Application of Bond Graph approach in dynamic modelling ofindustrial gas turbineMorteza Montazeri-Gh* and Seyed Alireza Miran Fashandi
Systems Simulation and Control Laboratory, School of Mechanical Engineering, Iran University of Science and Technology,Tehran, Iran
*e-mails: ms.alireza
Received: 19 January 2017 / Accepted: 22 May 2017
Abstract.Nowadays, gas turbines play a significant role in industry and power generation units. Therefore, anyincrease in their performance efficiency, is designers’ major concern. Power generation system’s principalconsiderations are performance, weight and reliability. Gas turbine engine is considered as a probable choice forsuch applications. This research develops and validates a Bond Graph model based on flow of energy andinformation of a gas turbine engine. Here, modelling of the gas turbine engine is achieved based on the pseudoBond Graph approach. Subsequently, by coupling the Bond-Graph component models, a unified framework formodel representation is presented. Also, to study the effect of changing external load on turbine’s performance,an industrial two-shaft gas turbine is simulated under large transient loads based on the previously developedcomponent models. Finally, the commercial gas turbine simulation program (GSP) is used to validate thesimulation results. Transient response simulations indicate an acceptable error between the GSP and BondGraph model outputs.
Keywords: Dynamic performance / industrial gas turbine / Bond Graph approach / simulation
1 Introduction
Industrial gas turbines have a considerable potential togenerate the electrical power and mechanical drive force.These turbines are used as the compressors derivers in themechanical applications and as the generators derivers inthe electrical applications for both open and combinedcycles. Modeling of industrial gas turbines plays animportant role in the design and development of thecontrol and diagnosis systems.
One method that is easily available to the engineers tostudy the dynamic behavior of gas turbine systems is todevelop mathematical models and do simulations in orderto better understand the system dynamic behavior.However, the availability of a set of general mathematicalmodels for gas turbine system modelling of the flexibilityand level of complexity for the specific problem at hand isoften limited. Also, it is necessary to model a complete gasturbine system available in different complexity levels toassemble into a full model for simulating by a desiredsimulator. Early models of gas turbines were the first-orderlinear models to relate the fuel flow (as an input parameter)and the turbine shaft rotational speed (as the output
parameter). These models, which their constant coeffi-cients were experimentally specified, were valid just in alimited performance range. Along with the development offirst-order models (in the frequency domain), moreparameters were gradually used for the calculation of theconstants. Also by developing the previous models usedonly for the single-shaft turbines, new models werepresented to simulate the two-shaft gas turbines [1–3].
After that time, due to the limited validity of thatmodels (with time constants) and in order to enhance theflexibility of the designed models and meet the more needs,the researchers paid attention to non-linear and morecomplicated models. The first non-linear model of the gasturbine was presented by Saravanamuttoo and Fawke [4].This thermodynamic model, obtained from the physicalcharacteristics of the system, was able to predict thedynamic behavior of the turbine over the full performancerange. Of course, later, more accurate and comprehensivemodels were introduced to simulate the transient behaviorof the gas turbine [5]. Effectively using and developing thereusable models rely on a consistent framework forrepresenting a successful model. BondGraphs is consideredas a probable choice to meet the requirements. To developthe gas turbine engine, the ever-increasing demand forgaining more power and lower fuel consumption hasresulted in designs at or near the thermal, aerodynamic and
Table 1. Design point characteristics of the examined gas turbine engine.
Quantity Value
Thermal efficiency, % 34.2Compressor pressure ratio 14Power, MW 24.77Exhaust gas temperature, °C 543Exhaust gas flow, kg s�1 80.4GG turbine speed, rpm 9705Power turbine speed, rpm 7700
2 M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017)
structural limits of the system components. It means thatthe effect of transient and dynamic instabilities which cancause the severe damage of the components must bequantified both from the individual components consider-ations, but also from aspect of a system approach. TheBond Graphs are such a modeling approach that has apotential to meet the needs [1,5].
The Bond Graph modeling approach, working based onthe energy balance and object-oriented concept, can causeto produce and develop a library of flexible models of thegas turbine system components. The Bond Graph methodis efficiently capable of modeling the systems that havenon-linear behaviors and are connected with different fieldsof the energy [6] (mechanical, hydraulic, electrical, pneu-matics and thermodynamics systems). Thoma [7] was oneof the first researchers in the field of thermo-fluid systemsmodeling by the Bond Graph method. He proposed thetemperature as an effort variable and the entropy flow asthe flow variable. Karnopp [8] in 1979 introduced theconcept of pseudo BondGraph formodeling of thermo-fluidsystems.
