intelligence 19 (2006) 721–730724

that vanishes when the solution is achieved. Thus therelated model can be seen as a forward plant simulator.

(2)

Status identification: In this kind of problem vectorsn ¼ n� and d ¼ d� are given. Plant DCS provides a setof monitored quantities xm corresponding to a subsetof plant variables x . The unknowns to be determinedare z ¼ ðxm�xÞ [ af.The objective function Fob is still the plant unbalanceand the matching constraint structure is still taken intoconsideration. The related model can be seen as anIdentification Model.

(3)

Optimum load allocation: In this case the unknown setof variables is represented by the DOFs that need to beoptimised no � n and the x quantities. Other DOFs notestablished by optimisation na are given ðna ¼ n�aÞ aswell as the boundary conditions (d ¼ d�). A costfunction (to be minimised) is introduced:

Fob ¼XN

i¼1

Fc;ipc;i �XM

j¼1

Fs;jps;j þ D. (7)

The first term on the right-hand side expresses theproduction cost: Fc,i is the amount of the ith quantityrequired (fuels, other consumables including the plantitself, electricity and heat bought from the externalnetworks, etc.) and pc,i the related cost. The second termrefers to incomes obtained by selling thermal and electricpower: Fs,j is the amount of the jth good sold to theexternal electric grid and thermal network and ps,j therelated selling price.

Matching constraints and therefore plant unbalance arestill considered. Various optimisation techniques based onEquality Constraint Recursive Quadratic Programming(ECRQP), Genetic Algorithms (GA) and SimulatedAnnealing (SA) as well as hybrid GA-ECRQP and SA-ECRQP have been applied and compared (Cerri, 1996;Cerri et al., 2005; Boccaletti et al., 2000). The choice of themost suitable one depends on the peculiar problem to besolved. For example, an optimisation algorithm based onquadratic programming has been successfully adopted by

Al-Shayji et al. (2005) to simulate and optimise multistageflash desalination processes, and by Elkamel (1998) todetermine the best oil recovery efficiencies in heterogeneousreservoirs.With reference to the case application presented in the

following, an optimisation technique developed by Cerri(1991, 1996) based on ECRQP has been adopted.The constrained optimisation problem represented by

Eq. (5) with the objective function expressed by Eq. (7) issolved through the introduction of two merit functions, thepenalty function:

Pðz; rÞ ¼ Fobþ ð1=rÞvTv. (8)

r being the penalty parameter and v being the vector ofactive constraints, and the Lagrange function:

Lðz; kÞ ¼ Fobþ kTv. (9)

k being the set of Lagrange multipliers related to theconstraints.The parameter r must be positive and when it tends to

zero the minimum of P(z,r) tends to the minimum of Fob.The minimum of L(z,k) also coincides with the minimumof Fob.The solution is found starting from an initial tentative

solution x1. At the generic kth iteration the step dk (whichmoves the tentative solution from zk to zk+1 ¼ zk+dk) issearched by solving a quadratic-programming problem.The objective function is a quadratic approximationof Fob:

Fq ¼ f kdk þ1

2dTkHkdk. (10)

fk being the gradient of Fob and Hk its Hessian matrix,both evaluated at point zk.Second-order Taylor’s series expansions around point zk

lead to approximate expressions of the penalty functiongradient:

rPðxk; rkÞ ¼ f k þHkdk þ2

rk

ðATk vk þ AT

kAkdkÞ (11)

and the Lagrange function gradient:

rLðxk; lkÞ ¼ f k þHkdk þ ATklk (12)

Ak being the Jacobian matrix of active constraintscalculated for z ¼ zk

The search of dk is performed by imposing the con-dition of minimum P ðrPðxk; rkÞ ¼ 0Þ and using furtherconditions resulting by equating the right terms of Eqs. (11)and (12).Therefore the steps towards the minimum of Fob(z) are

performed along the locus of penalty function minima.In the implemented algorithm, first order derivatives of

fk and Ak are evaluated by adopting a finite differencescheme. The Hessian matrix is updated by using theBroyden–Fletcher–Goldfarb–Shanno (BFGS) formula.

