Fuzzy Controller For Reducing Oscillation On Large Power System

Fuzzy Controller For Reducing Oscillation On Large Power System

Jeremias Leda

Department of Electrical Engineering

The University of Atma Jaya Makassar Indonesia

Abstract

This paper describes a novel of power system stabilizer (PSS) based on fuzzy logic theory for damping electromechanic oscillations focusing on inter-area modes of South Sulawesi power grid. An innovative approach for the determination of associated domains considered with the fuzzy logic power system stabilizer (FLPSS) is obtained by computer simulations when subjected to small disturbances under stressed operating conditions. The digital simulation results show that proposed controller proves its effectiveness in term of calculation process rather than optimal power system stabilizer and improves system damping compare to lead-lag controller under MATLAB Simulink environment.

Keywords: Fuzzy Logic Controller, Inter-area Modes, Oscillation, Stabilizer.

1. Introduction

   Power grid of South Sulawesi Indonesia as depicted in figure.1 stretches from Makassar to Mamuju through Pangkep – ParePare – Pinrang – Bakaru then through Jeneponto – Bulukumba – Sinjai – Bone – Soppeng Sengkang. That system is the largest grid engineered by Perusahaan Listrik Negara or PLN, for east region of Indonesia. PLN is the National Electric Company of Indonesia. During the last decades, the growth of South Sulawesi power grid is also the largest in east part of Indonesia; its about 14,5 percent in average. According to PLN, power installed in 2010 is 623 MW for supply the total load of 541 MW through the length of 1,926 km of transmission lines.

   The operation of such interconnected system can taking advantage of diversity of loads, availability of sources and fuel price in order to supply the electricity to the loads at minimum cost with a required reliability. However, as power transfers grow, the interconnected system becomes increasingly more complex to operate and the system becomes less secure. It may lead to large power flows with inadequate control, large dynamic swings among different part of the system

   which could produce instability of the system, and then create tendencies of less security and reduced quality of supply thus the potential advantages can not be utilized.

   Fig. 1. 150 kV Grid Line of South Sulawesi Indonesia

   This paper introduce the advantages of a novel FLPSS to reduce electromechanic-oscillation of South Sulawesi power grid in Indonesia which has weak ties structure. The poorly damped of oscillations typically occur in power systems with longitudinal structure or weak ties. The supplementary excitation controllers are used as additional feedback signals to enhance system damping and to improve the dynamic stability of power systems. These controllers are known as power system stabilizers. They have been widely used for years with many types.

   Some of them depend on conventional control theory such as PI or lead-lag controllers that can not provide a total satisfactory response when the operating conditions change widely. These controllers have main trouble for weekly connected power systems as a trade off will appear at the design process between local- modes and inter-area modes.

   Optimal controllers which are based on feedback signals from all or some states of the system will guarantee the damping of both local and inter-area modes. These controllers always suffer a lot from on- line iterative solution to Ricatti equation beside the many feedback gain channels.

   Another type of controllers is the adaptive control, which can do the entire job, but it is time consumption for real-time system identification. Simulations associated with steady state stability are quite

   oscillation to pass unchanged. The gain block determines the amount of damping introduced by PSS. Phase compensation block provides an approriate phase lead characteristics to compensate phase lagging between exciter input and generator electrical torque.

   Fig. 2. AVR + PSS Torque Characteristic Diagram

   K1+K1A+K1

   expensive in computational efforts, so these controllers can not be used for fast on-line assessments. Additionally many controllers such as self-tuning control, sliding-mode control and H-infinity control are a suggested solution to both local and inter-area modes of oscillation but they are not the perfect solution.

   TM

   _

   1 / Ms

   1 / Ms

   _

   D+DA+DP

   / s

   / s

   Torque Resultant

   New types of controllers such as rule-based, neural networks and fuzzy logic controllers have been used in many power system applications. These types do not require any kind of computational complexity. That point is vital for multi-machine or large-scale system.

