29-753 - DSP Based Simulator for Excitation Control of Synchronous Generator

7/28/2019 29-753 - DSP Based Simulator for Excitation Control of Synchronous Generator

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DSP based simulator for excitation control of synchronous generator

DAMIR SUMINA, IGOR ERCEG, GORISLAV ERCEG

Faculty of electrical engineering and computing

University of Zagreb

Unska 3, ZagrebFaculty of electrical engineering

University of Osijek

Kneza Trpimira 2, Osijek

CROATIA

[email protected]

Abstract: - This paper proposes a DSP based simulator for the implementing and testing control algorithms.The simulator is used to control a synchronous power plant model in real time. The simulator consists of a PC,on which the synchronous generator connected to AC network is simulated, connected through a

communication channel to a DSP into which the control algorithm has been implemented. The simulatorenables verification of the control algorithm on a simulation model in real time. In real time the simulator

enables faster processes of engineering, implementing and verifying control algorithms not only for the voltagecontrol system of a synchronous generator, but also for other systems able of having mathematical andsimulation models. This paper shows a comparison in the case when both the system model and the control

structure are simulated and for a case when the model is simulated on a computer and the control structureimplemented in the DSP. The implementation of a conventional and a nonlinear synchronous generator voltage

control structure has been presented. These methods were tested in the cases of voltage reference change,mechanical power change and the case of a short circuit on the transmission line.

Key-Words: -Real time simulation, DSP based simulator, synchronous generator, excitation control, nonlinearcontrol

1 IntroductionTesting a controller in complex process controlsystems demands a real control system or anadequate laboratory model. After engineering thenecessary electronic circuits, simulating and

implementing the control algorithm, the controller'soperation on a real system must be verified. With

complex systems, such as a power system,engineering an adequate laboratory model isdifficult and expensive, and the real, operatingsystems are rarely put to a stop so as to examine theoperation of its controller. It is desirable, for

technical and economic reasons, to have asimulator, which would simulate the physical

behaviors of real, complex systems [1], [2], [3].The implementation of a control algorithm and

the testing of a controller within a synchronous

generator's voltage control system by a simulatorare presented in this paper. A synchronous

generator's dynamic behavior is simulated in realtime using a Matlab/Simulink program package.The control algorithm was implemented on a

TMS320F2812 digital signal processor (DSP) byTexas Instruments. DSP based simulator (fig. 1)

consists of a PC simulating a synchronous

generator, connected by a communication channel(through a parallel port) to a DSP into which thecontrol algorithm has been implemented.

The data exchange between the PC and the DSPis carried out by a JTAG (Join Test Action Group)emulator through the realtime data exchange

interface (RTDX). This kind of simulator for thetesting of controller operation in a system is lesstechnically and economically demanding than if thetesting was conducted on a lab model, or on a realsystem. Different control processes can be

simulated with the mathematical and simulationmodels and the input/output signals can be broughtdirectly to the controller, while testing its operation(processor/hardware in the loop simulations).

Fig. 1 DSP based simulator

WSEAS TRANSACTIONS on SYSTEMS and CONTROL Damir Sumina, Igor Erceg, Gorislav Erceg

ISSN: 1991-8763 531 Issue 11, Volume 4, November 2009


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Fig. 2 Synchronous generator connection to AC

network

The simulator contains commercial electroniccomponents that are easily accessible andeconomically acceptable.

In this paper the voltage control system ofsynchronous generator is examined.

The synchronous generator is connected to anetwork through a transmission line (fig. 2)(reactance of transmission line is 0.2 p.u.). Fig. 3shows the generator's voltage control system blockscheme.

The generator's voltage control system consistsof a proportional excitation current controller and aPI voltage controller which is super-ordinate to it[4], [5]. The control system's input signals are twomeasured phase currents, two line voltages and the

generator's excitation current, while the system'soutput signal is a PWM signal for an AD/DCconverter.

