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392 Decision Making Applications in Modern Power Systems
15.2.2 Energy demand
The energy demand (E d ) of the DC microgrid consists of the energy con-
sumption in the appliances, total energy losses (E loss,t ).
T;n
X a
E d 5 P aj ðtÞτ h 1 E loss;t ð15:1Þ
t51;j51
where P aj is the power consumption in jth appliance, n a is the number of
appliances, T is the scheduling horizon of the optimization, and τ h is the
optimum time step 1 minute.
The total energy loss consists of the energy losses in the converters (E loss,c ),
line, and energy loss (E loss,b ) in the battery during charging/discharging due to
chemical reactions in it. As the system is prototyped and the cable length is
very small, the line losses are considered negligible. The total energy losses
(E loss,ac ) in the AC system can be expressed as
T;n ca
X
E loss;t 5 P loss;cj ðtÞτ h 1 P loss;b ðtÞτ h ð15:2Þ
t51;j51
where n c 5 (n a 1 n s ) is the number of converters in the autonomous micro-
grid with AC distribution system, and n s is the number of power sources.
While total energy demand with the DC system includes the energy con-
sumption in the appliances and energy losses in the battery, the energy con-
sumption can be expressed as
T;n
X a
E d 5 P aj ðtÞτ h 1 E loss;b ð15:3Þ
t51;j51
where E loss,b is the energy loss in the batteries.
15.2.3 Estimation of photovoltaic and battery size
The PV plant is the only power generator in this autonomous DC micro-
grid. Moreover, the ES (i.e., BB) is used to store the surplus PV plant
energy as well as to supply the surplus energy demand of the building.
Therefore estimation of their size is required to get the uninterrupted power
supply. The power rating of the PV plant and BBs can be calculated as
follows:
PV size: The PV Watt-hours needed per day are the combination of the
total power consumption in the appliances and power losses in the system.
The size of the PV plant depends on the Watt-hours needed from the PV
plant and a number of average sun hours per day in the whole year [14] and
can be expressed as
