Energy Function based Fuzzy Logic DiscreteControl with SSSC for stability improvement

R. ThirumalaivasanSchool of Electrical Engineering

VIT UniversityVellore, Tamilnadu.

Email: janaki.m@vit.ac.in

M. JanakiSchool of Electrical Engineering

VIT UniversityVellore, Tamilnadu.

Email: thirumalai.r@vit.ac.in

Nagesh PrabhuDepartment of EEE

NMAM Institute of TechnologyNitte, Karnataka.

Email: prabhunagesh@rediffmail.com

Abstract—Static Synchronous Series Compensator is a flexibleAC transmission System device which can improve the stability ofthe system, increases the power transfer capability and is usefulfor the fast control of power flow. This paper analyzes the use ofSSSC with discrete control to improve the transient stability ofpower system. During transient period SSSC is switched betweeninductive or capacitive or operating value and whose referencevalue of reactive voltage is obtained from Fuzzy Logic DiscreteController (FLDC). The fuzzy logic discrete controller is based onenergy function. Transient simulation is carried out to analyze thesystem. The results of the case study system adapted from IEEEFirst Benchmark Model demonstrate the effectiveness of fuzzylogic discrete controller in stabilizing the rotor angle oscillation.Linear analysis is performed on D-Q model of the system withFLDC and SSSC.

Keywords—Voltage Source Converter(VSC), FACTS, Static Syn-chronous Series Compensator (SSSC), Fuzzy Logic Discrete Con-troller (FLDC).

I. INTRODUCTION

In a transmission system, the stability aspect limits thepower transfer capability. The series connected FACTS con-trollers, like Thyristor Controlled Series Capacitor (TCSC) andStatic Synchronous Series Compensator (SSSC) can improvethe stability of transmission system and increases the powertransfer capability [1]. SSSC has several advantages overTCSC [2], and it can control reactive voltage, i.e. one degreeof freedom [3].

Transient stability is concerned with the stability of powersystems when subjected to severe or large disturbance like athree phase to ground fault. For a specified transient stabilitylimit, a judicious combination of switched and fixed seriescapacitors result in smaller rating of the capacitors whencompared to the case when all are fixed (or unswitched). Theinsertion of series capacitors also reduces angular swing andthe voltage fluctuations (the load especially those near the elec-trical center of the system [3]. Switching of series capacitors orits bang-bang control has been suggested to improve the powersystem transient stability along with the fast damping of lowfrequency rotor oscillations following a large disturbance [4]-[6]. Direct methods based on energy are useful for the analysisand control of transient stability [7],[8]. The availability of fastcontrol with Thyristor Controlled Series Compensator (TCSC),a FACTS controller enables the realization of this concept.The use of energy functions for discrete control of TCSC isproposed in [9].

In this paper, the investigations on transient stability usingSSSC is presented. The analysis and design of fuzzy logicdiscrete controller for SSSC to improve the power systemtransient stability is carried out. The study system is IEEEFBM with SSSC. SSSC is based on 3-level 24-pulse [1] VSCwith Type-1 controller [11]. Fuzzy Logic Discrete controlchanges the control variables, such that the system reachesstable operating point after a large disturbance. The SSSCinjected voltage is considered as a control variable and thereference value of reactive voltage is obtained from fuzzy logicdiscrete controller.

The paper is organized as follows: In section II, Modelingof SSSC and, Section III details a case study and discretecontrol logic. The design of Fuzzy Logic Discrete Controllerand transient simulation are given in Section IV. Conclusionsdrawn based on case studies are given in Section V.