Fig. 3 Generator's voltage control system

2 Simulation model of thesynchronous generatorBefore implementing and testing controlleroperation in a real system, it is necessary to make amathematical and simulation model of the realsystem. The mathematical model of synchronous

generator is determined by the followingdifferential equations [4]:

qd

s

dddt

diru +

+

1= (1)

d

q

s

qqdt

d

iru

+

1

= (2)

dt

diru

f

s

fff

+

1= (3)

dt

dir D

s

DD

+

1=0 (4)

dt

dir

Q

s

QQ+

1=0 (5)

The equations defining the relations between thefluxes and currents are:

DdDfadddd ixixix ++ = (6)

QqQqqq ixix + = (7)

DfDffdadf ixixix ++ = (8)

DDffDddDD ixixix ++ = (9)

QQqqQQ ixix + = (10)

The aggregate motion equations are:

( ) sdt

d

1= (11)

( )emm

mmTdt

d

1= (12)

The electromagnetic torque of the generator isdetermined by equation:

qddqe iim = (13)

Connection between the synchronous generatorand AC network is determined by the following

equations:

sdqed

s

eedd uix

dt

dixriu +++

= (14)

sqde

q

s

eeqq uix

dt

dixriu ++

= (15)

( )sin= ssd Uu (16)

cos= ssq

Uu (17)

The mathematical model of a synchronousgenerator connected to a power system is simulatedin the Matlab/Simulink program tool.

In the first case the simulation model (fig. 4)includes a proportionally integral (P.I.) voltagecontroller and a proportional (P) generatorexcitation current controller.

After performing the tests on a simulationmodel it is necessary to implement the controlalgorithms into the existing excitation system.Nowadays, digital signal processors (DSP) are

often used as control units in the excitation controlsystem of a synchronous generator due to the large




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4 Using simulator for implementing

and testing of algorithmsSeveral changes need to be made for implementing

the control algorithm into the DSP system. Thesimulator works with a 32-bite fixed-point

TMS320F2812 DSP. Therefore, all the floating-point input signals must be converted into fixed-point signals. The voltage reference signal,

measured voltage and measured excitation currentsignals have been converted from floating-point intofixed-point signals using the IQMath blocks (Floatto IQN).

Fig. 8 shows the synchronous generator control

algorithm implemented in the simulator based onthe DSP. A PID controller block from the DMClibrary was used for the synchronous generator's PIvoltage control and P excitation current control.

Control algorithms with the simulator are block-programmed using Matlab/Simulink R2008a (withTC2 Target Support Package) [6], [7], [8].Using Real Time Workshop, Embedded Link IDECC, the block algorithm of the synchronousgenerator's excitation system is automaticallytranslated into C/C++, and also automaticallylowered into the DSP. The communication betweenthe PC and the DSP takes place via a parallelcommunication port using the RTDX interface [9].

4.1 Implementing of conventional algorithmThe generator's voltage control system's operationhas been tested for the cases of reference voltagestep change and of a three-phase short circuit on thetransmission line.

Fig. 9 show the generator responses in the caseof a short circuit which happened at 0,3 seconds andlasted 100 ms, for a system with a simulated discreteand DSP implemented controller.

Fig. 10 show the generator responses forgenerator's reference voltage change from the initialvalue of 1 p.u. to the value of 0,8 p.u., for a systemwith a simulated discrete and DSP implementedcontroller.

The simulation model controlled by the simulator(DSP) in real time has an 0,8 ms delay compared toa case, where the simulated model of the controlled

system is performed on a PC. The simulator's delaycompared to a synchronous generator's discreteexcitation system is caused by the delay in dataexchange between the DSP and the PC.

Fig. 8 Synchronous generator control algorithm on DSP based simulator




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0 0.5 1 1.5 2

0.5

1

1.5

t[s]

u[p.u.

]

Voltage

Simulated

DSP

0 0.5 1 1.5 2

-1

0

1

2

t[s]

p[p.u.

]

Active pow er

Simulated

DSP

0 0.5 1 1.5 2

-60

-40

-20

0

20

t[s]

[p.u.]

Load angle

Simulated

DSP

Fig. 9 Synchronous generator's voltage, active power

and load angle for short circuit with simulateddiscrete and implemented in DSP PI voltagecontroller and P excitation current controller

0 0.5 1 1.5 2

0.8

0.9

1

1.1

t[s]

u[p.u.

]

Voltage

Simulated

DSP

0 0.5 1 1.5 20.3

0.4

0.5

0.6

t[s]

p[p.u.

