Adaptive type 2 fuzzy controller for

International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No.1, January 2014

DOI : 10.5121/ijfls.2014.4102 13

ADAPTIVE TYPE-2 FUZZY CONTROLLER FORLOAD FREQUENCY CONTROL OF ANINTERCONNECTED HYDRO-THERMALSYSTEM INCLUDING SMES UNITS

Dr. R.Vijaya Santhi1 and Dr. K.R.Sudha2

1 Assistant Professor,Department of Electrical Engineering, Andhra University, India2 Professor,Department of Electrical Engineering, Andhra University, India

ABSTRACT

This present paper includes the study Load Frequency Control (LFC) of power systems with several non-linearities like Generation Rate Constraint(GRC) and Boiler Dynamics (BD) including SuperconductingMagnetic Energy Storage (SMES) units using Type-2 Fuzzy System (T2FS) controllers . Here, Loadfrequency control problem is dealt with a three – area interconnected system of Thermal-Thermal-Hydalpower system by observing the effects and variations of dynamic responses employing conventionalcontroller, Type-1 fuzzy controller and T2FS controller considering incremental increase of steppertubations by 10% in the load. The salient advantage of this controller is its high insensitivity to largeload changes and plant parameter variations even in the presence of non-linearities. As the non-linearitieswere considered in the system, the conventional and classical Fuzzy controllers does not provide adequatecontrol performance with the consideration of above nonlinearities. To overcome this drawback T2FSController has been employed in the system. Therefore, the efficacy of the proposed T2FS controller isfound to be better than that of conventional controller and Type-1 Fuzzy controller in cosidreration withovershoot, settling time and robustness.

KEYWORDS

Load Frequency Control(LFC), Type-2(T2) Fuzzy Controller, Generation Rate Constraint (GRC), BoilerDynamics(BD), Superconducting magnetic energy storage (SMES).

1. INTRODUCTION

Inorder to maintain system frequency and inter-area oscillations within limits, Load FrequencyControl (LFC) plays a vital role in large scale electric power systems. Both area frequency andtie-line power interchange varies with variation in power load demand. The motives of loadfrequency control (LFC)[1][2] are to minimize the transient deviations in theses variables and toensure their steady state errors to be zeros. When dealing with the LFC [3] problem of powersystems, certain unexpected pertubations, parametric uncertainties and the model uncertainties ofthe power system leads for the designing of controller. In large interconnected power system ,


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generation of power is done by thermal, hydro, nuclear and gas power units.Usually, nuclearunits are kept at base load close to their maximum output owing to their high efficiency with noparticipation in system Automatic Generation Control (AGC)[4]. Since these type of plantsproduces a very small percentage of total system generation, so such plants donot play ansignificant role in AGC of a large power system. In order to meet peak demands, Gas plants areused. Thus the natural choice for LFC falls on either thermal or hydro units.

In past, the area of LFC constrained to interconnected thermal systems and relatively lesserattention has been focussed to the LFC of interconnected hydro-thermal system [5] involvingthermal and hydro subsystem of widely different characteristics. Concordia and Kirchmayer [6]have studied the AGC of a hydro-thermal system considering non-reheat type thermal systemneglecting generation rate constraints and boiler dynamics. Since frequency has become acommon factor, a change in active power demand at one point is reflected throughout the system,.Mostly in the load frequency control studies, the boiler system effects and the governor dead bandeffects are neglected. But for the realistic analysis of system performance, these should beincorporated as they have considerable effects on the amplitude and settling time of oscillations.From the past literature, under continuous-discrete mode with classical controllers, Nanda,Kothari and Satsangi [7] are the first to present comprehensive analysis of LFC of aninterconnected hydrothermal system.

In the past decades, fuzzy logic controllers (FLCs) have been successfully developed for analysisand control of nonlinear systems [8][9]. The fuzzy reasoning approach is motivated by its abilityto handle imperfect information,especially uncertainties in available knowledge. Stimulated bythe success of FLCs, Talaq [10], Yesil and Chang[11] proposed different adaptive fuzzyscheduling schemes for conventional PI andor PID controllers. These methods provide goodperformances but the system transient responses are relatively oscillatory.