Modeling of the gas turbine engine performance by theBond Graph approach was done in 1972 [9] at MITUniversity for the first time. The pressure, temperature andtorque were considered as the effort variables, and the massflow and engine speed (rpm) were considered as the flowvariables. Then a simple cycle of the single-shaft gasturbine was modeled by implementing the physical lawsand performance characteristic curves of the elements inthe form of Bond Graph method. Also in 1988, Krikelis andPapadakis [10] modeled a simple cycle of the single-shaftgas turbine using the Bond Graph model and then bylinearization of the model around an operation point, theydesigned a PI controller for it. They used the pressure,temperature and torque as the effort variables, and themass flow and engine speed (rpm) as the flow variables. In1993, Shoureshi and Brackney [11] in his research, on theuse of adaptive active noise control in the engine, modeled acycle of gas turbine using the Bond Graphmethod based onthe procedure outlined in reference [10]. In 1999, Diston [12]carried out a unified modeling of aerospace systems by theBondGraph approach. Hemodeled a virtual aircraft engineby the Bond Graph. In 2001, Pedersen [1] performed thetransient performance modeling of the gas turbine systemusing the Bond Graph method. He developed the energyfields presented by Karnopp and modeled the componentsof gas turbine system based on them. In his research, the
pressure, temperature, torque and fuel factor wereconsidered as the effort variables, and the mass flow,energy flow, engine speed and mass flow of burnt fuel wereconsidered as the flow variables. Thoma and Mocellin [13]in 2006 modeled the components of a gas turbine such asthe convergent nozzle, divergent nozzle, stator and rotorusing the Bond Graph. In their research, the temperaturewas considered as the effort variable and the entropy flowas the flow variable. In 2011, Movaghar and Novinza-deh [14] modeled and simulated an ideal turbocharger usingthe Bond Graph. The purpose of the modeling was to findthe system state space equations. In 2014, Sanei et al. [15]considered the effects of kinetic energy and momentum (inthe convergent-divergent nozzles with supersonic fluidflows), using the pseudo Bond Graph approach. They alsodeveloped the energy field which was able to model theposition of vertical shock in the divergent nozzle. Since thisfield can model the non-isentropic flows, this field can beused to model the thrust of rocket engines and thrusters inthe transient states. In 2015, Uddin and Gravdahl [16]developed the Bond Graph model of a radial compressorsystem to develop the control system. The analysis of BondGraph model investigates the energy flow of compressorperformance in the surge region. Also, they developed somemethods to prevent the surge in the compressor. In 2015,Montazeri and Miran Fashandi [17] showed the applicationof the BondGraph approach inmodeling of cold start phaseof the microjet engine. They investigated the possibility ofusing the combination of compressed air injection with theelectric starter by the Bond Graph approach in the coldstart phase of the engine. They used a simplified model ofmicrojet engine performance to study the cold start phase.
According to the literature, up to now, no study onmodeling and simulating of the dynamic performance of anindustrial gas turbine has been done by the Bond Graph.This modeling needs to consider the effects of the inletguide vanes. Also in earlier studies, the information bondshave not been used to transfer the information to the enginecomponents and to modulate them. But in this paper, theenergy fields (as the engine components) were modulatedby receiving the information from the information bonds.The objective of this study is to model and simulate thedynamic performance of the industrial gas turbine by theBond Graph method.
This paper is prepared in seven sections. First, theexamined industrial gas turbine engine is described. Next,the thermodynamic C and R fields (pseudo Bond Graph
Fig. 1. Schematic of the two-shaft gas turbine.
M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017) 3
elements) proposed by Karnopp are developed for theengine components. Subsequently, the complete dynamicmodel of the gas turbine engine is constructed aftercoupling the Bond-Graph component models. In thefollowing, the control system is described. Then, theanalysis and comparative study of the BG model and GSPsimulation results are presented. Finally, the discussionsand conclusions are given.
