Enhancing optimal excitation control by adaptive fuzzy logic rules

Electrical Power and Energy Systems 63 (2014) 226–235

Contents lists available at ScienceDirect

Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Enhancing optimal excitation control by adaptive fuzzy logic rules Hengxu Zhang ⇑, Fang Shi, Yutian Liu Key Laboratory of Power System Intelligent Dispatch and Control of Ministry of Education (Shandong University), 17923 Jingshi Road, Jinan 250061, PR China

a r t i c l e

i n f o

Article history: Received 15 December 2013 Received in revised form 6 April 2014 Accepted 2 June 2014

Keywords: Automatic Voltage Regulator (AVR) Power System Stabilizer (PSS) Excitation controller Fuzzy logic rules Coordination control

a b s t r a c t Generator excitation system plays an important role in maintaining power system stability. A new fuzzy control strategy is introduced to enhance excitation control by online coordinating Automatic Voltage Regulator (AVR) and Power System Stabilizer (PSS) control tunnels. The method automatically adjusts the weights of the AVR tunnel and PSS tunnel on-line according to different operating conditions by a set of fuzzy logic rules, aiming to improve the overall optimal excitation control performance by the coordination of voltage control and dynamic stability control. The requirements of excitation control in different circumstances are studied, and the fuzzy rules of the coordination are presented. The structure of the presented controller is simple and clear while the conventional design methods in AVR and PSS control tunnels can be kept without change. Numerical simulation results on two cases under different disturbances demonstrate that the proposed controller can get a good performance for a variety of the operating conditions. Ó 2014 Elsevier Ltd. All rights reserved.

Introduction Power system stability has been proved to be of great importance for power system secure operation and uninterrupted electric power supply [1]. The dramatic blackouts in North America, Europe and India caused by power system instability [2], especially in the past twenty years, have provided compelling evidence of this phenomenon. Historically, transient instability is the dominant stability problem and has drawn considerable attention in both literature and industry. Thanks to the Automatic Voltage Regulator (AVR) controller in generator excitation system, the generator terminal voltage can be maintained by controlling the amount of current supplied to the generator field winding by the exciter [3]. With some up-to-date algorithms, the AVR system can be optimally designed to strengthen the transient stability of power system [4]. Consequently, the transient instability probability has statistically decreased in recent years. However, the high gain exciters would deteriorate the damping of the system which leads to low-frequency oscillations of the power system [5]. The instability and blackouts resulted from oscillations has enormously increased with the expansion of the interconnection capacity of power system [6]. The potential jeopardy especially lies in the power system which needs a transmission of bulk amount power over long distance through ⇑ Corresponding author. Tel.: +86 531 88392838; fax: +86 531 88392369. E-mail addresses: [email protected] (H. Zhang), [email protected] (F. Shi), [email protected] (Y. Liu). http://dx.doi.org/10.1016/j.ijepes.2014.06.001 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.

relatively weak tie lines. To end this problem, various controllers have been designed such as Power System Stabilizer (PSS) [3], supplemental damping control of HVDC and FACTS [7–9]. Among these methods, PSS is the most cost-effective one and has been proved to be useful in practical applications [10]. Therefore, a number of generators in power system have been equipped with PSS control loops so as to enhance the damping of the electromechanical oscillations of the generators. Furthermore, a number of algorithms have been proposed aiming to optimize the PSS control effect, the currently available dominant ones are based on the linearized methods, such as pole-assignment and eigenvalue analysis [11]. The inevitable disadvantage of these methods is that the control effect is closely interrelated to the operation state, thus the fixed predefined parameters of the stabilizers may result in poor performance when operating point changes [12]. Addressing this crucial issue, in the last ten years, kinds of modern control techniques have been proposed for PSS self-adaptive tuning in order to provide sufficient damping for the power system under various operating conditions [13–15]. Despite some new approaches have been proposed in literature for generator excitation control, the most commonly used ones in a practical multi-machine power system are still the conventional PI, PID and Lead-lag controllers in which the parameters are tuned by classical, experiential or trial-and-error approaches [16]. The reasons are two-fold: (i) In practical power systems, the controllers with simple structure are particularly desirable since the everchanging parameters makes it time-costly and infeasible to design the controller with some newly proposed but fairly complicated

