A new method for detection of fake data and adaptive fuzzy PI control for power system stability

Abstract

This paper presents a fuzzy PI controller as a power system stabilizer. The fuzzy PI controller has been designed in order to prepare an auxiliary signal for the excitation system of the synchronous generator. The proposed controller utilizes a combination of a fuzzy logic controller (FLC) and a PI controller, which are the most recent researches in the problem at hand. In comparison with the conventional fuzzy controllers, the proposed fuzzy PI controller takes advantage of both FLC and conventional PI controller to overcome all kind of disturbances. The damping of oscillations local modes in a power system will substantially be controlled by employing this controller as a replacement for conventional PSS. Furthermore, the presented paper considers the conventional PSS and compares its performance with respect to three proposed types of fuzzy PI controller. Correspondingly, the effects of the supplementary signals in damping oscillation have been shown. Finally, to scrutinize the effectiveness of the proposed controller in damping oscillations, a three-phase short circuit condition is studied in order to clarify the application of the developed methodology. The achieved outcomes show that the proposed controller for stabilizing power system can provide very good damping characteristic.

Keywords

Fuzzy control power system stabilization operating condition

1 Introduction

In order to enhance the dynamic responses and to control the terminal voltages of the power generators they are conventionally accompanied with automatic voltage regulators (AVRs). But, AVRs lead to negative damping torques, which affect the stability adversely. Since disturbances, such as short circuits and operating point variations of power systems, may exhibit undesirable oscillations or lose synchronism [1]. In order to suppress and damp the aforementioned oscillations the conventional power system stabilizers (CPSS) are usually utilized. In addition, other types of PSS such as proportional integral (PIPSS) and proportional integral derivative (PIDPSS) have also been proposed in this paper. According to the linearized model of the power system around a nominal operating point, the gain settings of these controllers are settled in order to attain optimal performance at this point [2]. Generally, the power systems are highly nonlinear and the operating conditions can change over a wide range due to the load changes, line switching, and unforeseeable major disturbances such as three phase faults. Hence, a controller must work in the nonlinear systems and give good damping characteristics over a broad range of operation conditions. The conventional PI controller with fixed gains has been designed at nominal operating conditions. So it weakens to provide the best control performance over a wide range of operating conditions and show poor dynamic performance. To overcome with this problem, adaptive-gain-scheduling techniques which are on the basis of the adoption of a fuzzy system for gain scheduling have been presented [3]. Fuzzy PI controllers have many benefits such as simple structure, and relatively easy to apprehend for mathematical model of the controlled system. They provide an effective way to overcome deficient information. They give flexibility in decision making processes and provide an interesting machine interface by simplifying rule extraction from human experts. Moreover, the variations of the parameters and operating conditions of the controlled system do not substantially affect the performance of the controller, and controller parameters can be altered very quickly by the system dynamics because no parameter estimation is required in designing controller for nonlinear systems. Therefore a fuzzy PI controller, which represents a model-free type of nonlinear control algorithms, can be a reasonablesolution [4].

Ghoshal et al. utilized bacteria foraging optimization (BFO) –a bio-inspired technique to tune the parameters of both single-input and two-input power system stabilizers in order to obtain the optimal transient performances [5]. Mtsuki et al. described the experimental results on an application of fuzzy control design to stabilization of electric power systems [6]. Cheng et al. proposed an integrated tabu–fuzzy knowledge based controller applied in order to boost the enactment of power system stabilizer (PSS) [7]. Hussein et al. presented a robust adaptive fuzzy controller as a power system stabilizer in damping inter-area modes of oscillation due to disturbances in power systems. He applied two fuzzy systems. The first system models the nominal values of the system’s nonlinearities, and the second system is an adaptive one used for modeling errors [8]. Elshafei et al. presented a new power system stabilizer based on adaptive fuzzy systems, that has the ability to adaptively tune its rule-base online [9]. Abou El-Ela et al. proposed multi-modes of fired fuzzy linguistic rules inside the security regions for different constrained power dispatch (CPD) controller centers [10]. Chung et al. studied a novel control strategy for High Voltage DC (HVDC) links in order to enhance oscillatory stability of interconnected power Systems [11]. Taher et al. proposed a novel robust fuzzy logic power system stabilizer design. He basically uses only one measurable Δω signal as the input [12]. But, in none of the aforementioned, fuzzy PI controller as a power system stabilizer was not taken into consideration. In this paper, we concern about the fuzzy PI controller abilities in power systems. It will be demonstrated that the proposed controller which is used for stabilizing the power system with respect to the conventional PSS can offer extraordinary damping characteristic.