The main motive of this paper is to determine the Load Frequency Control and inter-area tiepower control problem for a wide area power system with following certain uncertainities. Fromthe literature, many authors have proposed fuzzy logic based controllers to power systems [12]inorder to take care of these uncertainties. This fuzzy logic, also called as Type-1 fuzzy, canfurther be modified to Type-2 fuzzy by giving grading to the membership functions which arethemselves fuzzy. Or in other words, in Type-2 fuzzy sets, at each value of the variable themembership is a function but not just a point value. Therefore, a Type-2 fuzzy set can bevisualized as a three dimensional. The advantage of the third dimension gives an extra degree offreedom for handling uncertainties. Taking this feature into consideration, a robust decentralizedcontrol scheme is designed using Type-2 Fuzzy logic [13][14][15]. The proposed controller issimulated for a three area power system in the presence of Generation Rate Constraint (GRC) andBoiler Dynamics (BD)[16] including Superconducting Magnetic Energy Storage(SMES) unitswas compared with conventional PI controller and Type-1 Fuzzycontroller. Results of simulationshow that the T2 fuzzy controllers guarantee the robust performance .

2. POWER SYSTEM MODELLING AND PROBLEM FORMULATION:

Usually, tie line power are used to interconnect control areas for a large scale power system.However, for the design of LFC a simplified and linearized model is usually used. The detailedpower system modeling of three area system containing two reheat steam turbines and one hydro-turbine tied together through power lines including Superconducting Magnetic Energy Storage


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(SMES) units with Generation Rate Constraint (GRC) and Boiler Dynamics (BD) for loadfrequency control is investigated in this study as shown in Fig.1 with Area Control Error(ACE)and its derivative are given as the inputs to the controllers [17]. Three areas have been installedwith SMES1, SMES2 and SMES3 inorder to stabilize frequency oscillations. The interconnectedpower system model is shown in Fig-3. The Parameters of the three areas is given in Appendix.Modelling of Speed Governors and turbines are discussed in [18]. Power generation can bechanged only to a specified maximum rate in a power system having steam plants. the generationrate for the steam plants can be restricted, by adding limiters to the governors. The GenerationRate Constraint (GRC) value for thermal units of 3%/min is considered. To prevent the excessivecontrol action, two limiters, bounded by ± 0.0005 within the automatic generation controller areused. By adding limiters to the turbines GRCs for all the areas are taken into consideration. Fig-2shows the model to represent the boiler dynamics. Representations for combustion controls arealso incorporated. This model is used inorder to study the responses of coal fired units withpoorly tuned combustions controls and with well tuned controls.The limiter of -0.01 ≤ ∆PSMi,i=1, 2 ≤ 0.01 [puMW] based on a system MW base is equipped for each SMES unit. “Parametersvalues of SMES1, SMES2 and SMES3 are set at Ksm1 = Ksm2 = Ksm3= 0.12 and Tsm1 = Tsm 2=Tsm3= 0.03 sec[19]”.

3.TYPE 2 (T2) FUZZY LOGIC CONTROLLERS:

Zadeh [20] introduced type-2 fuzzy sets. The fuzzification of a type-1 fuzzy set gives theType-2 sets. To describe the membership function by numbers, type-1 fuzzy sets requiresthe developer, in the discrete case, or by a function, where continuous membership function isgiven by the fuzzy . So, `non-fuzzy' (or crisp) representation is given by the fuzziness of asystem which employs fuzzy sets . A fuzzy system that uses Type-2 fuzzy sets and/or fuzzy logicand inference is called a Type-2 (T2) fuzzy system. Infact, a Type-1 (T1) fuzzy system can bedefined as the system that employs ordinary fuzzy sets, logic, and inference. In order to solvemany practical problems, T1 fuzzy systems, especially fuzzy logic controllers and fuzzy modelsare modelled. As per Mendel,“A Type-1 fuzzy set (T1 FS) has a grade of membership that iscrisp, whereas a Type - 2 fuzzy set (T2 FS) has a grade of membership that is fuzzy, so T2 FS are‘fuzzy-fuzzy’ sets”. To represent the fuzzy membership of fuzzy sets footprint of uncertainty(FOU) is employed, which is a 2-D representation, with the uncertainty about the right end pointof the right side of the membership function and with the uncertainty about the left end point ofthe left side of the membership function. The type-1 fuzzy sets, which represents uncertainty bynumbers in the range [0, 1] can be handled by the general framework of fuzzy reasoning .