]

Active power

Simulated

DSP

0 0.5 1 1.5 215

20

25

30

t[s]

[p.u.]

Load angle

Simulated

DSP

Fig. 10 Synchronous generator's load angle for

generator's reference voltage change with simulateddiscrete and implemented in DSP PI voltagecontroller and P excitation current controller

0.3 0.305 0.31 0.315

0.996

0.998

1

t[s]

u[p.u

.]

Voltage

Simulated

DSP

Fig. 11 Time delay of the simulator

4.2 Implementing of nonlinear algorithmThe parameters and characteristics of a conventional

voltage regulator are determined based on alinearized synchronous generator model operating at

a specific work point so this regulator is not robustto generator work point changes, i.e. to systemstructure changes (transmission line falling out,short circuit on a transmission line etc.). The power

system keeps making bigger demands to the powerunits and thereby to the generator excitation controlsystem. This imposes the need to explore othertypes of structures and synchronous generatorexcitation system control algorithms. Starting from

the demands of the power system makes on thepower aggregate, i.e. on generator excitation, a new,nonlinear excitation controller has been developedand implemented by using Lyapunov's directstability method. The nonlinear regulator not only

keeps the voltage on generator clamps equal to thereference voltage, but also damps the electro

mechanic oscillations of the power unit.Lyapunov's direct method [10], [11], [12] was




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used to develop the nonlinear voltage regulator aswell as a third order mathematical model of ahydrogenerator (active resistances of the stator coilsand transient processes in damping coils wereneglected), which is connected to an AC network

via transformer and transmission line (fig. 2).Vector diagram of a hydrogenerator connected toAC network is presented on the fig. 12.

q

d

IUs

UgjXeId

Id

Iq

Usd

Usq

jXqIq

jXqIq

jXdId

jXd'IqjXeIq

E'=Eq'

E=Eq

Fig. 12 Vector diagram of hydrogenerator connected

to AC network

The mathematical model of synchronousgenerator connected to AC network is given by [1],[2], [11], [12]:

( ) sdt

d

1= (18)

( )emm

ppTdt

d

1= (19)

( )adffd

qxiE

Tdt

dE

'

1=

'

0

(20)

where is the load angle, rotation speed and Eqtransient induced voltage in the q axis q osi. Pedenotes generator active power which comes to:

( )

( ) ( )( )

++

+

+

2sin'

2

sin'

'=

2

eqed

qds

ed

sq

e

xxxx

xxU

xx

UEp

(21)

Lyapunov's direct method is one of the moreimportant tools for analyzing stability of nonlinearsystems today. Lyapunov's methods are also used inthe synthesis of nonlinear control algorithms, knownas Control Lyapunov Function (CLF) [13], [14],[15], [16], [17]. The existance of the CLF is both anecessity and condition enough for system stability.

Using the CLF can lead to the development ofvarius rules of control which will asymptotically

stabilize the system. The CLF's greatestdisadvantage is there is no exact way to find aCLF for a nonlinear system.

Further on, a control algorithm has beendeveloped for the control of a synchronous

generator excitation system, which will confirm thesystem's stability according to Lyapunov.

Assuming Lyapunov's function (22), where is theerror between voltage reference value and the realvoltage value on generator clamps (23):

2

2

1= eV (22)

uUe ref = (23)

Adding (23) into (22), and differentiating theequation (22) will lead to:

dtdue

dtdV = (24)

Supstitution of generator voltage22= qd uuu + to

the equation (24) will lead to:

+

dt

duu

dt

duu

u

e

dt

dV qq

dd= (25)

From the generator's vector diagram (fig 12),voltages ud i uq can be calculated:

( )eq

q

sdxx

xUu

+ sin= (26)

( )ed

ds

ed

eqq

xx

xU

xx

xEu

++

+

'

'cos

''= (27)

respectively:

( )

( )

+

+

s

eq

qs

eq

q

sd

xxxU

dt

d

xx

xU

dt

du

cos=

cos=

(28)

( )

( )

( )

+

+

+

+

sed

d

s

ed

eadff

d

ed

ds

ed

eqq

xx

xU

xx

xxiE

T

dt

d

xx

xU

xx

x

dt

dE

dt

du

'

'sin

''

1=

'

'sin

'

'=

0

(29)