227

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235

algorithms. (ii) The reliability of the controllers in electric industry is more import compared with some less conservative but more risky ones. Therefore, the traditional AVR and PSS control systems are still widely used although theoretically these methods could not maintain good dynamical performance in a wide range of operating conditions and disturbances. Conventionally, the AVR and PSS design process are two separate sequential stages. Specifically, the AVR is firstly designed to meet the specified voltage regulation performances; secondly, the PSS is tuned to strengthen the damping and improve the dynamic stability performance. However, it has been long recognized that, essentially, the AVR and PSS have inherent conflicting objectives, which might deteriorate each other in some operating circumstances [16]. More pessimistically, as AVR and PSS are actually executed via a unique control signal, that is field voltage, the successful achievement for simultaneously improving the dynamic stability and voltage regulation might be impossible [17]. The coordination and trade-off between voltage regulation and damping enhancements are feasible solutions to the abovementioned issue. A coordinated design procedure is described in [18], thereby, the design of individual PSSs and AVRs is separated and coordinated to achieve a near-optimal overall power system stability performance. In [19], a new comprehensive criterion for the coordinated AVR–PSS design method is proposed for trading-off between voltage regulation and small signal stability in large-scale power systems. In this paper, a new fuzzy logic excitation controller (FLEC) is designed to enhance excitation control by online coordination between AVR and PSS control tunnels. Although AVR and PSS are both exerted on the exciter, their primary aims differ from each other during the two different stages after a disturbance. The generator bus voltage will be strongly deviated by a nearby transmission line short circuit fault. Therefore, the AVR needs to respond right away in order to maintain the desired voltage. After a relative long period after the disturbance, the PSS is then primarily needed to damp the ongoing oscillations. Consequently, the proposed method automatically achieves the trade-off between AVR and PSS controllers by dynamically adjusting their participation factors via a supplementary proportional component of which the weights are tuned based on online measurement and a fuzzy logic controller. The advantages therein are that the existing AVR and PSS controllers need no modification. Therefore the upgrading can be accomplished conveniently with an expected improvement of the overall control performance. The rest of the paper is organized as follows. In Section ‘Structural design of new excitation controller’, the structure of the conventional AVR and PSS controllers are introduced and then the FLEC is illustrated by a supplementary proportional component in which the proportionality factors can be adaptively tuned based on online measurements. The fuzzy logic rules and the detailed implementation of the fuzzy controller are explicitly illustrated in Section ‘Design of fuzzy logic controller’. In Section ‘Simulation results’, a single machine infinite bus (SMIB) power system and a multi-machine power system both equipped with the FLEC controller are tested, in which the PSS are parameterized by the above-mentioned linear optimal control method and conventional pole assignment method, respectively. Numerical simulation results show the effectiveness and feasibility of the proposed method. Some conclusions are drawn in Section ‘Conclusion’.

Structural design of new excitation controller The structure of the classical excitation controller Excitation control system usually can be described as Fig. 1, DVt is the deviation between terminal voltage and the reference value.

ΔVt

Voltage regulation tunnel

+ Exciter Auxiliary signals

Output voltage

+ Auxiliary stabilizing tunnel Fig. 1. Excitation system schematic diagram.

The auxiliary signals, normally PSS controller, generally include the deviations of rotor speed, active power and the change rate of speed deviations. In excitation control system design process, voltage regulation and damping control are the two important goals, which are of great importance for the performance of the controller. The AVR controller, normally tuned by PID method, has excellent performance and high steady state accuracy in voltage regulation [20]. However, it cannot provide sufficient damping torque when the system is subjected to oscillations. Therefore, PSS control tunnel is needed to improve the dynamic stability performance. In design of the conventional PSS, the AVR tunnel is designed as the main tunnel and also taken its negative impacts on dynamic stability into account. This meets the demand of voltage regulation and enhances the dynamic stability in some extent. However, it is hard to choose the optimized control parameters and the controller has bad robustness and low convergence for variation of model parameters. And worse still, it is lack of coordination among different generators. All these defects limit its practical applications [21]. In design of the linear optimal excitation controller (LOEC), AVR tunnel and PSS tunnel are put together with fixed coefficients which are calculated according to a certain steady state. Its performance can satisfy the requirements of dynamic stability in a range of operating conditions, but it cannot meet the requirements of voltage regulation very well. The proposed new FLEC aims to enhance the excitation controller’s performance by coordinating two control tunnels on-line. The AVR tunnel is still based on PID method which uses the generator terminal voltage deviation, DVt, as the feedback signal. The transfer function of the voltage regulation tunnel is

GðsÞ ¼

yðsÞ KI ¼ KP þ þ KDs DV t ðsÞ s

ð1Þ

where KP is proportional coefficient, KI is integral coefficient and KD is differential coefficient, y is the output control signal. The auxiliary stabilizing tunnel is designed to provide damping torque which can be calculated based on linear optimal control theory or pole assignment methods. A linear optimal control method will be presented in the sequel. Design of auxiliary stabilizing tunnel The function of the auxiliary stabilizing tunnel, or PSS tunnel, is dedicated to increase damping torque, and then improve the dynamic stability of the whole system. A linear optimal control method is proposed herein for the auxiliary stabilizing control design in the SMIB system, DVt, Dx and DPe are input variables, and their corresponding coefficients are determined by linear optimization method. It combines system state variables and non-state variables, according to the principle of minimum variable deviation and the least cost control rules, to determine a control variable vector. The behavior of a power system can be described by a set of nonlinear ordinary differential equations. Through appropriate transformations and simplifications, the

228

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235

third-order equations of SMIB system can be linearized at the given equilibrium point as following

X_ ¼ AX þ BU

ð2Þ

KP

ΔVt

where

2

Dx DV t 

S0E SV T 0d SV

6 6 A ¼ 6  xH0 4

SE SV T 0d RV SV

h

+

K1

+

SK D

X ¼ ½DPe

B¼

+

KI / S

R0E T 0d0

0

T

S0E

 TRV0 SSE

 HD S0E SV RV

0

R0E T 0d0 RV

d V

 T 0SES d V

Fuzzy controller

3

ΔPe

7 7 7 5

Δω

iT

K Pe

Exciter +

+ +

K2

Kω

Fig. 2. Structure of fuzzy logic excitation controller.

