Page 271 - Decision Making Applications in Modern Power Systems

234 Decision Making Applications in Modern Power Systems

60 to 30 minutes reduces the overall system’s HC. Afterward, the uncertainty
in DG size and location was investigated. From the DG size perspective, it
was found that using a deterministic size of the studied DG instead of using
relevant probability distribution curve for the size of the DG unit leads to a
considerable underestimation of the system’s HC. From the DG location per-
spective, the authors highlighted that considering a conservative approach for
allocating the DG units at the farthest buses leads to a noticeable reduction
in the system’s HC. Thus it is highly advisable to properly allocate the DG
units considering appropriate uniform distribution functions to allow for
higher HC levels.

9.5 Problem formulation
The problem of optimal DG sizing and sitting is solved by both deterministic
and probabilistic approaches considering the HC maximization as the prob-
lem objective function (OF). The problem OF and constraints are described
in the following subsections [23].

9.5.1 Objective function
In this work the maximization of the injected active power from connecting
DG units is considered as a problem objective that represents the HC maxi-
mum allowable level. The HC is expressed as given in Eq. (9.1), where PDG
represents the injected active power from the DG unit and S rated is the appar-
load
ent power of the load.
P DG
HCð%Þ 5 3 100 ð9:1Þ
S rated
load
Thus the OF can be formulated as
OF 5 Maximize HC 5 HCðDG size; DG locationÞ ð9:2Þ
where DG size and DG location represent the optimal size and location
achieved so far to satisfy the OF while complying with the preset
constraints.

9.5.2 Constraints
In this study, five constraints are considered as follows:
1. Bus voltage constraint
The bus rms voltage ðV rms Þ should be kept within its specified mini-
L
mum and maximum limit, thus
V rms # V rms # V rms ð9:3Þ
min L max