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Adding the equations (28) and (29) to the equation(25) will lead to:

+

++

++

+

ss

ed

d

ed

eadf

d

q

ed

ef

d

q

ss

qe

q

d

Uxx

x

xx

xxi

Tu

xxxE

Tu

Uxx

xu

u

e

dt

dV

)(sin'

'

''

1

''1

)(cos=

0

0(30)

Control rule has been selected:

[

+

++

+

+

+

ss

ed

d

ed

eadf

d

q

ss

qe

q

d

qe

eddf

Uxx

x

xx

xxi

TuK

Uxx

xuK

eK

ux

xxTE

)(sin'

'

''

1

)(cos

1''=

0

3

2

10

(31)

where K1, K2 i K3 are parameters which force

Lyapunov's function differentiation to be negative atevery generator work point.

Implementing control rule (31) into the equation(30) will lead to:

])(1)(1

)(cos=

32

2

1

KYuK

Uxx

xu

u

e

u

eK

dt

dV

qs

s

qe

q

d

+

++

(32)

where:

+

+

ss

ed

d

ed

e

adfd

Uxx

x

xx

x

xiTY

)(sin'

'

''

1

=0 (33)

In order for the system to be stable according toLyapunov, the following must be valid at every

generator work point: 0u atevery generator work point), whereas the second

part depends on , , du and qu . If the

differentiation of Lypunov's function (32) is to be

negative, the following equation must be valid:

] 0


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0 1 2 3 4 5 6

0.8

0.9

1

1.1

u[pu]

t[s]

Voltage

PI Nonlinear

0 1 2 3 4 5 60.4

0.6

0.8

1

p[pu]

t[s]

Active pow er

PI Nonlinear

0 1 2 3 4 5 620

40

60

80

[

]

t[s]

Load angle

PI Nonlinear

Fig. 13 Synchronous generator's responses for

voltage reference change for implemented PI controlstructure and nonlinear control structure

0 1 2 3 4 5 6

0.85

0.9

0.95

u[pu]

t[s]

Voltage

PI Nonlinear

0 1 2 3 4 5 60.2

0.4

0.6

0.8

1

p[pu]

t[s]

Active power

PI Nonlinear

0 1 2 3 4 5 6

30

40

50

60

[

]

t[s]

Load angle

PI Nonlinear

Fig. 14 Synchronous generator's responses formechanical power change for implemented PIcontrol structure and nonlinear control structure

Fig. 15 Nonlinear voltage control structure




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0 0.2 0.4 0.6 0.8 10.2

0.4

0.6

0.8

1

u[pu]

t[s]

Voltage

PI Nonlinear

0 0.2 0.4 0.6 0.8 1-1

0

1

2

p[pu]

t[s]

Active pow er

PI Nonlinear

0 0.2 0.4 0.6 0.8 130

40

50

60

70

[

]

t[s]

Load angle

PI Nonlinear

Fig. 16 Synchronous generator's responses for shortcircuit on transmission line for implemented PIcontrol structure and nonlinear control structure

5 ConclusionDSP based simulator in real time enables fasterprocesses of engineering, implementing andverifying control algorithms not only for the voltagecontrol system of a synchronous generator, but also

for other systems able of having mathematical andsimulation models. The engineering of controlalgorithms is based on block programming, so theprogram code is automatically generated, translatedand downloaded into the DSP using Real TimeWorkshop and Matlab Embedded Link IDE CC.The simulator verifies the control algorithm by asimulation in real time, where the simulated modelof the controlled system is performed on a PC. Thispaper shows a comparison in the case when both thesystem model and the control structure aresimulated and for a case when the model issimulated on a computer and the control structureimplemented in the DSP. It has been concluded that

in the case when the control structure implementedin the DSP there is a 0,8ms time delay. Also, theimplementation of a conventional and a nonlinearsynchronous generator voltage control structure hasbeen presented. These methods were tested in the

cases of voltage reference change, mechanicalpower change and the case of a short circuit on thetransmission line. The nonlinear structure has shownbetter results as the conventional structure.