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DCS

COGENERATION

PLANT

regulators

INM

OLANM

af

PONT

d, ξaxopt, ξopt

xm

Fig. 2. Plant optimisation neural tool.

G. Cerri et al. / Engineering Applications of Artificial Intelligence 19 (2006) 721–730 725

3. Plant neural model

As already stated, the solution of the traditionalsimulator may require long CPU time to be evaluated.Thus the NN approximation function approach has beenpursued. By using traditional plant simulators the compu-tational effort (in terms of computing time and memoryoccupancy) needed to populate the training DBs could bereally heavy. To reduce such effort a method based on NNsused in a cascade arrangement has been adopted.

The best approach has been found by considering thatall the above three stated problems require the solution of amatching problem. This means that a suitable choiceconsists in establishing the balanced correspondencebetween input and output for each component by solvingfor xk the problem represented by Eqs. (1) and (2).Component modules have a relatively simple structurethus their solution do not require relevant computationalefforts. This allows an easy production of a componentdatabase (CDB) of suitable size for each componentinvolved. For matching purposes the CDB is used toestablish the following one-to-one correspondence (whereF.C.S. stands for forward component simulator):

nk [ dk [ afk !F:C:S:

xk. (13)

This can be reproduced by a NN. Thus for each of the Ncomponents a component neural model (CNM) can bebuilt. The matching problem is then solved by substitutingthe traditional modules with the CNMs in Fig. 1. Thisreduces the computational load to get balanced plantsolutions because only matching constraints must be takeninto consideration. This matching procedure allows theestablishment of the one-to-one correspondence throughthe forward plant simulator (F.P.S.):

n [ d [ af !F:P:S:

x. (14)

The related DB can be used to build two kinds of neuralmodels. A plant forward neural model (FNM) can be setup to reach a fast solution to the matching problemaccording to Eq. (14).

Moreover, each vector in Eq. (14) can be divided intotwo sub-vectors (e.g. x ¼ x0 [ x00; d ¼ d0 [ d00, etc.). Theplant simulator (P.S.) represented by Eqs. (3) and (4)allows the establishment of a one-to-one correspondenceamong the elements of the vector v0 ¼ n0 [ x0 [ d0 [ af 0 andthose of the vector v00 ¼ n00 [ x00 [ d00 [ af 00:

v0 !P:S:

v00. (15)

v00 can be arbitrarily chosen provided that the inversesolution of the implicit functions representing the plantsimulator with respect to the variables constituting v00

exists. In practice, v00 contains the actuality functioncoefficients while the quantities constituting v0 are chosenamong those reliably measured by the plant DCS. Thus thefollowing correspondence representing the identification

plant simulator (I.P.S.) can be established:

n [ d [ xm !I:P:S:

af; (16)

where quantities in the left term are given (n and d) ormeasured by the DCS (xm). Consequently, an INMreproducing the correspondence expressed by Eq. (16)can be set up.Optimum load allocation (i.e. the best allocation of

electrical and thermal loads on machines and apparatuses)is achieved by using the CNMs already defined. Againoptimum load allocation is made according to the schemeof Fig. 1. The resulting DB establishes the correspondencebetween given DOFs na, boundary conditions d, compo-nent statuses (af) and the optimum load allocationexpressed by nopto and xopt:

na [ d [ af !O:L:A:P:S:

nopto [ nxopt, (17)

where O.L.A.P.S. stands for optimum load allocation plantsimulator. Such a correspondence can be reproduced witha NN indicated as OLANM.Finally, INM and OLANM are connected in a cascade

arrangement to obtain a plant optimisation neural tool(PONT), schematically presented in Fig. 2, which directlyrelates measured data from DCS and given quantities tooptimum load allocation:

na [ d [ xm !P:O:N:T:

nopto [ xopt. (18)

4. Case application

The described approach has been applied to a realcogeneration system. With reference to the selectedapplication, the following section describes and discussesthe various steps that lead to the realisation of theoptimisation tool.