II. MODELING OF SSSC

The schematic diagram of SSSC is depicted in Fig. 1. InSSSC power circuit, the converter is generally either a multi-pulse or a multilevel configuration.

vdc

bc

g c

V i i

idc

VSC

+

Fig. 1. Schematic representation of SSSC

In the realization of SSSC, a 24-pulse 3-level configurationis used. In two level converter topology, with constant DCvoltage, the Pulse Width Modulation (PWM) of ac voltageoutput magnitude requires high switching frequency, whichcauses increased losses, wherein 3-level converter topology,to control ac voltage output magnitude, dead angle β is variedwith fundamental switching frequency [10], [3]. The converters

which facilitates the control over the magnitude and phaseangle of their output voltage are termed as TYPE-1 converters[11]. The harmonic distortion is significantly reduced withthree level converter topology. The 3-phase model of SSSCis developed by representing the operation of converter byswitching functions. The switching function for phase ’a’ isshown in Fig. 2.

0.42 0.425 0.43 0.435 0.44 0.445 0.45−1.5

−1

−0.5

0

0.5

1

1.5

Time (sec)

P a(t) 2β

Line current ia (t)

Pa (t)

Fig. 2. Switching function for a three level converter

The phase ’b’ and ’c’ switching functions are same as phase’a’ however phase shifted successively by 120o. Assuming thedc side capacitor voltages Vdc1 = Vdc2 = Vdc

2 , the terminalvoltages of converter with respect to dc side mid point ’N’can be written as,

V iaN

V ibN

V icN

=

[

Pa(t)Pb(t)Pc(t)

]

Vdc

2(1)

and the output voltages of converter with respect to transformerneutral can be written as,

V ian

V ibn

V icn

=

[

Sa(t)Sb(t)Sc(t)

]

Vdc (2)

where, Sa(t) = Pa(t)2 −

[

Pa(t)+Pb(t)+Pc(t)6

]

Sa(t) is the switching function for phase ’a’ of a 6-pulse 3-level VSC. Likewise Sb(t) for phase ’b’, and Sc(t) for phase’c’ can be obtained. The maximum value of the fundamentaland harmonics in phase ’a’ voltage V i

an can be found byemploying Fourier analysis, and it is expressed as,

V ian(h) =

2

hπVdccos(hβ) (3)

Where h=1,5,7,11,13 and β is the dead angle during which theconverter output voltage is zero. The 5th and 7th harmonicscan be eliminated by using a twelve-pulse VSC.

The switching functions for first twelve-pulse converter areas follows:S12

1a(t) = S1a(t) + 1√3(S

′

1a(t) − S′

1c(t)),S12

1b (t) = S1b(t) + 1√3(S

′

1b(t) − S′

1a(t)),

S121c (t) = S1c(t) + 1√

3(S

′

1c(t) − S′

1b(t))where

S′

1x(t) = S1x

[

t +2π

ωo

1

12

]

S1x(t) = Sx

[

t +π

ωo

1

24

]

, x = a, b and c (4)

The switching functions for second twelve-pulse converter areas follows:S12

2a(t) = S2a(t) + 1√3(S

′

2a(t) − S′

2c(t)),S12

2b (t) = S2b(t) + 1√3(S

′

2b(t) − S′

2a(t)),S12

2c (t) = S2c(t) + 1√3(S

′

2c(t) − S′

2b(t))where

S′

2x(t) = S2x

[

t +2π

ωo

1

12

]

S2x(t) = Sx

[

t −π

ωo

1

24

]

, x = a, b and c (5)

The switching functions for a twenty four-pulse converterare as follows:

S24x (t) = S12

1x(t) + S122x(t), x = a, b and c (6)

Neglecting the harmonics and approximating the switchingfunctions by their fundamental components, the converteroutput voltage for a 24-pulse 3-level converter is given by,

V ian =

8

πVdccos(β)sin(ωot + φ + γ) (7)

and V ibn,V i

cn are phase shifted successively by 1200.

The line current is expressed as, ia =√

23Iasin(ωo + φ) and

ib, ic are phase shifted successively by 120o. The phase angle γis the value by which the converter output voltage fundamentalcomponent leads the line current. It is to be noted that γ isnearly equal to ±π

2 when SSSC injects inductive or capacitivevoltages. When the losses in the converter are neglected, theexpression for dc capacitor current is as,

[ idc ] = −[

S24a (t) S24

b (t) S24c (t)

]

[

iaibic

]

(8)

For 2β = 180o

h, a particular harmonic becomes zero. At

βoptimum = 3.75o, the 3-level 24-pulse converter performsnearly like a 2-level 48-pulse converter as 23th and 25thharmonics are negligible.

