PVArea i Á PVInt i ¼ F max p i 8i 2 PV
ð6:20Þ
The electricity produced by wind turbines is limited by wind speed, as shown in
the following equations:
X
u
EGen i,m,d,h,u þ ESal i,m,d,h þ IElec i,m,d,h NInv i Á Wp i,m,d,h 8i
2 wind, m, d, h
ð6:21Þ
Wp i,m,d,h ¼ F max p i Á
V
k
m,d,h À V
k
c i
V
k
R i
À V
k
c i
8i 2 wind, V c i V m,d,h V R i
ð6:22Þ
Wp i,m,d,h ¼ F max p i 8i 2 wind, V R i V m,d,h V F i
ð6:23Þ
Wp i,m,d,h ¼ 0 8i 2 wind, V m,d,h < V c i UV m,d,h > V F i
ð6:24Þ
A constraint is set by how much heat can be recovered from each type of DER
technology for both immediate usage and diversion to storage, as described in
Eq. (6.25).
X
u
RHeat i,m,d,h,u þ IHeat i,m,d,h
α i
X
u
EGen i,m,d,h,u þ ESal i,m,b,h þ IElec i,m,d,h
!
8i, m, d, h
ð6:25Þ
Additional constraints are needed to ensure the correct operation of the storage
tank. Equation (6.26) shows the heat inventory balance constraint. It states that the
total amount of heat stored at the beginning of an hour is equal to the non-dissipated
heat stored at the beginning of the previous hour, plus recovered heat diverted
toward storage during the hour, minus stored heat released to meet end-use loads
during the hour. Equation (6.27) is the specific case of Eq. (6.26) for the first hour of
the day. Here, the total heat stored at the beginning of the first hour of the day is
equal to the non-dissipated heat stored at the beginning of the last hour of the
previous day, plus the inflow and minus the outflow of heat during the hour.
Equation (6.28) is similar to Eq. (6.27). Equation (6.29) prevents stored heat from
being used by end-use loads such as electricity only. Equation (6.30) prevents the
quantity of heat stored from exceeding the storage capacity. Equation (6.31) resets
the heat stored to zero, and Eq. (6.32) indicates that stored heat is released at the end
of the year. Equation (6.33) prevents the use of heat from storage during the first
hour of the year. Equation (6.34) prevents the use of heat recovered from generation
or storage for a particular end use unless an appropriate CHP technology is installed.
Finally, Eq. 6.35 prevents the use of stored heat unless a heat storage unit has been
purchased.
6 Development of a Tool to Optimize Urban-Rural Linkage and a Decentralized Power. . . 129
ð6:20Þ
The electricity produced by wind turbines is limited by wind speed, as shown in
the following equations:
X
u
EGen i,m,d,h,u þ ESal i,m,d,h þ IElec i,m,d,h NInv i Á Wp i,m,d,h 8i
2 wind, m, d, h
ð6:21Þ
Wp i,m,d,h ¼ F max p i Á
V
k
m,d,h À V
k
c i
V
k
R i
À V
k
c i
8i 2 wind, V c i V m,d,h V R i
ð6:22Þ
Wp i,m,d,h ¼ F max p i 8i 2 wind, V R i V m,d,h V F i
ð6:23Þ
Wp i,m,d,h ¼ 0 8i 2 wind, V m,d,h < V c i UV m,d,h > V F i
ð6:24Þ
A constraint is set by how much heat can be recovered from each type of DER
technology for both immediate usage and diversion to storage, as described in
Eq. (6.25).
X
u
RHeat i,m,d,h,u þ IHeat i,m,d,h
α i
X
u
EGen i,m,d,h,u þ ESal i,m,b,h þ IElec i,m,d,h
!
8i, m, d, h
ð6:25Þ
Additional constraints are needed to ensure the correct operation of the storage
tank. Equation (6.26) shows the heat inventory balance constraint. It states that the
total amount of heat stored at the beginning of an hour is equal to the non-dissipated
heat stored at the beginning of the previous hour, plus recovered heat diverted
toward storage during the hour, minus stored heat released to meet end-use loads
during the hour. Equation (6.27) is the specific case of Eq. (6.26) for the first hour of
the day. Here, the total heat stored at the beginning of the first hour of the day is
equal to the non-dissipated heat stored at the beginning of the last hour of the
previous day, plus the inflow and minus the outflow of heat during the hour.
Equation (6.28) is similar to Eq. (6.27). Equation (6.29) prevents stored heat from
being used by end-use loads such as electricity only. Equation (6.30) prevents the
quantity of heat stored from exceeding the storage capacity. Equation (6.31) resets
the heat stored to zero, and Eq. (6.32) indicates that stored heat is released at the end
of the year. Equation (6.33) prevents the use of heat from storage during the first
hour of the year. Equation (6.34) prevents the use of heat recovered from generation
or storage for a particular end use unless an appropriate CHP technology is installed.
Finally, Eq. 6.35 prevents the use of stored heat unless a heat storage unit has been
purchased.
6 Development of a Tool to Optimize Urban-Rural Linkage and a Decentralized Power. . . 129