This study presents a new approach to the optimal placement of voltage sag monitors considering the uncertainties associated with transition resistance. The influence of transition resistance on the magnitude of voltage sags triggered by symmetrical and unsymmetrical faults is analyzed. Then the transition resistance interval set array for voltage sags is established, on the basis of which, a random vector model on voltage sag observability is proposed and related observability indices are defined in the form of conditional probability. The optimal placement model is established by taking the available number of monitors as the constraint condition and the maximum sag global observability index as the objective function. Binary particle swarm optimization (BPSO) is implemented to obtain the optimal placement results. Finally, simulation is carried out on IEEE 30-bus system, and it is shown that the proposed optimal monitor placement method is more applicable compared with the traditional MRA method. INDEX TERMS Binary particle swarm optimization, conditional probability, observability indices, optimal monitor placement, random vector model, transition resistance, uncertainties, voltage sags. I. INTRODUCTION Voltage sags are the most frequently occurring power quality disturbances, mainly caused by faults in a power system. Voltage sag is typically defined as the reduction of RMS voltage from 0.1 to 0.9 p.u. with a typical duration of 0.5 cycle to 1 min, which is usually characterized by its magnitude (the magnitude of during-fault voltages) and duration (the time during which the RMS voltage stays below a given threshold, usually 0.9 p.u.) [1]-[4]. Many studies conducted around the world have shown that voltage sags cause customers of various sectors significant financial losses, for instance, in a semiconductor manufacturing industry, economic losses per voltage sag have been estimated 3.8 million e[5], [6]. But it is unrealistic to expect that the grid will provide a completely financialloss-free power quality environment for all customers [6]. Before implementing adequate countermeasures, it is necessary to establish a monitoring system by using appropriate power quality monitors (PQMs) and this system should The associate editor coordinating the review of this manuscript and approving it for publication was Hui Ma .

Harmonic impedance estimation and suitable evaluation index selection are the key steps of harmonic contribution evaluation. Most of the traditional harmonic impedance estimation methods are only applicable to the scenario, where the background harmonic is stable and the utility impedance is constant. However, this scenario will change in many cases due to the fluctuation of harmonic, the change of system operation mode and so on. In order to improve the estimation accuracy for harmonic impedance, a harmonic impedance estimation method is proposed in this paper based on similarity measure and ordering points to identify the clustering structure (OPTICS). The total harmonic contribution index and harmonic comprehensive contribution index are proposed based on subjective analytic hierarchy process to simplify the evaluation results. Simulation analysis and their comparison with the traditional methods reveal that the proposed harmonic impedance estimation method can reduce the influence of background harmonic voltage fluctuation and utility impedance change, making the harmonic impedance estimation result more accurate. Besides, the proposed total harmonic contribution index and harmonic comprehensive contribution index can effectively simplify contribution evaluation results, which provide a new methodology for the evaluation of harmonic contribution.