ADAPTIVE TYPE-2 FUZZY CONTROLLER FOR LOAD FREQUENCY CONTROL OF AN INTERCONNECTED HYDRO-THERMAL SYSTEM INCLUDING SMES UNITS

Transcription

1 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 ADAPTIVE TYPE- FUZZY CONTROLLER FOR LOAD FREQUENCY CONTROL OF AN INTERCONNECTED HYDRO-THERMAL SYSTEM INCLUDING SMES UNITS Dr. R.Vijaya Santhi and Dr. K.R.Sudha Assistant Professor,Department of Electrical Engineering, Andhra University, India Professor,Department of Electrical Engineering, Andhra University, India ABSTRACT This present paper includes the study Load Frequency Control (LFC) of power systems with several nonlinearities like Generation Rate Constraint(GRC) and Boiler Dynamics (BD) including Superconducting Magnetic Energy Storage (SMES) units using Type- Fuzzy System (TFS) controllers. Here, Load frequency control problem is dealt with a three area interconnected system of Thermal-Thermal-Hydal power system by observing the effects and variations of dynamic responses employing conventional controller, Type- fuzzy controller and TFS controller considering incremental increase of step pertubations by % in the load. The salient advantage of this controller is its high insensitivity to large load changes and plant parameter variations even in the presence of non-linearities. As the non-linearities were considered in the system, the conventional and classical Fuzzy controllers does not provide adequate control performance with the consideration of above nonlinearities. To overcome this drawback TFS Controller has been employed in the system. Therefore, the efficacy of the proposed TFS controller is found to be better than that of conventional controller and Type- Fuzzy controller in cosidreration with overshoot, settling time and robustness. KEYWORDS Load Frequency Control(LFC), Type-(T) Fuzzy Controller, Generation Rate Constraint (GRC), Boiler Dynamics(BD), Superconducting magnetic energy storage (SMES).. INTRODUCTION Inorder to maintain system frequency and inter-area oscillations within limits, Load Frequency Control (LFC) plays a vital role in large scale electric power systems. Both area frequency and tie-line power interchange varies with variation in power load demand. The motives of load frequency control (LFC)[][] are to minimize the transient deviations in theses variables and to ensure their steady state errors to be zeros. When dealing with the LFC [3] problem of power systems, certain unexpected pertubations, parametric uncertainties and the model uncertainties of the power system leads for the designing of controller. In large interconnected power system, DOI :.5/ijfls.4.4 3

2 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 generation of power is done by thermal, hydro, nuclear and gas power units.usually, nuclear units are kept at base load close to their maximum output owing to their high efficiency with no participation in system Automatic Generation Control (AGC) [4]. Since these type of plants produces a very small percentage of total system generation, so such plants donot play an significant role in AGC of a large power system. In order to meet peak demands, Gas plants are used. 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 lesser attention has been focussed to the LFC of interconnected hydro-thermal system [5] involving thermal 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 system neglecting generation rate constraints and boiler dynamics. Since frequency has become a common 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 band effects are neglected. But for the realistic analysis of system performance, these should be incorporated 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 an interconnected hydrothermal system. In the past decades, fuzzy logic controllers (FLCs) have been successfully developed for analysis and control of nonlinear systems [8][9]. The fuzzy reasoning approach is motivated by its ability to handle imperfect information,especially uncertainties in available knowledge. Stimulated by the success of FLCs, Talaq [], Yesil and Chang[] proposed different adaptive fuzzy scheduling schemes for conventional PI andor PID controllers. These methods provide good performances but the system transient responses are relatively oscillatory. The main motive of this paper is to determine the Load Frequency Control and inter-area tie power control problem for a wide area power system with following certain uncertainities. From the literature, many authors have proposed fuzzy logic based controllers to power systems [] inorder to take care of these uncertainties. This fuzzy logic, also called as Type- fuzzy, can further be modified to Type- fuzzy by giving grading to the membership functions which are themselves fuzzy. Or in other words, in Type- fuzzy sets, at each value of the variable the membership is a function but not just a point value. Therefore, a Type- fuzzy set can be visualized as a three dimensional. The advantage of the third dimension gives an extra degree of freedom for handling uncertainties. Taking this feature into consideration, a robust decentralized control scheme is designed using Type- Fuzzy logic [3][4][5]. The proposed controller is simulated for a three area power system in the presence of Generation Rate Constraint (GRC) and Boiler Dynamics (BD) [6] including Superconducting Magnetic Energy Storage(SMES) units was compared with conventional PI controller and Type- Fuzzycontroller. Results of simulation show that the T fuzzy controllers guarantee the robust performance.. 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 detailed power 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 4