Uncertainity cannot be determined with its exact value, because of its complexity and rathertype-1 fuzzy sets gives much senser than using crisp sets [21]. So, it is difficult to measure anuncertain membership function . To overcome this difficulty, we require another type of fuzzysets, those which has ability to handle these uncertainties. Those type of fuzzy sets are calledtype-2 fuzzy sets. As the type-2 fuzzy logic has better capability to cope up with linguisticuncertainities , type-2 is a good replacement for type-1 fuzzy system..

Infact, the Type 1- fuzzy and Type-2 fuzzy sets operation are similar, but while using withinterval fuzzy system; by limiting the FOU, fuzzy operator is being done as two T1 membershipfunctions, UMF and LMF inorder to produce firing strength which is shown in Fig - 4.Defuzzification is a mapping process from fuzzy logic control action to a non-fuzzy (crisp)control action. Defuzzification on an interval Type2 fuzzy logic system using centroid method is


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shown in Fig -4. In Type-2 fuzzy set, at each value of primary variable the membership is afunction and it is not just a point value; the secondary membership function whose domain, i.e.,the primary membership is in the interval [0,1], then their range, the secondary grades may alsobe in the interval [0,1]. Since, the foot of membership functions is not a single point but designedover an interval, therefore Type -2 fuzzy logic controller can also be refered as Interval Type-2fuzzy logic controller. Interval type2 fuzzy logic operation is shown in Fig. 4.The Interval Type-2membership functions and operators are designed and are employed in the IT2FLS toolbox. AnInference FS is a rule base system that uses fuzzy logic, instead of Boolean logic that is utilized indata analysis. Its basic structure includes four components (Fig - 5):

Fuzzification: Translates inputs (real values) to fuzzy values.Inference System: To obtain a fuzzy output, fuzzy reasoning mechanism is applied.Type Defuzzificator/Reductor: To transduces one output to precise values, defuzzificator isemployed; the type reductor converts a Type 2 Fuzzy Set into a Type- 1 Fuzzy Set.

Knowledge Base:It contains data base which consists of set of fuzzy rules, and a membership

functions set. The two normalized input variables, ACE∆ and ECA ∆ , are first fuzzified by two

interval T2 fuzzy sets (Fig -6), namely “positive” and “negative” represented by )( ACEP ∆ and

)( ACEN ∆ respectively. The primary memberships are generated by blurring the trapezoidal

T1 fuzzy sets 1 )( ACEP ∆ , )( ACEN ∆ , )( ECAP∆ , and )( ECAN

∆ . The interval T2

fuzzy sets secondary membership functions are all constant.

The definitions of the T1 fuzzy sets are as follows:

∞−∆+

−−∞=∆

),[1],[2/))((

],(0)(

1

1111

1

LLLLACEL

LACEp -----(1)

After shifting the membership functions of the T1 fuzzy sets upward and downward by θ1∈[0,0.5] for )( ACEP ∆ and )( ACEN ∆ along the membership axes, the boundary membership

functions of the primary memberships of the interval T2 fuzzy sets[22][13] (i.e.), )( ACELP ∆ ,

)( ACEPU ∆ , )( ACENL ∆ , )( ACENU ∆ ). These boundary membership functions form

the shaded bands in Fig -6 which are called footprints of uncertainty (FOU). The designparameters θ1and θ 2are used to control the degree of uncertainty of the interval T2 fuzzy sets.Inorder to realize the AND operations in the rules, Zadeh fuzzy logic AND operator (i.e., min( ))is used.