where P is the solution of the following Riccati equation

U ¼ ½DEfd 

AT P þ PA  PBR1 BT P þ Q ¼ 0

The vector X is referred to as the state vector; A is the state matrix of size 3  3, in which the matrix elements are the partial derivatives of the corresponding differential equation with respect to the variables; B is the control matrix of size 3  1, the matrix elements are the partial derivatives of differential equation with respect to the input control signals; U is the input vector, and here it only comprises one variable. For a synchronous generator with salient poles,

Eq V s xd R  xq R SE ¼ cos d þ V 2s cos 2d xd R xdR xqR

Output voltage

+

ð3Þ

ð12Þ

The existence of the unique solutions of Eq. (12) is a classical linear-quadratic optimal regulator problem [22]. It has been proven that if the matrix A and B are controllable, the there exists a unique non-negative, symmetrical solutions of P. These conditions are normally satisfied for the practical power systems [23,24]. Therefore, the optimal control variables can be obtained

U ¼ DEfd ¼ K Pe DPe  K x Dx  K u DV t

ð13Þ

Then KPe and Kx are taken as the coefficients in the auxiliary stabilizing tunnel.

while for a generator with round rotor

SE ¼

Eq V s cos d xd R

Design of auxiliary stabilizing tunnel

ð4Þ

For both kinds of generator

S0E ¼

E0q V s x0  xqR cos d þ V 2s dR0 cos 2d 0 P xd xd R xq R

ð5Þ

RE ¼ V s sin d=xdR

ð6Þ

R0E ¼ V s sin d=x0d P

ð7Þ

RE RV ¼ @V t

ð8Þ

@Eq

SV ¼ SE  RV

@V t @d

ð9Þ

where Eq is the electric potential along q-axis, E0q is the transient electric potential along q-axis, Vs is the voltage of the infinite bus, Vt is generator terminal voltage, d is the angle difference between Eq and Vt, T 0d is the transient time constant of the excitation winding when the stator windings are closed, T 0d0 is the transient time constant of excitation winding when the stator windings are open, x P

A fuzzy controller is developed to coordinate the above mentioned two tunnels according to operating on-line conditions. In order to reflect the dynamics of system operating state, the fuzzy controller takes generator terminal voltage deviation DVt, rotor speed deviation Dx and output active power deviation DPe as input variables. The output variables are the weight of the AVR tunnel, K1, and that of the PSS tunnel, K2. The structure of the proposed fuzzy logic excitation controller is depicted in Fig. 2. The initial control parameters of the AVR tunnel and PSS tunnel are still based on the conventional mathematical method. Then a supplementary proportional component is added to coordinates the trade-off between the above two mentioned control tunnels. The proportionality coefficients K1 and K2 represent the participation weights of AVR tunnel and PSS tunnel, respectively. These two parameters can be automatically adjusted according to the operating states using a set of fuzzy logic rules in order to keep the steady state voltage regulation accuracy, and to improve system damping and dynamic stability. The improvement is quite clear in physical meaning and is feasible in practical application. The algorithm of the fuzzy controller is significant to the effectiveness of the proposed method, so it will be specifically designed in the sequel.

d

and xq P are the sum of synchronous reactance along d-axis and qaxis respectively, x0d P is the sum of the transient reactance along daxis. Detailed derivation of the linearization is available in Ref. [5]. In the proposed design, the objective function is defined as

J¼

1 2

Z

1

ðX T QX þ U T RUÞdt ¼ J min

ð10Þ

0

where Q is a diagonal matrix, R = r = 1. According to the linear optimal control theory, the optimal feedback gain matrix is

K ¼ R1 BT P ¼ ½K Pe ; K x ; K u T

ð11Þ

Design of fuzzy logic controller Rules of coordinated fuzzy control When the power system is subjected to a disturbance, the generator terminal voltage may surpass the acceptable operating limits. The excitation controller’s primary task is to eliminate the deviation as soon as possible, so the AVR tunnel should be given more weight accordingly. When the voltage deviation is small enough, its main task switches to damp the system oscillation, so the PSS tunnel should be given more weight. Obviously, to improve

229

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235

the system dynamic performances greatly, the two control tunnels should have different weights under different operation conditions. Thus a fuzzy regulation module needs to be suitably designed to accomplish this specific task. Based on Refs. [25–27] and further analysis, the coordination principles for the two tunnels are shown as following: (a) In steady state, the state variables are all within allowable limits and the primary task of excitation control is to improve voltage regulation accuracy. Therefore, the AVR tunnel should be given normal weight and the PSS control should be reduced or even canceled. (b) When the system is subjected to a small disturbance, the general deviations of variables usually are not very large. The primary aim at this time is switched to increase the system damping torque to suppress oscillation, then the weight of the PSS control should be increased correspondingly. (c) During the short period directly after a large disturbance, the voltage variations could be very huge. To improve system security, the most important task of the excitation control is to draw the generator terminal voltage back to operating limits immediately. Thus, during this period, make the AVR tunnel play its role as well as possible, its weight should be increased and that of the PSS tunnel should be decreased temporarily. (d) In the dynamic process after a large disturbance, voltage variations will become smaller, but generator angles are still oscillating which also makes the output active power oscillate. Under such circumstance, the goal of the excitation control should be switched to increase system damping torque to depress such oscillations. At this point, the weight of PSS tunnel should be increased. Those four principles mentioned above are reasonable and understandable, based on which a fuzzy rule set is obtained. Hence the participation factors of AVR and PSS, i.e., K1 and K2 in Fig. 2, can be automatically adjusted.