A. Modelling of SSSC in D-Q variables

Neglecting the harmonics and approximating the switchingfunctions by their fundamental components, SSSC is modelledby transforming the 3-phase voltages and currents to D-Qusing Kron’s transformation [12]. The functionality of SSSCcan be represented as shown in Fig. 3.

In Fig. 3, the resistance and reactance of VSC interfacingtransformer are denoted as Rst and Xst. To control the

φ + γ

φ

R st

X st

V i

I

Fig. 3. equivalent circuit of SSSC as viewed from AC side

converter output voltage magnitude, dead angle β is variedwith constant dc voltage.

The representation of converter output voltage in D-Qframe is as follows:

V i =√

V iD

2+ V i

Q

2 (9)

V iD = kmVdc sin(φ + γ) (10)

V iQ = kmVdc cos(φ + γ) (11)

where km = k ρ cos βse; k = 4√

6π

for a 24 pulse converter. ρis the transformation ratio of the interfacing transformer.

The active (VP (se)) and reactive (VR(se)) voltages injectedby SSSC are represented in D-Q variables (V i

D and V iQ) as

follows.VR(se) = V i

D cosφ − V iQ sin φ (12)

VP (se) = V iD sinφ + V i

Q cos φ (13)

Here, positive VR(se) signifies, SSSC injects inductive voltage,and positive VP (se) signifies, SSSC absorbs real power to meetthe converter losses.

The differential equation of dc side capacitor is as,

dVdc

dt= −

gcωb

bcVdc − idc

ωb

bc(14)

where idc = − [kmsin(φ + γ)ID + kmcos(φ + γ)IQ], ID andIQ are the line current D-Q components.

B. Type-1 controller

In this controller, magnitude and phase angle of converteroutput voltage can be controlled and the dc capacitor voltageis maintained constant by varying the injected voltage activecomponent VP (se). For control of real voltage, the referencevalue of real voltage VP (se)(ord) is obtained from dc voltagecontroller, and for reactive voltage control, a constant reactivevoltage reference VR(se)(ord) is considered.

It is to be noted that, harmonic content of SSSC injectedvoltage depends upon the operating point as the magnitudecontrol also governs the switching. In 3-level 24-pulse con-verter, depending on reactive voltage reference, the referencevalue of capacitor voltage can be adjusted to achieve optimumharmonic performance at βse = 3.75o in steady state.

The type-1 controller for SSSC is shown in Fig. 4, whereγ and βse are calculated as

γ = tan−1

[

VR(se)(ord)

VP (se)(ord))

]

(15)

Vdcref

1 + s Tmd

1

dcV

k p

k is

R(ord)V

VP(ord)

calculator

γ and β

β

γ

+Σ

−

+

+

Σ

Discrete ControllerFuzzy Logic

Fig. 4. Type-1 controller with FLDC for SSSC

X sys

X tRt

XlR l

Vg θgb

VSC

+

SSSC

Generator

0E

cb

cg

+

i

Fig. 5. Modified IEEE First Benchmark Model with SSSC

βse = cos−1

√

V 2P (se)(ord) + V 2

R(se)(ord)

kmVdc

(16)

III. A CASE STUDY

The system under study is adapted from IEEE FBM [13],[14], long transmission line and SSSC injecting a series voltagein the transmission line is shown in Fig. 5.

The analysis is carried out by considering the followingassumptions and initial operating condition.

1) The generator supplies power (Pe) of 0.1 p.u. to thetransmission line.

2) The mechanical input power to the turbine is madeconstant.

3) The study is carried out for the cases without DiscreteControl and with Fuzzy Logic Discrete Control.

