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366  Decision Making Applications in Modern Power Systems


            issues [2,3]. As a result, in the literature [4,5], great efforts were presented to
            solve the problem of optimal sizing and proper placement of DG units in DNs,
            such as analytical, numerical, and heuristic-based methods. In addition, for the
            determination of the optimal DG PL, bus rms voltage limits and current limits
            related to the allowable thermal loading capabilities of the lines/cables and
            transformers were traditionally considered constraints in the literature [6].
               Today, extensive employment of nonlinear loads and large-scale grid-
            connected DG units has led to considerably distorted voltages and currents in
            the distribution systems [7 9]. Accordingly, in the recent studies
            [2,4,10 13], the harmonic distortion limits placed in the international stan-
            dards have been considered additional constraints for optimal planning of the
            DG units with power electronic based interfaces. These studies clearly
            show that harmonic distortion considerably limits the hosting capacity of the
            system for those kinds of DG units.
               In addition, the distribution systems always have unbalanced voltages and
            currents due to the unequal distribution of single-phase loads over the three
            phases, asymmetry of lines, and/or unbalanced power system faults [14].
            Apart from that, single-phase and nondispatchable DG units of residential
            customers can be another important reason for the unbalance problem since
            they are often randomly distributed in the system [15 17]. Thus the voltage
            unbalance should be considered a constraint for the determination of the sys-
            tem’s DG hosting capacity [18 20].
               Induction machines are widely used as motors in consumer-connected
            devices and as generators in the small-to-medium-sized fixed-speed wind
            energy conversion systems (FSWECSs) due to their advantages such as small
            size, low cost, and high reliability [21]. Under unbalanced and/or distorted grid
            voltages the induction machines have poor power factor, torque pulsations, and
            extra losses resulting in overheating problem [21 24]. The torque pulsations
            and overheating problems lead to their fast aging. Accordingly, in the literature
            [14,25], to avoid the loss of life related to extra losses under these voltage con-
            ditions, it is suggested that their permissible loading ratio, the so-called derating
            factor (DF), should be limited by equalizing the highest phase current to the
            rated value. However, few studies paid attention to the maximum loading ratios
            or permissible PL (PPL)ofinduction generators (IGs) [26,27].
               To mitigate unbalance and/or harmonic distortion in the systems with DG
            units, there are several custom power devices, such as dynamic voltage
            restorers, static synchronous compensators, active power filters, and unified
            power quality conditioners [28 30]. On the other hand, when compared to
            these compensation devices, passive harmonic filters [2,12,13] and Steinmetz
            compensator [31 33] are simple and cost-effective solutions for harmonic
            distortion and unbalance mitigation, respectively.
               In this paper, first, an algorithm is presented to determine PPL of a
            FSWECS with squirrel cage IG (SCIG) operating in the unbalanced and non-
            sinusoidal distribution system. The simulated system is modeled through
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