(O, PVS, PS, PLM, PM, PML, PL) O PVS PS PLM PM PML PL

Zero Positive Positive Positive Positive Positive Positive

Very Small Small Light Medium Medium Medium Large Large.

The universe of the input and output variables The input and output variables of a fuzzy controller usually change within a certain range, which is called the basic universe of the variable. The variables in basic universe are accurate, however, their exact variation range usually cannot be confirmed precisely. So, the actual range needs to be projected to a proper closed interval to facilitate the calculation and control. According to the operation guides, voltage deviation and frequency deviation are usually permitted to change within ±10% and ±1% of their normal operation values, respectively. The generator terminal voltage deviation, DVt, is projected to the interval of [0.15, 0.15]; if it is greater than 0.15 or less than 0.15, treated as 0.15 and 0.15 respectively. The active output power deviation, DPe, is projected in the range of [0.30, 0.30]; if it is greater than 0.30 or less than 0.30, taken as 0.30 and 0.30 respectively. The rotation speed variation of a generator rotor is projected to the interval of [0.015, 0.015]; if it is’s more than 0.015 or less than 0.015, taken as 0.015 and 0.015 respectively. These variables are per-unit values. The output variables of fuzzy controllers, K1 and K2, are restricted to the range of [0.0, 1.5]. The number of elements in the basic universe should be more than twice of the total number of fuzzy linguistic terms to ensure that the fuzzy sets can cover the domain well, and avoid losing important information. Here, the universes of DVt, DPe, Dx are:

ð7; 6; 5; 4; 3; 2; 1; 0; 1; 2; 3; 4; 5; 6; 7Þ The universe of the output variables, K1 and K2 are:

Design of fuzzy controller

ð0; 1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13Þ

The design of a fuzzy controller usually includes three parts: (1) selecting proper linguistic terms which can describe the input and output variables properly; (2) defining fuzzy sets for all fuzzy variables; (3) establishing control rules for fuzzy controller [10]. Linguistic terms of the input and output variables One of the most important steps toward using fuzzy logic for problem-solving is representing fuzzy terms in the problem. Here, four linguistic terms, ‘‘Large’’, ‘‘Medium’’, ‘‘Small’’ and ‘‘Zero’’ are picked out to describe the input and output variables; appending positive or negative sign to nonzero terms, thus totally seven terms are used to describe input variables DVt, DPe, Dx in the fuzzy system: (NL, NM, NS, O, PS, PM, PL) NL NM NS O PS PM PL

Negative Large Negative Medium Negative Small Zero Positive Small Positive Medium Positive Large

K1, K2 are the output variables, which represent the dynamic weights of the two control tunnels, seven terms of none negative value is required:

Membership functions The values of the membership function are all in the interval [0, 1], where 0 means that the object is not a member of the set and 1 means that it belongs entirely. Defining a fuzzy subset is to determine the curve shape of its membership function. A fuzzy subset comes from the membership function curves directly; so, different curve shapes generally correspond to different control characteristics. The different behavior and response of the fuzzy logic controller with different membership functions have been thoroughly studied and compared in [28,29], which is out of this paper’s scope. It is believed that Gaussian membership functions can provide more efficient result in fuzzy control under most circumstance. However, in this paper, the rapid response and the low overshoot/undershoot of the desired output signals, rather than the optimized design of the member function, are our first priority. The triangular and trapezoidal member functions only consist of simple straight line segments and are very easy to practically implement in fuzzy control. And it has been proved that, in a SMIB power system stabilizer design process, triangular and trapezoidal member functions have a very close performance compared to Gaussian membership functions [29]. So, the triangular and trapezoidal membership functions are employed in this paper. The membership functions of input variables are shown in Fig. 3. The triangle function lies in the middle; the trapezoidal functions lie on both sides. When the input signals are small,

230

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235 Table 1 The fuzzy logic rules of the knowledge base.

NL

NM

NS

PS

1 O

PM

PL

DxPe

DV t O

O -7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

Fig. 3. Membership functions of input variables.