4) In transient simulation, a large disturbance of stepchange in mechanical input power from 0.1 p.u to0.9 p.u is considered at 0.5 sec and the disturbanceis cleared after 1 sec.

A. Discrete Control Logic

Transient stability of the power system can be improved bydamping the oscillations in generator rotor angle. When a largedisturbance occurs, the electrical power Pe is to be maximizedrapidly by reducing the decelerating and accelerating areassequentially and hence the rotor oscillations are damped [15].The power angle curve is used for developing the controlstrategy, and the three power angle curves in respect of basepower (with base or operating value of SSSC control variable),maximum power and minimum power are shown in Fig. 6. Byappropriately selecting the SSSC control variable VRref , thepower flow can be maximized and minimized. Pm is the inputmechanical power and δs is the initial and post-fault steadystate rotor angle of SMIB system. When a large disturbanceoccurs, say a change in input mechanical power or threephase to ground fault at generator terminals, the corresponding

accelerating area in power angle curve is ′abcda′. δcl is therotor angle at fault clearing time. At the time of fault clearance,the kinetic energy stored in generator rotor causes the rotor tooscillate beyond δcl. And the rotor angle reaches a maximumvalue δmax when decelerating area ′defgd′ becomes equal tothe accelerating area ′abcda′. Hence to decrease δmax, it isnecessary to increase (to maximum value of) the electricalpower. The power angle curve with points e and f correspondsto the maximum power. The power flow in the line can becontrolled by changing SSSC control variable.

At δ = δmax, dδdt

= 0. The rotor angle δu in power anglecurve is the unstable equilibrium point which corresponds tothe post-fault steady state values of the SSSC variable. Forvalues of δmax ≤ δu, if SSSC control variable is switchedto the operating value at the moment when δ = δmax, therotor angle is steered to a stable equilibrium value δs. Whenδ = δs, dδ

dtis at negative minimum, the power flow in the line

is varied to minimum by switching SSSC control variable, andthe undershoot of the generator rotor angle reduces. The rotorangle arrives a minimum value δmin when the acceleratingarea ′aijka′ becomes equal to the decelerating area ′ghag′.At the moment δ = δmin, dδ

dt= 0, if SSSC control variable

is switched to the operating value, the rotor angle is steeredto a stable equilibrium value δs. When δ = δs, dδ

dtis at

maximum, the power flow in the line is varied to maximumby switching SSSC control variable, and the overshoot of therotor angle reduces. Hence it is to be noted that, to reduceundershoot and overshoot of the generator rotor angle, powerflow is minimized when δ < δs, dδ

dt< 0 and the power flow is

maximized when δ > δs, dδdt

> 0.

0 20 40 60 80 100 120 140 160 180−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

δ in deg

base powermaximum powerminimum power

Pm

Pe

k a

l

j

i

b c

d

e

f

h

g

δmin

δs δ

cl δ

max δ

u δ’

u

Fig. 6. Power angle curves

The potential energy WPE of SMIB is given by

Wpe(δ) =

∫ δ

δo

(Pe − Pm)dδ (17)

where Pe and Pm are steady state value of electrical powerand turbine mechanical power respectively before and afterfault.

The control strategy is developed is as follows

1) The control variable VRref is selected such that tomaximize the power Pe the moment a large distur-bance is detected.

2) The control variable is switched to operating valuewhen dWpe

dt= 0 and dδ

dt≤ 0.

3) The control variable is selected such that to minimizethe power when dδ

dtis minimum and dδ

dt< ε.

4) The control variable is switched to the operating valuewhen dδ

dtbecomes zero.

5) The control variable is selected such that to maximizethe power when dδ

dtis at maximum and dδ

dt> ε. The

control action is repeated from step 2 to 5 till themagnitude of dδ

dt≤ ε.

