General Solution and Stability of Quattuordecic Functional Equation in Quasi β-Normed Spaces

In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi β-normed spaces by using the fixed point method.

Solving Optimal Power Flow Using Modified Bacterial Foraging Algorithm Considering FACTS Devices

In this paper, a new Modified Bacterial Foraging Algorithm (MBFA) method is developed to incorporate FACTS devices in optimal power flow (OPF) problem. This method can provide an enhanced economic solution with the use of controllable FACTS devices. Two types of FACTS devices, thyristor controlled series compensators (TCSC) and Static VAR Compensator (SVC) are considered in this method. The basic bacterial foraging algorithm (BFA) is an evolutionary optimization technique inspired by the foraging behavior of the E. coli bacteria. The strategy of the OPF problem is decomposed in two sub-problems, the first sub-problem related to active power planning to minimize the fuel cost function, and the second sub-problem designed to make corrections to the voltage deviation and reactive power violation based in an efficient reactive power planning of multi Static VAR Compensator (SVC). The specified power flow control constraints due to the use of FACTS devices are included in the OPF problem. The proposed method decomposes the solution of such modified OPF problem into two sub problems’ iteration. The first sub problem is a power flow control problem and the second sub problem is a modified Bacterial foraging algorithm (MBFA) OPF problem. The two sub problems are solved iteratively until convergence. Case studies are presented to show the effectiveness of the proposed method.