K1: K2: K1: K2: K1: K2: K1: K2:

PS PM PL

O

1

PS

PVS

PML

PM

PLM

PS PM O PS PLM PVS PML O PL

K1: K2: K1: K2: K1: K2: K1: K2:

PM PS PM PML PS PML PS PL

PM

PL

K1: PML K2: O K1: PM K2: PVS K1: PLM K2: PM K1: PS K2: PML

K1: K2: K1: K2: K1: K2: K1: K2:

PML O PM PVS PL PM PL PL

PL

IFjDV t jis PS and jDPe j is PS and jDxj is PS THENK 1 is PM; K 2 is PML 0

1

2

3

4

5

6

7

8

9

10

11

12

13

Fig. 4. Membership function of output variables.

greater resolution of the membership function is required to improve control accuracy. So, different slopes are used when designing the membership functions: the closer the trapezoid lies to the origin point, the larger its slope is. Both the linguistic terms and universes of input variables DVt, DPe and Dx are all the same. Therefore, those input variables share the same membership function, displayed in Fig. 3. The membership functions of output variables, K1 and K2, are a little simpler than that of the input variables, presented in Fig. 4. Rules of fuzzy control and simplification Based upon the above developed rules of coordination control, the rules of fuzzy control ones are defined. Due to space limitation, only a few representative rules are listed:

 IFjDV t jis O and jDPe j is PM and jDxj is PM THENK 1 is PVS; K 2 is PMS  In this paper, fuzzy controller only needs to consider determine how much the input variables deviate from the given value. Moreover, only the absolute deviations of the variables need to be considered; this simplifies the number of fuzzy control rules from 7  7  7 = 343 to 4  4  4 = 64, which greatly reduces the amount of computation in the control process. However, it is still too complicated for full illustration and practical application since a fuzzy controller prefers the least number of rules in the knowledge base. Taking advantage of the close relation between the rotor velocity and the active power of the generator, we combine these two variables as one input signal DxPe (shown in Fig. 5), and at the same time, the number of the fuzzy rules are reduced to 4  4 = 16, the detailed tuning rules are explicitly illustrated in Table 1 according to the IF & THEN rules mentioned above.

Rule 1): auxiliary stabilizing control quit in steady states

IFjDV t jis O and jDPe j is O and jDxj is O THENK 1 is PM; K 2 is O  Rule 2): shortly after large disturbance, the weight of auxiliary stabilizing control is limited to ensure voltage regulation performance.

IFjDV t jis PL and jDP e j is PL and jDxj is PS THENK 1 ¼ PL; K 2 ¼ PM  IFjDV t jis PL and jDP e j is PM and jDxj is PS THENK 1 is PL; K 2 is PVS  Rule 3): the weight of auxiliary stabilizing control is increased when the disturbance is small.

Simulation results Two study systems, a parameterized SMIB system and the wellknown four-machine two-area test system, are used to evaluate the performance of the proposed FLEC controller. The descriptions of the two systems are given as follows. Case study I: SMIB system The SMIB power system is shown in Fig. 6. The parameters are set as: T 0d0 ¼ 5:0 s, x0d ¼ 0:13p:u:, xT = 0.1p.u., x1 = 0.4p.u., x2 = 0.4p.u., where T 0d0 is the transient time constant of excitation winding when the stator windings are open; x0d is the d-axis transient reactance of the generator; xT is the reactance of the transformer; x1 and x2 are the resistances of the two transmission lines. The dynamics of the system after two different disturbances are observed and compared when equipped with different excitation

Fig. 5. The structure of the simplified Fuzzy controller.

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235

Vt

xT

231

x1

G

x2 Bus A

Bus B

Infinite Bus

Fig. 6. Single machine infinite bus system.

controllers, i.e., PID, LOEC and FLEC that proposed in this paper. It should be noted here that the PID controller is the specified control method of the AVR and the LOEC controller serves the same function as PSS. There are 3 input signals in the FLEC so as to verify the effectiveness of the full-dimensional fuzzy logic principles. The comparison is carried out under the operating point (d0 = 55°, Vt = 1.033p.u.) and the disturbances are: (A) 10% step change in the generator terminal voltage reference; (B) a simulated transmission line out because of three phase short circuit. The generator terminal voltage and rotor angle responses to disturbance A and B are shown in Figs. 7 and 8, respectively. The simulation results show that, with the dynamic coordination of the two control tunnels in different operating conditions, the proposed fuzzy excitation controller has almost the same voltage regulation accuracy with PID controller; it has better performance in voltage regulation than LOEC, and has better damping of angle

Fig. 9. Four machine two-area power system.

oscillation than PID and LOEC. In some sense, it can optimize the excitation controller’s performance and then enhance the system dynamic stability. Case II: Four-machine, two-area system In order to verify the practical effectiveness of the proposed FLEC controller using reduced input signals for multi-machine power system, the simulations are carried out on the four-machine two-area test system shown in Fig. 9. All the network parameters and the initial state values can be found in [5]. Three different scenarios are chosen to test the dynamics of the system under three different controller configurations: (i) with conventional AVR only, (ii) with AVR and PSS parameterized with classical linear theory, (iii) with the FLEC that proposed in this paper. The dynamic responses of generator G1 and G2 under the three different controllers after the three disturbances are comparatively observed in detail, which will be illustrated separately in the sequel. The results reported were obtained from simulations carried out in MATLAB/Simulink using ODE23 technique with a maximum step time of 1/60 ms. The generator G4 is chosen as the reference and the power difference is defined as the subtracted value between the prime mover power and the electromagnetic power. The error differences of the other variables are the differential values between the state variables and their initial values. Scenario 1: Instantaneous short circuit fault at bus 9

Fig. 7. Generator rotor angle and terminal voltage responses to disturbance A.

