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This paper presents an approach for optimum reactive power dispatch through the power network with flexible AC transmission systems (FACTSs) devices, using adaptive fuzzy logic controller (AFLC) driven by adaptive fuzzy sets (AFSs). The membership functions of AFLC are optimized based on 2nd-order fuzzy set specifications. The operation of FACTS devices (particularly, static VAR compensator (SVC)) and the setting of their control parameters (

Optimal power flow (OPF) control in power systems has a direct impact on system security and economic dispatch. Early OPF approaches were based on classical mathematical programming methods and successfully showed their capability in this field [

FACTS controllers can be generally classified as series controllers, shunt controllers, and combined series-shunt controllers [

The aim of this paper is to investigate the power network performance under the following terms:

to develop an adaptive-fuzzy-logic-controller- (AFLC-) based method for optimal reactive power

to investigate the effect of SVC controller on the performance of the power system using adaptive fuzzy logic controller approach (AFLC).

Consider

Maintaining the voltage within tight control helps the system to be stable and more secure. The objective function expresses this idea by minimizing the sum of the voltage deviations of all load buses. This can be mathematically expressed as follows:

The minimization of (

From (

The inequality constraints on security limits are presented as follows.

The generator voltage (

generator voltage of each

where

Transformer tap (

Transformer taps are varied between lower and upper limits as shown below:

where

Switchable VAR compensations (

shunt compensation units are subjected to their lower and upper limits as follows:

where

Load bus voltage (

where

Fuzzy control systems are rule-based systems. The outcome of certain system can be corrected by a set of fuzzy rules that represent the fuzzy logic controller (FLC) technique. The FLC also provides a strategy which can change the linguistic control approach, based on expert knowledge, to automatic control ones. Figure

Generic structure of fuzzy logic controller.

The fuzzy input vector, of each static fuzzy logic controller (SFLC) has two variables, which can briefly summarized by the voltage deviation error (

In this paper, the operation of SVC devices and the setting of their control parameters

The lookup table which defines the relation between input and output variables in a fuzzy set form for five fuzzy sets for SFLC.

Voltage deviation error ( |
Change error of voltage deviation ( |
||||
---|---|---|---|---|---|

NL | NS | Z | PS | PL | |

NL | NL | NL | NL | NS | Z |

NS | NL | NL | NS | Z | PS |

Z | NL | NS | Z | PS | PL |

PS | NS | Z | PS | PL | PL |

PL | Z | PS | PL | PL | PL |

The lookup table which defines the relation between input and output variables in a fuzzy set form for three fuzzy sets for SFLC and AFLC.

Voltage deviation error ( |
Change error of voltage deviation ( |
||
---|---|---|---|

NL | Z | PL | |

NL | NL | NL | Z |

Z | NL | Z | PL |

PL | Z | PL | PL |

Membership Functions of inputs and output variables for SFLC.

The fuzzy input vector of each AFLC consists of the previous variables used in SFLC with three linguistic variables using adaptive fuzzy sets. Each input and output variable fuzzy set uses only three linguistic variables (LVs), as shown in Figure

Membership Functions of inputs and output variables. The SFLC indicated by the solid lines while the dotted lines for AFLC.

In this study, the adaptive fuzzy set derived from GA is employed for the adaptive fuzzy logic controller (AFLC). AFLC uses three fuzzy sets for input and output variable. It means that the full rule base is 9 rules. Reference [

If vector

In addition, the membership function (

Moreover, the adapted genetic algorithm with adjusting population size (AGAPOP) is used to optimize the membership function parameters of the FLCs. The simulation results using the AFLC controller are denoted in dotted lines as shown in Figure

Flowchart of AGAPOP algorithm for optimizing MFs.

The fuzzy set parameters of FL are formulated by the AGAPOP technique. The values of static fuzzy set parameters is primarily activate the fuzzy set parameters of FL controllers, where (

The coded parameters are adjusted based on their constraints to shape a chromosome of the population [

The selection policy usually manages how to pick individuals to be parents for new “children” and applies some selection weight [

Roulette wheel Selection Scheme [

The crossover is applied, and the mating pool is created. Then, the mutation procedure is utilized followed by AGAPOP algorithm given in [

GA deals with the problem of optimizing a nonlinear objective function in the presence of nonlinear equality and inequality constraints. The main goal here is to construct the optimum GA algorithms (AFLC) for SVCs control.

One objective function was created as follows:

To study and design the system controller with

overload test up to 132%,

load rejection test up to 80%.

In each test, the optimum values of the control variables (

In order to investigate the controller design performance, the proposed techniques have been applied to the IEEE 30-bus system.

The increase in loads up to 132% overload (Loading factor

Load bus voltage magnitudes, the optimum VAR of each SVC, and voltage bus error as a function of load bus number using AFLC technique.

The SFLC technique is used for the same system condition; Figure

the network bus voltages are within the acceptable (1 p.u.

SVC 1, 2,

Load bus voltage magnitudes, the optimum VAR of each SVC, and voltage bus error as a function of load bus number using SFLC technique.

In this case, all network loads were partially rejected, and the technique was applied to determine the optimum VAR and system losses. The same previous techniques are applied to show their effectiveness. AFLC technique helped the system to remain within its limits as shown in Figure

Load bus voltage magnitudes, the optimum VAR of each SVC, and voltage bus error as a function of load bus number using AFLC technique.

Load bus voltage magnitudes, the optimum VAR of each SVC, and voltage bus error as a function of load bus number using SFLC technique.

It is noted from the presented figure that SVCs 12, 15, and 23 worked as capacitor while the remain SVCs worked as inductors. Moreover, the network bus voltages are within the suitable (1 p.u.

The SFLC achieved a remarkable conclusion shown in Figure

The SVC is considered as an effective tool for shunt reactive compensation devices for the use on high voltage power systems. The main purpose of the current study is to present a new design of controllers with the advantage of AFLC and SFLC techniques that control the VAR flow in the power system network. The designed control parameters affect the quantity of reactive power injected to or taken from the network during normal and emergency conditions. In this paper, an adaptive fuzzy set is introduced and tested through a simulation program. The proposed adaptive fuzzy controller driven by genetic algorithm improves the simulation results; it shows the superiority of the adaptive fuzzy controller. Furthermore, the effectiveness of the suggested AFLC with adaptive fuzzy set design as a remarkable approach can be observed. Specifications of parameter constraints related to input/output reference fuzzy sets are based on 2nd-order fuzzy sets. The GA with changeable crossover and mutation probabilities rates analyzes and solves the problem of constrained nonlinear optimization. The computational time of the FLC is decreased by the proposed AFLC using AFS, where the number of rules is reduced from 25 to 9 rules. In addition, the proposed technique adaptive FLC driven by genetic algorithm has reduced the fuzzy model complexity. The proposed techniques would be particularly a useful tool to assist the system operator in making control decisions to improve the voltage profiles (with overvoltages and undervoltages) in the system. The method has been successfully tested on standard IEEE 30-bus system.

The author would like to thank Professor Yusuf Al-Turki and Dr. Abdel-Fattah Attia for their help and guidance during this work. Also, this paper was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah. The author, therefore, acknowledges with thanks the DSR technical and financial support.