   The controller proposed in this paper has advantages of its simplicity, systematic design and combine functions of AVR and PSS. The performance of this controller is investigated for South Sulawesi power grid during year 2012 which is starting with collecting data, modelling, simulation, analysis, interpretating and then results discussion. Simulation work is done at computer laboratory of electrical engineering department at the University of Atma Jaya Makassar using multi-machine

   K1P+DP

   0

   K1A+DA

   K1 + D

   detail model under MATLAB Simulink environment.

2. Basic Concept of PSS

   Though a generator output power is decided by turbine mechanical torque but that output also can be changed by changing the excitation value transiently. PSS detects the changing of generator output power, control excitation value and reduced power swing rapidly. A PSS which is installed in the automatic voltage regulator of a generator could improve power system stability and has excellent cost performance compared to other modifications.

   PSS is designed to work together with generator excitation system in order to produce positive damping torque to ensure system stability in which can be explain by torque vector diagram as figure 2. K1 is syncronizing torque, K1A is syncronizing torque by AVR and K1P is syncronizing torque by PSS. Where D is damping torque DA is damping torque by AVR and DP is damping torque by PSS. In principle generic PSS has three components as seen on figure 3. They are washout, gain and phase compensation. The washout block serves as high pass filter with time constant high enough to allow signal associated with electromechanic

   Fig. 3. Generic PSS Block Diagram

   The input is rotor speed which came from the relation of change among mechanical power, electrical power and accelerating power as illustrated on diagram below.

   Fig. 4. Power and Rotor Speed Relation Diagram

   PSS has three types of application. The most simple type is single input type such as P, or f which maybe used for individual generator oscillates against the system with frequency of 1 Hz approximately and named local mode power oscillation. For this case P type is more effective. The second type is used for the whole system oscillates with long distance and large power transfer system connection that known as inter-

   area mode power oscillation or long-cycle. In this case

   or f is more effective. The third type PSS is used for complex power oscillation mode such as local mode and inter-area mode. In this case multiple input is more effective. For instance P + or P + f type of PSS input. The connection of those three type of PSS is shown in figure 5.

   Fig. 5. Connection Diagram of PSS

3. Fuzzy Logic Controller

   In this section th design of a novel PSS controller based on fuzzy logic theory is explored. With the goal of damping the oscillations associated with power systems under the effect of small signals for inter-area modes must be damped. A simple fuzzy controller based on the experience can damp only local modes. To damp inter-area modes of oscillation, the experience is difficult to be obtained. Thus the design process needs a systematic method for obtaining the rule base and domain ranges through optimal control theory.

   1. Controller Stucture

      The proposed controller uses triangular shaped fuzzy sets as nb: negative big, nm: negative medium,

      ns: negative small, z: zero, ps: positive small, pm: positive medium and pb: positive big, as in figure 6, the Max-Min inference method and the center of gravity deffuzification strategy. Two input signals are suggested, the generator speed deviation signal and generator speed error change d. The output signal

      UPSS is damping control signal as seen on figure 7. The point wise input controllers must be fuzzified (determination of their association to each defined fuzzy set in the domain).

      Fig. 6. Classified Fuzzy Sets

      Fig. 7. Exciter and FLPSS Structure Diagram

   2. Controller Training

      The main properties to construct this controller are physical domains and rule base. Physical domains contain normalized counterparts, normalization and denormalization scaling factors and the ranges of fuzzy membership sets. The rule base defines the relationship between the fuzzy controller inputs and its output in fuzzy manner. Forty-nine rules for the proposed controller are to be extracted. These requirements for the proposed controller can be achieved using optimal controllers which guarantee the damping of inter-area modes. For the non-linear system described by the state space equation, the optimal control signal u that minimizes the performance index is a linear function in terms of the system state variable x as:

      1 Speed

      Speed deviation change d

      J (xT Qx uT Ru) dt

      (1)

      Dev.

