Page 74 - Decision Making Applications in Modern Power Systems

Uncertainty management in decision-making Chapter | 2 45

along with the dispatchable units (diesel generators and energy storage sys-
tem), which can exchange the power with the upstream network.
In this problem the main objective is profit maximization, which is
obtained by the revenues minus the system costs. The objective function can
be formulated as follows:
Maximize Profit 5 RV 2 TC ð2:1Þ

where RV is the microgrids (MGs) revenue ($), TC is the total cost ($) of
MG. The revenue for MGs is calculated according to
N ω T L T
X X X X
N
N
L
RV 5 π ω λ P l;t;ω 1 r λ P ; ω 5 1; 2; ...; N ω ð2:2Þ
t;ω
t
t
ω51 t51 l51 t51
L th
where λ is the power market price that the consumers pay at t time, P l;t;ω
t
th
th
th
is the active power demand of l load at t time in ω scenario, P N t;ω is the
N
power sold to the upstream network at tth time, λ is the price of selling/pur-
t
th
th
chasing power with the upstream network at t time in ω scenario, r is the
binary variable that separates selling or purchasing state; if r is 1 MG sells
power to the upstream network, t is the index of time, i is the index of dis-
patchable unit, l is the index of load, ω is the index of the scenario, and N ω
is the number of scenarios.
The total operation cost of MG includes fuel cost, startup and shutdown
cost, emission cost of the dispatchable units, and the cost of purchasing
power from the upstream network that is calculated as follows:
N Ω N T
X X X
TC 5 π ω ðFðP i;t;ω ÞX i;t;ω 1 SU i;t;ω 1 SD i;t;ω
ω51 i51 t51
ð2:3Þ
T
X
N
1 ðC emi Uτ i UP i;t;ω ÞÞ 1 ð1 2 rÞ λ P b
t t;ω
t51
th
where π ω is the probability of the ω scenario, and N Ω is the number of total
th th th
scenarios. P i;t;ω is the power output of i generator at t time and ω scenario.
th th th
X i;t;ω is the commitment state of i generator at t time and ω scenario.
th
th
FðP i;t Þ is the fuel cost consumption function of the i generator at t time that
is calculated as follows:
2
FðP i;t Þ 5 a i 1 b i P i;t 1 c i ðP i;t Þ ; iAN; tAT ð2:4Þ
th
where a i , b i , and c i are the cost coefficients of i generator.
The second and the third terms of (2.2) show the technical cost of genera-
tor named startup and shutdown cost, respectively. The fourth term repre-
th
sents the emission cost of i generator, τ i is the emission factor (kg/kWh) of
th
th
i generator, and C emi is the emission cost of i generator ($/kg) [32].The
fifth term represents the cost of purchased power, and P b t;ω is the purchased
th
th
power from the upstream network at t time and ω scenario.