If ACE∆ is P and ECA ∆ is P, then U is N

For an interval T2 fuzzy interface, the firing set becomes a firing interval

[RL,RU]=[min( ACE∆ PL, ECA ∆ PL,U NL), min( ACE∆ PU, ECA ∆ PU,UNU)]The rules are shown in Table-1.


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4. SIMULATION RESULTS

To illustrate robust performance of the proposed Type-2 Fuzzy controller we have chosendifferent cases:

Case I(a),Case I(b) & CaseI(c): Step increase in demand of the first area ∆ PD1: In this case,step increase in demand of the first area ∆ PD1 is applied. The frequency deviation of the firstarea, Δf1, the frequency deviation of the second area, Δf2, the frequency deviation of the thirdarea, Δf3, and inter area tie-power signals of the closed-loop system are shown in Fig -7,Fig -8.Step increase in demand of the second area ∆ PD2 is applied. The frequency deviation of the firstarea, Δf1, the frequency deviation of the second area, Δf2, the frequency deviation of the thirdarea, Δf3, and inter area tie-power signals of the closed-loop system are shown in Fig -9, Fig -10.Step increase in demand of the third area ∆ PD3 is applied. The frequency deviation of the firstarea, Δf1, the frequency deviation of the second area, Δf2, the frequency deviation of the thirdarea, Δf3, and inter area tie-power signals of the closed-loop system are shown in Fig -11, Fig -12.Using proposed method, the frequency deviations and inter area tie-power quickly driven backto zero and controller using T2 fuzzy controller has the best performance in control and dampingof frequency and tie-power in all responses when compared with conventional PI and Type-1Fuzzy controller [12].

Case II: Step increase in demand of the first area ∆ PD1 , second area ∆ PD2 and third area ∆ PD3

is applied. This is the condition, for which perturbation is given in all the three areas. In this case,a step increase in demand of the first area ∆ PD1 , the second area ∆ PD2 and third area ∆ PD3 isapplied. The frequency deviation of the first area Δf1 , the frequency deviation of the second areaΔf2, the frequency deviation of the third area Δf3 is shown in Fig -13,fig-14. The frequencydeviations and inter area tie-power quickly driven back to zero by employing proposed controller.Type- 2 fuzzy controller has the best performance in control and damping of frequency and tie-power in all responses when compared with conventional PI and Type-1 Fuzzy controller[12].

The robust performance for the above cases is shown numerically at a particular operatingcondition is listed in Table-2. In this study, settling time, overshoot and undershoot are calculatedfor 10% band of the step load change in each area and in all three areas and simulation resultsfor 10% band of step load change for the operating point shown in Appendix. Upon examinationof Table-2, reveals that the performance of the proposed Type-2 Fuzzy controller is better thanconventional PI and Type-1 Fuzzy controller.

5.CONCLUSIONS

From the Table-2, the power system results are shown with the variation of 10% load. UnderHydro-thermal-thermal combination, the proposed Type-2 Fuzzy control gives a better dynamicperformance and also reduces the oscillations of frequency deviation and the tie line power..Simulation results proves that the proposed controller guarantees the robust stability performancelike frequency tracking and disturbance attenuation under a wide range of parameter uncertaintyand area load conditions. The results shows that under large parametric uncertainty, the proposedtype-2 fuzzy controller provided decentralized stability of the overall system. To demonstrateperformance robustness of proposed method, the Settling Time , Maximum Overshoot , and


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Undershoot are being considered.. It gave an appreciable performance as compared toconventional PI controller and Type I Fuzzy controller for the given operating condition.

