## 6 Congestion Management
However, for small-scale power systems the most acceptable optimization techniques are non-linear programming and sequential quadratic methods because they contain power system variables. Similarly, various analytical or sensitivity-index-based optimization techniques are also used with FACTS devices to mitigate congestion in deregulated systems. In the literature [221], locational marginal price and congestion-rent-contribution-based approaches are used with a series FACTS device, the TCSC, in the IEEE-14, 30, and 57 bus systems for providing congestion management. Results show that the congestion rent contribution approach is more effective than locational marginal price techniques in deregulated electricity markets. Another sensitivity-based approach named the \"power flow index\" is discussed in [196] to optimally place series FACTS devices and relieve congestion in cases of line outage in deregulated power systems. Similarly, in another study [222] real power flow and transmission line relief security indices in the IEEE-14 bus test system are used to relieve congestion. Some other analytical approaches such as single contingency sensitivity [223], branch overloading line [224], bus voltage violations [213], the extended voltage phasors approach [225], etc. are used to relieve congestion. However, meta-heuristic optimization algorithms are more popular for FACTS device optimization [104] due to the following reasons [226]: they are simple to implement and rely on simple concepts, effective and adaptable, bypass local optima, do not require gradient information, can be utilized in a wide range of multi-disciplined problems, and useful to solve complex and discrete optimization problems [227]. Meta-heuristics optimization is divided into four different subtechniques [228], shown in Figure 3, because it draws from physical phenomena, animal behavior, and nature-inspired phenomena. Therefore, in the literature [229], the genetic algorithm and differential evolution techniques are used to minimize transmission loss and simultaneously reduce operational cost by optimally placing FACTS devices (SVC, TCSC, and UPFC) in the IEEE-30 network bus system. In addition, in a comparative study [230] the modified whale optimization algorithm, whale optimization algorithm, genetic algorithm, differential evolution, and fast evolutionary programming are used to curtail congestion loss and improve system losses and voltages in the IEEE-118 bus system and New England 39 bus systems. It is concluded that the modified whale optimization programming algorithm superseded the other compared algorithms. In addition, it provides the fastest convergence mobility for congestion management problems. [PERSON] et al. [231] presented another meta-heuristic approach named the biogeography optimization method for power system security constraints with UPFCs in the IEEE-30 bus system. In addition, the authors calculate various indices such as the sensitivity index, overload index, and voltage violation index with or without optimally placed UPFCs in the IEEE-18 bus system. It is observed that the overload and voltage violation index are significantly reduced using optimally placed UPFCs with biogeography optimization methods. Furthermore, biogeography-based optimization method performance is compared with genetic algorithm and partial swarm optimization methods. It is concluded that biogeography optimization performance is superior. In [232], another meta-heuristic approach, the gravitational search algorithm, was found to be a superior algorithm while comparing it with the genetic algorithm, differential evolution, and partial swarm optimization. Further, it was concluded that gravitational search algorithms are effective to reduce congestion in terms of increasing load-ability and minimizing operating costs and total active power loss in power systems (IEEE-30 and 57 bus systems).