2 Fuzzy control algorithms

The linear control theory utilizes a mathematical model of a plant and some specifications of the anticipated behavior in the closed loop in order to design a controller. These controllers are positively applied in the linear systems and show quite a good behavior. These systems can be supposed as linear in specific range of their operation and pre-determined conditions [13, 14]. The method of root-locus design worked out in the linear control design. Since having non-suitable results and difficulty to obtain a mathematical model, would not be dealt in this paper. In some cases, system does not have constant parameters or has interdependence with other parameters. Therefore the linear control strategies would be limited in both its design and performance. These reasons cause the human knowledge to add various types of information and to mix different control strategies. These strategies cannot be added in an analytical control law and do not need a precise mathematical model. The knowledge-based fuzzy control uses the experience and the knowledge of an adept about the system behavior [15, 16]. A kind of knowledge-based fuzzy control is the rule-based fuzzy control. The human knowledge is approached by means of linguistic fuzzy rules in the form if-then, which describes the control action in a special condition of the system. Designing a linear control enjoys no success because of the nonlinear behavior of the machine. By knowing the privileges of the fuzzy control, investigated before, a nonlinear fuzzy control might be desirable as a power system stabilizer. The fuzzy controller provides a supplementary signal to the excitation system of the synchronous generator. The control proposed for the controller is a Mamdani controller. It is usually used as a feedback controller because the rule base represents a static mapping between the preceding and the consequent variables. For stabilizing power system in a fuzzy controller, the Fuzzy Inference System (FIS) uses the error and/or error derivative as an input. However, the output of controller is injected to excitation system of the synchronous generator.

The fuzzy logic controller unlike conventional controllers does not require a mathematical model of the system [17]. Nonetheless, an understanding of the system and the control necessities is vital. The fuzzy controller designer must illuminate how the information is processed (control strategy and decision), and information flows out of the system (solution/output variable). The fuzzy logic controller consists of three basic blocks: 2.1) Fuzzification; 2.2) Inference Mechanism; 2.3) Defuzzification.

2.1 Fuzzification

The fuzzy logic controller requires that each control variables which define the control surface be described in fuzzy set symbols using linguistic rules. In order to dismember each system variables into fuzzy domain, the membership functions must be defined. The membership functions symbolize the domain that which variable is a member of a particular rule. This procedure of transforming input/output variables to linguistic rules is designated as fuzzification that is performed by usage of the rule bases. The control rules are constructed based on the characteristics of the step response. For instant, if the output is falling far away from the determined set point, a large control signal that pushes the output toward the set point is awaited, due to this reason that a small control signal is required when the output is close enough or approaching the set point [19, 20].

2.2 Inference mechanism

The behavior of the control surface which illustrates the input and output variables of the system, is accomplished by a set of rules. A characteristic of rules would be: If (fuzzy suggestion) Then (fuzzy suggestion) Where the fuzzy suggestion is of the type “x is y” or “x is not y”, x being a scalar variable and y is a fuzzy set associated with that variable. The aforementioned rules are applied in order to indicate the proper control action. When a set of input variables are read, each of the rules that has any grade of truth (a nonzero value of membership grade) in its domain is fired and cause creating of the control surface by appropriately adapting to it. When all the rules are fired, the resulting control surface, is described as a fuzzy set to represent the controllers output. These rules are used to produce a fuzzy set that semantically represents the concept related to the rule. To have a smooth and stable control surface, an overlap between adjoining rules is provided such that the sum of the vertical points of the overlap should never be greater than one. In the proposed controller the error and/or error derivative is fuzzified and described as fuzzy sets.

2.3 Defuzzification

The fuzzy set which describes the controller output in linguistic rules has to be converted into a feasible solution variable before it can be used to control the system. This is attained by usage of a defuzzification. Various methods of defuzzification are available. The most commonly used methods are a) Mean of Maxima (MOM) and b) Center of Area (COA). COA method is applied in this paper, for the reason that this method calculates the center of gravity of the final fuzzy space and products a result which is sensitive to all the rules performed. Hence the results tend to move smoothly upon the control surface.

3 Implementation of fuzzy PI controller

In the presented paper, an adaptive fuzzy PI controller is implemented in order to damp oscillations in one machine, connected to network Fig. 5.