4.1. Cogeneration plant description

The cogeneration unit discussed here is a section of theFiat Mirafiori power plant in Turin, Italy. A schematic

ARTICLE IN PRESS

1= Electric Grid; 2= Feed Water Grid; 3= Fuel Grid;

4= Steam Manifold; 5= Hot Water Manifold; A= GT1;

B= HRSG1; C= GT2; D= HRSG2; E= SB; F= SWHE.

2

E

Steam to theFactory

A

D

1

3

4

5

F

FUELS

HRSG

External Electric Grid

SWHE

SB

Water to the Factory

WH

2

2

B

C

Fig. 3. Scheme of the cogeneration section.

G. Cerri et al. / Engineering Applications of Artificial Intelligence 19 (2006) 721–730726

diagram of the section is presented in Fig. 3. There are 2identical parallel groups constituted by a Gas Turbine(GT) (A and C) with a heat recovery device (HRD) (B andD) constituted by a HRSG and a water heater (WH). TheGT is a TG16 Fiat Avio with a ISO base load of about18MW. In the HRSG steam is produced at 360 1C and2.3MPa and subsequently de-superheated to 320 1C to befed into a MP manifold. The steam capacity is about 22 t/h.The WH follows the HRSG downstream on the gas path; itproduces about 650 t/h of hot water at 140 1C and 0.9MPa.A natural circulation steam boiler (E) is also connected tothe MP steam manifold. It can be fuelled by oil or bynatural gas and its steam capacity is 100 t/h at 320 1C and2.4MPa.

Hot water production also takes place in a group of eightsteam/water heat exchangers (SWHE) (F) fed by steamextracted from the MP manifold. The various machinesand devices are connected by fluid grids (feed water (2),fuel (3), steam (4), hot water (5) and electric grid (1)),through which water, steam and electricity can be suppliedaccording to factory demands.

4.2. Set up of the neural network simulator

As a first step, traditional physical-empirical simulatorsof plant subsystems have been used to produce databasescontaining input and relevant output quantities represent-ing the various operating points. The chosen subsystems,according to the scheme presented in Fig. 3, are 2 GT units,2 HRD units (consisting of a HRSG followed by a WH),one steam boiler and a battery of SWHE. This choice waspractically possible because the production of one DB

string for the GT units requires an average of 10 s and thatfor the other units is slightly less. Thus for example theproduction of the training DB for GT1 took about 12 h ona high-performance PC, which is acceptable.Since the size of the NN training DB depends heavily on

the number of input and output quantities and on thephysical complexity of the problem in study, theseconsiderations have been taken into account when produ-cing the various DBs. DB sizes are summarised in Table 1.The size is equal for GT unit and HRD of both Group 1and 2. Input quantities are ambient conditions, af andDOFs, i.e. the quantities specifying the operating point.Outputs are relevant quantities (powers, temperatures,mass flows, etc.) in the various plant stations. Each DBstring is thus representative of an actual operating point.Each DB has been used to train the correspondent FNM

and INM. From literature and Authors’ previous experi-ence (Boccaletti et al., 1999; Boccaletti et al., 2001; Cerriet al., 2003) Single-Layer Feed-Forward NNs trained withan error back-propagation algorithm have been selectedfor all the networks. The sigmoid activation function hasbeen adopted.In order to train the NN, input and output quantities are

divided into two subsets: training and validation data. NNsare trained through an iterative process of weight adjust-ments. The training of the NN is carried out using datastored in the training DB and presenting each example tothe NN for a certain number of iterations (epochs). Thelearning process is controlled through the known desiredoutput (supervised learning process). During this process,the learning algorithm modifies the weights associated witheach neuron to minimise the mean square error (MSE)

