Steam Turbine Hardware in the Loop SimulationJan Reitinger, Pavel Balda and Miloš Schlegel

NTIS - New Technologies for the Information SocietyFaculty of Applied SciencesUniversity of West Bohemia

Technická 8, 306 14 Plzen, Czech RepublicEmail: reitinge@ntis.zcu.cz, pbalda@ntis.zcu.cz, schlegel@ntis.zcu.cz

Abstract—In this paper, a new tool for teaching purposesis presented. The tool is a low-cost Hardware in the Loopsimulation with separated process model and control algorithmon standalone hardware which runs in real-time. In this paper,the simulation is used to control the steam turbine modelwith shaft and generator, but it can be used on wide rangeof complex physical models. The used model is evaluated onramp-up simulation in Simulink, and after that mathematicalequations are implemented in Modelica language and exportedinto Functional Mock-up Unit (FMU). The controlled and controlmodels are both simulated on Raspberry Pi minicomputers inreal-time and one can observe the control strategy on the secondRaspberry with prepared control task and Human MachineInterface (HMI). Both Raspberries are connected through theModbus over TCP/IP protocol and one can get familiar withthis wide-used communication. Furthermore, there is possibilityto control the system, change regulators parameters and handlethe trade-off between various performances. Regulation can beoperated in so-called island or grid mode. The aim of systemcontrol is to comply shaft speed demands described in norms.

Index Terms—steam turbine, Hardware in the Loop sim-ulation, modelling, Functional Mock-up Interface, Modelica,Raspberry Pi

I. INTRODUCTION

Hardware in the Loop Simulation (HiL below) is a finalstep of rapid development cycle validation and is very usefulin both academic and industrial spheres. This simulation isreal-time and consists of a combination of simulated and realcomponents. Simulated components are generally representedwith mathematical model, which runs on separated hardwareand is connected with real components through real com-munication. HiL reduces significantly the time integration ofnew technology into operation, because many problems canbe detected in laboratory environment [1]. The physical sepa-ration of controlled and control system is suitable for teachingpurposes too. Many students understand control theory betterwhen they see HiL simulation.

There was written many papers and articles about HiL.Quite often is used Matlab/Simulink to model simulation andused hardware is a PC in cooperation with an interface card[2], dSpace [3] or Arduino microcontroller [4]. All this ap-proaches have serious disadvantage - the mathematical modelis simulated on the PC in expensive Simulink environment.

Nowadays, it is not unthinkable to create a custom HiL.Computing power of currently offered affordable devices is

already sufficient for implementing soft real time simulations.Moreover, in the past few years, erupted literally "boom" inthe market for minicomputers that can be used for example forhome automation and contain such a variety of input/outputinterfaces that can be used in HiL. In this paper is useda modified existing mathematical model of a steam turbine,which is going to be the core of HiL simulation on widelyavailable hardware - Raspberry Pi 2B (RPi). The modelwas implemented into open source Modelica language andexported into Functional Mock-up Unit, which is part ofFunctional Mock-up Interface - a tool independent standard tosupport both model exchange and co-simulation of dynamicmodels [5]. The second RPi will be used to control the steamturbine model. The connection between Raspberries will beestablished using Modbus over TCP/IP protocol.

Steam turbine model was chosen because it is a complexproblem which can be modelled with different levels of detailfor various purposes. There exist both static [6], and dynamicmodels. Turbine system is nonlinear and for its descriptionare often used simple linearised models [7], sets of linearisedmodels for different operating points [8] and nonlinear models[9]. Modelling of the steam turbine is a widely studied topic,because detailed mathematical model allows proper adjustmentof controllers in a large operating range of the turbine, andthus significantly increases efficiency, or even prevents damageduring unexpected situations. Various authors approach theproblem differently. There are a number of works that are usedto describe an identification method based on the obtained datafrom real turbine. However the result of this modelling areparameters that do not have a clear physical meaning [10].Another way is physical modelling based on the expressionof relationships in the system using the mass and energyconservation laws [11]. Alternatively, there is a combinationof both of these approaches [8]. In this paper was used amodified model, which is described together with two othermodels in detail in [11]. This model was developed by SiemensPower Generation, one of the leading manufacturers of steamturbines. The model parameters have clear physical meaningand blocks describing the turbine sections may be in the futurereplaced with others, that will better reflect the thermodynamicbehaviour of the system.