List of symbols

du d-axe component of the generator

terminal voltage

qu q-axe component of the generator

terminal voltage

fu excitation voltage

su infinite busbar voltage

sdu d-axe component of the infinite

busbar voltage

squ q-axe component of the infinite

busbar voltage

di d-axe component of the generator

stator current

qi q-axe component of the generator

stator current

fi field current

Di d-axe field damper current

Qi q-axe field damper currentr generator stator resistance

fr excitation resistance

Dr d-axe damper resistance

Qr q-axe damper resistance

generator rotor speed

s synchronous speed

d d-axe flux linkage

q d-axe flux linkage

f field flux linkage

D d-axe field damper flux linkage

Q q-axe field damper flux linkage

dx d-axe synchronous reactance

qx q-axe synchronous reactance

fdx field reactance

Dx d-axe damper reactance

Qx q-axe damper reactance

'dx d-axe transient reactance




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adx armature reaction reactance

LTe xxx += transformer and transmission line

reactance

LTe rrr += transformer and transmission line

resistance

rotor angle

mm mechanical torque

em electromagnetic torque

mp mechanical power

ep electromagnetic power

mT mechanical time constant

'qE q-axe component of transient EMF

fE field voltage

Appendix AThe synchronous generator's rated parameters are:

Voltage 400 VCurrent 120 A

Power 83 kVAFrequency 50 Hz

Speed 600 r/minPower factor 0,8Excitation

voltage

100 V

Excitationcurrent

11.8 A

Appendix BControllers parameters are:

Voltage controllerKp 10Ki 15Excitation current controller

Kp 10Nonlinear controllerK1 50K2 -7K3 1

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SYSTEMS and CONTROL, 6(3), 2008

[2] C. Lupu, D. Popescu, A. Udrea, Real-timeControl Applications for Nonlinear Processes Basedon Adaptive Control and the Static Characteristic,WSEAS TRANSACTIONS on SYSTEMS andCONTROL, 6(3), 2008

[3] I. Dumitru, I. Fagarasan, S. St. Iliescu,G.Stamatescu, N. Ardhira, V. Barbulea,,A modular

process simulator with PLC, Proc. 9th WSEAS

International Conference on Simulation, Modellingand Optimization, 2009.[4] Prabha Kundur, Power System Stability andControl, Power System Engineering Series,

McGraw-Hill, 1993.[5] Paul M. Anderson, A. A. Fouad,Power SystemContol and Stability, IEEE Press, IEEE PowerSystem Engineering Series, 1994.[6] The Mathworks, Real Time Workshop

User's Guide, 2008.[7] The Mathworks,Embedded IDE Link CC 3User's Guide, 2008.[8] The Mathworks, Target Support PackageTC2 3 User's Guide, 2008.

[9] Texas Instruments: TMS320F2810,TMS320F2811, TMS320F2812, Digital Signal

Processors, Data Manual, 2004.[10] A. Kazemi, F. Mahamnia, Improving ofTransient Stability of Power Systems bysupplementary Controllers of UPFC Using DifferentFault Conditions, WSEAS TRANSACTIONS on

POWER SYSTEMS, 7(3), 2008[11] Jan Machowski, Janusz Bialek, and Dr JimBumby, Power System Dynamics: Stability andControl, Wiley, 2008[12] Qiang Lu, Yuanzhang Sun, and ShengweiMei, Nonlinear Control Systems and Power SystemDynamics, Springer, 2001

[13] R. A. Freeman, P. V. Kokotovic, Robustnonlinear Control Design State Space and LyapunovTehniques, Birkhauser, 1996[14] M. Krstic, I. Kanellakopoulos, P. V.Kokotovic,Nonlinear and Adaptive Control Design,

John Wiley and Sons, 1995[15] E. D. Sontag, A universal construction ofArtsteins theorem on nonlinear optimization, Syst.Control Lett., pp. 117-123, 1989[16] R. A. Freeman, J. A. Primbs, ControlLyapunov functions: New ideas from an old source,Proc. 35th IEEE Conf. Decis. Control, Kobe, Japan,

pp. 3926-3931. 1996[17] J. Machowski, S. Robak, J.W. Bailek, J.R.Bumby, Decentralised Lyapunov-Based PowerSystem Stabiliser, International Conference onElectric Utility Deregulation and Restructuring andPower Technologies, 2000



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29-753 - DSP Based Simulator for Excitation Control of Synchronous Generator