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Determination of the optimal configurations of identical point charges on a unit sphere, known as Thomson's problem, is a well-known energy optimization problem in physics. In this paper we have determined the minimum energy for various values of using Symbiotic Organisms Search (SOS) algorithm, up to = 200. The energy values considered in the study are found to be in good agreement with the existing values. Results are presented for various values of ranging from 3 to 200 along with the convergence graph. We found that SOS algorithm provides better optimal values of energy compared to hybrid approach of Evolutionary algorithm and Spectral Gradient for unconstrained condition (EA_SG2) method.

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The application of Differential Evolution (DE) to compute the Total Transfer Capability (TTC) in deregulated market is proposed in this paper. The objective is to maximize a specific point-to-point power transaction without violating system constraints using DE. This algorithm is based on full ac optimal power flow solution to account for the effects of active and reactive power flow, voltage limits, and line flow limits. The real power output of generators in source area and the real power of the loads in the sink area were adjusted to obtain the maximum transfer capability. In order to calculate TTC more accurately, Transmission Reliability Margin is incorporated in the calculation of TTC by considering single and multiline outages and also a three phase to ground fault near a bus and clearing it by isolating the faulty line after certain time interval. The performance of the proposed method is tested on the modified IEEE-30 bus system and results are compared with that of Particle Swarm Optimization method (PSO). Further, the results are compared with other published results using CPF and EP. It is found that DE provides more reliable results than other methods.