APPENDIX

The typical values of parameters of Hydro-thermal-thermal system for nominal operatingcondition are as follows[13][5]

K p1 = K p2 = Kp3= 120 , Tp1 = Tp2 = Tp3= 10 , Kr1 = Kr2 = 0.333, Tr1 = Tr2 =10Tg1 = Tg2 = 0.2 , R1 = R2 = R3= 2.4, B1 = B2 = B3= 0.425 , Tt1 = Tt2 = 0.3T12 =T23=T31= 0.0707 , a12 =a23=a31= -1 Kd = 4 Kp = 1 Ki = 5Tw = 1 f = 60 hz

Boiler Dynamics data:

K1= 0.85, K2= 0.095, K3= 0.92, Cb= 200, Td= 0 , Tf= 10,Kib= 0.03, Tib= 26, Trb= 69

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[12] Shayeghi H, Jalili A, Shayanfar H.A, (2005)“Fuzzy PI Type Controller for Load Frequency ControlProblem in Interconnected Power System”, 9th World Multi Conf. on Systemic Cybernetics andinformation, Orlando, Florida, U.S.A., July 10-13, pp. 24-29.

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Fig-1: Three - Area Interconnected Power System including SMES units

Fig- 2: Boiler dynamics

SMES 1 SMES 2

Load Disturbance Load Disturbance

Tie line

Reheat Thermal PlantArea 2

Reheat Thermal PlantArea 1

SMES 3

Load Disturbance

Hydal Plant Area 3


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Fig-3:Block Diagram of Three Area Interconnected system


22

Fig- 4: Membership Function and Interval Type-2 Fuzzy Reasoning

Fig- 5:The structure of the T2 fuzzy PI controller

Fig- 6: Membership functions of the Interval T2 fuzzy sets

FuzzificationFuzzy

Inference Type-Reducer

Defuzzification

Fuzzy RuleBases

inputs

E(n)R(n)

outputU(n)

)ACE(

NL NUN PL P PU

L2+P2L2-P2 L2-L2+P2- L2-L2-P2

θ2-0.5

θ2+0.5

Universe of Discourse


23

0 1 2 3 4 5 6 7 8 9 10-6

-5

-4

-3

-2

-1

0

1

2

3

4x 10-4

time,secs

delta

f1

conventional PI controllerType-1 Fuzzy (Shayegi's)controllerProposed Type-2 Fuzzy controller

0 1 2 3 4 5 6 7 8 9 1 0-2

-1 .5

-1

-0 .5

0

0 .5

1x 1 0 -4

t im e ,s e c s

de

lta

f2

c o n ve n t io n a l P I c o n t ro lle rTy p e -1 F u z z y (S h a y e g i's )c o n t ro lle rP ro p o s e d Ty p e -2 F u z z y c o n t ro lle r

0 1 2 3 4 5 6 7 8 9 1 0- 2 . 5

- 2

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5x 1 0 - 4

t i m e , s e c s

de

lta

f3

C o n ve n t i o n a l P I c o n t r o l l e rT y p e - 1 F u z z y ( S h a y e g i 's ) c o n t r o l l e rP r o p o s e d T y p e - 2 F u z z y c o n t r o l l e r

Fig -7: ∆f1,∆f2,∆f3 with step increase in first area ∆PD1 with GRC,BD including SMES Units


24

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0- 8

- 6

- 4

- 2

0

2

4

6x 1 0 - 5

t i m e , s e c s

de

lta

Pti

e1

2C o n ve n t i o n a l P I c o n t r o l l e rT y p e - 1 F u z z y ( S h a y e g i 's ) c o n t r o l l e rP r o p o s e d T y p e - 2 F u z z y c o n t r o l l e r

0 1 2 3 4 5 6 7 8 9 1 0- 2

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

2

2 . 5x 1 0 - 5

t i m e , s e c s

de

lta

Pti

e2

3


0 1 2 3 4 5 6 7 8 9 1 0- 8

- 6

- 4

- 2

0

2

4

6

8x 1 0 - 5

t i m e , s e c s

de

lta

Pti

e3

1

C o n v e n t i o n a l P I c o n t r o l l e rT y p e - 1 F u z z y ( S h a y e g i 's ) c o n t r o l l e rP r o p o s e d T y p e - 2 F u z z y c o n t r o l l e r