3 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 (SMES) units with Generation Rate Constraint (GRC) and Boiler Dynamics (BD) for load frequency control is investigated in this study as shown in Fig. with Area Control Error(ACE) and its derivative are given as the inputs to the controllers [7]. Three areas have been installed with SMES, SMES and SMES3 inorder to stabilize frequency oscillations. The interconnected power 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 [8]. Power generation can be changed only to a specified maximum rate in a power system having steam plants. the generation rate for the steam plants can be restricted, by adding limiters to the governors. The Generation Rate Constraint (GRC) value for thermal units of 3%/min is considered. To prevent the excessive control action, two limiters, bounded by ±.5 within the automatic generation controller are used. By adding limiters to the turbines GRCs for all the areas are taken into consideration. Fig- shows the model to represent the boiler dynamics. Representations for combustion controls are also incorporated. This model is used inorder to study the responses of coal fired units with poorly tuned combustions controls and with well tuned controls.the limiter of -. PSMi, i=,. [pumw] based on a system MW base is equipped for each SMES unit. Parameters values of SMES, SMES and SMES3 are set at Ksm = Ksm = Ksm3=. and Tsm = Tsm =Tsm3=.3 sec[9]. 3.TYPE (T) FUZZY LOGIC CONTROLLERS: Zadeh [] introduced type- fuzzy sets. The fuzzification of a type- fuzzy set gives the Type- sets. To describe the membership function by numbers, type- fuzzy sets requires the developer, in the discrete case, or by a function, where continuous membership function is given by the fuzzy. So, `non-fuzzy' (or crisp) representation is given by the fuzziness of a system which employs fuzzy sets. A fuzzy system that uses Type- fuzzy sets and/or fuzzy logic and inference is called a Type- (T) fuzzy system. Infact, a Type- (T) fuzzy system can be defined as the system that employs ordinary fuzzy sets, logic, and inference. In order to solve many practical problems, T fuzzy systems, especially fuzzy logic controllers and fuzzy models are modelled. As per Mendel, A Type- fuzzy set (T FS) has a grade of membership that is crisp, whereas a Type - fuzzy set (T FS) has a grade of membership that is fuzzy, so T FS are fuzzy-fuzzy sets. To represent the fuzzy membership of fuzzy sets footprint of uncertainty (FOU) is employed, which is a -D representation, with the uncertainty about the right end point of the right side of the membership function and with the uncertainty about the left end point of the left side of the membership function. The type- fuzzy sets, which represents uncertainty by numbers in the range [, ] can be handled by the general framework of fuzzy reasoning. Uncertainity cannot be determined with its exact value, because of its complexity and rather type- fuzzy sets gives much senser than using crisp sets []. So, it is difficult to measure an uncertain membership function. To overcome this difficulty, we require another type of fuzzy sets, those which has ability to handle these uncertainties. Those type of fuzzy sets are called type- fuzzy sets. As the type- fuzzy logic has better capability to cope up with linguistic uncertainities, type- is a good replacement for type- fuzzy system.. Infact, the Type - fuzzy and Type- fuzzy sets operation are similar, but while using with interval fuzzy system; by limiting the FOU, fuzzy operator is being done as two T membership functions, 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 Type fuzzy logic system using centroid method is 5

4 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 shown in Fig -4. In Type- fuzzy set, at each value of primary variable the membership is a function and it is not just a point value; the secondary membership function whose domain, i.e., the primary membership is in the interval [,], then their range, the secondary grades may also be in the interval [,]. Since, the foot of membership functions is not a single point but designed over an interval, therefore Type - fuzzy logic controller can also be refered as Interval Type- fuzzy logic controller. Interval type fuzzy logic operation is shown in Fig. 4.The Interval Type- membership functions and operators are designed and are employed in the ITFLS toolbox. An Inference FS is a rule base system that uses fuzzy logic, instead of Boolean logic that is utilized in data 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 is employed; the type reductor converts a Type Fuzzy Set into a Type- 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 AC E, are first fuzzified by two interval T fuzzy sets (Fig -6), namely positive and negative represented by ( P ACE) and N ( ACE) respectively. The primary memberships are generated by blurring the trapezoidal T fuzzy sets P ( ACE), N ( ACE), P ( AC E), and N ( AC E). The interval T fuzzy sets secondary membership functions are all constant. The definitions of the T fuzzy sets are as follows: (, L ] p ( ACE) = ( L + ( ACE)) / L [ L, L ] -----() [ L, ) After shifting the membership functions of the T fuzzy sets upward and downward by θ [,.5] for ( ACE) and ( ACE) along the membership axes, the boundary membership P N functions of the primary memberships of the interval T fuzzy sets[][3] (i.e.), ( ACE P ), L PU ( ACE), NL ( ACE), NU ( ACE) ). These boundary membership functions form the shaded bands in Fig -6 which are called footprints of uncertainty (FOU). The design parameters θ and θ are used to control the degree of uncertainty of the interval T 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 AC E is P, then U is N For an interval T fuzzy interface, the firing set becomes a firing interval [RL,RU]=[min( ACE PL, AC E PL,U NL), min( ACE PU, AC E PU,UNU)] The rules are shown in Table-. 6

