Abstract--In this paper, the problem of the synchronization of

previously proposed fuzzy stabilizers is investigated. In particular, a Fuzzy Power System Stabilizer and a Fuzzy FACTS Device Stabilizer have been considered. Some significant numerical results on the IEEE three machine power system illustrate the improvements provided by the proposed synchronized fuzzy stabilizers on power system dynamic performance.

Index Terms--Damping oscillation, FACTS, FACTS device stabilizer, Fuzzy logic controller, Power System Stabiliser, STATCOM.

I. INTRODUCTION ARGE extended power systems are often characterized by inter-area oscillations, usually spontaneous, which may be

caused by small disturbances such as changes in load that take place continually. Some oscillations are associated with the linear response of the system and represent natural modes of oscillation. Other ones are associated with the non-linear response of the system that appears only when the system is subjected to large disturbances such as sudden and large load changes or system faults. Inter-area oscillations are very harmful and may cause a total breakdown of the power transfer, especially when there are transmission lines weakly coupled in power systems carrying large loads.

As well known, a voltage regulation in the power system could be necessary to improve transient stability and power system oscillation damping properties. Each machine is so generally equipped with an Automatic Voltage Regulator (AVR) and some most “critical” ones with Power System Stabilizers (PSSs).

Nowadays, for power system oscillations damping, besides PSSs, the use of Flexible AC Transmission Systems (FACTS) devices has reached equal importance. FACTS devices can provide power modulation for power oscillation damping by a supplementary damping controller, conventionally referred as FACTS device stabilizer (FDS). Generally, the FDS has the same structure of a conventional PSS (a linear controller) [1].

D. Menniti, A. Burgio, A. Pinnarelli, N. Sorrentino work with the

Department of Electronic, Computer and System Science, University of Calabria, Via Pietro Bucci, Arcavacata of Rende- 87036, ITALY, (e.mail: sorrentino@deis.unical.it).

The power system operating conditions and topologies are time varying and the disturbances are unforeseeable especially in the new scenario of deregulated market. These uncertainties make very difficult to effectively deal with power system stability problems by conventional controllers, based on system model linearised around a specific operating point. As consequence, conventional PSS and FDS may fail, threatening the stability of the system so that a lot of interest has been placed in the use of more robust non-conventional controllers. A very powerful and widely used non-conventional controller is based on the use of fuzzy logic. A fuzzy controller is a non-linear controller and it is not so sensitive to system topology, parameter and operating condition changes as the conventional ones. However, still now the investigation on Fuzzy controller is mainly in PSS design [2-3]. Only in recent years, this investigation has been extended in FDS design [4].

On the basis of above considerations, in this paper, a Fuzzy FDS (FFDS) is synchronized with a Fuzzy PSS (FPSS), both proposed by the authors in [5] and [4] respectively, in order to avoid eventual negative effects due to their simultaneously presence in the power system. In particular, the FPSS conjoins the speed deviation and the electric power deviation of the machine where it is installed. This controller has proved to be effective in a wide range of operating conditions and different test power systems.

The FFDS is designed for a Static Synchronous Compensator (STATCOM) to enhance the inter-area power oscillation damping and both power system dynamic and transient stability. The control input signals of FFDS are the STATCOM dc-link voltage deviation and an opportune speed deviation. In particular, to perform the synchronization of FFDS with FPSS, in the paper, the speed deviation of the machine where the PSS is placed is adopted as feedback control input for FFDS.

In the paper, in the Section II the test power system and STATCOM effects in voltage regulation are briefly recalled. In Sections III and IV the fuzzy controllers features and how their parameters are chosen are illustrated. In the last section, some numerical results show how the proposed synchronized FPSS and FFDS significantly improve power system dynamic behavior.

Synchronizing Fuzzy Power System Stabilizer and Fuzzy FACTS Device Stabilizer to damp

electromechanical oscillations in a multi-machine power system

D. Menniti, Member IEEE, A. Burgio, A. Pinnarelli, N. Sorrentino, Member IEEE

L

II. POWER SYSTEM WITH A STATCOM INSTALLED Let consider the IEEE three machine test power system [6]

with a STATCOM installed on the tie line 4-5, as shown in Fig. 1.

