Simulation of Boiler Model in a Cloud Environment

Transcription

1 Proceeings of Avances in Control an Optimization of Dynamic Systems Simulation of Boiler Moel in a Clou Environment Saikrishna PS, Ramkrishna Pasumarthy, Pujita Raman, Sukanya Chakrabarty, L. Siva Kumar Abstract A nonlinear ynamic moel for a rum-boiler simulate in a clou environment is presente. The boiler moel escribes the ynamics of the rum, owncomer, riser, superheater, reheater an economizer by means of ifferential algebraic equations (DAEs). Conservation equations an characteristic curves are use to moel the components of the boiler. From these mathematical moel equations, a program combining DAEs is evelope using MATLAB. The entire setup has been hoste on a private clou, with LabVIEW enabling ata exchange with MATLAB an proviing HMI for remote access. Inex Terms Simulators, Clou, Boiler ynamics I. INTRODUCTION A Power plant simulator is a computer program that simulates the real plant environment for training an research [4], [7]. One of the important reasons for having a simulator is for operator training, as it eliminates the number of plant trips thereby increasing availability an savings/mw of power generate. Beyon their use for training an control system engineering, simulators can be profitably applie to the testing of new technologies. They can act as research test bes to ai the esign, testing, an ebugging of new power plant technologies, such as avance plant control schemes an automation systems. In brief simulators are neee for the following: Operator Training: incluing unerstaning of plant ynamics, operations an HMI Functions. Stuy of control system functions Engineering analysis an optimizing control loops. The broaer motivation for the present work is to evelop a power plant simulator that works efficiently in a Clou environment. The iea of clou is essentially base on taking atasets away from physical servers an placing them on multiple servers on the internet (the clou) [6], [1], [11]. The inherent avantages of clou computing lies in cost-savings, increase spee, flexibility an higher performance to name a few. This iea has alreay been implemente in sectors such as government an financial services. We here explore the possibility of applications in inustrial automation an in particular simulators for power plants. In the present work we restrict the simulator only to hanle the boiler moule of the power plant. Saikrishna PS, Pujita Raman an Sukanya Chakrabarty are with the Department of Electrical Engineering, BITS-Pilani, Hyeraba Campus, Inia. saikrishna.ps,@bits-hyeraba.ac.in, { pujitaraman, chakrabarty.sukanya}@gmail.com Ramkrishna Pasumarthy is with the Department of Electrical Engineering, IIT Maras, Inia. ramkrishna@ee.iitm.ac.in L. Siva Kumar is with the Srikrishna College of Engineering an Technology, Coimbatore, Inia. lingappansivakumar@gmail.com To evelop mathematical moels for boilers capturing the entire ynamics is a aunting task. Many papers present the moels of a boiler at ifferent levels of complexity. Some complicate moels have more than ten non-linear ifferential equations an over one hunre non-linear static equations escribing the esign of all the parts of the boiler [10]. Another class of moels are erive for very limite purposes e.g. overall performance of power station or control of any particular variable. In this case many ynamic equations are neglecte an many variables are not inclue [9]. For a comprehensive survey of these moels we refer to [5] an the references there in. In the current work, the moel presente is something between two categories mentione above an is etaile enough to inclue the ynamics of all the variables which are important in CC/CHP (Combine Cycle/Combine heat an Power) applications, but on the other han it must be simple enough to permit effective control algorithm. The boiler moels, together with the furnace moel, an the incorporation of the attemporation flow into the moel has been etaile in [5] an is use as the main builing block for eveloping moels in the current work. In this paper we simulate the boiler ynamics in a clou environment. For simulation purposes, we use Matlab in aition to Labview for the Human Machine Interface (HMI). We implement a single-cluster installation, using Ubuntu server eition. We have one physical