      2 0

      u Kx R-1BT Px

      dw- dw- dw- dw-z dw- dw- dw-

      	nb	nm	ns		ps	pm	pb
      w-nb	u-nb	u-nb	u-nb	u-nb	u-nm	u-ps	u-z
      w-nm	u-nb	u-nm	u-nm	u-nm	u-ns	u-z	u-ps
      w-ns	u-nb	u-nm	u-ns	u-ns	u-z	u-ps	u-pm
      w-z	u-nb	u-nm	u-ns	u-z	u-ps	u-pm	u-pb
      w-ps	u-nm	u-ns	u-z	u-ps	u-ps	u-pm	u-pb
      w-pm	u-ns	u-z	u-ps	u-pm	u-pm	u-pb	u-pb
      w-pb	u-z	u-ps	u-pm	u-pb	u-pb	u-pb	u-pb

      	nb	nm	ns		ps	pm	pb
      w-nb	u-nb	u-nb	u-nb	u-nb	u-nm	u-ps	u-z
      w-nm	u-nb	u-nm	u-nm	u-nm	u-ns	u-z	u-ps
      w-ns	u-nb	u-nm	u-ns	u-ns	u-z	u-ps	u-pm
      w-z	u-nb	u-nm	u-ns	u-z	u-ps	u-pm	u-pb
      w-ps	u-nm	u-ns	u-z	u-ps	u-ps	u-pm	u-pb
      w-pm	u-ns	u-z	u-ps	u-pm	u-pm	u-pb	u-pb
      w-pb	u-z	u-ps	u-pm	u-pb	u-pb	u-pb	u-pb

      Q and R are the weighting matrices, K is the feedback gain matrix for the output u and P is the solution of the linear matrix Riccati equation :

      ATP PA- PBR-1BTP Q 0

      (2)

      Physical domains can be calculated from the generated data for simulation by the optimal controller assuming different disturbances. For the rule base, the relationship between the fuzzy controller inputs and its output can be extracted from algorithm below.

      Step1: simulate the optimal controller

      Step 2: Save each sample value of (, change in , Upss)

      Step 3: At each sample time t:

      the class with max membership among (_nb,

      _nm, _ns, _z, _ps, _pm, _pb) so at sample time is _1 … (a)

      change in the class with max membership among (d_nb, d_nm, d_ns, d_z, d_ ps, d_ pm, d_ pb ) so at sample time t , is d_1 … (b)

      This will form the contents of the rule-antecedent (If-part of a rule)

      Upss the class with max membership among (u_nb, u_nm, u_ns, u_z, u_ps, u_pm, u_pb )

      so at sample time t , Upss is u_1 …(c)

      This contents of the rule-consequent (then-part of the rule). And a total rule can be formed as:

      From (a), (b) and (c) : the rule If is _1 and change in is d_1 then Upss is u_1

      After generation rules, only small amount of samples can violate to the rule base. These samples are denied according to the results on table 1.

      TABLE I

      RULE BASE OF THE PROPOSED FUZZY LOGIC CONTROLLER

4. The Simulation, Results And Discussion

The single line diagram of the South Sulawesi power grid with 4 machine as shown in figure 8 is used to examine inter-area oscillation problem. The grid-ring is simplified and created especially for analysis study of oscillation problem under Simulink configuration. As shown in the single line diagram there are four generators, GEN1, GEN2, GEN3 and GEN4, and four 11.5/150 kV step-up transformers. There are 8 loads in the system except at bus no.7. The transformer and line impedances for the system are given in Appendix and also data of generators. Some of the set up parameters based on their preset value by MATLAB.7-Simulink is acceptable due to the lack of information.

Fig. 8. Single Line Diagram of South Sulawesi Power Grid

This system exhibits seven electromechanical modes of oscillations. Three inter-area mode which the generating units in one area oscillates against those in the other area. The frequency of this mode varies from 0.35-0.75 Hz depending on operating conditions. And four local modes which represent oscillations generating units internally within each area against system. The loads are modeled as constant impedances. A 135 MW electrical power transfer from GEN1 of area#1 to area#2 of GEN2 and area#3 of GEN3 and GEN4 is the main case study which is very stressed operating point.

