Adaptive Firefly Algorithm Based OPF for AC/DC Systems

J Electr Eng Technol.2016; 11(4): 791-800 ISSN(Print) 1975-0102 http://dx.doi.org/10.5370/JEET.2016.11.4.791 ISSN(Online) 2093-7423 Adaptive Firefly Algorithm based OPF for AC/DC Systems B. Suresh Babu† and S. Palaniswami* Abstract – Optimal Power Flow (OPF) is an important operational and planning problem in minimizing the chosen objective functions of the power systems. The recent developments in power electronics have enabled introduction of dc links in the AC power systems with a view of making the operation more flexible, secure and economical. This paper formulates a new OPF to embrace dc link equations and presents a heuristic optimization technique, inspired by the behavior of fireflies, for solving the problem. The solution process involves AC/DC power flow and uses a self adaptive technique so as to avoid landing at the suboptimal solutions. It presents simulation results of IEEE test systems with a view of demonstrating its effectiveness. Keywords: Optimal power flow, AC/DC power flow, Firefly optimization 1. Introduction systems, rapid adjustments for direct power flow controls, ability to improve the stability of AC systems, mitigation The optimal power flow (OPF) has been widely used in of transmission congestion, enhancement of transmission power system operation and planning since its introduction capacity, rapid frequency control following a loss of by Carpenter in 1962 [1]. The OPF determines optimal generation, ability to damp out regional power oscillations settings for certain power system control variables by following major contingencies and offering major optimizing a few selected objective functions while economic incentives for supplying loads. Flexible and fast satisfying a set of equality and inequality constraints for DC controls provide efficient and desirable performance given settings of loads and system parameters. The control for a wide range of AC systems. The existing OPF problem variables include generator active powers, generator bus can be modified to handle AC/DC systems [2-3]. The voltages, transformer tap ratios and the reactive power resulting optimization problem, designated as OPF with generation of shunt compensators. In general, the total fuel DC links (OPFDC), is a large scale, non-linear non-convex cost (FC) is commonly used as the main objective for OPF and multimodal optimization problem with continuous and problems. However, the other objectives, such as reduction discrete control variables. The existence of nonlinear of real power loss (RPL), improvement of the voltage power flow constraints and the DC link equations make the profile (VP) and enhancement of the voltage stability (VS) problem non-convex even in the absence of discrete control can also be included, as it has progressively become easy variables [4]. to formulate and solve large-scaled complex problems with In the recent decades, numerous mathematical pro- the advancement in computing technologies. The equality gramming techniques such as gradient method [1], linear constraints are the power flow balance equations, while the programming [5], nonlinear programming [6], interior inequality constraints are the limits on the control variables point method [7] and quadratic programming [8] with and the operating limits of the power system dependent various degrees of near-optimality, efficiency, ability to variables. handle difficult constraints and heuristics, have been The recent developments in power electronics have widely applied in solving the OPF problems. Although introduced DC transmission links in the existing AC many of these techniques have excellent convergence transmission systems with a view of achieving the benefits characteristics, they have severe limitations in handling of reduced network loss, lower number of power non-linear and discontinuous objectives and constraints. conductors, increased stability, enhanced security, etc. The gradient method suffer from the difficulty in handling They are often considered for transmission of bulk power inequality constraints; and the linear programming requires via long distances. The attributes of DC transmission links the objective and constraint functions to be linearized include low capacitance, low average transmission cost in during optimization, which may lead to the loss of accuracy. long distances, ability to prevent cascaded outages in AC Besides they may converge to local solution instead of global ones, when the initial guess is in the neighborhood † Corresponding Author: Dept. of Electrical and Electronics Engi- neering, Odaiyappa College of Engg & Tech, Theni (Dist), India. of a local solution. Thus there is