machine which is the clou controller an other machine which acts as a noe controller, which serves as a simple illustration for the simulator in the clou environment. This paper is organize as follows: In Section II, we present the equations escribing the ynamics of the various stages of a rum type boiler. Section III A gives a brief introuction to the clou setup an clou computing. In Section III B we present the basic architecture of setting up the boiler moel in a clou base environment using Matlab, Labview interface. Finally, in SectionIV we present simulation results in the client-server setting on the clou. All the variables an the parameters of the boiler, with their values, have been liste in the Appenix (Section VI) at the en of the paper. II. BOILER DYNAMICS AND SUMILATIONS A typical rum type boiler epicte in Figure 1 is consiere here for case stuy from a fictitious CC/CHP configuration calle Skegton unit [5]. The overall system consists of the following: A single shaft gas turbine 1

2 Proceeings of Avances in Control an Optimization of Dynamic Systems Fig. 2. The boiler subsystem Fig. 1. A rum type boiler Boiler-Single rum, natural circulation, with integrate earator, a superheater, a esuperheater an with an aitional firing Conensing, triple stage steam turbine. Conenser situate at the outlet of the steam turbines Fee water system Steam amission valve, throttle valves an high pressure steam extraction valves for the steam turbine. The boiler subsystem (Figure 2) consists of the following: Combustion chamber Drum Waterwalls (the risers) Superheater Reheater Economizer The exhaust gas from the gas turbine is irecte to the boiler accoring to the steam eman; the rest of the exhaust gas is ischarge to the atmosphere. A waste heat recovery boiler with aitional firing prouces steam which is use by steam turbines to generate power. For a typical rum type boiler feewater is supplie to the rum, in the rum the evaporation of water occurs. The water flows into the owncomers, then enters the risers. In the risers, the heat from the furnace is use to increase the water temperature an eventually cause evaporation. Thus, the circulation of water, steam, an water an steam mixture takes place in the rum, the owncomers an the risers. Steam generate in the risers is separate in the rum from where it flows through the superheater on to the high pressure turbines. It may then be recycle to the boiler in the reheater where its energy content is increase. Desuperheate spray water is introuce in the superheater for control of main steam temperature. The combustion path is also shown in Figure 1. The risers absorb the raiant heat in the furnace. The hot gases leaving the furnace transfer heat by raiation an convection to the superheater. Then the heat is transferre by convection to the reheater an finally to the economizer before exiting the boiler via stack. The burner tilt mechanism is use to change the raiation heat istribution between the risers an the superheater. The boiler is ivie into six moules corresponing to furnace, risers, owncomers, rum, superheater, reheater an economizer. The Skegton Unit: Although capable of representing any particular CC/CHP configuration, the skegton unit currently implemente is not base on existing inustrial installation. The availability of comprehensive CC/CHP plant operating ata in the open literature is virtually nil. This is largely ue to commercially sensitive nature of such information. Consequently the sizing of Skegton unit has been base upon incomplete ata. Detaile information for the boiler moel is available from references cite in [5]. Thus other moules were size to match the boiler. The resulting fictitious CC/CHP plant may or may not be realistic in terms of Engineering practicality, overall efficiency an size. Regarless of this, the Skegton unit satisfies the main esign objectives an represents a valuable tool to conuct research. Sizing ata for Skegton Unit: Corresponing to the steay state operating conitions presente in Appenix for a 45MW (34MW gas turbine + 11MW Steam Turbine). Skegton unit salient full loa operating ata are as follows: Gas Turbine: Output Power 34MW Exhaust gas flow 47 kg/sec Exhaust gas temperature 1016 K Compression ratio 10:1 Boiler (waste heat recovery with supplementary firing): Superheate Steam Pressure 45 bar Superheate Steam Temperature 717 K Superheate Steam Flow 12 kg/sec 2