The outline of the paper is as follows: Section II presents amodified mathematical model that will be used. In Section III,

2017 21st International Conference on Process Control (PC)June 6–9, 2017, Štrbské Pleso, Slovakia

978-1-5386-4011-1/17/$31.00 c©2017 IEEE 380

used control structure is introduced, parameters of regulatorsare set according to the mentioned requirements and the modelis tested on a simulation of the ramp-up of the system. SectionIV introduces the HiL simulation with the HMI and timestatistics of the simulation. The conclusions and ideas forfuture work are given in Section V.

II. USED MODEL

A relatively simple dynamical model described in [11] wasused for HiL simulation. The overall scheme of the model isshown in Fig. 1. There are some simplifications especially inthermodynamic part of the model, so the model fits the turbinebehaviour well mainly in operating point neighbourhood. Themodel was modified for simulation with zero initial conditionsagainst the original. The main differences are in the shaft part.

G

steam generatorreheater

boiler

shaft

electric grid

condenser

generator

low-pressureintermediate-p.high-pressure

Turbine blocks:

controller

hRShMS

Pgenn

Fig. 1: Overall scheme of the model

A. Turbine block

The work of steam turbine is based on the Clausius-Rankinecycle, which uses changes in working fluid (commonly water)and its phases. In this case, steam expansion from hightemperature ϑin and high pressure pin to low temperatureϑout and low pressure pout is used. This expansion is causedby the loss of specific enthalpy h and it can be assigned as∆h = hin−hout . Thermodynamic power can be expressed withthis enthalpy drop ∆h and mass flow of the steam Ûm(t) as

P(t) = ∆h Ûm(t). (1)

From the law of conservation of mass, it is known that massof steam variance in turbine section Ûm is equal to the differencebetween input and output mass flows. Integrating this equationone get steam mass storage with zero initial condition

m(t) =∫( Ûmin(τ) − Ûmout (τ)) dτ. (2)

It will be considered that the pressure inside the sectionis proportional to the stored mass of the steam around theoperating point:

p(t) = KM m(t) = KM

∫( Ûmin(τ) − Ûmout (τ)) dτ, (3)

which is fulfilled for ideal gases.

The next consideration is that the mass flow through theturbine segment is especially around the operating point pro-portional to the pressure:

Ûmout (t) = Kp p(t). (4)

This statement holds true for higher pressure values. ConstantsKM and Kp will be chosen for operating point and inaccuracyaround other values will be neglected.

The mass flow into the overall system is controlled by thevalve and it thus depends on the pressure in front of the valvepin(t) and a function of the main steam valve lift hMS(t):

Ûmin(t) = pin(t) ∗ hMS(t). (5)

From equations (3) and (4) one get the mathematical modelfor steam turbine section:

Ûmout (t) = Kp KM

∫( Ûmin(τ) − Ûmout (τ)) dτ, (6)

where for high-pressure section is the input given by (5) andfor others is the input equals to output in front of the section.The substitution K := KpKM will be used for simplification.For distinction between turbine sections, it will be establishedthe HP subscript for high-pressure section, IP for intermediate-pressure and LP for the low-pressure section.

Turbine model outputs are mass flows Ûmout (t) and thethermodynamic power P(t), which is defined by equation (1).It is considered in this model, that the enthalpy drop ∆h isconstant for all turbine sections and it is also model parameter.

