Assessment of impact of unbalancing power allocation on calculating Maximum Loading Point

In traditional Power Flow (PF) formulations, the unbalancing power that caused by the transmission power loss (TPL) is provided by sole slack bus, which introduces some errors. Such errors are involved in the results of Continuation Power Flow (CPF) which is based on the parameterized PF formulations. Moreover, for certain class of systems, this kind of errors could be significant and few research centres on assessing the CPF with multiple slack buses (MSB). In addition, the impact of the allocations of the slack buses on PF and CPF results has not been well demonstrated. Therefore, this paper analyses the performances of the PF and CPF formulations involving MSB by applying them to calculate the Maximum Loading Point (MLP). It captures the allocation of the unbalancing power by assigning it to MSB according to a set of proportionality coefficients. Since the formulations could generate different results according to various sets of the proportionality coefficients, it is obvious that optimization techniques could be adopted to give optimal coefficients aiming at specific objectives. A particle swarm optimization (PSO) and CPF based approach is presented to help search the optimal proportionality coefficients for the MSBs with the objective of minimizing the TPL. The case studies based on the IEEE 5-bus test system and the IEEE 14-bus test system show the efficiency of the proposed approaches.