Generally, to improve transient stability and damping oscillation properties a voltage regulation control action in the power system is necessary. Each machine is so basically equipped with an Automatic Voltage Regulator (AVR) and some most “critical” ones are equipped with Power System Stabilizers (PSSs), as in Fig. 2.

A further voltage regulation control action may be performed by a STATCOM. STATCOM consists of a step-down transformer with leakage impedance and a three phase GTO based voltage source inverter (VSI) with a DC capacitor (CDC). Representing the VSI as a controllable voltage source

0V (see Fig. 3), the reactive power exchange between the STATCOM and the power system is determined by the difference between 0V and V (terminal bus voltage).

This power flow can be controlled by adjusting the magnitude and the phase of 0V ( 0V =cVDC(sinωt+ϕ)) by the modulation ratio c and the phase ϕ of the PWM switching control strategy of VSI. The data of STATCOM considered in the paper are reported in Table I.

STATCOM provides a voltage regulation at the midpoint of the transmission line (see Fig. 4). The midpoint compensator segments the transmission line into two independent parts: the first segment carries power flow from the sending end to the midpoint and the second one from the midpoint to the receiving end. The phasor diagram in Fig. 5 shows the relationship among voltages and line segment currents.

Theoretically, the transmittable power flow would double with each doubling of the segments for the same overall line length [7]. Thus, it is reasonable to expect that, with suitable and fast controls, STATCOM will be able to change the power flow in the system during and following dynamic disturbances so as to increase the transient stability limit and improve power system dynamic stability.

In particular, being the power oscillation a sustained dynamic event, the STATCOM control scheme must be designed to vary the midpoint voltage of the transmission line to counteract the accelerating and decelerating swings of the disturbed machine (s).

Fig. 1 IEEE three machine power system with a STATCOM installed

A typical STATCOM control scheme consists of a DC voltage regulator controls the DC voltage across the capacitor of the STATCOM DC-link (VDC) to the reference value VDCref, and of AC voltage regulator, which regulates the terminal bus voltage (V) to the reference value, Vref [8].

Fig. 2 Machine equipped with AVR and PSS

Fig. 3 Representation of power system with STATCOM installed

TABLE I STATCOM DATA

V0 [pu] Xsh[pu] ϕ0 [rad]

c CDC[pu]

1.0292 0.025 -0.0570 0.61 20

Fig. 4 Representation of a line with a STATCOM in the midpoint

Fig. 5 Phasor diagram electric circuit of Fig. 4 (V40, V50 pre-compensation voltage values)

Conventionally, the DC voltage regulator contributes negative damping to the power system. Instead, the AC voltage regulator has positive but little influence on system damping. An auxiliary stabilizing signal u∆c may be so introduced and superimposed on the AC voltage control loop in order to increase this influence [8].

The basic idea of a functional control for damping power oscillations, referred as FDS, is to modify the voltage reference Vref opportunely. Accordingly, the auxiliary stabilizing signal u∆c, corresponding to the variation of the real power or of the system frequency, is summed to the voltage reference Vref (see Fig. 6). By this added signal the STATCOM output current oscillates around the fixed operating point controlling the midpoint voltage so as aiding power system damping.

In particular, the midpoint voltage is increased when the speed deviation is positive (in order to increase the transmitted electrical power and thereby to oppose the acceleration of the machines) and it is decreased when the speed deviation is negative (to reduce the transmitted electrical power and thereby oppose the deceleration of the machines) [7].

III. THE FUZZY PSS Several types of PSS were proposed in literature in order to

improve power system stability. Among them, a lot of interest has been placed in PSS based on fuzzy logic. A powerful one has been proposed in [6].

The PSS target is to stabilize the synchronous machine, where it is installed, and improve its damping oscillations. At this scope, in the paper, the machine speed deviation (∆ω) and the active power deviation (∆Pe) are selected as feedback control inputs for adopted FPSS (see Fig. 7).

