Fractional-Order Power System

Fractional-Order Power System

Dhivya Grace Varghese,

Power System Scholar

Guide

Hassena K A Assitant Professor Saintgits College Of Engineering, Kottayam

Abstract A fractional-order power system stabilizer (FoPSS) is introduced to control the frequency and the terminal voltage deviation in a power system connected to an infinite bus. FoPSS yields satisfactory results when there is drastic load change in long transmission lines. MATLAB/Simulink simulation is used to show the improvement of systems performance when FoPSS is used. FoPSS is more superior to the classical integer-order power system stabilizers (IoPSS)

Keywords

FoPSS Fractional order Power System IoPSS Integer order Power System

PSS Power System Stabilizer

q-axis Quadrature Axis

1. xis Direct Axis

   FOC Fractional Order Controller

   AVR Automatic Voltage Regulator

   1. INTRODUCTION

      The PSS compensates the local and inter-area mode of frequency oscillations that appears in power systems connected to long transmission lines. These oscillations could go up to ±1 Hz off the nominal value. The stability analysis of power systems using adaptive or sliding mode techniques is not straightforward especially when it comes to online tuning. For instance, different techniques of sequential design of PSSs were adapted to damp out inter area mode of oscillations one at a time. However, this approach may not lead finally to an overall optimal choice of PSS parameters; the stabilizers designed to damp one mode can produce adverse effects in other modes.

      A classical integer-order lead PSS with a washout component is usually used to stabilize power systems. Since most of these controllers have at least five parameters to tune, and exhibit narrow band phase compensation around a desired operating point, there is a need to implement more robust PSS with fewer number of parameters to adjust.

   2. FRACTIONAL-ORDER POWER SYSTEM STABILIZERS

      A FoPSS was successfully implemented to control a single machine connected to an infinite-bus system. The FoPSS enjoys a memory effect, which exhibits a satisfactory performance in most practical applications. In spite of the design complexity of the FoPSS, this feature gives the fractional-order compensators a leading edge over their integer-order counterparts. A typical FoPSS may be described by the following transfer function:

      (1)

      where is the Laplace operator of the fractional derivative of order ; < 0 1, where, Tj; j = 1, 2 4, while TW and KW are real constants Obviously, as = 1, .

      For completeness, the Laplace transform of a fractional-order derivative of f(t) of order n-1 < 1 is given by :

      (2)

      Clearly, if the signal f(t) is initially at rest, then , which will be assumed throughout this work.

      Due to the memory effect of the fractional-order dynamics, a single-stage FoPSS of the form:

      (3)

      will be sufficient to stabilize an interconnected system. sKw/((s) + 1). The large bandwidth exhibited by (3) can replace the washout component

      In order to implement a finite-dimensional FoPSS, one may replace the fractional-order integrator, 1/s, (s in the case of a differentiator), by a finite-order transfer function. The half-order integrator, 1/s, can be replaced by:

      =

      Consequently, the FoPSS in (3) can be rewritten as:

      (4)

      where 1, 2 and K are the controller parameters that will be selected to provide sufficient damping signals to the power system.

      III MODEL 2.1

      This representation is intended to maintain a balance by using two windings (one field, one equivalent damper)on d-axis and one equivalent dampers on q-axis. Following assumptions have been used for analysis of the model:

      1. Main field flux decay is considered.

      2. One equivalent damper winding included in q axis.

      3. One equivalent damper winding included in d axis.

      4. Speed is assumed constant.

      5. Saturation is neglected.

      1. Block Diagram Modeling of Synchronous Generator

         The stator resistance is assumed to be negligible.

         The following equations in the s-domain characterize Model 2.1.