5 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 4. SIMULATION RESULTS To illustrate robust performance of the proposed Type- Fuzzy controller we have chosen different cases: Case I(a),Case I(b) & CaseI(c): Step increase in demand of the first area P D : In this case, step increase in demand of the first area P D is applied. The frequency deviation of the first area, Δf, the frequency deviation of the second area, Δf, the frequency deviation of the third area, Δf 3, 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 P D is applied. The frequency deviation of the first area, Δf, the frequency deviation of the second area, Δf, the frequency deviation of the third area, Δf 3, and inter area tie-power signals of the closed-loop system are shown in Fig -9, Fig -. Step increase in demand of the third area P D3 is applied. The frequency deviation of the first area, Δf, the frequency deviation of the second area, Δf, the frequency deviation of the third area, Δf 3, and inter area tie-power signals of the closed-loop system are shown in Fig -, Fig -.Using proposed method, the frequency deviations and inter area tie-power quickly driven back to zero and controller using T 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- Fuzzy controller []. Case II: Step increase in demand of the first area P D, second area P D and third area P D3 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 P D, the second area P D and third area P D3 is applied. The frequency deviation of the first area Δf, the frequency deviation of the second area Δf, the frequency deviation of the third area Δf 3 is shown in Fig -3,fig-4. The frequency deviations and inter area tie-power quickly driven back to zero by employing proposed controller. Type- fuzzy controller has the best performance in control and damping of frequency and tiepower in all responses when compared with conventional PI and Type- Fuzzy controller[]. The robust performance for the above cases is shown numerically at a particular operating condition is listed in Table-. In this study, settling time, overshoot and undershoot are calculated for % band of the step load change in each area and in all three areas and simulation results for % band of step load change for the operating point shown in Appendix. Upon examination of Table-, reveals that the performance of the proposed Type- Fuzzy controller is better than conventional PI and Type- Fuzzy controller. 5.CONCLUSIONS From the Table-, the power system results are shown with the variation of % load. Under Hydro-thermal-thermal combination, the proposed Type- Fuzzy control gives a better dynamic performance and also reduces the oscillations of frequency deviation and the tie line power.. Simulation results proves that the proposed controller guarantees the robust stability performance like frequency tracking and disturbance attenuation under a wide range of parameter uncertainty and area load conditions. The results shows that under large parametric uncertainty, the proposed type- fuzzy controller provided decentralized stability of the overall system. To demonstrate performance robustness of proposed method, the Settling Time, Maximum Overshoot, and 7