2 Gas turbine description
The gas turbine engine studied in this paper is a mediumsize industrial two-shaft gas turbine, which can beemployed in both power generation and mechanical-driveapplications [18], and here, the power generation applica-tion is considered. This gas turbine engine which known asSGT600, includes an axial compressor with 10 stages thatthe first two stages have the variable inlet guide vanes. Theexamined engine also has two bleed valves that open duringstart and stop to bypass some of the air to avoid surging.The engine specifications in design point condition arelisted in Table 1 [18]. The industrial gas turbine understudy consists of two distinct parts; the gas generator (GG)and power turbine (PT). The gas generator provides theenergy needed to rotate the power turbine and the powerturbineuses this power to rotate the generator or compressordepend on the application. As shown in Figure 1, maincomponents of the gas turbine are the compressor, combus-tion chamber, GG turbine and power turbine. This enginehas two separate shafts. The first shaft related to the gasgenerator is the connector between the compressor and GGturbine and the second shaft connects the power turbine tothe compressor or generator (external load).
3 Bond Graph modelling of gas turbineengine components
A field is amultiport BondGraph element. In the following,the engine components have been considered as energyfields. The variables of effort and flow in this section are asthe same variables as introduced and selected byKarnopp [19] in the thermo-fluid systems. The selectionof these variables causes that the use of the pseudo BondGraph is more useful than the true Bond Graph. One of thepseudo bonds considers the energy flow as the flow variableand the temperature as the effort variable. The otherpseudo bond takes into account the pressure as the effortvariable, and the mass flow as the flow variable. Also in themodeling of the compressor and turbine, the torque isselected as the effort variable and the engine speed as the
flow variable. Bond Graph modelling of gas turbinesystems for dynamic performance has to comply withsome very important guidelines to provide useful results:the model must be able to predict steady state performanceover a wide area of operating conditions. The model shouldbe as simple as possible, yet able to predict the dynamicoperation of interest. The model should include a fairlycomplete model of the control system, i.e. speed control,temperature limitation, acceleration and decelerationlimitation, rate of fuel injection limitation, etc. To developa workable model for a complete gas turbine system anumber of simplifications has to be introduced. First thetotal system is divided into a number of subsystems such asthe compressor, the combustor and turbine. Each of thesecomponents having their own model description which areinfluencing the exchange of mass, energy and work betweeneach of the subsystems. In addition they may introducechanges in the composition of the working medium.Describing the thermodynamic processes which take placein each of the subsystems following the working mediumthrough the complete system is the common denominatorof the engine models to be developed.
In developing models for the compressor or turbinebasically two different approaches are normally taken.Starting from the fundamental equations for the turbomachine may lead to a correct model, but the number ofapproximations that must be introduced soon give a modelof limited accuracy, at least over a wide operation area.Such an approach also requires a very detailed informationof the machine that most manufacturers are extremelyreluctant to provide. An approach which is simpler is tostart from the steady state performancemaps that youmayget from the manufacturers. These maps contain the mostcondensed accurate information of the performance of themachine over a large operational area. The modelsdeveloped here all use these maps in deriving the modelequations (10).
3.1 Compressor
For a compressor the mass and energy flow through themachine can be found from compressor performance maps.These maps although they are presented in slightlydifferent versions from different manufacturers, expressesthe mass flow and isentropic efficiency as a function ofpressure ratio and rotor speed. The assumption that thereare no mass or energy accumulation within the compressorand that the time scale for the flow through the compressoris very small compared to the system time scales, allow usto use a quasi-steady approach for the compressor. Thismeans that the steady state performance map for themachine is assumed valid also during transient operation.The performance map of the gas turbine engine understudy considers the corrected mass flow rate (GC) andisentropic efficiency (his,C) of the compressor as a functionof the compressor pressure ratio (pC), corrected rotor speed(NC,cor) and position of the inlet guide vanes (uVIGV). Thecompressor characteristic curve of the gas turbine engineunder study is shown in Figure 2. With regard to equations(1) and (2), the corrected mass flow rate and isentropicefficiency are achieved from the compressor performance
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
) RPC (oitaR
erus ser Prosserp
moC
0.65
0.80.82
0.850.87
0.89
0.920.94
0.960.98
Surge Line
Line
Ncor=1
Fig. 2. Compressor performance map.
GG
Fig. 3. Compressor pseudo-Bond Graph model.
4 M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017)
where d=Pin/Pref and u=Tin/Tref respectively representthe dimensionless pressure and temperature and Pref andTref represent the standard pressure and temperature(ISA), respectively. NGG and _mc also introduces the gasgenerator speed and compressor air mass flow respectively.