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Table 1

Components DB Size

GT unit FNM HRD FNM GT unit INM HRD INM SWHE FNM SWHE INM SB FNM SB INM

Training+validation 4095 4995 7875 17,271 4950 4365 4797 2313

Test 400 500 700 1000 400 400 500 200

0.0E+00

5.0E-05

1.0E-04

1.5E-04

2.5E-04

3.0E-04

3.5E-04

4.0E-04

4.5E-04

5.0E-04

65 70 75 80 85 90M

ean

Sq

uar

e E

rro

r (M

SE

) Number of Hidden Neurons

2.0E-04

MSE TRAININGMSE TEST

Fig. 4. GT1 FNM—optimisation of the number of hidden neurons.

0 4000 6000 8000 10000 12000 14000

Mea

n S

qu

are

Err

or

(MS

E) 0.010

0.0090.0080.0070.0060.0050.0040.0030.0020.0010.000

2000Number of Epochs

GT1 Direct NN Architecture 12 - 80- 16

Training Set 4095

Fig. 5. GT1 FNM–MSE vs. number of epochs.

G. Cerri et al. / Engineering Applications of Artificial Intelligence 19 (2006) 721–730 727

between the target, i.e. the desired value, and the networkactual output. To avoid instabilities the intensity of thismodification is limited by a coefficient known as learningrate, put equal to 0.9.

Validation dataset (10% of the total DB) is used forcross-validation during the learning process: it is presentedto the NN every NV epochs and if the calculated MSE islower than the previous one, the new weights are accepted.The learning process terminates when the expected error isachieved or all the epochs have been performed. Thisprocedure is repeated to find the optimum number ofhidden neurons while keeping others NN parametersconstant.

Lastly, after the optimisation of the number of hiddenneurons, the general performance of the NN is assessedusing a new set of data (test DB) by comparing calculatedand the desired (expected) values. For sake of brevity, onlythe optimisation of the HN number for GT1 Unit FNM ispresented in Fig. 4.

Fig. 5 shows the MSE as a function of the number ofEpochs for the optimised number of HN. An analysis ofthe errors shows that nearly all of the calculated pointspresent absolute errors that are less than 3 1C fortemperatures, 4 kPa for pressures, 0.1MW for powers.This level of accuracy is regarded as satisfactory foroptimisation and status recognition purposes, consideringthat these errors are of the same order of magnitude of theuncertainty characterizing the monitored quantities. Forexample fuel consumption, which represents the mostrelevant contribution to the plant running costs, isestimated with an accuracy of some 0.5%. A big advantageof these neural models is their speed: one calculation withFNMs of GT units takes on average 140 ms, for HRD105 ms are needed, while FNMs of SWHE and SB employ40 and 50 ms, respectively. INMs are of comparable times.

These NNs have been matched to further proceedtowards the construction of the DB of whole cogenerationsection.

By matching the INMs of plant subsystems a DB of18,000 strings has been generated to train the INM of thewhole cogeneration section. One calculation with this INMtakes on average 50ms whilst the corresponding physical-empirical identification simulator employs 100 s, resulting2000 times faster. Regarding the forward calculation of thewhole section, a matching programme has also been set up.The corresponding traditional forward simulator takesabout 30 s for one run. Since the matching programme withFNMs has proved to be very fast, the decision has beentaken to proceed directly with the production of the DB of

the optimum load allocation, according to Eq. (17),without passing for the non-optimised DB of the wholesection described by Eq. (14). An optimisation techniquebased on ECRQP has been adopted. With this programmeeach run takes approximately 65ms, allowing a really fastproduction of the DB of 25,000 strings with whichOLANM has been trained.Finally, the INM and OLANM have been matched to

produce a DB to train what has been called PlantOptimization Neural Tool (PONT). Plant data gatheredby DCS enter the PONT which also receives input datasuch as factory electricity and heat demands, fuel andconsumable costs, and gives as output all the quantitiesrequired to specify optimum plant operations: productioncost and thermal and electric load distribution on parallelmachines and apparatuses and the values of the set point

ARTICLE IN PRESSG. Cerri et al. / Engineering Applications of Artificial Intelligence 19 (2006) 721–730728

quantities required by the plant control system. Thecorresponding physical-empirical plant simulator takesseveral minutes to perform the optimisation of one point,depending on the number of iterations required to get thesolution. Therefore only by applying neural models it ispossible to produce a suitable, practical tool for optimumload allocation.