6 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 Undershoot are being considered.. It gave an appreciable performance as compared to conventional 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 operating condition are as follows[3][5] K p = K p = Kp3=, Tp = Tp = Tp3=, Kr = Kr =.333, Tr = Tr = Tg = Tg =., R = R = R3=.4, B = B = B3=.45, Tt = Tt =.3 T =T3=T3=.77, a =a3=a3= - Kd = 4 Kp = Ki = 5 Tw = f = 6 hz Boiler Dynamics data: K=.85, K=.95, K3=.9, Cb=, Td=, Tf=, Kib=.3, Tib= 6, Trb= 69 REFERENCES [] Chaturvedi D.K., Satsangi P.S. & Kalra P.K, (999), Load Frequency Control: A generalized Neural Network Approach, Int. Journal on Electric Power and Energy Systems, Elsevier Science, Vol., [] Gayadhar Panda, Sidhartha Panda and Ardil C, (9), Hybr id Neuro Fuzzy Approach for Automatic Generation Control of Two Area Interconnected Power System, International Journal of Computational Intelligence, Vol. 5, pp [3] Sudha K.R, Butchi Raju Y, Chandra Sekhar A, (), Fuzzy C -Means clustering for robust decentralized load frequency control of interconnected power system with Generation Rate Constraint IJEPES,Volume 37, Issue, Pages [4] Nanda J, Sakkaram J. S, Automatic generation control with fuzzy logic controller considering generation rate constraint, Proceedings of thc 6th International Confcrrnce on Advances in Power System Control, Operation and Management, November [3]. [5] Kothari M.L, Kaul B.Land Nanda J,(98) Automatic Generation Control of Hydro-Thermal system, journal of Institute of Engineers(India), vo.6, Pt EL, pp [6] Concordia C and Kirchmayer L.K, (954) Tie-Line Power and Frequency Control of Electric Power System - Part It, AIEE Transaction, vol. 73, pp [7] Nanda J, Kothari M.L, Satsangi P.S, (983) Automatic Generation Control of an Interconnected hydrothermal system in Continuous and Discrete modes considering Generation Rate Constraints, IEE Proc., vol. 3, pp [8] lndulkar C.S and Raj B,(995) Application of Fuzzy controller to automatic generation control, Electrical Machines and Power Systems, vol. 3, pp. 9-. [9] Chown G.A and Hartman R.C,(998) Design and experiment with a fuzzy controller for AGC, IEEE Trans. Power Systems, vol. 3, pp [] Talaq J and Al-Basri F,(999) Adaptive fuzzy gain scheduling for load frequency control, IEEE Trans. Power Systems, vol. 4, pp [] Chang C.S and Fu W,(997) Area load-frequency control using gain scheduling of PI controllers, Electric Power Systems Research, vol. 4, pp

7 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 [] Shayeghi H, Jalili A, Shayanfar H.A, (5) Fuzzy PI Type Controller for Load Frequency Control Problem in Interconnected Power System, 9th World Multi Conf. on Systemic Cybernetics and information, Orlando, Florida, U.S.A., July -3, pp [3] Sudha K.R, Vijaya Santhi R,() Robust decentralized load frequency control of interconnected power system with Generation Rate Constraint using Type- fuzzy approach, Electrical Power and Energy Systems, Vol. 33, pp [4] Oscar Castillo, Patricia Melin, () A review on the design and optimization of interval type - fuzzy controllers, Appl. Soft Comput., (4): [5] Oscar Castillo, Patricia Melin, Witold Pedrycz, () Design of interval type- fuzzy models through optimal granularity allocation,appl. Soft Comput, (8): [6] Anand Band Ebenezer Jeyakumar (9) A Load Frequency Control with Fuzzy Logic Controller Considering Non-Linearities and Boiler Dynamics ICGST-ACSE Journal, Volume 8, Issue III, ISSN [7] Mendel J. M,(7) Advances in type- fuzzy sets and systems, Information Sciences, vol. 77, pp [8] Tripathy S.C, Balasubramanian R, Chandramohanan Nair P.S, (99) Effect of SMES on automatic generation control considering governor deadband and boiler dynamics, IEEE Trans Power Syst, vol. 7,pp [9] Chaimongkon Khamsum, Saravuth Pothiya, Chuan Taowklang and Worawat Sagiamvibool (6) Design of Optimal PID Controller using Improved Genetic Algorithm for AGC including SMES Units GMSARN International Conference on Sustainable Development: Issues and Prospects for GMS, 6-7. [] Zadeh L.A, (975) The Concept of a Linguistic Variable and its A pplication to approximate Reasoning I, Information Sciences, vol. 8, pp [] Dobrescu M, Kamwa I,(4) A New Fuzzy Logic Power System Stabilizer Performances, IEEE. [] Yesil E, Guzelkaya M and Eksin L, (4) Self tuning fuzzy PID type load and frequency controller, Energy Conversion and Management, vol. 45, pp

8 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 Reheat Thermal Plant Area SMES SMES Tie line Reheat Thermal Plant Area Load Disturbance Hydal Plant Area 3 SMES 3 Load Disturbance Load Disturbance Fig-: Three - Area Interconnected Power System including SMES units Fig- : Boiler dynamics

9 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 Fig-3:Block Diagram of Three Area Interconnected system