The first disturbance is defined as following: at the time spot 1s, an instantaneous short circuit fault occurs at bus 9 and clears after 200 ms. The system is expected to recover to its initial operation states after the disturbance as there is no structure or parameter changing. The differential responses of the rotor angle, generator active power output, generator terminal voltage and rotating speed are shown in Figs. 10–13, respectively. From these figures, we can see that the system will lose synchronization after a short oscillation when only the traditional AVR controller is applied. With the additional functions of the classical PSS controller, the system will keep in synchronization and recover to its initial operating states after an oscillation. Under the proposed FLEC, the system can recover more rapidly with less power fluctuations and better generator voltage maintaining capabilities, which are also helpful for improving the transient stability of the system. The simulation results verify the correctness and effectiveness of the proposed fuzzy logic controllers. Scenario 2: Transmission line tripping off after a short circuit fault

Fig. 8. Generator rotor angle and terminal voltage responses to disturbance B.

In order to verify the effectiveness of the fuzzy logic controller under different disturbance, the second scenario is as follows: at 1s, a three-phase short-circuit fault occurs at Bus 8, 0.1s later, and the fault is cleared by tripping the line between Bus 7 and Bus 9. The fault resistance is chosen as 0.001 X. The differential responses of the rotor angle, generator active power output, generator terminal voltage and rotating speed are shown in Figs. 14–17, respectively.

232

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235

100 0 -100

AVR AVR+PSS FLEC

0.01

AVR AVR+PSS FLEC

Δω1 /(p.u)

Δδ1 /(°)

200

0 -0.01

0

1

2

3

4

5

6

7

8

9

0

10

1

2

3

4

0 -100

6

7

8

9

10

AVR AVR+PSS FLEC

0.01

AVR AVR+PSS FLEC

Δω2 /(p.u)

Δδ2 /(°)

200 100

5

t/s

t/s

0 -0.01

0

1

2

3

4

5

6

7

8

9

0

10

1

2

3

4

5

6

7

8

9

10

t/s

t/s

Fig. 13. Differential generator rotating speed responses of G1 and G2 for Scenario 1. Fig. 10. Differential rotor angle responses of G1 and G2 for Scenario 1.

150 AVR AVR+PSS FLEC

AVR AVR+PSS FLEC

0

Δδ 1 /(°)

Δ p1 /(p.u)

0.5 100 50 0

-0.5

0

0

1

2

3

4

5

6

7

8

9

1

2

3

4

5

6

7

8

9

10

t/s

10

t/s 150

AVR AVR+PSS FLEC

0.5 0

Δδ 2 /(°)

Δ p2 /(p.u)

1

-0.5 -1

AVR AVR+PSS FLEC

100 50 0 0

0

1

2

3

4

5

6

7

8

9

10

1

2

3

4

5

6

7

8

9

10

t/s

t/s Fig. 14. Differential rotor angle responses of G1 and G2 for Scenario 2. Fig. 11. Power difference responses of G1 and G2 for Scenario 1.

Δ U1 /(p.u)

0.4 AVR AVR+PSS FLEC

0.2 0 -0.2

0

1

2

3

4

5

6

7

8

9

10

t/s

Δ U2 /(p.u)

0.4 AVR AVR+PSS FLEC

0.2 0 -0.2

From these figures, it can be seen that when equipped with the AVR controller only, the system will lose synchronization although the generator terminal voltage has a better performance during the fault period. Obviously, it is easy to understand this phenomenon since the AVR only aims for maintaining the generator terminal voltage. With the help of the PSS (AVR + PSS controller), both the rotor stability and the voltage stability can be readily realized but the voltage fluctuations are larger. With the FLEC controller that proposed in this paper, the participation weights of AVR and PSS are dynamically regulated according to the fuzzy logic rules with respect to state variables. Hence the voltage fluctuations can be efficiently diminished efficiently and both the generator rotor angle deviation and rotating speed deviation can be enormously suppressed. Therefore both the transient angle stability and voltage stability of the system can be improved. Scenario 3: A different operation conditions with line short circuit fault

0

1

2

3

4

5

6

7

8

9

10

t/s Fig. 12. Differential generator terminal voltage responses of G1 and G2 for Scenario 1.

To further evaluating the applicability and robustness of the proposed controller under various operating conditions, the system is also tested at a different prescribed initial operating point. In this scenario, the active power load at Bus 9 has declined

233

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235 0.4

AVR AVR+PSS FLEC

Δδ 1 /(°)

Δp1 /(p.u)

0.2 0 -0.2

20 0 -20

0

2

4

t/s

6

8

0

10

1

2

3

4

0

Δδ2 /(°)

0.1 -0.1 -0.2

20

9

10

0

2

4

6

8

0

10

1

2

3

4

6

7

8

9

10

Fig. 18. Rotor angle responses of G1 and G2 for Scenario 3.