3 Proceeings of Avances in Control an Optimization of Dynamic Systems Reheate Steam Pressure 13 bar Reheate Steam Temperature 727 K Furnace fuel flow (supplementary firing) 14kg/sec Total output power generate by steam turbine 11MW Moel Assumptions: 1) The moel inclues only the time erivatives of variables, spatial erivatives are not consiere. 2) Polynomial fits to steam tables are use to establish the relations between the steam parameters such as enthalpy, ensity, temperature, pressure. 3) Superheate steam an furnace exhaust gases are treate as ieal gases. 4) Constant volumetric flow is maintaine in owncomers by circulation pumps. 5) Mass flow ynamics for riser an reheater is moele as first orer lag. 6) The moel inclues only the main parts of the boiler using lumpe characteristics for those parts which consist of more than one section (e.g. two sections of a superheater an an attemporator between them, these are lumpe to form one section calle superheater plus atemporator). The boiler is ivie into six interconnecte subsystems as shown in Figure 2. The overall block iagram shows the interconnections between moules in the boiler moel. Each iniviual moule is given accoring to the equations liste below. In orer to have a moel structure to implement it as an algorithm in MATLAB, certain moifications are require, in particular all the algebraic equations are rearrange an reorere in such a way that all the variables on the right han sie are known at the time of calculation. There are 18 state variables namely x F 1, ρ EG, h r, T rt, w r, m L, x D1, x D2, ρ s, T st, X s1, ρ rh, T rh, x RH1, w ro, ρ e, T et, X e1 an forty five algebraic variables epenent on the state variables. h EG = x F 1 ρ EG, p G = R EG ρ EG T g, Q ir = θkv F σt 4 g /ρ EG, T g = h EG h ref + T ref c pg w EG = k F p G Q gs = Q is + k gs weg(t 0.6 g T st ) T gr = T g (Q is Q gs ) c gs w EG Q is = (1 θ)kv F σt 4 g /ρ EG Q rs = k rs w 0.6 EG(T gr T rh ), T ge = T gr 1 c gs 1 w EG Q rs Q es = k es weg(t 0.6 ge T et ), T g1 = T ge 1 1 Q es c gs w EG 1 y = 100(w A + γw G w F R s ) w F R s Differential equations t x F 1 = 1 (C F w F + h A w A + V F h G w G Q ir Q is w EG R s (1 + t ρ EG = 1 (w F + w A + w G w EG ) V F Q ir, Q is, Q rs, Q es, p G Risers: Inputs: w, Q ir, h w, h v, h wv, T v, ρ wv, ρ v K r, V r, M r, C rt, τ r ρ r, h r, T rt, w r Algebraic equations: y 100 ))h EG x = h ( r h wv x, ρ r = + 1 x ) 1 h v h wv ρ v ρ wv Q r = k r (T rt T v ) 3 Differential equations: A. Dynamical equations The following equations escribe the boiler ynamics: Furnace: w r, x t h r = 1 (w h w w r h r + Q r ) ρ r V r t T 1 rt = (Q ir Q r ) M r C rt t w r = 1 (w w r ) τ r Inputs: w F, w A, h G, w G, θ, T st, T rh, T et, h A Drum: k F, k, k gs, c gs, k rs, V F, C F, R s, γ, k es, h ref, T ref Inputs: w e, x, w r, w V, h e, v ow ρ EG, x F 1 V, k ec, r Algebraic equations: m L, x D1, x D2 3

4 Proceeings of Avances in Control an Optimization of Dynamic Systems Algebraic equations h w = x D1 m L, p w = f 3 (h w ), ρ w = f 4 (h w ) T w = f 5 (h w ), w = v ow ρ w, V L = m L ρ w V v = V V L, ρ v = x D2, V v h v = f 5 (ρ v ) T v = f 7 (ρ v ), p v = f 8 (ρ v ), h wv = f 9 (ρ v ) w ec = k ec (T w T v ), L = f 1 10 (V L) f 10 (L) = 1 3 πl2 (3r L) (W 2r)r2 (θ sin θ) ( ) r L where θ = 2 cos 1 r Differential equations: t m 1 = w e + (1 x)w r w w ec t x D1 = w e h e + (1 x)w r h wv w h w w ec h v t x D2 = w ec + xw r w v p v, p w, ρ wv, ρ v, h v, h w, h wv, w Superheater an Attemporator: Inputs: w a, w s, p v, ρ v, Q gs, h v, h a f s, k s, V s, M s, C st, c ps, T ref, h ref p s, T st, x s1 Algebraic equations: h s = x s1, T s = h s h ref + T ref ρ s c ps p s = R s ρ s T s, h f = f 13 (p s ) (p v p s )ρ v w v =, Q s = K s wv 0.8 (T st T s ) f s Differential Equations t ρ s = 1 (W v W s ) V s 1 M s C st (Q gs Q s ) t T st = t X s1 = 1 (Q s + w v h v w s h s + (h a h f )w a ) V s W v, T st, P s, T s Reheater Inputs: P ri, w ri, T ri, Q rs, ρ ri, h ri τ r, k rh, V rh, M r, C rh, c pr, T ref, h ref p rh, T rh, x RH1, w ro Algebraic equations h ro = x RH1, T r = h ro h ref + T ref ρ rh c pr p ro = R r ρ rh T r, Q rh = K rh wri 0.8 (T rh T r ) Differential equations t ρ rh = 1 (W ri W ro ) V rn t T 1 rh = (Q rs Q rh ) M r C rh t x RH1 = 1 (Q rh + w ri h ri w ro h ro ) V rh t w ro = (w ri w ro )/τ rh T rh, P ro, T r, w ro Economiser Inputs: p ei, w ei, w eo, T ei, Q es f e, k e, V e, M e, C e ρ e, T et, X e1 Algebraic Equations: h eo = X e1 /ρ e T eo = h eo h 2 eo p eo = (0.1245h eo h 2 eo h 3 eo) Q e = k e w 0.8 ei (T et T eo ); Differential Equations: t ρ e = w ei w eo V e t T et = Q es Q e M e C e t X e1 = Q e + w ei h ei w eo h eo V e T et, p eo, T eo, ρ e, h eo III. THE CLOUD SETTING A clou is simply a group of interconnecte computers. It can be broaly classifie into two types: public an private. A public clou is available to the general public or a large user group. It is owne by an organization or thir party offering clou services. A private clou is operate solely for an organization. It may be manage by the organization or a thir party an may exist on premise or off premise [6]. Clou Computing is a moel in which a group of computers, forming a clou, offer various services such as storage, servers, infrastructure, applications etc. to a set of users, accessible via the internet. Components of Clou computing In clou computing, users connect to the clou from their computers using the internet. The harware in the clou (an the operating system that manages the harware connections) is invisible to them. A clou is mae up of three elements: 1) Clients: Clients are the computers using the clou service. Users interact with the clou through these client computers. 2) Datacenter: The atacenter is the collection of servers where the ata we store, or the application to which we subscribe is locate. 4

5 Proceeings of Avances in Control an Optimization of Dynamic Systems 3) Distribute Servers: All the servers of the clou nee not be in the same location. In fact, servers are eliberately locate in ifferent places. This gives the service provier more flexibility an security [6].. Boiler Simulations in the Clou Environment Over the years, there has been constant increase in the evelopment of inustrial automation through remote monitoring an iagnosis virtually. By surveying own the existing remote monitoring system use for process plants, we focus on the recent trens an evelopments in the control of equipments an evices in the inustries by remote monitoring through Internet. The objectives of remote monitoring an iagnosis are prevention of unplanne owntime, making optimal control operation an maximizing the operational life of plant assets [3]. An online integrate web base boiler simulator on a private clou takes real-time simulation ata which helps the remote client for further analysis of the process behavior uner ifferent excitations. The reasons for running simulator on a clou are the following: 1) Reuce Cost: Clou technology is pai incrementally, saving organizations money in training their operators. 2) Increase Storage an computational power: Organizations can store more ata than on private computer systems. 3) Highly Automate: No longer o IT personnel nee to worry about keeping software up to ate. 4) Flexibility: Clou computing offers much more flexibility than past computing methos. 5) More Mobility: Operators/clients can access information wherever they are, rather than having to remain at their esks. A. The clou setup Introuction to UEC an Eucalyptus: In orer to run the boiler simulator in a clou environment, we have set up a private clou consisting of three computers within our organization. The clou has been setup using the Ubuntu Enterprise Clou (UEC), which is a stack of applications inclue in the Ubuntu Server Eition The UEC is powere by Eucalyptus [2] which is an open source platform that helps in creating an managing private clous. In an Eucalyptus clou, there are two top level components calle the Clou Controller (CLC) an Walrus. These two components manage the clusters. A cluster is a group of physical machines, calle noes, which host the virtual instances. In each cluster, there are two components that interact with the top level components- Cluster Controller (CC) an Storage Controller (SC). Moreover, each noe will run a Noe Controller (NC) that will control the hypervisor for managing the virtual instances. The various components an their functions are explaine in greater etail below: This setup is shown in Figure 3. 