         (5)

         (6)

         (7)

         (8)

         (9)

         (10)

         (11)

         This model is defined by equations (5)(10). The transfer matrix representation of (11) is obtained, where

      2. System coefficients and transfer functions

         (

      3. Stabilization with an AVR

      Excitation system is a key element in the dynamic performance of any electrical power generator. Since accurate excitation is of great importance in bringing the machine into synchronization, and since an AVR malfunction could destabilize the overall system. It is needed to investigate the effect of both stabilizers onto the system with and without an AVR.

      Fig 1 Block Diagram for model 2.1

      1. NUMERICAL RESULTS

         The maximum amount of phase needed depends on the fractional order of the FoPSS. Cascading more than one power system stabilizer would yield the amount of phase required to stabilize the system. The performance of the system is investigated using MATLAB/Simulink environment. It is assumed that the system with the exciter is working properly and a 0.05 p.u. step change in both Vref and Tm is applied to it at t=0.5s and t=2s, respectively. The IoPSS implemented is [3]:

         For fractional-order controllers, two lead FoPSS is cascaded and followed by a limiter without a washout component to form a complete FoPSS controller. Where is selected from Table II, and = 0.5, 1 =30, and 2 = 1

         Fig 2 Frequency deviation due to 0.05 p.u. step change in both Vref and Tm when D = 2, 1 = 30, 2 = 1

         Fig 3 Voltage deviation due to 0.05 p.u. step change in both Vref and Tm when D = 2, 1 = 30, 2 = 1

         Fig 3 Frequency deviation without an AVR when D = 2, 1 = 30, 2 = 1

         Fig 4Voltage deviation without an AVR when D = 2, 1 = 30, 2 = 1

      2. CONCLUSIONS

The FoPSS improved the performance of the infinite bus system and achieved a faster and smoother performance than its integer-order counterpart. Frequency and terminal voltage deviation over sever conditions were quickly absorbed when using FoPSS. FoPSSs has a larger bandwidth than its integer-order counterpart, and is expected to accommodate wider range of operating conditions. The increase in order in the case of FoPSS can be compensated by implementing already existing fast processors.

APPENDIX

Parameters for Model 2.1

,

ACKNOWLEDGMENT

First and foremost, I offer my gratitude to God Almighty for his blessings. I express my heartfelt gratitude to our Principal Dr.M C Philipose, Saintgits College of Engineering, for providing the required facilities. I am grateful to my internal guides, Er.Haseena.K.A, Assistant Professor for their whole hearted support. I would also like to thank Associate Professor Er.Radhika.R for her innovative ideas. I hereby extend my sincere gratitude to all the staff members. Last, but not the least, I extend my sincere thanks to my family and friends for their valuable help and encouragement in my endeavor.

REFERENCES

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2. R. El-Khazali, and N. Tawalbeh Multi-Machine Fractional-Order Power System Stabilizers ,2012

3. Anderson, P.M and Fouad, A.A., Power System Control and Stability. New Jersy: IEEE Press, 1994

4. Aboreshaid, S., and S. O. Faried, Teaching Power System Dynamics and Control using SIMULINK,

   J. King Saud Univ., Vol. 12, Eng. Sci. (1), pp. 139-152, 2000

5. Charef, A., Sun HH, Tsao YY, and Onaral B. ,Fractal system as represented by singularity function, IEEE Trans. on Aut. Control 1992.

6. Kundur, P. Power System Stability and Control. New York: McGraw-Hill, 1994.

7. Oldham, K. B. and J. Spanier, Fractional calculus, Academic Press, New York, 1974.

8. Podlubny, I. Petras, B.M. Vinagre, P. OLeary, and L. Dorcak, Analogue Realization of Fractional- Order Controllers, Nonlinear Dynamics, Vol. 29, pp. 281-296, 2002.

9. Saidy, M. and Hughes, F.M. Block diagram transfer function model of a generator including damper windings. IEE Proceedings on Generation, Transmission and Distribution, 1994.

Table I Synchronous Machine Parameters

maximum error.

H(s) = N(s)/D(s) 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Table II Transfer function approximation of fractional-order integrators with 2 dB