Published in IET Generation, Transmission & Distribution Received on 3rd April 2009 Revised on 19th November 2009 doi: 10.1049/iet-gtd.2009.0422 ISSN 1751-8687 Reactive power dispatch and planning using a non-linear branch-and-bound algorithm C.R.N. Estevam 1 M.J. Rider 1 E. Amorim 2 J.R.S. Mantovani 1 1 Departamento de Engenharia Ele ´trica, Faculdade de Engenharia de Ilha Solteira, UNESP – Universidade Estadual Paulista, Ilha Solteira – SP, Brazil 2 Departamento de Engenharia Ele ´trica da, Universidade Federal de Mato Grasso do Sul-UFMS, Campus de Campo Grande, Campo Grande – MS, Brazil E-mail: mjrider@dsee.fee.unicamp.br Abstract: This study proposes the use of a non-linear branch-and-bound (B&B) algorithm to solve the reactive power dispatch and planning problem of an electrical power system. The problem is formulated as a mixed integer non-linear programming (MINLP) problem. The MINLP is relaxed resulting in a set of non-linear programming (NLP) problems, which are solved at each node of the B&B tree through a primal dual-interior point algorithm. The non-linear B&B algorithm proposed has special fathoming criteria to deal with non-linear and multimodal optimisation models. The fathoming tests are redefined, adding a safety margin value to the objective function of each NLP problem before they are fathomed through the objective function criteria, avoiding convergence to local optimum solutions. The results are presented using three test systems from the specialised literature. The B&B algorithm found several optimum local solutions and the best solution was found after solving some NLP problems, with little computational effort. Notation The notation used throughout this paper is reproduced below for quick reference. NB Set of system buses. M and N Set of candidate buses where continuous and discreet reactive power sources are already installed or where new ones are permitted. I Set of buses where reactive sources are already installed or where the installation of new ones is permitted (I = M < N ). G, L Set of generation and load buses of the system, respectively. J Set of candidate buses with fictitious injection of reactive power sources. NT Set of transformers with automatic tap control. U Set of buses with installed discrete controllable reactive power sources. w Objective function. CFX i Fixed cost for allocation of reactive power sources in bus i. Cc i , Cr i Varying costs due to the allocation of new reactive capacitive and inductive reactive power sources, respectively, in bus i. qc i , qr i (i [ I ) Investment variables: Capacitive and inductive reactive power source, respectively, either existing in the system or to be installed in the chosen bus i. y1 j , y2 j ( j [ J ) Fictitious injection of capacitive and inductive reactive power, respectively, in bus j. r i Binary decision variable: if r i = 1 then allocate the reactive power sources in bus i; if r i = 0 then do not allocate the reactive power source in bus i. g Penalty factor. ( V, u, t) Voltage magnitude, phase angle of bus- bar voltage and transformer tap ratio, respectively. IET Gener. Transm. Distrib., 2010, Vol. 4, Iss. 8, pp. 963–973 963 doi: 10.1049/iet-gtd.2009.0422 & The Institution of Engineering and Technology 2010 www.ietdl.org