Fig -8: ∆Ptie12, ∆Ptie23, ∆Ptie31with step increase in first area ∆PD1 with GRC, BD including SMES Units


25

0 1 2 3 4 5 6 7 8 9 1 0-2

-1 . 5

-1

-0 . 5

0

0 . 5

1x 1 0 - 4

t im e , s e c s

de

lta

f1 C o n ve n t io n a l P I c o n t ro l le r

T y p e -1 F u z z y (S h a y e g i 's )c o n t ro l le rP ro p o s e d T y p e -3 F u z z y c o n t ro l le r

0 1 2 3 4 5 6 7 8 9 1 0-6

-5

-4

-3

-2

-1

0

1

2

3

4x 1 0 - 4

t im e , s e c s

dlt

a f

2

C o n ve n t io n a l P I c o n t ro l le rT y p e -1 F u z z y (S h a y e g i 's )c o n t ro l le rP ro p o s e d T y p e -2 F u z z y c o n t ro l le r

0 1 2 3 4 5 6 7 8 9 1 0- 2 . 5

- 2

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5x 1 0 - 4

t i m e , s e c s

de

lta

f3


Fig -9:∆f1,∆f2,∆f3 with step increase in second area ∆PD2 with GRC, BD including SMES Units


26

0 1 2 3 4 5 6 7 8 9 1 0- 4

- 2

0

2

4

6

8x 1 0 - 5

t i m e , s e c s

de

lta

Pti

e1

2


0 1 2 3 4 5 6 7 8 9 1 0- 8

- 6

- 4

- 2

0

2

4

6

8x 1 0 - 5

t i m e , s e c s

de

lta

Pti

e2

3


0 1 2 3 4 5 6 7 8 9 1 0- 2 . 5

- 2

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5

2x 1 0 - 5

t im e , s e c s

de

lta

Pti

e3

1


Fig -10: ∆Ptie12, ∆Ptie23, ∆Ptie31with step increase in second area ∆PD2 with GRC and SMES Units


27

0 1 2 3 4 5 6 7 8 9 1 0- 3

- 2 . 5

- 2

- 1 . 5

- 1

- 0 . 5

0

0 . 5

1

1 . 5x 1 0 - 4

t im e , s e c s

de

lta

f1


0 1 2 3 4 5 6 7 8 9 1 0-3

-2 . 5

-2

-1 . 5

-1

-0 . 5

0

0 . 5

1

1 . 5x 1 0 - 4

t im e , s e c s

de

lta

f2


0 1 2 3 4 5 6 7 8 9 1 0- 8

- 6

- 4

- 2

0

2

4x 1 0 - 4

t i m e , s e c s

de

lta

f3


Fig -11: ∆f1,∆f2,∆f3 with step increase in third area ∆PD3 with GRC, BD including SMES Units


28

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0-3

-2

-1

0

1

2

3x 1 0 - 6

t im e , s e c s

de

lta

Pti

e1

2


0 1 2 3 4 5 6 7 8 9 1 0- 8

- 6

- 4

- 2

0

2

4

6

8

1 0x 1 0 - 5

t im e , s e c s

de

lta

Pti

e2

3

C o n ve n t i o n a l P I c o n t r o l l e rT y p e - 1 F u z z y ( S h a y e g i 's ) c o n t r o l l e rP r p o s e d T y p e - 2 F u z z y c o n t r o l l e r

0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0-1 0

-8

-6

-4

-2

0

2

4

6

8x 1 0 - 5

t im e , s e c s

de

lta

Pti

e3

1

C o n ve n t i o n a l P I c o n t ro l l e rT y p e -1 F u z z y (S h a y e g i 's ) c o n t ro l l e rP ro p o s e d T y p e -2 F u z z y c o n t ro l l e r

Fig -12: ∆Ptie12, ∆Ptie23, ∆Ptie31with step increase in third area ∆PD3 with GRC, BD including SMES Units