always a need for simple ([email protected]) and efficient solution methods for obtaining global optimal * Principal and Professor, Dept. of Electrical and Electronics solution for the OPF problems. Engineering, Government College of Engineering, Bodinayakkanur, Theni (Dist), India. ([email protected]) Apart from the above methods, another class of Received: February 9, 2015; Accepted: December 15, 2015 numerical techniques called evolutionary search algorithms 791 Copyright ⓒ The Korean Institute of Electrical Engineers This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/ licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Adaptive Firefly Algorithm based OPF for AC/DC Systems such as genetic algorithm (GA) [9], evolutionary Minimize Φ(,)x u (1) programming [10], particle swarm optimization (PSO) [11], differential evolution [12], frog leaping [13], harmony Subject to search optimization (HSO) [14], gravitational search [15], clonal search [16], artificial bee colony [17] and teaching- bxu(,)= 0 (2) learning [18] have been widely applied in solving the OPF gxu(,)≤ 0 (3) problems. Having in common processes of natural evolution, these algorithms share many similarities; each where maintains a population of solutions that are evolved through random alterations and selection. The differences x = [,VQPL GG ,] (4) between these procedures lie in the techniques they utilize ijs GG Cdc to encode candidates, the type of alterations they use to uPVTQI= [,,,,]kjvqp (5) create new solutions, and the mechanism they employ for ⎧ GD ⎫ PPV−− VG(cosδδ + B sin)0 = selecting the new parents. These algorithms have yielded ⎪ m m m∑ n mn mn mn mn ⎪ n∈ΩΠ{},` satisfactory results across a great variety of power system ⎪ ⎪ ⎪ GD ⎪ problems. The main difficulty is their sensitivity to the bxu(,)= ⎨QQVm−− m m∑ VG n(sin mnδδ mn − B mn cos)0 mn =⎬ (6) ⎪ n∈ΩΠ{},` ⎪ choice of the parameters, such as the crossover and ⎪ ⎪ mutation probabilities in GA and the inertia weight, ⎪ ⎪ ⎩⎭hxu(,)= 0 acceleration coefficients and velocity limits in PSO. Recently, firefly optimization (FO) has been suggested GGG(min) (max) ⎧PPPkkk≤≤ ⎫ ⎪ ⎪ by Dr. Xin-She Yang for solving optimization problems QQQGGG(min)≤≤ (max) [19]. It is inspired by the light attenuation over the distance ⎪ jjj⎪ ⎪QQQCCC(min)≤≤ (max) ⎪ and fireflies’ mutual attraction rather than the phenomenon ⎪ qqq⎪ of the fireflies’ light flashing. In this approach, each ⎪TTTmin≤≤ max ⎪ gxu(,)= vvv problem solution is represented by a firefly, which tries to ⎨ GGG(min) (max) ⎬ (7) ⎪VVVjjj≤≤ ⎪ move to a greater light source, than its own. It has been ⎪VVVLLL(min)≤≤ (max) ⎪ applied to a variety of engineering optimization problems iii ⎪ dc(min) dc dc (max) ⎪ and found to yield satisfactory results. However, the choice ⎪IIIppp≤≤ ⎪ of FO parameters is important in obtaining good con- ⎪ max ⎪ ⎩⎭SSLi≤ Li vergence and global optimal solution. This paper formulates the problem of OPFDC, suggests ⎧VschVcosdc−+= acθ s cX c I dc 0⎫ ⎪ mm2mwmm3mm ⎪ a solution methodology involving a self adaptive FO (SFO) dc ac ⎪VschVcosmm2mwm−=0.995 φ 0 ⎪ with a view of obtaining the global best solution and ac ac dc ⎪QVchIsin−=φ 0 ⎪ ⎪ ww2mmm ⎪ demonstrates its performance through simulation results on ⎪ ac ac dc ⎪ the modified IEEE 30, 57 and 118 bus systems. hxu(,)=−⎨ Pww2mmm V c h I cosφ =0 ⎬ (8) ⎪PVI0dc−= dc dc ⎪ ⎪ mmm ⎪ dc dc dc dc ⎪IVVR0mmnmn−−() = ⎪ 2. Problem Formulation ⎪ dc dc dc dc ⎪ ⎩⎭⎪VVIR0mnmmn−− = ⎪ s The exercise is to identify the optimal control m = 1 for rectifier and -1 for inverter c = 32π c = 3 π parameters such as generator active powers, generator bus 2 3 i ∈ Ω j ∈Π voltages, transformer tap ratios and the reactive power v ∈ℜ generation of shunt compensators, besides determining the k ∈ Ψ p ∈ ℑ q ∈ℵ DC control parameters. The formation of the problem involves both the AC and DC sets of equations. The AC set Φ(,)x u of equations are the standard AC power balance equations The objective function can take different forms. whereas the DC set equations represent power, current and Seven different cases involving FC, RPL, VP and VS, voltage balance equations at both DC and AC terminal which are calculated from the power flow solution, are buses of DC links. Moreover the DC link can be operated considered in tailoring the objectives in this paper. in different modes such as constant current, constant power, Case-1: Minimization of fuel cost etc [8]. In this formulation, DC links with constant current control are considered. The OPFDC problem is formulated GG2 as a constrained nonlinear optimization problem through Minimize Φ1 (,)x uaPbPc=+++∑ jj jj j j∈Π combining the standard OPF problem and the DC link GG equations as dePjjjsin(

Load more