1) Clou Controller: The Clou Controller (CLC) is the front en to the entire clou infrastructure. It monitors the availability of resources on various components of the clou as escribe above. It also ecies which Fig. 3. The Clou Setup clusters will be use for provisioning the instances. In aition, it monitors the running instances. 2) Walrus Storage Controller: The Walrus Storage Controller (WS3) provies a persistent, simple storage service. It stores the machine images, an snapshots, an is responsible for serving an storing files. 3) Cluster Controller: The Cluster Controller (CC) manages the Noe Controllers an eploys/manages the instances on them. It also takes care of the networking for the instances running on the noes. It communicates with the CLC on one sie an the Noe Controllers(NC) on the other. It receives requests from the CLC to eploy instances, selects which NC to use for the same, an controls the network available to the instances. It also collects information about the NCs registere with it an reports it to the CLC. 4) Storage Controller (SC): The Storage Controller (SC) provies persistent block storage for use by the instances. It also allows creation of snapshots of volumes. 5) Noe Controller (NC): The Noe Controller (NC) runs on each noe an controls the life cycle of instances running on the noe. The NC interacts with the OS an the hypervisor running on the noe on one sie an the Cluster Controller (CC) on the other sie. The NC queries the operating system running on the noe to iscover the noes physical resources an also to learn about the state of VM instances running on the noe an propagates this ata up to the CC [2]. B. Clou Configuration In our case, we have implemente a single-cluster installation; using the Ubuntu Enterprise Clou (inclue in Ubuntu Server Eition 11.04).The setup consists of three machines. The first machine encompasses the Clou Controller, Walrus, Cluster Controller an Storage Controller. The secon an thir machines are the Noe Controller an the client respectively. All three machines are connecte to the enterprise network through a switch, an obtain IP aresses from the 5

6 Proceeings of Avances in Control an Optimization of Dynamic Systems TABLE I CLOUD CONFIGURATION SPECIFICATIONS Server#1 Server #2 Client Ubuntu Version Ubuntu server eition Ubuntu server eition Ubuntu server eition Functionality Clou Controller, Walrus, Cluster Controller Storage Controller Noe Controller Bunling Web UI Client Disk Space 150 GB 150 GB 150 GB CPU 2.4 GHz 2.4 GHz 2.40 GHz Virtualization Technology(VT) enable enterprise DHCP server. Proceure: For creating the virtual machine (VM), KVM (Kernel-base Virtual Machine) hypervisor was installe on the NC. Winows XP was use as the guest OS for the VM, running on Ubuntu platform. On this VM, MATLAB an LABVIEW were installe an integrate, in orer to eploy the boiler simulator on the clou. This was followe by bunling an registering of the Winows XP image on UEC. Finally, instances of the Winows XP image were run on the NC, each obtaining an IP aress from the enterprise DHCP server. Using this IP aress, the instance on the NC was accesse from the client using remote esktop connection. This enables the boiler simulator to run inepenently on the client esktop. Glossary Virtual machine: A virtual machine is a completely isolate guest operating system installe within a normal host operating system (OS). A VM can run its own OS an applications as if it were a real computer. It behaves exactly like a physical computer an contains its own virtual (software base) CPU, RAM har isk, NIC. Image: An image is static ata containing the software (OS an applications, configuration an ata files) that the VM will run once starte. Instance: An instance is a running VM. It is starte from an image an is capable of running an OS an processes, computations, I/O etc. Unlike an image, an instance is ynamic an interactive. Hypervisor: A hypervisor is a software that runs on the host OS an uses the services of the OS to provie timesharing of resources IV. SIMULATIONS The system that is moele in MATLAB can be simulate in LabVIEW using MATLAB script noe. The script noe provies a seamless integration between MATLAB an LABVIEW. With its pure software oriente real time igital simulation an no harware components involve this metho can be implemente with minimal cost an can be easily extene further. LabVIEW