δ u
The amount of heat that can be allocated to end use u from unit kW of
stored heat that is released
λ u
The amount of electricity that can be allocated to end use u from unit
kW of stored electricity that is released
ε H
The amount of heat that is not lost due to dissipation during 1 h from
unit kWh of stored heat
ε E
The amount of electricity that is not lost due to dissipation during 1 hour
from unit kWh of stored electricity
ω
Unit start and stop cost (Yen)
θ
Minimum percentage of electricity purchase (%)
Wp i,m,d,h
Power generation of wind technology i (kW)
V ci
Cut in speed of wind turbine (m/s)
V ri
Rated speed of wind turbine (m/s)
V fi
Cutoff speed of wind turbine (m/s)
M
A very large number
Decision variables
DC
Indicator variable for installation of a direct-fired natural gas AC
HS
Indicator variable for installation of heat storage unit
ES
Indicator variable for installation of electricity storage unit
Operate i,m,d,h Number of units of technology i, set to run at hour h, day d, in month
m
PElec m,d,h,u
Purchased electricity from the distribution company by the customer
during hour h, day d, and month m for end use u (kW)
PGas m,d,h,u
Purchased natural gas during hour h, day d, and month m for end use
u (m
3 )
EGen i,m,d,h,u
Generated power by technology i during hour h, day d, month m and
for end use u to supply the customer’s load (kW)
IHeat i,m,d,h
Amount of heat from technology i that is diverted toward the heat
storage unit during hour h, day d, and month m (kW)
IGElec m,d,h
Amount of grid electricity that is diverted toward the electricity
storage unit during hour h, day d, and month m (kW)
IElec i,m,d,h
Amount of generated electricity from technology i that is diverted
toward the electricity storage unit during hour h, day d, and month m
(kW)
FStart i,m,d,h
Indicator variable for the start of technology i
FStop i,m,d,h
Indicator variable for the stop of technology i
NInv i
Number of units of technology i installed by the customer
OHeat m,d,h,u
Amount of stored heat that is released to meet the load of end use u
during hour h, day d, and month m (kW)
RHeat i,m,d,h,u Amount of heat recovered from technology I that is used to meet end
use u during hour h, type of day t, and month m (kW)
HSmax
Capacity of heat storage unit (kWh)
ESmax
Capacity of electricity storage unit (kWh)
122
H. Ren and W. Zhou
The amount of heat that can be allocated to end use u from unit kW of
stored heat that is released
λ u
The amount of electricity that can be allocated to end use u from unit
kW of stored electricity that is released
ε H
The amount of heat that is not lost due to dissipation during 1 h from
unit kWh of stored heat
ε E
The amount of electricity that is not lost due to dissipation during 1 hour
from unit kWh of stored electricity
ω
Unit start and stop cost (Yen)
θ
Minimum percentage of electricity purchase (%)
Wp i,m,d,h
Power generation of wind technology i (kW)
V ci
Cut in speed of wind turbine (m/s)
V ri
Rated speed of wind turbine (m/s)
V fi
Cutoff speed of wind turbine (m/s)
M
A very large number
Decision variables
DC
Indicator variable for installation of a direct-fired natural gas AC
HS
Indicator variable for installation of heat storage unit
ES
Indicator variable for installation of electricity storage unit
Operate i,m,d,h Number of units of technology i, set to run at hour h, day d, in month
m
PElec m,d,h,u
Purchased electricity from the distribution company by the customer
during hour h, day d, and month m for end use u (kW)
PGas m,d,h,u
Purchased natural gas during hour h, day d, and month m for end use
u (m
3 )
EGen i,m,d,h,u
Generated power by technology i during hour h, day d, month m and
for end use u to supply the customer’s load (kW)
IHeat i,m,d,h
Amount of heat from technology i that is diverted toward the heat
storage unit during hour h, day d, and month m (kW)
IGElec m,d,h
Amount of grid electricity that is diverted toward the electricity
storage unit during hour h, day d, and month m (kW)
IElec i,m,d,h
Amount of generated electricity from technology i that is diverted
toward the electricity storage unit during hour h, day d, and month m
(kW)
FStart i,m,d,h
Indicator variable for the start of technology i
FStop i,m,d,h
Indicator variable for the stop of technology i
NInv i
Number of units of technology i installed by the customer
OHeat m,d,h,u
Amount of stored heat that is released to meet the load of end use u
during hour h, day d, and month m (kW)
RHeat i,m,d,h,u Amount of heat recovered from technology I that is used to meet end
use u during hour h, type of day t, and month m (kW)
HSmax
Capacity of heat storage unit (kWh)
ESmax
Capacity of electricity storage unit (kWh)
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H. Ren and W. Zhou