4.3. Results

In this section, some examples showing the capability ofthe neural tool to achieve the optimum load allocation arepresented and discussed.

As stated before, the plant produces steam and hot waterto satisfy the factory thermal demands. Furthermore, theelectric power can be exchanged with the electric grid (soldor purchased).

Optimum load allocation is performed through theminimisation of a cost objective function like that ofEq. (7). In particular, this function includes the cost of fuel(natural gas) and consumables (water, lubricants, etc.), theplant amortisation and depreciation, the latter accountingfor when a component is operated outside its designconditions. Earnings from the sale of electric power arealso included.

The identification of the actual status of plant compo-nents has been performed by using a suitable subset ofavailable DCS data. For sake of brevity, and because oftheir relevance to the performance of the plant, in thefollowing only the GT actuality functions are detailed.

Table 2

GT1 and GT2 actuality function coefficients

GT1 GT2

Compressor afl_c 0.970 0.990

afw_c 0.992 0.991

afb_c 0.984 0.986

Expander afl_e 0.973 0.998

afw_e 0.995 0.999

afb_e 0.986 0.997

Filter af_fil 0.978 1.000

Table 3

Tariffs and factory requests

Case # Tariffs

Fuel (h/Nm3) Pel,purchased (h/kWh) Pel,s

1 0.2 — —

2 0.2 — —

3 0.2 0.140 0.12

4 0.4 0.040 0.03

5 0.2 0.092 0.08

6 0.2 0.040 0.03

Pel: electric power; ms: steam mass flow; Qw: thermal power from hot water.

Such functions are related to: (i) compressor losses(afl_c); (ii) compressor work exchange capability (afw_c);(iii) compressor effective flow functions (afb_c); (iv)expander losses (afl_e); (v) expander work exchangecapability (afw_e); (vi) expander effective flow functions(afb_e); (vii) filter pressure losses (af_fil). The number ofavailable data suggested the adoption of a zero-orderpolynomial form. af coefficients for the GT units of bothGroups 1 and 2 are presented in Table 2.It can be noted that the af coefficients calculated for the

GT1 are lower than those of GT2. This implies that the gasturbine of the first group presents a higher level ofperformance deterioration.The neural tool for optimum load allocation has been

applied to some cases. Data representing the boundaryconditions are reported in Table 3. Fuel costs andelectricity prices have been chosen to highlight how theirvariation influences plant operations. Results are given inTable 4.Case # 1 is taken as the reference one. It is assumed that

no exchange of electric power with the external grid canoccur. A reduced electric load is allocated on GT1 by theneural tool because of the higher deterioration of themachine.Case # 2 refers to the same boundary conditions and

requests of Case # 1, but all the components are assumed as‘‘New and Clean’’. As expected, the same electric load isallocated on the GT units of both groups. When the gasturbine operates with a higher performance, the exhaustgas temperature is lower. As a consequence, the productionof steam and hot water in the HRSG and WH followingthe GT is lower than that of Case #1. Factory thermalrequests are satisfied by an increase in the steam mass flowgenerated in the steam boiler. Comparison between the2 cases shows the influence that the actual status ofcomponents has on the results of the optimum loadallocation. This fact highlights the importance of havinga tool for status recognition to obtain results responding toreal situations. This tool could also be useful in the decisionof cleaning interventions.In the remaining cases, it is assumed that the electric

power can be exchanged with the external grid. Case # 3 ischaracterised by a high selling price of the electric power

Factory requests

old (h/kWh) Pel (MW) ms (kg/s) Qw (MW)