applications have a unique user interface for each user instea of isplaying a common user interface to all users. In other wors, multiple users can control the front panel of a VI (Virtual Instrument) i.e. simulator in our case, at the same time without affecting any other users connecte to the same remote front panel. The simulations are performe here on the server machine hosting the LabVIEW an from a client machine connecte to the server machine via a web browser. The MATLAB program for boiler simulator is calle from MATLAB script noe of LabVIEW program. Assumptions mae for Simulation: Since we are not simulating the complete plant but boiler alone the some assumptions have been mae pertaining to interaction of boiler subsystem with other subsystems. The following are as uner: 1) The furnace has the following steay state inputs as per [5]. These inputs give interaction with gas turbine subsystem. W F = , W A = , h G = 6.9E5, w G = , θ = ) The economizer has the following steay state inputs as per [5]; it is assume that assume here that water flows at a constant rate into the boiler through the economizer. These inputs give the interaction with feewater system w ei = 12.5, p ei = , h ei = ) The reheater has the following steay state inputs as per [5]. It is assume here that steam after passing through the HP turbine enters the reheater at a constant rate of w ri = This input gives the interaction with HP turbine subsystem. A. Results Simulation with step change in Fuel flow rate: The results of simulation of the boiler parameters of interest i.e. T g, Q ir, Q gs, w EG, p G, Q s, Q es are performe uner conitions of 10% change in input fuel flow (w F ) from kg/s to kg/s are shown in figures below. The MATLAB program uses oe15s with time uration of 500 secons. The results of the simulation are shown on the HMI of LABVIEW. It is seen from the results that for a step change in fuel rate in the boiler the furnace gas temperature, pressure an mass flow rate of exhaust gas increases leaing to increase in heat transfer to risers, super heater an economizer an also the steam generate. The simulations are performe on a client using remote esktop connection an on the noe controller of the clou setup an it is observe that there is no change in the results. The important factors contributing to the elay in observe results in simulation on the client are the spee of Ethernet an processing spee of the clou setup. V. CONCLUSIONS AND FUTURE WORK The motivation of this work was to create an infrastructure that woul simulate the ynamics of a rum type boiler in a clou environment. To emonstrate an valiate the boiler 6

7 Proceeings of Avances in Control an Optimization of Dynamic Systems (a) Client with remote esktop connection (a) Client (b) Server Fig. 4. Simulations on Server an Client using remote esktop in a clou setting, we have presente various test cases an simulations at the client an server sie, performing simulations in real-time. The clou infrastructure evelope provies a very goo tool for further analysis an research. Many issues remain open from the system theoretic point of view, namely system ynamics with reference to choice of service noes an initial assignment of customers to service noes. Other issues which are to be explore inclue optimization problems in a multiple customer, multiple client environment, scheuling an sequencing, for which work is unerway. REFERENCES [1] M. Miller, Clou Computing Web Base Applications That Change The Way You Work An Collaborate Online, Que Publishing, 2009 [2] D. Johnson, Kiran Murari, Murthy Raju, Suseenran RB, Yogesh Girikumar, Eucalyptus Beginner s Guie UEC Eition (Ubuntu Server Luci Lynx), v1.0, 25 May [3] R. Kirubashankar, K. Krishnamurthy, J. Inra, B.Vignesh. Design an Implementation of Web Base Remote Supervisory Control an Information System, International Journal of Soft Computing an Engineering (IJSCE) ISSN: , Volume-1, Issue-4, September (b) Server Fig. 5. Simulations as seen on server an the client using remote esktop with a 10% variation in fuel flow rate [4] ANSI/ISA , Fossil Fuel Power Plant SimulatorsFunctional Requirements. [5] A.W.Orys, A.W.Pike, M.A. Johnson, R.M.Katebi, M.J.Grimble. Moelling an Simulation of Power Generation Plants,Springer-Verilag, Lonon [6] Anthony T. Velte, Toby J. Velte, Robert Elsenpeter. Clou Computing: A Practical Approach, McGraw Hill, [7] Brian Elmegaar, Software for Simulation of Power Plant Processes: Part B Proceeings of International symposium on efficiency, costs, optimization, simulation an environmental aspects of energy systems, Berlin Germany, July 11-12, , [8] Simon Warley, Etienne Goyer, Nick Barcet. Technical White Paper- Ubuntu Enterprise Clou Architecture, August 2009 [9] K. J. Astrom an R. D. Bell, Drum-boiler ynamics, Automatica 36 (2000), pp [10] R. Cori, R, T. Busi (1977). Parameter ientification of a rum boiler power plant. 