B. Reheater

The output mass flow Ûmout (t) can be directly controlled bythe reheater steam valve and the final output of the systemÛmout f (t) can be defined as:

Ûmout f (t) = hRS(t) Ûmout (t), (7)

where the hRS(t) is the actual lift for reheater steam valve.Using the equations (2), (3) and (4) with Ûmout f (t) instead ofÛmout (t) can be reached the final mathematical model as:

Ümout (t) = KpKM ( Ûmin(t) − hV (t) Ûmout (t)) . (8)

For all reheater parameterers and variables will be used thesubscript RH.

C. Valves

In this paper are used two valves (main and reheater steam)with subscripts MS and RS. Both valves are modelled as a firstorder systems with steady state gain equals to 1, time constantT = 1

KVand the required valve lift u(t) in range 〈0; 1〉. The

differential equation for the actual valve lift (generally markedas hV (t)) is defined as

ÛhV (t) = −KV hV (t) + KV u(t). (9)

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D. Shaft

Using torques equilibrium, it can be estimated the variationof the shaft angular velocity as

J Ûω(t) = Mf (t) − Mload(t) − Mf ric(t), (10)

where ω(t) [rad s−1] is angular velocity, J[kg m2] is moment

of inertia, Mf (t) [Nm] forcing torque produced by the thermo-dynamic power P(t), Mload(t) torque caused by the load andMf ric(t) is the frictional torque. Establishing ω(t) = 2πn(t),Mf (t) = P(t)

ω(t) , Mf ric(t) = Bω(t)

Ûn(t) = 1J2π

(P(t)

2πn(t) − Mload(t) − 2πBn(t)). (11)

This system has discontinuity for rotation speed n(t) = 0and thus it is necessary to modify it for simulations with zeroinitial conditions. For this purpose, it will be assumed thatthe rotation speed holds zero as long as the power P(t) isless than minimal power P0. After that forcing torque Mf (t)will be equal to constant torque Mfconst > Mstatic , whereMstatic is the static friction torque. Mf (t) will be constantuntil P(t)

2πn(t) > Mfconst and n(t) > n0. From this moment willbe valid the equation (11). This behaviour can be described as

Ûn(t) =

0 , if P(t) < P0,1

J2π(Mfconst − Mload(t) − 2πBn(t)) , if P(t) ≥ P0,

1J2π

(P(t)

2πn(t) − Mload(t) − 2πBn(t))

, if n(t) > n0∧P(t)

2πn(t) > Mfconst .

(12)

E. Generator

In [11], there was a generator designed as an asynchronousmachine, which works on induction motors principle. Ingenerators case, the machine produce the electrical powerthanks to the slip σ(t) = n(t) − f (t) between turbine speedn(t) [rev/s] and grid frequency f (t) [Hz]. The machine worksas generator for n(t) > f (t) and as motor in other case. If speedand frequency will be considered as phasors, it is possible toestimate actual angle between them as

ε(t) =∫(n(τ) − f (τ)) dτ. (13)

This angle defines current position of rotor and stator.The load torque Mload(t) caused by generator, which affect

the shaft, is composed of a forcing torque Mf orc(t) and adamping torque Mdamp(t). The forcing torque is proportionalto the sine of the angle ε(t), so

Mf orc(t) = K1 sin(ε(t))and the damping torque is proportional to the slip σ(t) :

Mdamp(t) = K2(n(t) − f (t)).Complete model is thus given by equation

Mload(t) = K1 sin(ε(t)) + K2(n(t) − f (t)). (14)

F. Complete model

Possibility of switching between two modes will be re-quested. In the first mode, the load torque Mload(t) will bethe input of the whole system and in the second mode will begenerated by the equation (14). For this purpose, those inputsof the complete model were proposed as:• uMS – required value of the main valve lift,• uRS – required value of the reheater valve lift,• MODE – switching between modes,• f – actual frequency of the grid,• Mloadin – torque which is due to the load in the first

mode.The outputs will be described as:• qout – mass flow of the steam from the system,• nmin – revolutions of the shaft per minute,• Pgen – generated power.The following mathematical model can be assembled from

equations (1), (5), (6), (8), (9), (12), (13) and (14) with somemodifications:ÛhMS(t) = −KMS hMS(t) + KMS uMS(t),ÜmHP(t) = −KHP ÛmHP(t) + pin KHP hMS(t),ÛhRS(t) = −KRS hRS(t) + KRS uRS(t),ÜmRH (t) = −KRH ÛmRH (t) hRS(t) + KRH ÛmHP(t),ÜmIP(t) = −KIP ÛmIP(t) + KIP hRS(t) ÛmRH (t),ÜmLP(t) = −KLP ÛmLP(t) + KLP ÛmIP(t),