IV. DESIGN OF FUZZY LOGIC DISCRETE CONTROL

The crispy logic in Boolean theory uses only two logiclevels (0 and 1), whereas fuzzy logic is a branch that allowsinfinite logic levels (from 0 to 1), and is used to solve aproblem that has uncertainties or imprecise situations. Thecontrol strategies in the FLC are based on the computationof the fuzzy membership function of control variables andthe linguistic control rules. Hence, if the designed controllerdoes not satisfy the system requirements owing to a changein the outside environment of the control system, the systemcontrol strategies have to be changed to meet the controlobjective. The possible approach to this problem is that themembership function of the fuzzy sets or the control rules canbe adjusted to meet the control objective. In [16], the transientstability improvement with fuzzy logic based unified powerflow controller is reported.

Σ X

ddtδ

Pm

PeVRref+

−

Fuzzy Logic

Discrete Controller

Fig. 7. Block Diagram of Fuzzy Logic Discrete Controller.

The control logic presented in section III is developed infuzzy logic and whose block diagram is shown in Fig. 7. TheFuzzy Logic Discrete Controller involves: (1) fuzzification (2)inference and (3) defuzzification unit.

1) Fuzzification: In this process, the input variables areconverted to fuzzy linquistic variables. Each fuzzifiedvariable holds certain membership function. The tri-angular membership functions is chosen for both theinput and output variables. There are three linguisticvariables for each input variable and output variable,such as, ’Negative Maximum’(NM), ’Zero’(Z), ’Pos-itive Maximum’(PM). The input to the fuzzy logiccontroller are [ dWpe

dt, dδ

dt].

2) Inference: The control actions are decided on thebasis of fuzzified linguistic variables. Inference sys-tem involves rules for resolving output decisions. Forthe input variables having three fuzzified variables,the fuzzy controller holds 9 rules for SSSC injectedvoltage control.

3) Defuzzification: The inference system output vari-ables are the linguistic variables. These linguisticvariables must be mapped to numerical values (out-put).

1) Transient simulation: The transient simulation is carriedout with the combined system with and without FLDC usingMATLAB-SIMULINK [17]. The control strategy is employedto the system with a large disturbance. It is assumed that, 0.1p.u is the initial power supplied by the generator with terminalvoltage of 1 p.u and the steady state value of reactive voltageinjected by SSSC is zero. A step change in input mechanicalpower from 0.1 p.u to 0.9 p.u at 0.5 sec is considered as alarge disturbance and the disturbance is cleared after 1 sec. Itis seen that, the system is unstable without discrete control. Theapplication of the discrete control strategy stabilizes the systemas the rotor angle oscillation decreases with time as shown inFig. 8. The SSSC injected voltage is shown in Fig. 9, and it isto be noted that when rotor angle is maximum, the electricalpower is maximized with SSSC capacitive voltage. When rotorangle is minimum, the electrical power is minimized withSSSC inductive voltage.

0 1 2 3 4 5 6 7 8 9 10−200

−150

−100

−50

0

50

100

150

200

250

300

Time in sec

Rot

or a

ngle

in d

eg

with FLDCwithout FLDC

Fig. 8. Variation of rotor angle with and without FLDC.

0 1 2 3 4 5 6 7 8 9 10−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0.2

0.25

Time in sec

SS

SC

inje

cted

vol

tage

in p

.u.

Fig. 9. SSSC injected voltage.

V. CONCLUSION

In this paper, the investigations on transient stability im-provement using SSSC with Fuzzy logic discrete controller

is presented. The SSSC is realized by 24-pulse three levelconfiguration. The transient stability can be improved byswitching SSSC reactive voltage reference between inductiveor capacitive or operating value where the reference valueof reactive voltage is obtained from Fuzzy Logic DiscreteController (FLDC). The predictions about the stability of thesystem is done with transient simulation using MATLABSimulink. FLDC involves changing the control variable (SSSCreactive voltage reference) such that the system reaches stableoperating point after a disturbance. The rotor oscillationsare damped by successively maximizing and minimizing theelectrical power using discrete control of SSSC and stabilizesthe system. The result shows the effectiveness of SSSC withfuzzy logic discrete control.

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