One set of fuzzy logic controllers (FLC) is used for each area. This set of controllers includes one FLC for the area and one FLC for each generator within the area. The test contains three inter-area. A comparison

between the results of a lead-lag, optimal and fuzzy controllers due to different disturbances is presented below. A comparisonbetween resultant performance of optimal and fuzzy controller is needed. So we present the results values for the relation among the controllers graphycally.

Models are simplifications thus there are relatively small numerical error and will not be valid exactly. However when used appropriately the simulation models provide an important results and useful information. Results of simulation are as follow:

Case #1. An increase of 5% in rotor speed at GEN1

0.05

0.02

Rotor speed deviation (rad./sec.)

Rotor speed deviation (rad./sec.)

0.015

0.01

0.005

0

-0.005

-0.01

-0.015

Proposed FLC

Optimal control

Lead-lag control

Proposed FLC

Optimal control

Lead-lag control

0 1 2 3 4 5 6 7 8

Time (sec.)

Fig. 12. Electromechanic-Oscillation on GEN4

Proposed FLC

The results for case #1 show that the fuzzy controller

Rotor speed deviation (rad./sec.)

Rotor speed deviation (rad./sec.)

0.04

0.03

0.02

0.01

0

-0.01

-0.02

10

Rotor speed deviation (rad./sec.)

Rotor speed deviation (rad./sec.)

8

6

4

2

0

Optimal control Lead-lag control

0 1 2 3 4 5 6 7 8

Time (sec.)

Fig. 9. Electromechanic-Oscillation on GEN1

x 10-3

performance index ranges approximately from 7%-15% greater than optimal controller as different disturbances but more effective and efficient in terms of calculation process. Compare to lead-lag controller, the FLC much better to damp oscillations and the result is presented graphycally on figures above Fig.9 – Fig.12 of proposed FLC, optimal and lead-lag controller respectively.

Case #2. An increase of 5% in rotor speed at GEN2

Proposed FLC

Proposed FLC

0.015

Optimal control

Optimal control

Lead-lag control

Lead-lag control

Rotor speed deviation (rad./sec.)

Rotor speed deviation (rad./sec.)

0.01

0.005

0

Proposed FLC

Optimal control

Lead-lag control

Proposed FLC

Optimal control

Lead-lag control

-0.005

-2

-4 -0.01

-6

0 1 2 3 4 5 6 7 8

Time (sec.)

Fig. 10. Electromechanic-Oscillation on GEN2

x 10-3

-0.015

0 1 2 3 4 5 6 7 8

Time (sec.)

Fig. 13. Electromechanic-Oscillation on GEN1

Proposed FLC

Optimal control

Lead-lag control

Proposed FLC

Optimal control

Lead-lag control

10

Rotor speed deviation (rad./sec.)

Rotor speed deviation (rad./sec.)

8 0.05

6 0.04

Proposed FLC

Optimal control

4

2

0

-2

-4

0 1 2 3 4 5 6 7 8

0.03

Rotor speed deviation (rad./sec.)

Rotor speed deviation (rad./sec.)

0.02

0.01

0

-0.01

Lead-lag control

Time (sec.)

Fig. 11. Electromechanic-Osci

llation on GEN3

-0.02

-0.03

0 1 2 3 4 5 6 7 8

Time (sec.)

Fig. 14. Electromechanic-Oscillation on GEN2

0.02

Rotor speed deviation (rad./sec.)

Rotor speed deviation (rad./sec.)

0.015

0.01

0.005

0

-0.005

-0.01

0.025

0 1 2 3 4 5 6 7 8

Proposed FLC

Optimal control

Lead-lag control

Proposed FLC

Optimal control

Lead-lag control

Time (sec.)

Fig. 15. Electromechanic-Oscillation on GEN3

Appendix

SYSTEM DATA

TABLE II

GENERATORS, LOAD AND TRANSFORMERS DATA

Proposed FLC

Optimal control

Lead-lag control

Proposed FLC

Optimal control

Lead-lag control

Rotor speed deviation (rad./sec.)

Rotor speed deviation (rad./sec.)