P(t) = ∆hHP ÛmHP(t) + ∆hIP ÛmIP(t) + ∆hLP ÛmLP(t),Ûε(t) = n(t) − f (t),

Mbr (t) = Mload(t) + 2πBn(t),

Ûn(t) =

0 , P(t) < P0,1

J2π(Mfconst − Mbr (t)

), P(t) ≥ P0,

1J2π

(P(t)

2πn(t) − Mbr (t))

, n(t) > n0∧P(t)

2πn(t) > Mfconst ,

Mload(t) ={

K1 sin ε(t) + K2(n(t) − f (t)) , MODE = 1,Mloadin (t) , MODE = 0,

and outputs

qout (t) = xLP(t),nmin(t) = 60 n(t),Pgen(t) = Mload(t)2πn(t).

Those equations were implemented in OpenModelica withfollowing parameters: KMS = 0,5

[s−1] , KHP = 3,333 3

[s−1] ,

KRS = 0,5[s−1] , KRH = 0,5

[s−1] , KIP = 2,5

[s−1] ,

KLP = 1,666 667[s−1] , ∆hHP = 0,25 · 106 [

J · kg−1] ,∆hIP = 0,3 ·106 [

J · kg−1] , ∆hLP = 0,45 ·106 [J · kg−1] , pin =

300 [bar], J = 10 000[kg ·m2] , B = 100

[Nm · s · rad−1] ,

P0 = 100π2 [W], Mfconst = 50Bπ [Nm], n0 = 0,05 [rev/s],K1 = 50 000 [Nm], K2 = 9 990 680 [Nm · s]. After thatwas model automatically exported into FMU. This process isquite straightforward and thus it will be omitted. Advantage

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of FMI/FMU is that, it is an open source tool independentstandard to support both model exchange and co-simulationof dynamic models [5] and is now supported in REX [12].

III. CONTROL REQUIREMENTS, RAMP-UP AND CONTROLSIMULATION

The output of the process energy conversion is electricalenergy in all types of power plants. This energy is suppliedinto electrical grid, which is composed of production sources(power plants), distribution lines and appliances. Grids canhave local character with small number of sources (usuallyone) and appliances. This small grids are commonly calledislands. On the other hand, grids can be very large, composedof big number of power plants, appliances and extensivedistribution lines. Those systems usually have transnationalcharacter and some kind of cooperation of sources is requiredthere. Power plants control their energy production with aview to preservation qualitative parameters of electricity inlimits. Parameters varies in dependence on actual appliancesconsumption and disruptive influences. The benefits of thisapproach are among other things:• better ability to react to disturbances and power outages,• lower transmission and distribution losses,• longer lifetime of power blocks thanks to smaller power

variance,• automatic support across the nations,• possibility of trading.The frequency and voltage are the main qualitative param-

eters. Power plants can directly control the mean value offrequency (without higher harmonics), which is in all parts ofthe grid equal. The limits for frequency variation are definedin CSN EN 50160 standard for Czech republic and can beobserved in tables I and II.