29

0 1 2 3 4 5 6 7 8 9 1 0-6

-5

-4

-3

-2

-1

0

1

2x 1 0 - 4

t im e , s e c s

de

lta

f1

C o n ve n t io n a l P I c o n t ro l le rT y p e -1 F u z z y (S h a y e g i 's )c o n t ro l le rP ro p o s e d T y p e -2 F u z z y a p p ro a c h

0 1 2 3 4 5 6 7 8 9 1 0- 6

- 5

- 4

- 3

- 2

- 1

0

1

2x 1 0 - 4

t i m e , s e c s

de

lta

f2


0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0-7

-6

-5

-4

-3

-2

-1

0

1

2

3x 1 0 - 4

t im e , s e c s

de

lta

f3


Fig -13: ∆f1,∆f2,∆f3 with step increase in first area ∆PD1, second area ∆PD2 and third area ∆PD3 with GRC,BD including SMES Units


30

0 2 4 6 8 10 12 14 16 18 20-1 .5

-1

-0 .5

0

0.5

1

1.5

2

2.5

3

3.5x 10 -6

tm e,s ec s

de

lta

Pte

12

C onvent iona l P I c on tro lle rTy pe-1 F uz z y (S hay eg i's )c on tro lle rP ropos ed Ty pe-2 F uz z y c on tro lle r

0 2 4 6 8 10 12 14 16 18 20-3

-2

-1

0

1

2

3

4

5

6x 10 -5

t im e,s ec s

delta

Ptie

23

Conventional P I c ontrollerTy pe-1 Fuz z y (S hay egi's )c ontrollerP ropos ed Ty pe-2 Fuz z y c ontroller

0 2 4 6 8 10 12 14 16 18 20-7

-6

-5

-4

-3

-2

-1

0

1

2

3x 10 -5

t im e,secs

delta

Ptie

31

Conventional P I controllerType-1 Fuzzy (S hayegi's )controllerP roposed Type-2 Fuzzy controller

Fig -14: ∆Ptie12, ∆Ptie23, ∆Ptie31with step increase in demand of first area ∆PD1, second area ∆PD2 and thirdarea ∆PD3 with GRC, BD including SMES Units