In particular, for the analyzed power system a FPSS is placed on machine 1.

A. Membership functions The membership functions map the crisp function values

into fuzzy variables. The chosen set of membership are NB, NM, NS, ZE, PS, PM, PB which stand for negative big, negative medium, negative small, zero, positive small, positive medium and positive big, respectively.

For sake of simplicity for both input and output variables the membership functions are two trapezoidal and five triangular with the 50% of overlapping. The membership function ranges are reported in Fig. 8.

Fig. 6 STATCOM AC voltage regulator and stabilizer

Fig. 7 Fuzzy PSS controller structure

Fig. 8 Adopted FPSS membership functions

B. Rule table Fuzzy rules are the relations between input-output fuzzy

sets. They usually are in the form: If A then B where A is the rule antecedent and B is the rule consequent. Each rule defines a fuzzy patch in the Cartesian product AxB.

For a system with two control variables and seven linguistic variables in each control variable range, this leads to a 7x7 decision table. For the case under examination the Table II has been adopted.

The antecedent of each rule conjoins the speed deviation and the active power deviation fuzzy set values. Using min inference rule the activation of the i-th consequent rule is a scalar value, which equals the minimum of the two antecedent conjuncts values.

The knowledge required to generate the fuzzy rules has been derived from an off-line simulation and expert operators.

Defuzzifycation of fuzzy decision inferred from the fired rules is done using the centroid method.

IV. THE FUZZY FDS In this section the proposed fuzzy FDS is illustrated. It is

based on the decentralised/hierarchical control architecture proposed by the authors in [9]. This control architecture is a two level control structure: a control signal of first level provides damping of local modes using local available signals while a control signal of second level, sent to STATCOM, provides damping of inter-area modes.

According to this hierarchical configuration, the VDC deviation (∆VDC) and the speed deviation (∆ω) of machine 1 where PSS is installed have been used as input signals for FFDS. The FFDS scheme is shown in Fig. 9, and it is replaced the stabilizer block in the AC voltage regulator scheme (see Fig. 6).

TABLE II RULES TABLE OF FPSS

∆ Pe NB NM NS ZE PS P

M PB

NB NB NB NB NB NM NS ZE NM NB NB NM NM NS ZE PS NS NB NM NM NS ZE PS PMZE NM NM NS ZE PS PM PMPS NM NS ZE PS PM PM PB PM NS ZE PS PM PM PB PB

∆ω

PB ZE PS PM PB PB PB PB

Fig. 9 Fuzzy FDS controller structure It is opportune to underline ∆VDC has been chosen as a

FFDS control input being the terminal voltage of STATCOM (V) function of VDC.

A. Membership functions The chosen set of membership are NB, NS, ZE, PS, PB

which stand for negative big, negative small, zero, positive small and positive big, respectively.

For sake of simplicity for both input and output variables the membership functions are two trapezoidal and three triangular with the 50% of overlapping. The membership function ranges are reported in Fig. 10.

B. Rule table The rule table has been valuated going with the following

steps. A conventional controller based on the linearised system model at a dominant operating point has been firstly designed. Then, several disturbances have been applied on the original non-linear system with conventional linear controller installed.

By time simulations a large number of FFDS input–output pairs have been collected and used as training samples. By the combination of the two input signals there will be 25 decision rules altogether.

The min inference rule and centroid defuzzyfication technique have been used in order to determine FFDS output signal, u∆c.

The most convenient way to represent the decision rules is to use a table as shown in Table III, in which each entry represents a particular rule.

Fig. 10 Adopted FFDS membership functions

TABLE III RULES TABLE OF FFDS

∆ω NB NS ZE PS PB

NB NB NB NB PB NS NS NS NS NS ZE PS ZE NS NS ZE PS PB PS NS ZE PS PS PS

∆VDC

PB PS NB PB PB PB

V. NUMERICAL RESULTS

Several numerical experiments on the adopted test power system have been performed to value the effect of the synchronization of the FFDS with the FPSS on power system dynamic performance.