In order to consider the effects of the angular position ofVIGV on the general performance of the engine, thecompressor scale factors should be modified correspondingto uVIGV changes. Since the data obtained from the gasturbine test is recorded and displayed by the turbotronicdevice and this device is merely capable of displaying thepercentage of VIGVs openings (a), therefore instead of theangular position of VIGV, the percentage of VIGVsopenings should be considered in the calculations.Experimental studies on some axial flow compressors showthat the relation between the percentage of VIGVsopenings and correction coefficients of the compressorperformance map parameters can be expressed throughequations (3) and (4) [21].
CPRcco ¼ G cco ¼ 2:90667 � 10�3aþ 0:819787 ð3Þ
hcco ¼ 1:66667 � 10�4aþ 0:9896667 ð4Þwhere CPRcco, G cco and hcco represent the correctioncoefficients of the pressure ratio, corrected mass flow andisentropic efficiency of the compressor, respectively. As canbe seen in equations, the amount of correction coefficient tomodify the mass flow and pressure ratio is considered thesame. By applying the mentioned correction coefficients,the scale factor for parameter Y (SFY) can be expressed as
equation (5).
SFY ¼ Y des
Y Map
� �Y cco ð5Þ
where Ydes and YMap respectively represent the values ofparameter Y (pressure ratio, corrected flow rate orisentropic efficiency) in the design point and referencemap, and parameter Ycco also introduces the relevantcorrection coefficient.
It should be noted that the purpose of changing theangular position of VIGV is reduction or increase in theflow rate of the compressor inlet air. Usually at low speedsto enlarge the safety performance range of the compressor,by changing the position of VIGV and decreasing thecompressor inlet air flow, the possibility of occurringaerodynamic instabilities and surge can be decreased. Thecompressor shaft torque and exhaust temperature [22] cansubsequently be calculated as:
MC ¼ 30
p
hV _mcðhis;out � hinÞhis;cN
� �;
Tout � Tin ¼ Tin
hC
Pout
Pin
� �g�1g
� 1
" #ð6Þ
where his,out and hin is the inflow enthalpy and outflowisentropic enthalpy, hV is the volumetric efficiency of thecompressor and g is the specificheat ratio.Theenergyflow inand out of the compressor can subsequently be expressed as:
_Ein ¼ _mChin;C
_Eout ¼ _mC hin;C þ hV ðhis;out;C � hin;CÞhis;C
� �ð7Þ
Now, reviewing themodel equations derived using a pseudo-Bond Graph approach, we find that they express a relationbetween the hydraulic, thermal and mechanical efforts and
M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017) 5
flows on the three ports of the component. The rotationalshaft and the fluid inflow and outflow terminals of thecompressor, i.e. it is a R-field relation as shown in Figure 3.
TheVIGV signal enters to the R-field by an informationbond. The information bond is determined in an open loopfashion. This field has the inputs of pressure, temperatureand rotational speed, and the outputs of compressor massflow, energy flow and torque. The preferred causalityindicated from the form of the performance maps and themodel equations are effort input on all fluid bonds and flowinput from the mechanical bond.
The 10-stage compressor is modelled as three com-pressors in series with two small volume (plenum) inbetween. From these volumes, two bleed valves areattached for bypassing an amount of air back to theupstream side of the compressor. This does help to avoidsurge for low pressures ratios and during acceleration. Theplenum is considered to be equivalent to an isentropicpassage where both flow speed and energy accumulationare assumed to be negligible [20]. Thus, the followingequation is considered across the plenum: T, P (inletplenum)=T, P (outlet plenum).
Also the pressure and temperature derivative, repre-senting the variation of pressure and temperature due tomass accumulation in the plenum, is calculated usingequation (8) that is considered as a C-field in completeBond Graph model of gas turbine engine in Figure 11.
V pdroutdt
¼ V P
dRTout
dpoutdt
¼ _min � _mout
dTout
dt¼ d
rcpV pððcpT _mÞin � ðcpT _mÞoutÞ
þ Tout
rV pð _mout � _minÞ ð8Þ
where VP is the volume of the plenum, cp and r are heatcapacity and density, respectively and d can be estimatedby the specific heat ratio [20].