31

Table-1: Control rules forT1 and T2 Fuzzy controller

Settling Timesecs

MaximumOvershoot

Undershoot

Case -I(a) ∆f1 Conventional PI >10 1.9x10-4 -1.7x10-4

Type-1 Fuzzy 10 2.0x10-4 -1.6x10-4

Type-2 Fuzzy 5.2 1.8x10-4 -0.9x10-4

∆f2 Conventional PI >10 0.57x10-4 -1.8x10-4

Type-1 Fuzzy >10 0.52x10-4 -1.7x10-4

Type-2 Fuzzy 6.1 0.187x10-4 -1.4x10-4


Type-1 Fuzzy >10 1.4x10-4 -2.3x10-4

Type-2 Fuzzy 8.8 0.74x10-4 -1.7x10-4

∆Ptie12 Conventional PI >10 4.1x10-5 -7.1x10-5

Type-1 Fuzzy >10 3.78x10-5 -6.7x10-5

Type-2 Fuzzy 5.9 2.33x10-5 -6.43x10-5


Type-1 Fuzzy >10 6.71x10-5 -5.85x10-5

Type-2 Fuzzy 6.39 6.41x10-5 -3.5x10-5


Type-1 Fuzzy >10 2.06x10-5 -1.78x10-5

Type-2 Fuzzy 8.6 1.23x10-5 -0.66x10-5

Case -I(b) ∆f1 Conventional PI >10 0.57x10-4 -1.8x10-4

Type-1 Fuzzy >10 0.48x10-4 -1.7x10-4

Type-2 Fuzzy 8 0.16x10-4 -1.3x10-4


Type-1 Fuzzy >10 2.0x10-4 -1.6x10-4

Type-2 Fuzzy 5.3 1.8x10-4 -0.9x10-4


Type-1 Fuzzy >10 1.47x10-4 -2.3x10-4

Type-2 Fuzzy 8.9 0.75x10-4 -1.7x10-4


Type-1 Fuzzy >10 6.9x10-5 -3.6x10-5

Type-2 Fuzzy 5.6 6.47x10-5 -2.17x10-5


Type-1 Fuzzy >10 5.9x10-5 -6.8x10-5

∆ACE

)( ECA ∆

N Z P

N P N N

Z N P P

P N N N


32

Type-2 Fuzzy 6.7 3.52x10-5 -6.4x10-5


Type-1 Fuzzy >10 1.8x10-5 -2.25x10-5

Type-2 Fuzzy 7.58 0.7x10-5 -1.28x10-5

Case –I(c) ∆f1 Conventional PI >10 1.3x10-4 -2.5x10-4

Type-1 Fuzzy >10 1.3x10-4 -2.49x10-4

Type-2 Fuzzy 7.35 0.81x10-4 -1.8x10-4


Type-1 Fuzzy >10 1.38x10-4 -2.5x10-4

Type-2 Fuzzy 7.12 0.71x10-4 -1.7x10-4


Type-1 Fuzzy >10 2.6x10-4 -2.1x10-4

Type-2 Fuzzy 6.3 2.0x10-4 -0.98x10-4

∆Ptie12 Conventional PI --- 1.3x10-6 ---Type-1 Fuzzy --- 2.13x10-6 -0.33x10-6

Type-2 Fuzzy 13.66 1.58x10-6 -2.7x10-6


Type-1 Fuzzy >10 9.43x10-5 -5.9x10-5

Type-2 Fuzzy 7.8 7.9x10-5 -3.3x10-5


Type-1 Fuzzy >10 5.7x10-5 -9.4x10-5

Type-2 Fuzzy 6.66 3.43x10-5 -7.8x10-5

Case –2 ∆f1 Conventional PI >10 1.3x10-4 ---Type-1 Fuzzy 10 1.2x10-4 ---Type-2 Fuzzy 9.4 0.53x10-4 -0.1x10-4

∆f2 Conventional PI --- 1.32x10-4 ---Type-1 Fuzzy --- 1.26x10-4 ---Type-2 Fuzzy 8.6 0.5x10-4 ---


Type-1 Fuzzy >10 1.7x10-4 -0.26x10-4

Type-2 Fuzzy 6.7 0.9x10-4 -0.05x10-4

∆Ptie12 Conventional PI --- 2.58x10-6 ---Type-1 Fuzzy --- 3.43x10-6 ---Type-2 Fuzzy 18.78 0.46x10-6 -1.36x10-6


Type-1 Fuzzy >10 5.9x10-5 -2.3x10-5

Type-2 Fuzzy 7.9 3.6x10-5 -0.95x10-5

∆Ptie31 Conventional PI 10 1.65x10-5 -5.6x10-5

Type-1 Fuzzy 9.6 2.1x10-5 -6.29x10-5

Type-2 Fuzzy 7.13 1.0x10-5 -3.6x10-5

Table -2: The numerical analysis


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Authors

Dr. R.Vijaya Santhi received her B.Tech. degree in Electrical and ElectronicsEngineering from S.V.H Engineering College, Machilipatnam, Nagarjuna University in2003.She did her M.Tech in Power systems, from JNTU Kakinada in 2008. awarded herDoctorate in Electrical Engineering in 2014 by Andhra University.Presently, she isworking as Assistant Professor in the Department of Electrical Engineering, AndhraUniversity, Visakhapatnam, India.

Dr.K.R.Sudha received her B.E. degree in Electrical and Electronics Engineering fromGITAM; Andhra University 1991.She did her M.E in Power Systems 1994. She wasawarded her Doctorate in Electrical Engineering in 2006 by Andhra University. During1994-2006, she worked with GITAM Engineering College and presently she is workingas Professor and Head in the Department of Electrical Engineering, AUCE(W), AndhraUniversity, Visakhapatnam, India.

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