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Uncertainty management in decision-making Chapter | 2 59

profit for 10 scenarios. The scenario number 7 with the maximum profit is
selected and described in the following.
The optimal generators and ESSs state for 24 hours are given in
Table 2.7. ESS charging, discharging, and idle states are represented by 21,
1, and 0. As can be seen in Table 2.2, generator number 3 is a high-cost gen-
erator, so it is committed in peak-load hours (13 16 hours).
The proposed algorithm detects that the price of exchanged power is low
at some hours (1 8 hours), so purchasing power from the upstream network
is rational for MG’s owner (r 5 0). In this interval, most of the ESS is
charged. At the higher exchanged power price (10 16 hours), it is beneficial
for MG to sell surplus power to the upstream network to achieve significant
benefits. In this interval, ESS is discharged and because the exchanged
power price exceeds the cost coefficients of all generators, generator number
2 (high-cost generator) is committed at 13 16 hours. While MG supplies
their loads, the surplus power is sold to the upstream network (r 5 1).
The monetary result of the problem consists of MG’s costs, revenues, and
profits, which are given in Table 2.8.
It is shown in Table 2.8, at the peak-load hours (11 16), in which the
value of the power price exceeds generators cost coefficients, MG sells the
surplus power (that generated by the high-cost generator) to the upstream
network and receives significant revenues; at this interval, r that shows the
exchanged power direction with the upstream network is equal to 1. Based
on the proposed optimal scheduling, the profit of MG is determined as
$7721.35 for scenario number 7.
Finally, the expected profit of 10 reduced scenarios based on the proba-
bility of each scenario can be calculated as follows:

10 10
X X
Expected profit 5 π ω f ω where π ω 5 1 ð2:25Þ
ω51 ω51
According to (2.25), the value of expected profit is $7528.9.

2.5 Conclusion

In this chapter a brief overview of uncertainty management in the modern
power system is studied. The penetration of renewable energy resources, as
well as load demand deviation, causes different challenges in the operation
and scheduling of modern power systems. After classifying a variety of
uncertain parameters in the power system, some useful methods for uncer-
tainty management are discussed. To demonstrate the uncertainty modeling
in the power system decision-making process, we considered that a micro-
grid consists of different generation units (dispatchable units and renewable
units such as PV and wind). The MG scheduling for profit maximization in
the presence of multiple uncertain parameters is examined. After the