The conventional PI controller is given by: $u (t) = k_{p} [e (t) + \frac{1}{T} \int e (t) dt]$ (1) where k _p, T, and e (t) are the proportional gain, integral time and error, respectively. Therefore, transfer function of the Equation (1) will be described as follow: $Fu (s) = \frac{U (s)}{E (s)} = k_{p} + \frac{k_{i}}{s}$ (2) where k _p and k _i are respectively the proportional and integral gains of the PI controller. These gains have been tuned by the fuzzy system in real time. Assume that the inputs to the fuzzy system are e (t) and/or . so the fuzzy system tuner comprises of dual two-input one-output fuzzy systems as shown in Fig. 1.

The three types of fuzzy system algorithms are presented in this paper: 3.1) a single input-single output control scheme, 3.2) another single input-single output control scheme and 3.3) two input-single output control scheme.

3.1 Single input-single output control scheme (type-1)

In the type (1) controller, the time derivative of rotor speed of generator $\overset{´}{ω}$ chosen as input and output of the fuzzy PI controller is used as a supplementary stabilizing signal, instead of PSS, to a digital AVR of the tested generator. The accelerating control of the study system is obtained by applying a positive stabilizing control signal to the excitation loop, while the decelerating control is obtained by applying a negative stabilizing control signal to the excitation loop. Regarding these, the control rule may be described as fuzzy conditional statements as follows: “if the speed derivative is negative, then the control applied is negative” and “if the speed derivative is positive, then the control applied is positive”. Thus, at least two rules are needed. To appreciate a more efficient control, a set of seven rules are settled in this study as follows where PL (positive large), PM (positive medium), PS(positive small), ZE(zero), NS(negative small), NM(negative medium) and NL(negative large). For each of these fuzzy sets, triangular membership function (MF) has been used. The membership function of $\overset{´}{ω}$ for tuning Kp is depicted in Fig. 2. Also the membership function of output for tuning Kp and the membership function of $\overset{´}{ω}$ and output for tuning Ki in the range of [−0.035 0.035], [−0.3 0.3] and [−1.5 1.5], respectively.

Rule 1: if $\dot{ω}$ is NL then U is NL.

Rule 2: if $\dot{ω}$ is NM then U is NM.

Rule 3: if $\dot{ω}$ is NS then U is NS.

Rule 4: if $\dot{ω}$ is ZR then U is ZR.

Rule 5: if $\dot{ω}$ is PS then U is PS.

Rule 6: if $\dot{ω}$ is PM then U is PM.

Rule 7: if $\dot{ω}$ is PL then U is PL.

3.2 Single input-single output control scheme (type 2)

In the type (2) controller, the acceleration of generator speed $d \dot{ω}$ is chosen as the input and signal U is the output of the fuzzy controller that tuned the K _p and K _i in the PI controller. Seven fuzzy subsets have been used in this scheme controller. A set of seven rules are defined in this study as follows. For each of these fuzzy sets, triangular membership function (MF) has been used. Four membership functions have been used in this scheme similar type (1) controller. The membership function of $\overset{´}{ω}$ and output for tuning Kp and the membership function of $\overset{´}{ω}$ and output for tuning Ki in the range of [−1. 3 1. 3], [−1 1], [−0.07 0.07] and [−0.15 0.15], respectively.

Rule 1: if $d \dot{ω}$ is NL then U is NL.

Rule 2: if $d \dot{ω}$ is NM then U is NM.

Rule 3: if $d \dot{ω}$ is NS then U is NS.

Rule 4: if $d \dot{ω}$ is ZR then U is ZR.

Rule 5: if $d \dot{ω}$ is PS then U is PS.

Rule 6: if $d \dot{ω}$ is PM then U is PM.

Rule 7: if $d \dot{ω}$ is PL then U is PL.

3.3 Two input- single output control scheme (type 3)

In the type (3) controller, the acceleration of generator speed ( $d \dot{ω}$ ) and the rotor speed deviation (dω) are selected as the inputs and signal U is selected as the output of the fuzzy controller. The parameters of the controller should be determined by trial and error using the simulation of system. Seven fuzzy subsets have been used in this scheme similar type (1). For each of these fuzzy sets, Gaussian membership function (MF) has been exploited. The membership function of $d \overset{´}{ω}$ for tuning Kp is displayed in Fig. 3. Also the membership function of dω and output for tuning Kp and the membership function of $d \overset{´}{ω}$ , $\overset{´}{ω}$ and output for tuning Ki in the range of [−0.4 0.4], [−0.03 0.03], [−0.1 0.1],[−0.4 0.4], and [−0.03 0.3], respectively. Fuzzy subsets outcomes through these fuzzy subsets for computing the output are presented in Table 1.