3r Power Plant Dynamics, Control an Testing Symposium, Knoxwille, Tennessee, September 7-9, [11] J. Weinman, Axiomatic Clou theory, working paper Weinman Axiomatic Clou Theory.pf

8 Proceeings of Avances in Control an Optimization of Dynamic Systems VI. APPENDIX: BOILER VARIABLES AND PARAMETERS A. The furnace Inputs w F = fuel flow to the furnace [kg/s] w A = air flow to the furnace [kg/s] h G = enthalpy of the exhaust gas from the gas turbine [J/kg] w G = exhaust gas flow from the gas turbine [kg/s] θ = tilt angle coefficient [-] (0 < θ < 1) T st = temperature of superheater metal tubes [K] T rh = temperature of reheater metal tubes [K] T et = temperature of economiser metal tubes [K] h A = inlet air enthalpy [J/kg] Q ir = heat transferre to the risers [J/s] Q is = heat transferre by raiation to the superheater [J/s] Q rs = heat transferre to the reheater [J/s] Q es = heat transferre to the economiser [J/s] p G = furnace air pressure [Pa] Q gs = total heat transferre to the superheater [J/s] h EG = enthalpy of exhaust gas from the boiler [J/kg] w EG = mass flow of exhaust gas from the boiler [kg/s] T g = gas temperature at the superheater [K] T gr = gas temperature at the reheater [K] T ge = gas temperature at the economiser [K] T g1 = boiler exhaust gas temperature [K] y ex = percentage excess air [%] x F l = h EG ρ EG [J/m 3 ] ρ EG = ensity of exhaust gas from the boiler [kg/m 3 ] K F = chimney flow coefficient [ms] K = attenuation coefficient [-] k gs = experimental heat transfer coefficient to the superheater [J/(kgK)] C gs = combustion gas specific heat capacity [(Js)/(kgK)] k rs = experimental heat transfer coefficient to the reheater [J/(kgK)] V F = combustion chamber volume [m 3 ] C F = fuel calorific value [J/kg] R s = stoichiometric air/fuel ratio [-] γ = content of fresh air in exhaust from gas turbine [-] k es = experimental heat transfer coefficient to the economizer [J/(kgK)] x F 1 = h EG ρ EG [J/m 3 ] ρ EG = ensity of exhaust gas from the boiler [kg/m 3 ] 1) Steay State Operating Conitions: Inputs: w F = kg/s, h G = J/kg, w A = kg/s w G = kg/s θ = ra, T st = K T rh = K, T et = K h A = J/kg K F = 0.001ms, K = 0.18 k gs = 3532J/(kgK), C gs = 1045(Js)/(kgK) k rs = J/(kgK), V F = 2000m 3 C F = J/kg, R s = 3.5 γ = 0.1, k es = J/(kgK) x F 1 = J/m 3 ρ EG = kg/m 3 Outputs Q ir = J/s, Q rs = J/s, p G = P a, w EG = 101.3kg/s, T g = K T gr = K, T g1 = K T ge = K, y ex = Q is = J/s Q es = J/s h EG = J/kg x F l = J/m 3, ρ EG = kg/m 3 B. The Drum Part Inputs: h e = specifie enthalpy of the water from the economizer [J/kg] v ow = volumetric water flow to the owncomer [m 3 /s] w e = water flow from the economizer [kg/s] Q ir = heat flow from the furnace [J/s] w v = steam flow to the superheater [kg/s] p v = rum outlet steam pressure [Pa] ρ v = rum outlet steam ensity [kg/m 3 ] h v = rum outlet steam specific enthalpy [J/kg] h r = liqui-vapor mixture specific enthalpy [J/kg] T rt = risers metal tube temperature [K] w r = liqui vapor mixture mass flow from the risers [kg/s] ρ w = rum water ensity [kg/m 3 ] w = water mass flow to the owncomer [kg/s] m l = rum liqui mass [kg] L = rum water level [m] x = steam quality [-] T w = rum water temperature [K] V = volume of the rum [m 3 ] k ec = evaporation coefficient [kg/(ks)] r = rum raius [m] w ec0 = steay state evaporation constant [kg/s] k r = experimental heat transfer coefficient [J/(sK )] V r = risers volume [m 3 ] M r = mass of risers metal tubes [kg] C rt = metal specific heat (J/(kgK)] A r = not use in version 1 L r = not use in version 1 f r = not use in version 1 8