3.2 Combustion chamber
In the combustion chamber, the combustion processhappens by mixing the fuel and compressed air. Combus-tion gases energy causes to rotate the turbine and generatethe work. The input fuel flow rate into the combustionchamber is determined by the control system. Thecombustion chamber is considered as a constant-volumetank. It is assumed that the process of mixing the fuel andair in the chamber has been completed, and therefore, thephysical and chemical properties in the whole of the tankare the same [23].
dT
dt¼ _minhin − _mouthout þ _mf ðhf þ L
C
P
mð _min − _mout þ _mf Þ
þ P
T
_minhin − _mouthout þ _mf ðhf þ LHV�CCVm
�
The non-linear equations of the combustion chamberhave been calculated by the conservation laws of mass (Eq.(9)) and energy (Eq. (10)). In this section, the dynamicequations of the model have been extracted by thefollowing steps:
dm
dt¼ _min � _mout þ _mf ð9Þ
dU
dt¼ _minhin � _mouthout þ _mfðhf þ LHV hCCÞ ð10Þ
where hin is the input enthalpy, hout the output enthalpy,LHV the fuel heat value and hCC the combustion chamberefficiency. In addition, the internal energy will be as:U=mCVT ; where CV is the specific heat at constantvolume. Derivative of the above equation can lead to obtainequation (11):
dU
dt¼ CV T
dm
dtþ CVm
dT
dtð11Þ
By equating equations (10) and (11), the state equation tocalculate the chamber exhaust temperature can be writtenas equation (12):
see equation (12) belowUsing the perfect gas law (PV=mRT) and equation
(12), the following equation to calculate the chamberoutput pressure will be obtained:
see equation (13) belowThe fuel–air ratio is calculated by the following
equation: f ¼ mf
mair¼ mf
m�mf
According to the above equations, the Bond Graphmodel of the combustion chamber is shown in Figure 4 as amodulated C-field with the information bonds. This fieldhas two mass flow and energy flow inputs through theenergy bonds as well as three pressure, temperature andfuel inputs through the information bonds. Also, the energyfield of the combustion chamber has two pressure andtemperature outputs through the energy bonds and a fuel–air ratio output through the information bond. Thepreferred causality indicated from the model equationsare flow input on all fluid bonds.
3.3 GG turbine
Expansion of the hot gases of the combustion andconversion of the gases kinetic energy into the mechanicalenergy lead to the shaft rotation. To describe the quasi-static behavior of the gas generator and power turbines, acharacteristic curve is used. The GG turbine characteristiccurve of the gas turbine engine under study is shown in
HV�CCÞ −CVTð _min − _mout þ _mf ÞVm
ð12Þ
C Þ−CVTð _min − _mout þ _mf Þ�¼ dP
dtð13Þ
Fig. 4. Combustion pseudo-Bond Graph model.
10
10.5
11
11.5
12
12.5
13
13.5
)s/gK(wolFssa
MdetcerroC
0.4
11.1
0.60.5
0.70.80.9
1.2Ncor
Fig. 5. GG turbine performance map.
Fig. 6. GG turbine pseudo-Bond Graph model.
Fig. 7. Power turbine pseudo-Bond Graph model.
6 M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017)
Figure 5. The turbine performance map provides thecorrected mass flow rate (GT) and isentropic efficiency(his,T) as a function of the expansion ratio (pT) andcorrected rotor speed (NT,cor). According to equations (14)and (15), the mass flow rate and isentropic efficiency areobtained using the turbine characteristic curves [22].
G T ¼ g1ðpT ;NT ;corÞ; his;T ¼ g2ðpT ;NT ;corÞ ð14Þ
G T ¼ _mT
ffiffiffiu
p
d; NT ;cor ¼ NGGffiffiffi
up ; pT ¼ Pin
Poutð15Þ
Similar to the compression process in the compressor, theexpansion process in the turbine is also considered as anisentropic process. The turbine output torque in anisentropic process can be calculated by equation (16).
MT ¼ 30
p
hT _mT ðhu � hd;isÞN
� �ð16Þ
The energy flow in and out of the turbine can subsequentlybe expressed as:
_Ein ¼ _mThu;T
_Eout ¼ _mT hu;T þ ðhu � hd;isÞhT
� �ð17Þ
Now, by reviewing the model equations, the modulatedR-field can be defined as shown in Figure 6. The chamberoutput pressure and temperature, rotational speed, GGturbine pressure and temperature are considered as the fieldinputs, and the GG turbine mass flow and energy flow andtorque as the field outputs. Using an information bond, thefuel–air ratio of the combustion chamber enters into the GGturbine and then it is sent to the power turbine and plenumby the other information bond. The plenum is put betweenthe GG turbine and the power turbine. The preferredcausality indicated from themodel equations are effort inputon all fluid bonds and flow input from the mechanical bond.