4 System description

The model of system, consists of a 200^MVA, 13.8^KV three phase, 60^Hz, 32 pole synchronous generator. The generator is connected to the network (10000^MVA, 230^KV) through a transmission line, as shown in Fig. 5. The basic parameters of the generator are revealed in the appendix. The generator is equipped with an AVR and PSS [19 –25].

5 Simulation results

To indicate the design process besides investigation of the effectiveness of the fuzzy PI controllers [26 –29], we set the three phase short circuit faults during [0.5 0.57] of time for two cases, namely AVR with PSS and AVR with Fuzzy PI Controller.

5.1 System responses under AVR and PSS

The basic elements designed the excitation system block are the voltage regulator and the exciter. The conventional power system stabilizer (CPSS) blockdiagram can be used to add damping signal to the rotor oscillations of the synchronous generator by controlling its excitation. The conventional power system stabilizer is modeled by the nonlinear system as shown in Fig. 4.

Figure 6 illustrates the dynamic behaviors of the generator for a three phase short circuit faults in the case of AVR and PSS in the one-machine connected to the network. The following variables are plotted: electrical output power (Pe) and rotor speed deviation (dω). The oscillations of the variables decay very slowly.

5.2 System responses under AVR and Fuzzy PI controller

Figure 7 shows the dynamic behaviors of the system under the type (1) fuzzy controller and AVR. From this figure, it can be comprehended that the oscillations are more quickly damped than those under AVR and PSS. The system under the type (2) and (3) fuzzy controller with AVR dynamic behaviors of are shown in Figs. 8, 9.

It is noteworthy to say that the performance of type (1) controller with 7 rules substantially amends the damping of the generator oscillations, in comparison with the conventional PSS. The results illustrate that a slightly improvement of the system stability was obtained by the type (2) fuzzy controller in comparison with type (1) controller.

Nevertheless, the performance of the fuzzy PI controller can be upgraded on the expense of using a significantly larger rule-base. So a considerable improvement of the system stability was obtained by type (3) fuzzy controller, with 49 rules, in comparison with that by the conventional power system stabilizer.

The significance of the projected controller can be enlightened as follows:

It follows a smooth gain scheduling design algorithm where a different controller is actually utilized in accordance with the need of the plant.

Fuzzy controllers are nonlinear mappings while the CPSS is a linear one. This nonlinearity donates more flexibility in shaping the control surface and providing better performance.

It is observed that system is settled absolutely fast. This justifies the robustness of the proposed controller, which is capable to stand up against the changes in dynamic parameters of system.

Classical controllers such as CPSS, have demonstrated not to be efficient enough under practical tests because of the optimization procedure used to setup their parameters.

6 Conclusions

In this paper, the control performances of the three proposed fuzzy PI controllers, instead of PSS, under various operating conditions are investigated. The proposed controller provides a supplementary signal to the excitation system of the synchronous generator. The obtained results show that for stabilizing power system a very good damping characteristic can provided by means of the proposed controller. This controller utilizes a combination of a FLC and a PI controller. Additionally, the suggested controller is simple to be implemented in real-time. In comparison with the conventional fuzzy controllers, the fuzzy PI controller incorporates the advantages of a FLC and a conventional PI controller. The design of the fuzzy PI controllers requires no mathematical model of generator and power system as would be needed by the conventional power system stabilizers. Regarding this and its simple control scheme also, the performances of the proposed fuzzy PI controllers were judiciously agreeable. Probably due to their nonlinearity, although determination of optimal fuzzy control parameters by trial and error was required.

Appendix

Machine Parameters:

The parameters of the tested generator are as follows:

x_d = 1.305	x_l = 0.18	$T_{d}^{'} = 1.01$
$x_{d}^{'} = 0.296$	$x_{q}^{''} = 0.243$	$T_{d}^{''} = 0.053$
$x_{d}^{''} = 0.252$	R_s = 2.85 × 10^-3	$T_{q 0}^{''} = 0.1$
x_q = 0.474		H = 3.2
PSS data:
K_pss = 100	T_W = 1.41	T₁ = 0.154
T₂ = 0.033	V_SMax = 0.2	V_SMin = -0.2

Footnotes

Acknowledgments

The authors would like to thank Islamic Azad University, Marvdasht, Iran for their finance support

References

1983 Electric power systems dynamics Academic Press

New York

Awed-Badeeb

2006

Damping of electromechanical modes using power system stabilizer

Journal of ElectricalEngineering 57 5 291 295

Juang

2006

Load-frequency control by hybrid evolutionary fuzzy PI controller

IEE Proc Gener Transm Distrib 153 2 196 204

Demiroren

Yesil

2004

Automatic generation control with fuzzy logic controllers in the power system including SMES units