9 Proceeings of Avances in Control an Optimization of Dynamic Systems D r = not use in version 1 τ r = mass flow time constant [s] m l = rum liqui mass [kg] x D1 = h w m l x D2 = ρ v V v where V v = volume of steam in the rum h r = liqui-vapor mixture specific enthalpy [J/kg] T rt = risers metal tube temperature [K] w r = liqui-vapor mixture mass flow from the risers [kg/s] 1) Steay state operating conition: Inputs: h e = J/kg, v ow = m 3 /s w e = 12kg/s, w v = 12kg/s V = 9.253m 3, r = 0.61m, Q ir = J/s k ec = kg/(Ks) w ec0 = 0kg/s k r = 444.2J/(sK), V r = 6.53m 3 M r = 2.25x10 4 kg, A r = 0.893m 2, L r = 7.315m C rt = 481.4J/(kgK) f r = 0.044, D r = 1.066m, τ r = 1s m l = kg, x D2 = kg, T rt = 567.9K, x D1 = J h r = J/kg w r = kg/s p v = P a, ρ v = kg/m 3 h v = 1, J/kg, T rt = 567.9K w r = kg/s, ρ w = kg/m 3 w = kg/s, m l = kg L = m, x = , T w = K C. Superheater an attemporator Inputs: W a = attemporation water flow [kg/s] w s = steam flow from the superheater [kg/s] p v = steam rum pressure [Pa] ρ v = ensity of saturate steam from the rum [kg/m 3 ] Q gs = heat flow from the furnace [J/s] h v = specific enthalpy of saturate steam from the rum [J/kg] h a = specific enthalpy of attemporation water [J/kg] w v = rum outlet steam pressure [Pa] T st = superheater metal tube temperature [K] p s = pressure of superheate steam [Pa] T s = temperature of superheate system [K] h f = specific enthalpy of evaporation [J/kg] Q s = heat transferre to the steam [J/s] ρ s = ensity of superheate steam [kg/m 3 ] x s1 = h s ρ s h s = specific enthalpy of superheate steam [J/m 3 ] f s = superheater friction coefficient [m 4 ] k s = experimental heat transfer coefficient [J/(kgK)] V s = superheater volume [m 3 ] M s = superheater mass [kg] C st = heat capacitance of superheater tubes [J/(kgK)] Cp ref = ieal gas reference specific heat [J/(kgK)] T ref = ieal gas reference specific temperature [K] h ref = ieal gas reference specific enthalpy [J/kg] ρ s = ensity of superheate steam [kg/m 3 ] T st = superheater metal tube temperature [K] x s1 = h s ρ s 1) Steay state operating conitions: : Inputs: W a = 0kg/s, w s = 12kg/s p v = P a, ρ v = kg/m 3 Q gs = , J/s, h a = J/kg f s = 2615m 4, V s = 8.462m 3, C st = J/(kgK), T ref = K, h v = J/kg k s = J/(kgK) M s = kg Cp ref = 2330 J/(kgK) h ref = J/kg ρ s = kg/m 3, T st = K, x s1 = J/m 3 w v = 12kg/s, T st = K p s = P a, T s = K h f = J/kg, Q s = J/s ρ s = kg/m 3, x s1 = J/m 3 h s = J/kg D. The Reheater Inputs: p ri = pressure of the steam at the inlet to the reheater [Pa] w ri = flow of steam at the inlet to the reheater [kg/s] T ri = inlet steam temperature [K] Q rs = heat flow from the furnace [J/s] h ri = specific enthalpy of inlet steam [J/kg] T rh = reheater metal tube temperature [K] p ro = outlet steam pressure [Pa] T r = reheater steam temperature [K] h ro = specific enthalpy of outlet steam [J/kg] Q rh = heat transferre to the steam [J/s] 9

10 Proceeings of Avances in Control an Optimization of Dynamic Systems ρ rh = steam ensity in the reheater [kg/m 3 ] x RH1 = h r0 ρ rh w r0 = flow of steam at the outlet from the reheater [kg/s] k rh = experimental heat transfer coefficient [J/(kgK)] V rh = reheater volume [m 3 ] M r = reheater mass [kg] C rh = heat capacitance of superheater tubes [J/(kgK)] Cp ref = ieal gas reference specific heat [J/(kgK)] T ref = ieal gas reference temperature [K] h ref = ieal gas reference temperature enthalpy [J/kg] ρ rh = steam ensity in the reheater [kg/m 3 ] T rh = reheater metal tube temperature [K] 1) Steay state operating conitions: Inputs: p ei = P a, w ei = 12.5kg/s w eo = 12kg/s, Q es = J/s k e = 98998J/(kgK)V e = 3m 2, M e = 7000kg C e = 43700J/(kgK) T et = K, p eo = T eo = K, ρ e = Kg/m 3, h eo = x RH1 = h r0 ρ rh w ro = outlet steam mass flow [kg/s] 1) Steay state operating conitions: : Inputs: p ri = P a, T ri = K, h ri = J/kg w ri = kg/s Q rs = J/s k rh = J/(kgK), V rh = 10m 3 M r = 7000kg, C rh = 481J/(kgK) Cp ref = 2200J/(kgK), T ref = K h ref = J/kg ρ rh = kg/m 3, T rh = K x RH1 = J/m 3, Steay state outputs: T rh = K, T r = K, w ro = kg/s p ro = P a h ro = J/kg Q rh = x 10 6 J/s, ρ rh = kg/m 3 x RH1 = J/m 3, E. Economizer Parameters w r0 = kg/s k e : an empirical coefficient T eo : Economizer liqui temperature P ei : Economizer inlet water pressure P eo : Economizer outlet water pressure h ei : inlet water specific enthalpy h eo : outlet water specific enthalpy Q es :Heat raiation absorbe by economizer T et : Economizer metal tube temperature 10