0.2

0.4

Δ p1 /(p.u)

AVR AVR+PSS FLEC

0.1

5

t/s

Fig. 15. Power difference responses of G1 and G2 for Scenario 2.

Δ U1 /(p.u)

8

AVR AVR+PSS FLEC

t/s

0

AVR AVR+PSS FLEC

0.2 0 -0.2 -0.4

0

1

2

3

4

5

6

7

8

9

10

0

1

2

3

4

5

6

7

8

0.4

0.2 0.1

Δp2 /(p.u)

AVR AVR+PSS FLEC

0

9

10

t/s

t/s

Δ U2 /(p.u)

7

-20 0

-0.1

6

40

AVR AVR+PSS FLEC

0.2

-0.1

5

t/s

0.3

Δp2 /(p.u)

AVR AVR+PSS FLEC

40

AVR AVR+PSS FLEC

0.2 0 -0.2

0

1

2

3

4

5

6

7

8

9

10

t/s

0

1

2

3

4

5

6

7

8

9

10

t/s Fig. 19. Power difference responses of G1 and G2 for Scenario 3.

Fig. 16. Differential generator terminal voltage responses of G1 and G2 for Scenario 2.

Δω1 /(p.u)

x 10 -3 5

AVR AVR+PSS FLEC

0

-5

0

1

2

3

4

5

6

7

8

9

10

t/s

Δω2 /(p.u)

x 10 -3 5

AVR AVR+PSS FLEC

0

-5

0

1

2

3

4

5

6

7

8

9

10

t/s Fig. 17. Differential generator rotating speed responses of G1 and G2 for Scenario 2.

by 20% against Scenario 1, and the output power of Generator 1 is accordingly resettled in order to obtain a feasible power-flow solution. The disturbance situation and the other parameters are the same as that in Scenario 1. The corresponding responses of the rotor angle, power difference, generator terminal voltage and rotating speed are illustrated from Figs. 18–21, respectively. As the load becomes lighter and transmission power is decreased, it is reasonable that the transient stability of the system will be improved correspondingly. Confirmatively, the system does not lose synchronization after undergoing the same disturbance as that in Scenario 1, as seen in the figures. However, an oscillation is still present after the disturbance when only the AVR controller is used despite the voltage of the generator can be automatically controlled. With the AVR + PSS controller, the oscillation can be ultimately eliminated but the first swing is considerably large since the parameters of PSS are suitably designed for the predefined operating points. Under the FLEC, only the deviation of the states are used as the control input and the participation weights can be dynamically self-adjusted, therefore the controller can be effective for various operation conditions. The contrast response curves in Figs. 18–21 demonstrate that FLEC controller still has the best performance with respect to AVR and AVR + PSS even the operating condition changed.

234

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235

Δ U1 /(p.u)

0.2

performance for a variety of the operating conditions and different disturbances.

AVR AVR+PSS FLEC

0.1

Acknowledgements

0 -0.1

0

1

2

3

4

5

6

7

8

9

10

t/s

Δ U2 /(p.u)

0.2

References AVR AVR+PSS FLEC

0.1 0 -0.1

0

1

2

3

4

5

6

7

8

9

10

t/s Fig. 20. Generator terminal voltage responses of G1 and G2 for Scenario 3.

x 10

-3

Δω1 /(p.u)

5 0 -5

AVR AVR+PSS FLEC

-10 -15

0

1

2

3

4

5

6

7

8

9

10

t/s x 10

-3

Δω2 /(p.u)

5 0 -5

AVR AVR+PSS FLEC

-10 -15

This work is supported by the National High Technology Research and Development Program of China (863 Program, No. 2011AA05A118).

0

1

2

3

4

5

6

7

8

9

10

t/s Fig. 21. Generator rotating speed responses of G1 and G2 for Scenario 3.

Conclusion In this paper, a new adaptive excitation control scheme is presented to automatically obtain the trade off between the AVR and PSS tunnel, then enhance the existing excitation control system. The structure, design steps and coordination rules as well as the simplification method of the input signals are thoroughly illustrated. The proposed FLEC method is simple since it only needs to pick up one rule online from a minimal rule set with 16 definite rules. Therefore, it is possible to realize the controller efficiently since the computation burden involved in the fuzzy reasoning is small. The proposed FLEC controller is evaluated on both the SMIB system and four-machine two-area power system. Simulation results from different kinds of disturbances demonstrate that it can provide good damping and improves the dynamics even the operating condition changes. Simultaneously, the transient stability as well as the voltage-sustaining capability can be effectively strengthened. Numerical simulation results on two test power system demonstrate that the proposed controller can get a good