3.4 Power turbine
The turbine performance map provides the corrected massflow rate and isentropic efficiency as a function of theexpansion ratio and corrected rotor speed. According to
(a)
(b)
Effort Sensor
Effort Sensor
Fig. 8. Bond graph representation of the engine shafts models:(a) GG shaft model and (b) PT shaft model.
Fig. 9. Schematic representation of the gas turbine enginecontrol circuit.
0 2000 4000 6000 8000 100000
20
40
60
80
100
VIGV
Pos
ition
(%)
Fig. 10. VIGV position against GG shaft speeds.
M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017) 7
equations (14) and (15), the mass flow rate and isentropicefficiency are obtained using the turbine characteristiccurves. The modulated R-field for the power turbine can bedefined as presented in Figure 7. The GG turbine outputpressure and temperature, rotational speed, ambientpressure and temperature are considered as the fieldinputs, and the power turbine mass flow and energy flowand torque as the field outputs. The fuel–air ratio of the GGturbine enters to the power turbine by an informationbond. The preferred causality indicated from the modelequations are effort input on all fluid bonds and flow inputfrom the mechanical bond.
3.5 Engine shaft model
The imbalance between the generated power by the turbine(output shaft) and the consumed power in the compressorcan cause the acceleration of the gas generator shaft. As thesame way, changes in the load applied to the power turbineshaft can also be a factor for changing the power turbinespeed and accelerating the connector shaft between thegenerator and power turbine. In a two-shaft gas turbine,the dynamic behavior of the gas generator shaft and powerturbine shaft can be described by equations (20) and (21),where in these equations, I andN respectively represent themoment of inertia and rotational speed of the gas generatorand power turbine shafts. ML in equation (21) representsthe consumed torque due to the imposed load on the powerturbine shaft (consumed generator torque). Mfric inequation (19) represents the friction torque that isproportional to the shaft torque from the turbine withcoefficient of the mechanical efficiency [22].
Mfric;GG ¼ hmech;GGMGG:Turb
Mfric;PT ¼ hmech;PTMPower:Turbð19Þ
dNGG
dt¼ 30
pIGGðMGG:Turb �MC �M fric;GGÞ ð20Þ
dNPT
dt¼ 30
pIPTðMPower:Turb �ML �M fric;PT Þ ð21Þ
The related Bond Graph models are shown in Figure 8.
Control System
Compressor
Combustion Chamber
GG Turbine
Power Turbine
GG Shaft modelPT Shaft modelBleed
Valve
Bleed
Valve
Plenum
Plenum
VIGV signal
Load
Plenum
Effort Sensor
Effort Sensor
Fig. 11. Complete bond graph model of the gas turbine engine.
0.5
0.6
0.7
0.8
0.9
1
Load
/Loa
d(de
s)
Fig. 12. Normalized input load.
8 M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017)
4 Description of control system
Figure 9 shows the schematic of the gas turbine enginecontrol circuit. Under the standard conditions, the turbo-generators control system has two forms; the droop controland isochronous control [24]. In this study, the isochronouscontrol strategy was used to control the turbo-generatorload/speed. When a turbo-generator unit is in theisochronous control mode, the control system must changethe control parameters in a way that the power turbine
speed (output frequency) remains constant. In fact, thechange of loading causes the power turbine speed deviationfrom the desired value and the controller is responsible forthe appropriate change in the fuel flow rate during theshortest possible time to restore the power turbine speed tothe initial value. The fuel controller block is depicted inFigure 9 includes an isochronous controller and a set oflimiters that in addition to stabilizing the power turbinespeed, is also responsible for satisfying the engine’s physicaland aerodynamic constraints.