0.02

0.015

0.01

0.005

0

-0.005

-0.01

-0.015

Data Source: PT. PLN AP2B Sistem Sulawesi Indonesia TABLE III

GENERATORS IMPEDANCE

-0.02

0 1 2 3 4 5 6 7 8

Time (sec.)

Fig. 16. Electromechanic-Oscillation on GEN4

Data Source: PT. PLN AP2B Sistem Sulawesi Indonesia

The simulation results of case #2 above look similarly to case #1. Again the FLC shows its effectiveness. For case #3, an increase of 5% speed in rotor at GEN3 and

#4, an increase of 5% speed in rotor at GEN4, look being almost the same if compare to case #1 and #2.

4. Conclusions

The work in this research involves fuzzy logic controller which is built based on data generated by an controller under MATLAB-Simulink environment. A systematic generation of fuzzy logic controller rule base and also input-output domain range has been investigated and tested on South Sulawesi power grid. It has found that the controller provides a more robust control over an excursion of the operating points versus optimal controller and lead-lag stabilizer. Most of the previous control methods either are not working sufficiently under whole range of operating conditions or they need complicated calculations as they require exact models. Decrease in calculations due to the fuzzy logic controller here is a fact.

Result of proposed controller has indicated damping increase and stability enhancement of inter-area modes and works nicely for South Sulawesi power grid in Indonesia in which certainly very useful for PLN as an alternative solution and policy for system stability.

TABLE IV

LINE TRANSMISSION IMPEDANCE

Data Source: PT. PLN AP2B Sistem Sulawesi Indonesia

Acknowledgements

This research was supported by Direktorat Penelitian & Pengabdian Masyarakat DITLITABMAS Ditjen DIKTI, National Ministry of Higher Education of Indonesia through Hibah Bersaing scheme project DIPA Kopertis Wilayah IX Sulawesi Tahun 2011 No.0763/023-04.2.01/23/2012 date 9 December 2011 Contract No. 344/009/KL/2012, date 6 February 2012.

References

1. Ahmad Rohani, M. Reza Safari T and Reza Noroozian, Combined Design of PSS and STATCOM Controllers For Power System Stability Enhancement, Journal of Power Electronics, Vol.11, No.5, September 2011, pp. 734-742.

2. A. Safari, R. Jahani, M. Hajinasiri, A.H. Araskalaei and

   H.A. Shayanfar, COA based coordinated design of FACTs and PSS output feedback controllers, International Review of Electrical Engineering, vol. 21, no. 6, 2010.

3. C J Wu and Y Y Hsu, Design of Self-tuning PID Power System Stabilizer for Multimachine Power System, IEEE Transactions on Power Systems, vol. 3, pp. 1059-1064, Aug. 1998.

4. C M Lim, Application of a new Fuzzy Logic Control Scheme for Stability Enhancement-Simulation and Experimental Results, IEEE International Conference on Fuzzy Systems, vol.3, pp. 1339-1346, March 1995.

5. Eltahir Mohamed Hussein and Bahar A.A.Elmahi, Fuzzy Logic Based VAR Stability for Power System Control, Journal of Science and Technology 12 (02) December 2011, ISSN 1605 427X.

6. Francis H. Raven, 1995 Automatic Control Engineering, McGraw-Hill International Edition, Singapore.

7. F. W. Keay and W. H. south, Design of Power System Stabilizer Sensing Frequency Deviation, IEEE Transactions on Power Apparatus and Systems, vol. 90, pp.707- 713, March 1971.

8. G. P. Chen, Y.Q. Qin , G.Y. Xu and O. P. Malik, Optimization Technique for The Design of a Linear Optimal Power System Stabilizer, IEEE Transactions on Energy Conversion, Vol.7, No.3, September 1992, pp.453-459.

9. H. Shayeghi, H. A. Shayanfar and O. Abedinia, Fuzzy PSS Design for a Multi-machine Power System Using Improved Genetic Algorithm, Computer Science and Engineering 2012, 2(1): 1-8, DOI: 10.5923/ j.computer. 20120201.01.

10. H Taliyat, J Sadeh and R Ghazi Design of Augmented Fuzzy Logic Power System Stabilizer to Enhance Power System Stability IEEE Transactions on Energy Conversion, vol 11, pp, 97-103, March 1996.