In the following one set of simulations is reported when on the no-linear model of power system a three-phase fault occurs near bus 7, cleared in 0.086 sec by opening line 5-7.

In Fig. 11 and Fig. 12 the results obtained with the only FFDS (FFDS) and when the two proposed fuzzy controllers work simultaneously (FFDS&FPSS) are reported.

As it can be noted the power system dynamic performance, already satisfactory with only the FFDS [4], is significantly improved by the FPSS and their synchronization.

Besides, the stabilizing effect of the proposed synchronization is more relevant comparing the power system dynamic performance when FPSS and FFDS are turn on separately and when they are turn on together (see Fig. 13 and Fig. 14).

Referring to machine 3 and its speed deviation, it’s evident how it is not obtained the same strong damping effect respect to machine 2 in the period following the first 2-3 seconds (see Fig. 14).

In order to value the whole dynamic power system performance the two following performance dynamic indices are calculated:

- ∑∫=

∆ ∆−∆=3

2

5

0 1i

i dtJ ωωω ;

- ∑∫=

∆ ∆−∆=3

2

5

0 1i

i dtJ δδδ .

It can be observed that the whole power system performance is almost similar when FFDS and FPSS work together with respect to only FPSS (see Table IV and Table V).

It is worth to underline that to extend the stabilizing effect on the whole observation period it should be opportune to implement a more strictly interaction between the FPSS and FFDS using for FPSS input also remote signals coming from STATCOM.

TABLE IV PERFORMANCE INDEX J∆ω FOR THE THREE DIFFERENT CONTROL

CONFIGURATIONS

FFDS FPSS FFDS&FPSS J∆ω 2.0992 1.1262 1.1517

TABLE V

PERFORMANCE INDEX J∆δ FOR THE THREE DIFFERENT CONTROL CONFIGURATIONS

FFDS FPSS FFDS&FPSS J∆δ 1418 913 903

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 -10 -8 -6 -4 -2 0 2

4 6

∆ω∆ω∆ω∆ω2-∆ω∆ω∆ω∆ω1 rad/sec

sec

FFDS FPSS&FFDS

Fig. 11 Dynamic performance of machine 2

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 sec -8

-6

-4

-2

0

2

4

rad/sec

FFDS

FPSS&FFDS

∆ω∆ω∆ω∆ω3-∆ω∆ω∆ω∆ω1

Fig. 12 Dynamic performance of machine 3

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5-0.6

-0.4

-0.2

0

0.2

0.4

0.6

rad

sec

FFDS

FPSS &FFDS

∆δ∆δ∆δ∆δ2-∆δ∆δ∆δ∆δ1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 sec-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

rad

FFDS only

FPSS&FFDS

∆δ∆δ∆δ∆δ3-∆δ∆δ∆δ∆δ1

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 sec -0.6

-0.4

-0.2

0

0.2

0.4

0.6

rad ∆δ∆δ∆δ∆δ2-∆δ∆δ∆δ∆δ1

FFDS FPSS FFDS&FPSS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 sec -10

-8

-6

-4

-2

0

2

4

6

rad/sec ∆ω∆ω∆ω∆ω2-∆ω∆ω∆ω∆ω1

FFDS FPSS FFDS&FPSS

Fig. 13 Machine 2: comparison of the three different controllers effects

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 sec -0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

rad ∆δ∆δ∆δ∆δ3-∆δ∆δ∆δ∆δ1

FFDS FPSS FFDS&FPSS

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 sec -8

-6

-4

-2

0

2

4

rad/sec ∆ω∆ω∆ω∆ω3-∆ω∆ω∆ω∆ω1

FFDS FPSS FFDS&FPSS

Fig. 14 Machine 3: comparison of the three different controllers effects

VI. CONCLUSIONS In this paper, the synchronization of a fuzzy logic stabilizer

(FFDS) for STATCOM with a fuzzy logic Power System Stabilizer (FPSS) is performed. It is possible thanks to decentralized /hierarchical control architecture of the FFDS. This control structure uses as control inputs both local and remote signals. In particular, using as remote signal the speed deviation of the machine where the FPSS is placed, the aforesaid synchronization is achieved.