[1] Kundur P, Paserba J, Ajjarapu V, Andersson G, Bose A, Canizares C, et al. Definition and classification of power system stability. IEEE Trans Power Syst 2004;19:1387–401. [2] Andersson G, Donalek P, Farmer R, Hatziargyriou N, Kamwa I, Kundur P, et al. Causes of the 2003 major grid blackouts in north America and Europe, and recommended means to improve System Dynamic Performance. IEEE Trans Power Syst 2005;20:1922–8. [3] Machowski J, Bialek JW, Bumby JR, NetLibrary I. Power system dynamics: stability and control. Wiley; 2008. [4] Gaing ZL. A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Trans Energy Convers 2004;19:384–91. [5] Kundur P. Power system stability and control. New York: McGraw-Hill; 1993. [6] Padhy BP, Srivastava SC, Verma NK. Robust wide-area TS fuzzy output feedback controller for enhancement of stability in multimachine power system. IEEE Syst J 2012;6:426–35. [7] Zhang Y, Bose A. Design of wide-area damping controllers for interarea oscillations. IEEE Trans Power Syst 2008;23:1136–43. [8] Chao L, Xiaochen W, Jingtao W, Peng L, Yingduo H, Licheng L. Implementations and experiences of wide-area HVDC damping control in China Southern Power Grid. In: 2012 IEEE power & energy society general meeting new energy horizons – opportunities and challenges; 2012, 7 pp. [9] Li Y, Rehtanz C, Rueberg S, Luo L, Cao Y. Wide-area robust coordination approach of HVDC and FACTS controllers for damping multiple interarea oscillations. IEEE Trans Power Delivery 2012;27:1096–105. [10] Gurrala G, Sen I. Power system stabilizers design for interconnected power systems. IEEE Trans Power Syst 2010;25:1042–51. [11] Jalayer R, Ooi B-T. Estimation of electromechanical modes of power systems by transfer function and eigenfunction analysis. IEEE Trans Power Syst 2013;28: 181–9. [12] Nechadi E, Harmas MN, Hamzaoui A, Essounbouli N. A new robust adaptive fuzzy sliding mode power system stabilizer. Int J Electr Power Energy Syst 2012;42:1–7. [13] Zhang J, Chung CY, Han Y. A novel modal decomposition control and its application to PSS design for damping interarea oscillations in power systems. IEEE Trans Power Syst 2012;27:2015–25. [14] Lin Y-J. Proportional plus derivative output feedback based fuzzy logic power system stabiliser. Int J Electr Power Energy Syst 2013;44:301–7. [15] Bhati PS, Gupta R. Robust fuzzy logic power system stabilizer based on evolution and learning. Int J Electr Power Energy Syst 2013;53:357–66. [16] Bevrani H, Hiyama T, Mitani Y. Power system dynamic stability and voltage regulation enhancement using an optimal gain vector. Control Eng Practice 2008;16:1109–19. [17] Bourles H, Peres S, Margotin T, Houry MP. Analysis and design of a robust coordinated AVR/PSS. IEEE Trans Power Syst 1998;13:568–74. [18] Dysko A, Leithead WE, O’Reilly J. Enhanced power system stability by coordinated PSS design. Power Syst, IEEE Trans 2010;25:413–22. [19] Golpira H, Bevrani H, Naghshbandy AH. An approach for coordinated automatic voltage regulator-power system stabiliser design in large-scale interconnected power systems considering wind power penetration. IET Gener Transm Distrib 2012;6:39–49. [20] Kim K, Schaefer RC. Tuning a PID controller for a digital excitation control system. IEEE Trans Ind Appl 2005;41:485–92. [21] Zhou E, Malik OP, Hope GS. Design of stabilizer for a multimachine power system based on the sensitivity of PSS effect. IEEE Trans Energy Convers 1992;7:606–13. [22] Bender DJ, Laub AJ. The linear-quadratic optimal regulator for descriptor systems. IEEE Trans Autom Control 1987;AC-32:672–88. [23] Matsuo T, Yasuda T, Suemitsu H, Okada H. Adaptive stabilizer for power systems based on Riccati equation. Trans Inst Electr Eng Japan, Part C 2001;121-C:366–74. [24] Ibraheem, Kumar P. A novel approach to the matrix Riccati equation solution: an application to optimal control of interconnected power systems. Electr Power Compon Syst 2004;32:33–52. [25] Hassan LH, Moghavvemi M, Almurib HAF, Muttaqi KM, Du H. Damping of lowfrequency oscillations and improving power system stability via auto-tuned PI stabilizer using Takagi-Sugeno fuzzy logic. Int J Electr Power Energy Syst 2012;38:72–83. [26] Liang R-H, Chen Y-K, Chen Y-T. Volt/Var control in a distribution system by a fuzzy optimization approach. Int J Electr Power Energy Syst 2011;33: 278–87. [27] Dudgeon GJW, Leithead WE, Dysko A, O’Reilly J, McDonald JR. The effective role of AVR and PSS in power systems: frequency response analysis. IEEE Trans Power Syst 2007;22:1986–94.

H. Zhang et al. / Electrical Power and Energy Systems 63 (2014) 226–235 [28] Zhao J, Bose BK. IEEE, IEEE Evaluation of membership functions for fuzzy logic controlled induction motor drive. In: Iecon-2002: Proceedings of the 2002 28th annual conference of the IEEE industrial electronics society, vols. 1–4. New York: IEEE; 2002. p. 229–34.

235

[29] Sambariya DK, Prasad R. Robust power system stabilizer design for single machine infinite bus system with different membership functions for fuzzy logic controller. In: Proceedings of the 2013 7th international conference on intelligent systems and control (ISCO); 2013. p. 13–9.