Nominalvalue

Allowed variance Maximaltimepercentage min max

50 Hz ±1 % 49,5 Hz 50,5 Hz 99,5 % of year+4 %/−6 % 47 Hz 52 Hz 100 % of year

TABLE I: Allowed values of frequency in the national grid

Nominalvalue

Allowed variance Maximaltimepercentage min max

50 Hz ±2 % 49 Hz 51 Hz 95 % of week±15 % 42,5 Hz 57,5 Hz 100 % of time

TABLE II: Allowed values of frequency in the island grid

Frequency regulation is usually composed of three degrees –primary, secondary and tertiary. Primary regulation is runningin each power plant and keep continuing balance betweenproduction and consumption of electrical energy. Secondaryregulation is the central control in each state, which setspower setpoints to individual power blocks to the purpose ofneglecting the remainder. This control serves to compensationof higher frequency variations too, which primary regulationcannot handle. Tertiary regulation is usually manual control,which can be used for creating power reserve, regain thebalance or in case of secondary regulation saturation [13].

Primary regulation is focused in this work and it meanspower output follows the setpoint from secondary regulation.There is needed connection between frequency grid and thepower output of the block. It is fulfilled with proportionalcontroller called frequency corrector. This corrector can par-tially affect the power setpoint and regulate the mean valueof frequency. The size of controller output has been given bycorrector gain Kc as ∆P(t) = Kc · ∆ f (t) = Kc · ( fnom − n(t)) ,where n(t) are revolutions of shaft per second. It can beexpressed in relative coordinates as ∆P(t)

Pnom= k ∆ f (t)fnom

, wherefnom and Pnom are nominal values, k is a relative gain withrelation to Kc defined as Kc =

k ·Pnom

fnom. The relative gain can

be expressed as a

k =

∆P(t)Pnom

∆ f (t)fnom

=1s,

where s is statics. It is often expressed in percentages, sos [%] = 1/k · 100. For frequency corrector, it is usually useds = 8 % and thus k = 12.5. Maximal controller output isconvenient to restrict ∆Pmax = ±5%Pnom. The block diagramof frequency corrector is shown in Fig. 2.

Gn

nnom = 50 rev/s Pnom

SpeedController

PowerController

Pgen

valves

Gn

Pnom

PowerController

Pgen

valvesfnom

K

Δf

ΔP=K.Δf

ΔPmax=±5%P

frequencycorrector

Fig. 2: Simplified schemes for ramp-up and primary regulationSpecial case of the control is the ramp-up. There is a

so called ramp-up diagram for every turbine provided bymanufacturer. Compliance with diagram will prevent damages,which are caused by different temperatures in individual partsor by rapid speed changes.

During cold start, small amount of steam is let into thesystem. Turbine is revolving by the engine in order to reachuniform warm up. The torque is increased with continuousadding of steam and engine is turned off when shaft isrevolving by itself. The speed regulation is turned on in thismoment.

The volume of steam is still increased and turbine will reachnominal rotational speed nnom during continuous warming up.Regulation is carried out by only speed controller for turbines,which has been operating in island mode. In other case, thereis needed to synchronise grid frequency with rotational speedand plug in the generator. The speed and grid frequency areequal and speed controller is not necessary any more.

The regulation is switched to power controller and the poweris continuously increased. It is still very important to notincrease the steam volume fast. After reaching the value ofnominal power Pnom, which is set by secondary regulation,

383

turbine is in normal operation [14]. The control scheme isshown in Figure 3.

speedcontroller

powercontroller

controllerswitcher

power ramp-up

speed ramp-up

f_grid

n_shaft switch

Phasing

n_min

f_nom

P_nom

deltaP

Frequency_corrector

0

M_load

1

u_RS 50

f

u1u2SW

y

SSW1

y

P_sp

50

f_req

Rate Limiter

[f_grid]

Goto

[f_grid]

From

[f_grid]

From1

Product

dvsppvtvhvMANIH

mv

dmv

de

SAT

PIDU_n_no_load

dvsppvtvhvMANIH

mv

dmv

de

SAT

PIDU_P_6e5_load

60

sec2min

u_MSu_RSMODEfM_load

q_out

n_min

P_gen

Turbine_system

Rate Limiter1

Fig. 3: Simulation scheme for control including ramp-up

The rotational speed controller was chosen as a PID regu-lator with two degrees of freedom and control law describedas

U(s) =K{bW(s) − Y (s) + 1

Tis[W(s) − Y (s)]

+Tds

TdN s + 1

[cW(s) − Y (s)]},

where U(s) is Laplace transform of the manipulated variable,W(s) is Laplace transform of the setpoint variable, Y (s) isLaplace transform of the process variable and K , Ti , Td , N , b,c are the parameters of the controller [12]. Power controller isa PI regulator and parameters of both controllers are in tableIII.