The numerical results obtained on the IEEE three machine power system show as the synchronized FPSS-FFDS improves power system dynamic performance with respect to the case of the two controllers work separately.

Future aim of the authors is to implement a more strictly synchronization between the FPSS and FFDS using for FPSS input remote signals coming from STATCOM.

VII. REFERENCES [1] G.J. Li, T.T. Lie, G.B. Shrestha, and K.L. Lo, “Implementation of co-

ordinated multiple facts controllers for damping oscillations”, Electric Power and Energy System, vol. 22, 2000, pp. 79-92.

[2] D. Menniti, N. Sorrentino "A decentralised fuzzy stabiliser for multi-machine power system" Proceedings of the 1999 IEEE Power Tech'99 conference, Budapest, Hungary, Aug 29 Sept 2.

[3] T. Hiyama, H. Sameshima “Fuzzy logic control scheme for on line stabilization of multi-machine power system” Fuzzy set and System, vol. 35, 1991, pp181-194.

[4] D. Menniti, A. Burgio, A. Pinnarelli, N. Sorrentino, “Design of STATCOM fuzzy controller to damp electromechanical oscillations in a multi-machine power system”, PMAPS 2002, Naples, 22-23 September, pp. 439-444.

[5] D. Menniti, N. Sorrentino, “A decentralised fuzzy power system stabilizers”, Proceedings of the 1999 IEEE Power Tech'99 conference, Budapest, Hungary, Aug 29 Sept 2.

[6] K.A.El-Metwally, D.P. Malik “Application of fuzzy logic stabilizers in a multi-machine power system environment” IEE proc. On generation, Transmission and Distribution vol. 143, n°3, May 1996, 263-267.

[7] N.G.Hingorani, L. Gyugi, “Understanding FACTS”, IEEE Press, 1999 [8] H. F. Wang, “Modelling STATCOM into Power Systems”, in

Proceedings of the 1999 IEEE Power Tech'99 conference, Budapest, Hungary, Aug 29 Sept 2.

[9] D. Menniti, A. Pinnarelli, N. Sorrentino, “Simultaneous design of damping controls for improving system dynamic performance- Part II: Decentralised/hierarchical control of FACTS device stabilisers and power system stabilisers”, PowerCon 2002, October 13-17, Kunming, China, 2002.

VIII. BIOGRAPHIES Daniele Menniti was born in Susa (TO), Italy on September 23, 1958. He

received the degree in Electrical Engineering from University of Calabria, Cosenza, Italy and the PhD. degree in Electrical Engineering from University of Naples, Italy, in 1984 and 1989 respectively. He is an Associate Professor at the Electronic, Computer and Systems Science Department of University of Calabria, Italy. His current research interests concern with electrical power system analysis, real-time control and automation. Dr Menniti is an IEEE Power Engineering Society member.

Anna Pinnarelli was born in Cosenza, Italy, on December 8, 1973. She received the degree in Management Engineering from University of Calabria in 1998 and the PhD in Electrotechnics Engineering in 2002 at Electrical Engineering Department of University of Naples, Italy. Her current research interests concern FACTS technology, harmonic analysis and electrical system automation and decentralised control.

Nicola Sorrentino was born in Cosenza, Italy, on October 26, 1970. He received the degree in Management Engineering in 1994 and the PhD in Computer and system Engineering in 1999 at the Electronic, Computer and Systems Science Department of University of Calabria, Italy. His current research interests concern electrical power systems decentralised control and analysis. Dr Sorrentino is an IEEE Power Engineering Society member.

Alessandro Burgio was born in Taurianova, Italy, on March 30, 1973. He received the degree in Management Engineering from University of Calabria in 1999. His current research interests concern electrical power systems decentralised control and analysis.