Electrical Power and Energy Systems 26 291 305

Ghoshal

Chatterjee

Mukherjee

2009

Bio-inspired fuzzy logic based tuning of power system stabilizer

Expert Systems with Applications 36 9281 9292

Mtsuki

Okada

1991

Application of fuzzy algorithms to stability control of power systems

International Conference on Industrial Electronics, Control and Instrumentation 2 1645 1650

Cheng

Elangovan

2003

Enhanced power system stabilizer via integrated tabu–fuzzy knowledge based controller

Electrical Power and Energy Systems 25 543 550

Hussein

Saad

Elshafei

Bahgat

2009

Robust adaptive fuzzy logic power system stabilizer

Expert Systems with Applications 36 12104 12112

Elshafei

Metwally

KAEL

Shaltout

2005

A variable-structure adaptive fuzzy logic stabilizer for single and multi-machine power systems

Control Engineering Practice 13 413 423

10.

Abou El-Ela

Bishr

Allam

El-Sehiemy

2007

An emergency power system control based on the multi-stage fuzzy based procedure

Electric Power Systems Research 77 421 429

11.

Chung

Da-zhong

2002

Fuzzy logic controller forenhancing oscillatory stability of AC/DC interconnected power system

Electric Power Systems Research 61 221 226

12.

Taher

Shemshadi

2007

Design of Robust fuzzy logic power system stabilizer

Proceedings of World Academy of Science, Engineering and Technology 21 1307 6884

13.

Aghaei

Niknam

Azizipanah-Abarghooee

Arroyo

2013

Scenario-based dynamic economic emission dispatch considering load and wind power uncertainties

International Journal of Electrical Power & Energy Systems 47 351 367

14.

Niknam

Azizipanah-Abarghooee

Roosta

2012

Reserve constrained dynamic economic dispatch: A new fast self-adaptive modified firefly algorithm

IEEE Systems Journal 6 4 635 646

15.

Niknam

Narimani

Azizipanah-Abarghooee

2012

A new hybrid algorithm for optimal power flow considering prohibited zones and valve point effect

Energy Conversion and Management 58 197 206

16.

Kavousi-Fard

Niknam

2014

Multi-objective stochastic distribution feeder reconfiguration from the reliability point of view

Energy 64 342 354

17.

Niknam

Olamaie

Khorshidi

2008

A hybrid algorithm based on HBMO and fuzzy set for multi-objective distribution feeder reconfiguration

World Applied Sciences Journal 4 2

18.

Niknam

Azizipanah-Abarghooee

Aghaei

2013

A new modified teaching-learning algorithm for reserve constrained dynamic economic dispatch Power Systems

IEEE Transactions on 28 2 749 763

19.

Niknam

Kavousifard

2012

Impact of thermal recovery and hydrogen production of fuel cell power plants on distribution feeder reconfiguration

IET Generation, Transmission & Distribution 6 9 831 843

20.

Niknam

2011

A new HBMO algorithm for multiobjective daily Volt/Var control in distribution systems considering distributed generators

Applied Energy 88 3 778 788

21.

Rodrigo

2009

Stability analysis of power systems considering AVR and PSS output limiters

Electrical Power and Energy Systems 31 153 159

22.

Hossein-Zadeh

Kalam

2002

An indirect adaptive fuzzy logic power system stabilizer

Electrical Power and Energy Systems 24 837 842

23.

Mohd Hasan

Minwon

In Keun

Murata

Tamura

2009

Enhancement of transient stability by fuzzy logic-controlled SMES considering communication delay

Electrical Power and Energy Systems 31 402 408

24.

Hosaeinzadeh

Kalam

1995

A Direct Adaptive Fuzzy Power System stabilizer

IEEE Transactions on EnergyConversion 14 4 1564 1571

25.

Elshafei

Metwally

KEL

Shaltout

2000

Design and analysis of a variable structure adaptive fuzzy-logic power system stabilizer

American Control Conference 6 3959 3963

26.

Hoang

Tomsovic

1996

Design and analysis of an adaptive fuzzy power system stabilizer

IEEE Transaction on Energy Conversion 11 455 461

27.

Lin

2004

Systematic approach for the design of a fuzzy power system stabilizer

International Conference on Power System Technology 1 747 752

28.

Pedrycz

1989

Fuzzy control and fuzzy systems

ResearchStudies Press Ltd.

29.

Hiyama

Nakano

1988

Application of fuzzy logic stabilizer to electrical power system

Proc of ’88 Kiee Annual Conference 33 37

Korea