As previously described, the examined gas turbinecompressor have variable inlet guide vanes and hence, inaddition to the fuel flow rate, the angular position of thevariable inlet guide vanes (i.e. uVIGV) can also be consideredas the second control parameter. For the examined gasturbine, the control of uVIGV is as open loop control basedon the data presented in Figure 10, which means that thedesired position of the variable inlet guide vanes is merely afunction of the gas generator speed. Also, the valvepositions of bleed valves are functions of the gas generatorspeed [25]. Loading block (in Fig. 9) receives the externalload and output power of the power turbine as inputs andby balancing the power for the power turbine rotor, theinstantaneous value of NPT can be determined. Thecontroller can also be extended to control a by-pass valvebetween different stages of the compressor.
0.550.6
0.650.7
0.750.8
0.850.9
0.95
1
FMF/
FMF(
des)
Fig. 13. Normalized fuel mass flow.
0 20 40 60 80 100 120 140 160 180 2000.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
1.04
EGT/
EGT(
des)
GSPBG
12 14 16 180.93
0.94
0.95
0.96
120 122 124 126
0.87
0.88
0.89
0.9
BG
GSP Sec. BGSP
BG
Sec. A
Fig. 14. Comparison of BG model and GSP for EGT.
0 20 40 60 80 100 120 140 160 180 2000
0.5
1
1.5
2
2.5
%Er
ror
(EGT
)
Mean Error
Fig. 15. The percentage of error between BGmodel and GSP forEGT.
M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017) 9
5 Complete Bond Graph model of gasturbine engine
The complete dynamic model of the gas turbine engine isconstructed after coupling the Bond-Graph sub-models. Asshown in Figure 11, there is a one-to-one map between thecomponents modeled by the Bond Graph and the gasturbine engine components shown in Figure 1. It shows the
ability of the Bond Graph approach in the modularmodeling of the system components. Using this feature amodel libraries which consists of the systemsmade from thegas turbine engine components can be developed.
In Figure 11, after determining the effort and flow in thegas turbine system, the type of engine component elementsmust be specified. In this study, the environment wasconsidered as a source of effort and the fuel mass flow as asource of flow. Due to the assumption that no energy isstored in the compressor and turbine, these were consid-ered as the energy dissipater elements (resistance). Thecombustion chamber and shaft dynamics were modeled asthe energy capacitor elements (i.e. capacitor and inertia).In the next step, after the Bond Graph modeling of theengine components, these elements were connectedtogether by the energy and information bonds, and zeroand one junctions. In the engine model, the energy entersinto the system via the source of effort (environment) andthe source of flow (fuel flow rate). The Bond Graph model,developed in this study, is based on the exchange of energyand power between the engine components. It means thatthe effort and flow are exchanged between the components.The product of these two parameters is representative ofthe power, and the integral of power represents the energy.
0 20 40 60 80 100 120 140 160 180 2000.96
0.97
0.98
0.99
1
1.01
1.02
1.03
NPT
/NPT
(des
)
GSPBG
25 30 351
1.005
1.01
110 112 1140.999
1
1.001
1.002
GSP
BGSec .A
GSP
BGSec .B
Fig. 16. Comparison of BG model and GSP for NPT.
0 20 40 60 80 100 120 140 160 180 2000
0.5
1
1.5
2
%Er
ror
(NPT
)
Mean Error
Fig. 17. The percentage of error between BG model and GSP for NPT.
0 20 40 60 80 100 120 140 160 180 2000.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
NGG
/NGG
(des
)
GSPBG
46 48 50
0.950.9550.960.965
140 1450.9880.990.9920.9940.996
GSPBG
Sec. A
Sec. B
BG
GSP
Fig. 18. Comparison of BG model and GSP for NGG.
10 M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017)
0 20 40 60 80 100 120 140 160 180 2000
0.2
0.4
0.6
0.8
1
%Er
ror
(NGG
)
Mean Error
Fig. 19. The percentage of error between BG model and GSP for NGG.
0 20 40 60 80 100 120 140 160 180 2000.75
0.8
0.85
0.9
0.95
1
1.05
1.1
CAM
F/CA
MF(
des)
GSPBG
152 154 156 158 160 1620.98
0.99
1
76 78 80
0.9
0.92
BG GSP
Sec. A
GSP
BG
Sec. B
Fig. 20. Comparison of BG model and GSP for CAMF.
0 20 40 60 80 100 120 140 160 180 2000
0.2
0.4
0.6
0.8
1
%Er
ror
(CAM
F)
Mean Error
Fig. 21. The percentage of error between BG model and GSP for CAMF.
M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017) 11
Table 2. BG model and GSP simulation results maximum and mean percent error.