Parameter Speed controller Power controllerK 5,298 · 10−5 4,251 · 10−8

Ti 8,041 8,172Td 1,624 -N 2 -b 0 1c 1 1

TABLE III: Parameters of speed and power controller

Results of simulation for ramp-up, phasing and turbinecontrol in the grid mode are shown in Figures 4, 5 and 6.There is an overshoot in rotation speed. The maximal value is3 140 rpm ≈ 52,33 Hz. This value is acceptable for shaft speed,because shaft have to be constructed at least for 57,5 Hz (seetable II).

The generated power follow the ramp quite well. There isan pulse in the switch moment and it is caused by inaccuratephasing. Figure 6 shows control action ∆P in dependence on∆ f of frequency corrector.

IV. HARDWARE IN THE LOOP SIMULATION

The REX Control System [12] and Functional Mock-upInterface (FMI) [5] were chosen for HiL simulation. Detaileddescription of used blocks and example of use can be foundin [15]. The final mathematical model from Section II was

0 50 100 150 200 250 300 350 400 450 5000

500

1000

1500

2000

2500

3000

rev/

min

setpointmanipulated variable

0 50 100 150 200 250 300 350 400 450 500

time [s]

2950

3050

3150

rev/

min

Fig. 4: Speed regulation

300 320 340 360 380 400 420 440 460

time [s]

0

0.5

1

1.5

2

2.5

3

pow

er [W

]

108

setpointmanipulated variable

Fig. 5: Power regulation

implemented in Modelica language and was automaticallyexported into FMU and loaded into REX Core running onRPi. Detailed model and HiL validation can be found in [16].

On the second RPi, there is running control task fromSection III, which is implemented in REX Control System.The HMI is available on this RPi through HTML browser,which is shown in Fig. 7. Both RPis are connected throughTCP/IP Modbus standard. Users can observe the state of thesteam turbine and generator system, change parameters of thecontrollers, frequency of the grid and set-point of the outputpower, which is usually controlled from secondary regulation.

The final HiL simulation, which runs on RPis, is shownin Fig. 8. Both model and control tasks are executed with5 ms period. Tasks ran for a day and the maximum timeof model executing was 0,618 7 ms and average time was0,115 3 ms. The maximum execution time of the control taskwas 0,920 4 ms and average time was 0,059 6 ms. Therefore itis possible to use more accurate and complicated mathematicalmodel.

V. CONCLUSION AND FUTURE WORK

A low-cost HiL simulation based on existing mathematicalmodel of steam turbine was developed in this paper. Thissimulation runs on two RPis and will be used for educationpurposes. The model was implemented in Modelica languageand exported into Functional Mock-up Unit via FMI. Thisprocedure can be applied to large group of models and thusvarious types of simulations can be created. Both model and

384

300 320 340 360 380 400 420 440 460 480 5000

0.05

0.1

f [H

z]

300 320 340 360 380 400 420 440 460 480 500

time [s]

0

1

2

P [W

]

106

Fig. 6: Control action of frequency corrector

Fig. 7: Human-machine interface

controller tasks run in REX [12] and communicate throughModbus over TCP/IP protocol. User can use existing regulatorstructure from Section III and control the steam turbine systemwith prepared HMI or easily modify the control task to achievebetter results. It is shown in Section IV that it can be used morecomplicated model for HiL and that will be the future work.The simulation will be connected with the solar and wind plantsimulations and appliances in the future.

ACKNOWLEDGEMENT

This work was supported by the Technology Agency ofthe Czech Republic – project No. TA04010364 and by theproject LO1506 of the Czech Ministry of Education, Youthand Sports under the program NPU I. The support is gratefullyacknowledged.

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