Page 80 - Decision Making Applications in Modern Power Systems

Uncertainty management in decision-making Chapter | 2 51

Step 5:If Ω and Ω are the final sets of selected and deleted scenarios,
s j

respectively, and ωAΩ ; calculate the probabilities of selected scenarios
s
as
X
π 5 π ω 1 π ω 0 ð2:24Þ
ω
ω 0 AJðωÞ
where JðωÞ is defined as the set of scenarios ω AΩ such that
0
j
ωAarg min υðωv; ω Þ.
0
ωvAΩ s
2.4 Case study
The proposed microgrid problem that is presented in the previous section is
implemented on the 33-bus microgrid (Fig. 2.1). The characteristic of three
generators is given in Table 2.2. Tables 2.3 2.5 show the characteristic of
PV, wind, and energy storage system, respectively.
Based on the uncertainty modeling for different parameters (PV and wind
power generation and load demand), which is described in Section 2.3.2.1,
the forecasted values of these parameters are depicted in Figs. 2.2 2.4.
The stochastic framework models the power output of WT and PV and
the load consumption using the corresponding PDF that is described in
Section 2.2. To model the uncertainties, 1000 scenarios are generated for
each variable, which is reduced to 10 scenarios using the scenario generation
algorithm (Section 2.3.2.2).

TABLE 2.2 The characteristic of generators of system.
Generator G1 G2 G3

P min ðkWÞ 25 75 25
P max ðkWÞ 300 150 300
a ($) 25 10 20
b ($/kW) 0.15 0.85 0.25
c ($/kW) 2 0.0023 0.012 0.003
Startup/shutdown cost ($) 0.96 1.9 0.96

TABLE 2.3 PV characteristics.
2
Technology T c ( C) P STC (kW) G STC (W/m ) K

PV 25 250 1000 0.001