Page 75 - Decision Making Applications in Modern Power Systems

46 Decision Making Applications in Modern Power Systems

2.3.1 Constraints
2.3.1.1 Power balance constraint
The sum of generated power by dispatchable (generators and energy storage
system (ESS)) and nondispatchable (PV and wind turbine (WT)) units and
exchanged power with the upstream network must be greater or equal to the
sum of forecasted power demand and power loss as follows:
N E K W
X X X X
P i;t;ω UX i;t;ω 6 P ESS e;t;ω UX e;t;ω 1 P PV k;t;ω 1 P WT w;t;ω 6 P grid t;ω $ P loss t;ω
i51 e51 k51 w51
L
X
1 P l;t;ω ; tAT; ωAN ω
l51
ð2:5Þ
th
th
is the charged/discharged power by the e ESS at t time in
where P ESS e;t;ω
ω scenario, X e;t;ω is the commitment state of the e ESS at t time in ω th
th
th
th
th
d
c
scenario. X e;t;ω and X e;t;ω are the binary variables denoting the e ESS charg-
th th
ing and discharging modes at t time in ω scenario, respectively. P PV k;t;ω is
the power output of k PV at t time in ω th scenario, P WT w;t;ω is the power
th
th
output of w th WT at t th time in ω th scenario, and P grid t;ω is the exchanged
power with the upstream network at t th time and ω th scenario, if r is 1,
5 P N and power sold to the upstream network, otherwise,
P grid t;ω t;ω
5 P b is the
P grid t;ω t;ω and power purchased from the upstream network. P loss t;ω
th
th
total power loss at t time in ω scenario.
2.3.1.2 Inequality constraints
The generated power by generators and exchanged power are bounded by
upper and lower limits as follows:
P min ðtÞ # P i ðtÞ # P max ðtÞ; tAT ð2:6Þ
i i
P min ðtÞ # P grid ðtÞ # P max ðtÞ; tAT ð2:7Þ
grid
grid
where P min and P max are the minimum and maximum power outputs of i th
i i
generator, respectively, P min and P max are minimum and maximum
grid grid
exchanged powers with the upstream network, respectively.
2.3.1.3 Energy storage constraints
The power that is charged or discharged by ESS is bounded by the upper
and lower limits:
d
d
P min ðtÞX # P ESS e ðtÞ # P max ðtÞX ; ’tAT; ’eAE ð2:8Þ
dis e e;t dis e e;t