10 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 Fig- 4: Membership Function and Interval Type- Fuzzy Reasoning Fuzzy Rule Bases Defuzzification output U(n) E(n) R(n) inputs Fuzzification Fuzzy Inference Type-Reducer Fig- 5:The structure of the T fuzzy PI controller NL ( ACE ) N NU PL P PU θ +.5 θ -.5 -L -P - L -L +P Universe of Discourse L -P L L +P Fig- 6: Membership functions of the Interval T fuzzy sets

11 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 4 x -4 3 conventional PI controller Type- Fuzzy (Shayegi's)controller Proposed Type- Fuzzy controller delta f time,secs x conventional P I controller Type- Fuzzy (S hayegi's)controller P ro p o s e d Ty p e - F u z z y c o n t ro lle r d e lt a f tim e, s e c s. 5 x - 4 C o n ve n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r. 5 d e l t a f Fig -7: f, f, f 3 with step increase in first area P D with GRC,BD including SMES Units 3

12 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 6 x C o n ve n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r d e l t a P t i e x d e l t a P t i e 3. 5 C o n v e n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r x C o n v e n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r 4 d e l t a P t i e Fig -8: P tie, P tie3, P tie3 with step increase in first area P D with GRC, BD including SMES Units 4

13 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 x d e lt a f -. 5 C o n ve n t io n a l P I c o n t ro lle r T y p e - F u z z y ( S h a y e g i's) c o n t r o lle r P r o p o s e d T y p e - 3 F u z z y c o n t r o lle r t im e, s e c s 4 x C o n ve n t io n a l P I c o n t ro lle r T y p e - F u z z y (S h a y e g i's)c o n t ro lle r P ro p o s e d T y p e - F u z z y c o n t ro lle r d lt a f t im e, s e c s. 5 x - 4 C o n v e n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r. 5 d e l t a f Fig -9: f, f, f 3 with step increase in second area P D with GRC, BD including SMES Units 5

14 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 8 x - 5 C o n ve n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r 6 4 d e l t a P t i e x C o n v e n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r 4 d e l t a P t i e x - 5 C o n ve n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r. 5 d e l t a P t i e Fig -: P tie, P tie3, P tie3 with step increase in second area P D with GRC and SMES Units 6

15 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4. 5 x - 4 C o n ve n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r. 5 d e l t a f x - 4 C o n ve n t io n a l P I c o n t ro lle r T y p e - F u z z y ( S h a y e g i's) c o n t r o lle r P r o p o s e d T y p e - F u z z y c o n t r o lle r. 5 d e lt a f t im e, s e c s 4 x - 4 C o n v e n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r d e l t a f Fig -: f, f, f 3 with step increase in third area P D3 with GRC, BD including SMES Units 7

16 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 3 x - 6 C o n ve n t io n a l P I c o n t ro lle r T y p e - F u z z y (S h a y e g i's)c o n t ro lle r P ro p o s e d T y p e - F u z z y c o n t ro lle r d e lta P tie t im e, s e c s x C o n ve n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r p o s e d T y p e - F u z z y c o n t r o l l e r 6 4 d e l t a P t i e x C o n ve n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r d e l t a P t i e Fig -: P tie, P tie3, P tie3 with step increase in third area P D3 with GRC, BD including SMES Units 8

17 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 x - 4 C o n ve n t io n a l P I c o n t ro lle r T y p e - F u z z y (S h a y e g i's)c o n t ro lle r P ro p o s e d T y p e - F u z z y a p p ro a c h - d e lt a f t im e, s e c s x - 4 C o n ve n t i o n a l P I c o n t r o l l e r T y p e - F u z z y ( S h a y e g i 's) c o n t r o l l e r P r o p o s e d T y p e - F u z z y c o n t r o l l e r - d e l t a f x - 4 C o n ve n t io n a l P I c o n t ro lle r T y p e - F u z z y (S h a y e g i's)c o n t ro lle r P ro p o s e d T y p e - F u z z y c o n t ro lle r - d e lt a f t im e, s e c s Fig -3: f, f, f 3 with step increase in first area P D, second area P D and third area P D3 with GRC, BD including SMES Units 9

18 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January x -6 3 Conventional P I controller Type- Fuzzy (Shayegi's)controller P ropos ed Ty pe- F uz z y c ontroller.5 delta P te tm e,secs 6 x -5 5 Conventional PI controller Type- Fuzzy (Shayegi's)controller Proposed Type- Fuzzy controller 4 3 delta Ptie tim e,s ec s 3 x -5 delta Ptie Conventional PI controller Type- Fuzzy (Shayegi's)controller Proposed Type- Fuzzy controller tim e,s ec s Fig -4: P tie, P tie3, P tie3 with step increase in demand of first area P D, second area P D and third area P D3 with GRC, BD including SMES Units 3