12 M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017)
In other words, the output effort or flow of each enginecomponent is algebraically or differentially related to theeffort or input flow to that element.
6 Analysis of the simulation and results
In this study, external loading has been changed based on agiven profile. The control system determines the instanta-neous value of the fuel flow proportional to the appliedload, to stabilize NPT and satisfy the system physicalconstraints. Figure 12 shows the procedure of loading onthe power turbine. On the other hand, in order to comparethe results of the Bond Graph model with the GSP [26](software), the external load profile was applied in GSPsoftware. Figure 13 shows the fuel flow variations in termsof the applied load. Using Figures 14, 16, 18 and 20 theperformance of the Bond Graph and GSP models inestimating the parameters EGT, NPT, NGG and CAMFcan be compared with each other. Figures 15, 17, 19 and 21show the error percentage of above parameters. Table 2shows the maximum and mean percent error of the BondGraph model EGT, NPT, NGG, and CAMF values fromthe GSP values over the simulations. As can be seen inTable 2, the maximum percent errors of performanceparameters are found to be below 2.2% over a wide loadranges, with the mean percent errors below 0.26%. Theseresults show that the Bond Graph model is acceptable forapproximating the GSP model output. As can be seen inFigure 16, by changing in the applied load, the powerturbine speed deviates from its nominal value but theisochronous mode controller, returns NPT to its nominalvalue during a short time by simultaneously managing thefuel flow and subsequently changing the turbine’s outputpower. Since the control system must keep the powerturbine speed constant, when the load applied on thesystem is reduced, the fuel injected into the combustionchamber is decreased. This causes to increase in theamount of air to fuel ratio, and rises the risk of flame-out.So, the control system regulates the angular position of thevariable inlet guide vanes and thus reduces CAMF(Fig. 20) to prevent the flame-out. As the load rises, bothFMF and uIGV are used to regulate NPT. In this way, theamount of FMF is increased to prevent NPT reduction. Arapid increase in the input fuel entering the combustionchamber, to achieve NPT around the full speed (100%) andto increase the system response speed, causes an inevitableincrease in EGT (Fig. 14). High values of EGT indicatehigh internal temperature which result in turbine bladedamage. In fact, because of increase in the input fuel in ashort moment, a greater power than the generator turbine
output power in the design point enters to the powerturbine and, therefore, the power turbine response speedincreases. In the first moments of accelerating, a suddenfuel injection into the combustion chamber and conse-quently the sudden increase in CPR and NGG (Fig. 18) arethe main causes of occurring the aerodynamic instabilitiessuch as surge and stall. The limiting loops such asrotational speed and acceleration loops preserve the gasturbine from exceeding the operational limitations. Inacceleration mode, since air and FMF are varying at thesame rate, sudden raise in EGT occurs but the EGTlimiting loop keeps it at safe region.
7 Conclusions
In this paper, modeling and simulation of the industrialgas turbine dynamic performance is achieved based on thepseudo Bond Graph approach. To do this, we first obtainedthe physical relationships governing each engine componentin conjunction with the performance characteristic curves ofthe compressor and turbine. Next, the modulated energyfields (pseudo BondGraph elements) were developed for thegas turbinecomponents.The complete dynamicmodel of thegas turbine is constructed after coupling the Bond Graphsub-models.Also, the gas turbine simulationprogram(GSP)is used to validate the simulation results. The maximumpercent errors of performance parameters are found to bebelow 2.2% over a wide load ranges, with the mean percenterrors below 0.26%. The presented comparisons show thegood accuracy of the results. The proposedmodel can readilybe used as a subsystem for the larger systems like powerplants. Itcanalsobeappliedasthebasis for innovativedesignof control and diagnosis systems associated with industrialgas turbines.
Nomenclature
BG
Bond Graph GSP gas turbine simulation program EGT exhaust gas temperature FMF fuel mass flow NGG gas generator speed NPT power turbine speed CAMF compressor air mass flow CPR compressor pressure ratio VIGV variable inlet guide vane GG gas generator PT power turbine N rotational speed e effort sensor
M. Montazeri-Gh and S.A.M. Fashandi: Mechanics & Industry 18, 410 (2017) 13
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Cite this article as: M. Montazeri-Gh, S.A.M. Fashandi, Application of Bond Graph approach in dynamic modelling of industrialgas turbine, Mechanics & Industry 18, 410 (2017)
