(a) Available capacity constraint of the plants
X p;t;d;y avp d;p i y
À Á Â Kp y;p
ð11Þ
where avp d;p i y
À Á
: availability factor of i-th type of power plant.
(b) Power demand and supply balances
X 6
p¼1
X p;t;d;y þ
X 2
s¼1
Dis s;d;t;y À Cha s;d;t;y
À
Á ¼ load d;t;y À Save d;t;y
ð12Þ
(c) Constraint on installable capacity
Kp y;p KPmax y;p
ð13Þ
Ks1 y;s KS1max y;s
ð14Þ
Ks2 y;s KS2max y;s
ð15Þ
where KPmax p : maximum installable capacity of p-th type of power plant in year
y (GW), KS1max y;s : maximum installable kW capacity of s-th type of power storage
facility in year y (GW), KS2max y;s : maximum installable kWh capacity of s-th type
of power storage facility in year y (GWh).
(d) Constraint on load following capability of the plants
X p;t þ 1;d;y X p;t;d;y þ increase p  avp d;p i y
À Á Â Kp y;p
ð16Þ
X p;t þ 1;d;y ! X p;t;d;y À decrease p  avp d;p i y
À Á Â Kp y;p
ð17Þ
where increase p : maximum output increase rate per unit time of p-th type of power
plant, decrease p : maximum output decrease rate per unit time of p-th type of power
plant.
(e) Charge and discharge balances of energy storage technology
Ss s;d;t þ 1;y ¼ 1 À sd s
ð
ÞÂSs s;d;t;y þ
ffiffiffiffiffiffi ffi
eff s
p
 Cha s;d;t;y Dis s;d;t;y
ffiffiffiffiffiffi ffi
eff s
p
ð18Þ
where sd s : self-discharge rate of s-th type of power storage facility, eff s : cycle
efficiency of electricity storage of s-th type of power storage facility.
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