19 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 ACE N Z P ( AC E) N P N N Z N P P P N N N Table-: Control rules fort and T Fuzzy controller Settling Time Maximum Undershoot secs Overshoot Case -I(a) f Conventional PI >.9x x -4 Type- Fuzzy.x x -4 Type- Fuzzy 5..8x x -4 f Conventional PI >.57x x -4 Type- Fuzzy >.5x x -4 Type- Fuzzy 6..87x x -4 f 3 Conventional PI >.45x x -4 Type- Fuzzy >.4x x -4 Type- Fuzzy x x -4 P tie Conventional PI > 4.x -5-7.x -5 Type- Fuzzy > 3.78x x -5 Type- Fuzzy x x -5 P tie3 Conventional PI > 7.3x x -5 Type- Fuzzy > 6.7x x -5 Type- Fuzzy x x -5 P tie3 Conventional PI >.3x x -5 Type- Fuzzy >.6x x -5 Type- Fuzzy 8.6.3x x -5 Case -I(b) f Conventional PI >.57x x -4 Type- Fuzzy >.48x x -4 Type- Fuzzy 8.6x x -4 f Conventional PI >.8x x -4 Type- Fuzzy >.x x -4 Type- Fuzzy 5.3.8x x -4 f 3 Conventional PI >.45x x -4 Type- Fuzzy >.47x x -4 Type- Fuzzy x x -4 P tie Conventional PI > 7.5x x -5 Type- Fuzzy > 6.9x x -5 Type- Fuzzy x x -5 P tie3 Conventional PI > 6.x x -5 Type- Fuzzy > 5.9x x -5 3

20 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 Type- Fuzzy x x -5 P tie3 Conventional PI >.7x -5 -.x -5 Type- Fuzzy >.8x x -5 Type- Fuzzy x x -5 Case I(c) f Conventional PI >.3x x -4 Type- Fuzzy >.3x x -4 Type- Fuzzy x x -4 f Conventional PI >.6x x -4 Type- Fuzzy >.38x x -4 Type- Fuzzy 7..7x x -4 f 3 Conventional PI >.7x x -4 Type- Fuzzy >.6x -4 -.x -4 Type- Fuzzy 6.3.x x -4 P tie Conventional PI ---.3x Type- Fuzzy ---.3x x -6 Type- Fuzzy x x -6 P tie3 Conventional PI > 9.43x -5-6.x -5 Type- Fuzzy > 9.43x x -5 Type- Fuzzy x x -5 P tie3 Conventional PI > 6.x x -5 Type- Fuzzy > 5.7x x -5 Type- Fuzzy x x -5 Case f Conventional PI >.3x Type- Fuzzy.x Type- Fuzzy x -4 -.x -4 f Conventional PI ---.3x Type- Fuzzy ---.6x Type- Fuzzy 8.6.5x f 3 Conventional PI >.8x x -4 Type- Fuzzy >.7x x -4 Type- Fuzzy 6.7.9x x -4 P tie Conventional PI x Type- Fuzzy x Type- Fuzzy x x -6 P tie3 Conventional PI > 5.53x x -5 Type- Fuzzy > 5.9x x -5 Type- Fuzzy x x -5 P tie3 Conventional PI.65x x -5 Type- Fuzzy 9.6.x x -5 Type- Fuzzy 7.3.x x -5 Table -: The numerical analysis 3

21 International Journal of Fuzzy Logic Systems (IJFLS) Vol.4, No., January 4 Authors Dr. R.Vijaya Santhi received her B.Tech. degree in Electrical and Electronics Engineering from S.V.H Engineering College, Machilipatnam, Nagarjuna University in 3.She did her M.Tech in Power systems, from JNTU Kakinada in 8. awarded her Doctorate in Electrical Engineering in 4 by Andhra University.Presently, she is working as Assistant Professor in the Department of Electrical Engineering, Andhra University, Visakhapatnam, India. Dr.K.R.Sudha received her B.E. degree in Electrical and Electronics Engineering from GITAM; Andhra University 99.She did her M.E in Power Systems 994. She was awarded her Doctorate in Electrical Engineering in 6 by Andhra University. During 994-6, she worked with GITAM Engineering College and presently she is working as Professor and Head in the Department of Electrical Engineering, AUCE(W), Andhra University, Visakhapatnam, India. 33