RESEARCH ARTICLE Voltage stability analysis based on optimal placement of multiple DG types using hybrid optimization technique Ali Selim 1 | Salah Kamel 2 | Francisco Jurado 1 1 Department of Electrical Engineering, University of Jaén, Jaén, Spain 2 Department of Electrical Engineering, Faculty of Engineering, Aswan University, Aswan, Egypt Correspondence Francisco Jurado, Department of Electrical Engineering, University of Jaén, 23700 EPS Linares, Jaén, Spain. Email: fjurado@ujaen.es Funding information NSFC (China)-ASRT (Egypt) Joint Research Fund, Grant/Award Number: 51861145406 Peer Review The peer review history for this article is available at https://publons.com/publon/ 10.1002/2050-7038.12551. Abstract This article proposes a hybrid analytical and metaheuristic optimization tech- nique for optimal allocation of multiple types of distributed generator (DG) in radial distribution networks. DG integration aims to minimize the total power losses and enhance the voltage stability of the distribution system. The proposed technique is formulated using the analytical technique which utilizes the exact loss formula to calculate the initial DG size at a certain bus. However, the ana- lytical technique may not be proper to allocate multiple DGs types due to the mass of calculations, hence, a metaheuristic optimization technique named Tree Growth Algorithm (TGA) is combined with the analytical technique to find the final solution of optimal DG locations and sizes. The hybridization between the analytical and metaheuristic optimization techniques combines the advantages of both techniques and eliminates the disadvantages. The proposed hybrid Ana- lytical TGA (ATGA) is validated using the stranded radial distribution feeders, IEEE 33-bus and 69-bus and practical 94-bus Portuguese system. A comprehen- sive comparison between the proposed technique and other competitive optimi- zation techniques is carried out to prove its effectiveness. The result shows that the proposed hybrid ATGA is efficient to allocate the multiple DGs types with minimum power loss and a high convergence rate. KEYWORDS DG location, hybrid optimization, power loss minimization, tree growth algorithm, voltage stability List of Symbols and Abbreviations: P loss , total power losses; P i , Q i , active and reactive power at bus i; N bus , the total bus number; α ik , β ik , branch coefficients; V, voltage magnitude; θ, phase angle; Z busik , bus matrix; w 1 ,w 2 , weighting factor; PD i , QD i , the demand active and reactive power at bus i; PG i , QG i , generated active and reactive power; n, numbers for DG type I; PG a1 , PG a2 , PG an , generated active power at a 1 , a 2 , …a n ; m, numbers for DG type II; QG b1 , QG b2 , QG m , generated reactive power at b 1 , b 2 , …b m ; C ai , coefficient matrix for DG type I; E bi , coefficient matrix for DG type II; G 1 ,G 2 , G 3 ,G 4 , the main group of Tree Growth Algorithm; k, iteration number; k max , maximum number of iterations; T k GB , global best tree at iteration k; T k i , tree position at iteration k; r, uniform distributed between [0,1]; d i , distance between trees; y, linear combination between trees; x 1 ,x 2 , two minimal distance solutions; μ, uniformly distributed factor [0,1]; α i , adjacent best tree angle [0, 1]; DGs, distributed generators; IA, improved analytical; ELF, exhaustive load flow; LSF, loss sensitivity factor; PSI, power stability index; VSI, voltage stability index; GA, genetic algorithm; PSO, particle swarm optimization; BSOA, backtracking search optimization algorithm; BFOA, bacterial foraging optimization algorithm; SKHA, stud krill herd algorithm; BAT, Bat algorithm; MVGWO, modified variant grey wolf optimizer; CSA, Cuckoo search algorithm; TGA, Tree Growth Algorithm; ATGA, analytical tree growth algorithm; LR, loss reduction. *Corresponding author, Tel.: +34 953 648 518; Fax: +34 953 648 586. E-mail addresses: fjurado@ujaen.es (F. Jurado), ali.selim@aswu.edu.eg (A. Selim), skamel@aswu.edu.eg (S. Kamel). Received: 3 July 2019 Revised: 4 May 2020 Accepted: 18 June 2020 DOI: 10.1002/2050-7038.12551 Int Trans Electr Energ Syst. 2020;e12551. wileyonlinelibrary.com/journal/etep © 2020 John Wiley & Sons Ltd 1 of 20 https://doi.org/10.1002/2050-7038.12551