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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