30.0 20.0 120.0

30.0 20.0 120.0

0 30.0 20.0 120.0

5 30.0 20.0 120.0

0 20.0 10.0 60.0

5 20.0 10.0 60.0

ARTICLE IN PRESS

Table 4

Results

Case # GT1 GT2 SB SWHE mf (kg/s) Pel,sold (MW) Ctot (h/h)

Pel (MW) ms (kg/s) Qw (MW) Pel (MW) ms (kg/s) Qw (MW) ms (kg/s) Qw (MW)

1 14.50 6.04 43.80 15.80 6.08 43.90 21.6 32.30 4.29 — 4529

2 15.17 5.35 41.80 15.17 5.35 41.80 24.52 36.40 4.28 — 4492

3 19.50 7.26 46.50 19.50 7.05 46.10 17.53 27.40 4.59 8.73 3954

4 13.55 5.66 42.60 14.80 5.66 42.80 23.25 34.60 4.24 �1.97 8749

5 19.50 5.34 28.60 19.50 4.88 26.30 2.78 5.10 3.70 18.84 2630

6 9.10 1.88 18.70 13.70 5.06 40.70 4.60 0.50 2.84 �2.63 2962

Pel: electric power; ms: steam mass flow; mf: fuel mass flow; Qw: thermal power from hot water; Ctot: total hourly costs.

G. Cerri et al. / Engineering Applications of Artificial Intelligence 19 (2006) 721–730 729

(0.12 h/kWh). For this reason, it is convenient to run boththe GT units at peak load, although GT1 is degraded andthus presents higher operational costs. The electric powerexceeding the factory electric demands (about 8.7MW)is sold to the external grid. Earnings from this sale resultin a cost reduction of some 12% compared with thereference case.

In Case # 4 the fuel price is double than that of Case # 1(0.4 h/Nm3) and a low price of the purchased electricity isassumed (0.04 h/kWh). Plant power production is lowerthan that required by the factory, because in this case it isconvenient to purchase about 2MW from the external grid.Nevertheless, the electric production is kept quite highbecause of the need to produce steam and hot water in theHRSG and WH to satisfy the thermal requests.

Case # 5 is characterised by reduced factory requests andquite high electricity prices, whilst the fuel price is the sameof Case # 1. The production of electric power is themaximum possible and some 19MW are sold to theexternal grid.

Case # 6 presents the same factory requests as Case # 5but with lower electricity prices. Cost minimisation impliesthe purchase of some 13% (2.6MW) of the requestedelectric power. It can be observed that, due to the diversedeterioration levels, loads allocated on the GT unitsare considerably different: 9.1MW on GT1 and 13.7MWon GT2.

The above calculations demonstrate the capability of theneural tool to modify the load allocation when boundaryconditions and the status of components vary.

Finally, it has to be pointed out that results are obtainedin a really short computational time (in the order of500 ms).

5. Conclusions

A methodology to set up neural tools to performoptimum load allocations on CHP plant components hasbeen designed and developed. Actual operating conditionsof machines and apparatuses are taken into considerationthrough a status recognition procedure based on plant-monitored quantities.

Traditional physical-empirical component models havebeen used to produce databases to train the neural tool. Inorder to reduce the related massive computational effort,an approach based on intermediate neural models used incascade arrangement has been pursued.The method has been applied to a real cogeneration

plant. The developed PONT has shown a good capabilityto modify load allocation when the status of componentsand boundary conditions vary.The computational time required is really small (some

500 ms). The accuracy in achieving the solution is compar-able with that of traditional physical-empirical plantsimulators.These achievements show the potentialities of the neural

approach for real time or quasi-real time applications tosupport plant management decisions.The application of neural tools for production planning

over a period of time is under investigation and will be thesubject of future work.

Acknowledgements

The Authors wish to express their gratitude to FeniceSpA, in particular to S. Salvador and F. Perin fortheir support and collaboration. Support from MURST,MIUR, EU is also acknowledged.

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