Page 77 - Decision Making Applications in Modern Power Systems

48 Decision Making Applications in Modern Power Systems

2.3.1.5 Ramp up/down constraint
th
Any increase or decrease in power output of i generator for two consecutive
periods of time must be limited by ramp up and ramp down, respectively,
which are as follows:
P i;t 2 P i;t21 # UR i ð2:14Þ

P i;t21 2 P i;t # UD i ð2:15Þ
where P i;t and P i;t21 are the power outputs of i th generator at t th and
t 2 1 th time, respectively. UR i and UD i are the up/down ramp rates of i th
generator, respectively.

2.3.2 Uncertainty modeling

As mentioned earlier, the penetration of renewable energy sources (RESs)
into MG can influence the scheduling and operation of MG. PVs and WTs
are one of the common types of RESs in active distribution networks and
MGs. The generated powers by PVs and WTs are coming from the solar irra-
diation and wind speed as a prime energy source, respectively [35]. Due to
the probabilistic nature of wind speed and sun irradiance, the generated
power of those resources causes a significant amount of uncertainties.
Furthermore, daily load behavior is considered as an uncertain parameter.
Therefore the proposed optimal profit maximization of MG scheduling con-
sists of a large number of uncertain parameters. The probabilistic analysis in
the presence of multiple uncertain parameters is a mighty tool for scheduling
and operation of power network. To address the uncertain parameters a prob-
abilistic scenario-based framework is presented in this section.

2.3.2.1 Scenario generation
2.3.2.1.1 WT power output
The power output of WT depends on the speed of wind. To model the uncer-
tainty of wind speed, it is assumed that the wind speed follows the Weibull
distribution [7].If V mean and σ are the mean and standard deviations of fore-
casted wind speed, respectively, the parameters of the Weibull distribution
are calculated as [36].

σ V mean
21:086
r 5 ; c 5 ð2:16Þ
V mean Gamma 1 1 1=r
According to the Weibull parameters (r, c), the Weibull probability distri-
bution function (PDF) is calculated as
r
r21
r V V
fðVÞ 5 exp 2 ð2:17Þ
c c c