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Distributed generation in deregulated Chapter | 9 243

in Ref. [23], DG units operating at 0.9 lagging PF help to achieve optimum
power loss reduction and hence higher HC levels. In this case, the DG unit
acts as a multirole player because the injected active power from DGs sup-
plies the load active power demands and compensates the system active
power losses, while the injected DG reactive power helps in improving the
voltage profile of the system, relieves the overvoltages arisen from the high
DG penetration, and increases the overall PF.

9.6.2 Probabilistic hosting capacity results
In the probabilistic HC approach, an MCS is utilized to develop a large num-
ber of probabilities of load active and reactive power, PV output power, and
WT output power. For each probability, the 95th percentile of the considered
parameter is calculated. In this work, each distribution was obtained from
MCS using 1000 samples [30]. An uncertainty tolerance level of 1% was
proposed for load power variations, PV output power, and WT output power.
The optimization problem in the presence of uncertain input parameters
is performed in the following sequence:

1. The input parameters of the problem are defined in addition to their rele-
vant uncertainty tolerance.
2. The 95th percentiles of the studied uncertain parameters are calculated
using MCS for the specified sample.
3. Then, the problem of optimal DG sizing and sitting is activated with a
preset objective.
4. To maximize the systems’ HC.
5. The OF (HC level) is evaluated, and the compliance with the problem
constraints is examined.
6. Steps 2 4 are repeated until reaching the maximum number of iterations.
7. The best value of the achieved objectives (highest obtained HC level) is
reported.
From the achieved results in Tables 9.5, 9.6 and 9.7, it can be noticed
that the probabilistic HC levels are higher than the deterministic HC results.
In other words, ignoring the uncertainty of electrical parameters, results in
optimistic that cause a noticeable underestimation to the HC levels achieved
from probabilistic assessments. The results obtained of the probabilistic HC
approach, with and without back-feed conditions, are presented in Table 9.7.

9.7 Conclusion

Uncertainty in the HC calculations took place due to numerous issues, such
as uncertain DG locations and size, the variable nature of the output powers
from renewable energy resources, such as wind and PV resources, and fluc-
tuations of load profiles along the day. Accordingly, the HC calculations