SOC	State of charge
V2H	Vehicle-to-home
H2V	Home-to-vehicle
PV	Photovoltaic
EV	Electric vehicle
ESS	Energy storage system
HEMS	Home energy management system
NT	Standard and nominal cell operating temperature conditions
$DOD$	Total number depth of discharge
D	Vehicle travel distance (km)
i	Interest rate
N	Lifetime
$N_{days}$	Total number of days during the year
$\gamma$	Contracted ratio for selling power to the grid
${\lambda }_t$	Electricity price during different periods of day
${\lambda }_k$	Peak price
${\lambda }_m$	Mid-peak price
${\lambda }_{off}$	Off-peak price
${\eta }_{EV}^d$	EV battery discharge efficiency
${\eta }_V$	Vehicle efficiency (kWh/km)
${\eta }_{PV}$	PV generator efficiency
${\eta }_R$	The PV generator efficiency at reference temperature
${\eta }_{ESS}^c$	Charging efficiency of ESS
${\eta }_{ESS}^d$	Discharging efficiency of ESS
${\eta }_{EV}^c$	Charging efficiency of EV battery
${\eta }_{EV}^d$	Discharging efficiency of EV battery
$\beta$	Binary variable
$\rho$	Temperature coefficient for cell efficiency
$P_{GL,t}$	Power from the grid-to-load (kW)
$P_{GESS,t}$	Power from the grid-to-ESS (kW)
$P_{GEV,t}$	Power from the grid-to-EV (kW)
$P_{PVG,t}$	Power from the PV-to-grid (kW)
$P_{ESSG,t}$	Power from the ESS-to-grid (kW)
$P_{PVL,t}$	Power from the PV-to-load (kW)
$P_{ESSL,t}$	Power from the ESS-to-load (kW)
$P_{EVL,t}$	Power from the EV-to-load (kW)
$P_{ESS,t}^c$	Charging power of ESS (kW)
$P_{ESS,t}^d$	Discharging power of ESS (kW)
$P_{EV,t}^c$	Charging power of EV (kW)
$P_{EV,t}^d$	Discharge power of EV (kW)
$P_{L,t}$	Household power demand at time t
$P_{max}^{grid}$	Maximum power that can be drawn from the grid (kW)
$P_{max}^{sell}$	Maximum power that can be sold back to the grid (kW)
$Cos{t}_{PV}^{\mathrm{capital}}$	Daily capital cost of the PV installation
$Cos{t}_{ESS}^{\mathrm{capital}}$	Daily capital cost of ESS installation
$Cos{t}_{EV}^{degradation}$	EV battery degradation cost due to V2H
$C_{PV}$	One-time installation cost of PV (USD/kW)
$C_{ESS}$	One time installation cost of ESS (USD/kWh)
$C_{EV}$	Replacement cost of EV battery
$C_f$	Full cycles number during battery lifespan
$Z_{PV}$	Rated capacity of PV array size (kW)
$Z_{ESS}$	Rated capacity of ESS (kWh)
$Z_{EV}$	Rated capacity of EV battery (kWh)
$E_{EV}^R$	Required energy for the EV travel distance in the typical day (kWh)
$I_{PV}$	Solar radiation (kWh/m2)
$I_{PV,NT}$	The average hourly solar irradiation incident on the array at NT
$T_A$	Ambient temperatures
$T_R$	Reference cell temperature
$T_C$	The cell temperature
$T_{C,NT}$	Cell temperatures at NT
$T_{A,NT}$	Ambient temperatures at NT
$SO{C}_{ESS,t}$	ESS SOC at time t
$SO{C}_{ESS,t-1}$	SOC of ESS in past period
$SO{C}_{ESS,max}$	Maximum SOC of ESS
$SO{C}_{ESS,min}$	Minimum SOC of ESS
$SO{C}_{EV,t}$	EV battery SOC at time t
$SO{C}_{EV,t-1}$	State of charge of EV battery at the past period
$SO{C}_{EV,max}$	Maximum SOC of EV battery
$SO{C}_{EV,min}$	Minimum SOC of EV battery
$SO{C}_{EV,R1}$	SOC required for the EV trip distance at the first departure time $t_{d1}$
$SO{C}_{EV,R2}$	SOC required for the remaining EV trip distance at the second departure time $t_{d2}$
$t_{d1}$	First departure time
$t_{d2}$	Second departure time
$X_{m,best,t}$	Variable m best value obtained for the best candidate
$X_{m,worst,t}$	Variable m worst value obtained for the worst candidate
$X_{m,n,t}^{{}^{\prime }}$	Modified value of $X_{m,n,t}$
$r_1$ and $r_2$	Are random values between zero and one