11. Jeremias Leda, The Analysis of Prospective Application of Power System Stabilizer and Shunt Capacitor For Reducing Electromechanics Oscillation of The South Sulawesi Power Grid, Proceeding of the National Conference of the Electro Technique Forum of Indonesia, 8-9 December 2011, page 53-66, Makassar Indonesia.

12. J H Chow and J J Sanchez-Gasca, Pole Placement Designs of Power System Stabilizers, IEEE Transactions on Power Systems, vol. 4, pp. 271-277, Feb 1989.

13. J. H. Hwang, D. W. Kim, J. H. Lee and Y. J. An, Design of fuzzy power system using adaptive evolutionary algorithm, Engineering Applications of Artificial Intelligence, vol. 21, pp. 86-96, 2008.

14. K A El-Metwally and O P Malik, Fuzzy Logic Based Power System Stabilizer, IEEE Proc- Gener.Transm. Distri., vol. 142, pp.277-281, May 1995.

15. M. E. Aboul-Ela, A. A. Sallam, J. D. McCally and A. A. Fouad, Damping Controller Design for Power System Oscillations Using Global Signals, IEEE Transactions on power apparatus and systems, Vol.11, No.2, May 1996, pp.767-773.

16. M. Caner, N. Umurkan, S. Tokat and S. V. Ustun. Deter-mination of optimal hierarchical fuzzy controller parameters according to loading condition with ANN, Expert systems with applications, Vol. 34, pp. 2650- 2655, 2008.

17. Narain G. Hingorani & Laszlo Gyugyi, Understanding FACTS, Concepts and Technology of Flexible AC Transmission System (Wiley-Intersience A. John Wiley & Sons, Inc. NY, USA, 2000).

18. Neeraj Gupta and Sanjay K. Jain, Comparative Analysis of Fuzzy Power System Stabilizer Using Different Membership Functions, International Journal of Computer and Electrical Engineering, Vol. 2, No. 2, April, 2010, 1793-8163.

19. P Kundur, Power System Stability and Control, McGraw-Hill 1994.

20. R. J. Fleming and J. Sun, An Optimal Multivariable Stabilizer For a Multi-Machine Plant, IEEE Transactions on Energy Conversion, Vol.5, No.1, March 1990, pp.15-22.

21. Robert H. Miller dan James H. Malinowski, Power System Operation (McGraw-Hill Co. Singapore, 1994).

22. R Gupta, D K Sambariya and R Gunjan, Fuzzy Logic Based Robust Power System Stabilizer for a Multi- machine Power System,IEEE ICIT, pp. 1037-1042, Dec 2006.

23. S. Cheng, Y. S. Chow , O. P. Malik and G. S. Hope, An Adaptive Synchronous Machine Stabilizer, IEEE Transactions on Power Apparatus and Systems, Vol. PWRS-1, No.3, August 1986, pp.101-106.

24. Stanley M. Shinners, Advanced Modern Control System Theory and Design (John Wiley & Sons, Inc.USA, 1998).

25. Syed A. Nasar, 1990. Electric Power Systems, Schaums ouT-lines, McGraw-Hill Co. USA.

26. T. J. Rose, Fuzzy Logic With Engineering Applications, McGraw-Hill.Inc, Newyork, 1997.

27. William D. Stanley, John R. Hackworth, Richard L. Jones, Fundamentals of Electrical Engineering and Technology (Thomson Learning, Inc. USA, 2007).

28. William D. Stanley, Technical Analysis and Applications with MATLAB (Thomson Learning, Inc. Canada, 2005).

29. William D. Stanley, John R. Hackworth, Richard L. Jones, 2007. Fundamentals of Electrical Engineering and Technology, Thomson Learning, Inc. USA.

30. Z. Barto, Robust control in a multimachine power system using adaptive neuro-fuzzy stabilizers, IEE Proceedings on Generation, Transmission and Distribution, vol. 151, No 2, pp. 261-267, 2004.