Table 4 The model concepts of sets, indices, parameters, and decision variables

From: Optimizing bus charging infrastructure by incorporating private car charging demands and uncertain solar photovoltaic generation

Sets

 

I

Set of EBs

L

Set of bus layovers

Y

Set of years

M

Set of months in a year

K

Set of solar PV power generation scenarios

T

Set of time slots (1 minute for each time slot in this study)

Indices

 

i

Index of EBs

l

Index of bus layovers

y

Index of years

m

Index of months in a year

k

Index of solar PV power scenarios

t

Index of time slots

Parameters

 

\({{\rm{\lambda }}}_{{\rm{bes}}}\)

Unit price of BES (CNY/kWh)

\({{\rm{\lambda }}}_{{\rm{pv}}}\)

Unit price of PV panel (CNY)

\({{\rm{\lambda }}}_{{\rm{t}}}\)

Unit price of electricity purchased from grid in time slot t (CNY/kWh)

\({{\rm{\beta }}}_{1}\)

Price factor for charger power (CNY10,000/kW)

\({{\rm{\beta }}}_{0}\)

Price intercept for charger power (CNY10,000)

\({{\rm{\delta }}}_{{\rm{grid}}}\)

Carbon emission cost of thermal power generation (CNY/kWh)

\({{\rm{\delta }}}_{{\rm{pv}}}\)

Carbon emission cost of solar PV power generation (CNY/kWh)

\({{\rm{\delta }}}_{{\rm{ev}}}\)

Service fee of providing charging infrastructure to EVs (CNY/kWh)

\({{\rm{\delta }}}_{{\rm{sell}}}\)

Electricity sales price of solar PV (CNY/kWh)

\({{\rm{\rho }}}_{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Probability of solar PV power generation scenario k in month m of year y occurring

\({{\rm{Q}}}_{{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Output power of a single PV panel in time slot t under solar PV power generation scenario k in month m of year y (kW)

\({{\rm{e}}}_{{\rm{i}},{\rm{l}}}\)

Energy consumption of EB i during the trip right before the layover l (kWh)

\({\rm{SO}}{{\rm{C}}}_{\min }\)

Minimum state of charge (SOC) of the batteries in EB and BES

\({\rm{SO}}{{\rm{C}}}_{\max }\)

Maximum SOC of the batteries in EB and BES

\({\rm{SO}}{{\rm{C}}}_{{\rm{ini}}}\)

The initial SOC of the batteries in EB and BES

\({\rm{C}}\)

Power battery capacity of EB (kWh)

\({\rm{du}}{{\rm{r}}}_{{\rm{i}},{\rm{l}}}\)

Duration of EB i during the layover l (h)

\({{\rm{P}}}_{{\rm{ev}},{\rm{t}}}\)

Charging demand of EVs in time slot t

\({\rm{\varepsilon }}\)

Charging and discharging efficiency of BES

\({{\rm{P}}}_{\max }\)

Maximum charging and discharging power of BES (kW)

\({{\rm{d}}}_{{\rm{m}}}\)

Number of days in month m

\({{\rm{\mu }}}_{{\rm{PV}}}\)

Residual value rate of solar PV

\({{\rm{r}}}_{{\rm{PV}}}\)

Annual PV module aging rate

\({{\rm{r}}}_{{\rm{BES}}}\)

Annual capacity degradation rate of BES

Variables

 

\({{\rm{C}}}_{{\rm{bes}}}\)

Capacity of BES at the bus depot (kWh)

\({{\rm{N}}}_{{\rm{ch}}}\)

Number of chargers deployed at the bus depot

\({{\rm{N}}}_{{\rm{pv}}}\)

Number of PV panels deployed at the bus depot

\({{\rm{N}}}_{{\rm{ev}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Number of chargers occupied by EVs in time slot t under solar PV power generation scenario k in month m of year y

\({{\rm{N}}}_{{\rm{bus}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Number of chargers occupied by EBs in time slot t under solar PV power generation scenario k in month m of year y

\({\rm{SO}}{{\rm{C}}}_{{\rm{bef}},{\rm{i}},{\rm{l}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

SOC of EB i right before the layover l under solar PV power generation scenario k in month m of year y

\({\rm{SO}}{{\rm{C}}}_{{\rm{aft}},{\rm{i}},{\rm{l}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

SOC of EB i right after the layover l under solar PV power generation scenario k in month m of year y

\({\rm{P}}\)

Maximum charging power of deployed chargers at the bus depot (kW)

\({{\rm{P}}}_{{\rm{i}},{\rm{l}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Charging power for EB i during the layover l under solar PV power generation scenario k in month m of year y (kW)

\(\overline{{{\rm{P}}}_{{\rm{i}},{\rm{l}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}}\)

1 if the \({{\rm{P}}}_{{\rm{i}},{\rm{l}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\) is larger than zero, otherwise 0

\({{\rm{E}}}_{{\rm{bat}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Energy remaining in BES in time slot t under solar PV power generation scenario k in month m of year y (kWh)

\({{\rm{P}}}_{{\rm{charge}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Charging power of BES in time slot t under solar PV power generation scenario k in month m of year y (kW)

\({{\rm{P}}}_{{\rm{discharge}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Discharging power of BES in time slot t under solar PV power generation scenario k in month m of year y (kW)

\({{\rm{P}}}_{{\rm{eb}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Charging power for all the EBs in time slot t under solar PV power generation scenario k in month m of year y (kW)

\({{\rm{P}}}_{{\rm{ev}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Charging power for private EVs in time slot t under solar PV power generation scenario k in month m of year y (kW)

\({{\rm{P}}}_{{\rm{grid}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Charging power for all the EBs from the grid in time slot t under solar PV power generation scenario k in month m of year y (kW)

\({{\rm{P}}}_{{\rm{pv}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Output power of solar PV system in time slot t under solar PV power generation scenario k in month m of year y (kW)

\({{\rm{P}}}_{{\rm{sell}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Power of solar PV energy sold to the grid in time slot t under solar PV power generation scenario k in month m of year y (kW)

\({{\rm{P}}}_{{\rm{usepv}},{\rm{t}}}^{{\rm{y}},{\rm{m}},{\rm{k}}}\)

Power of solar PV energy used to charge vehicles in time slot t under solar PV power generation scenario k in month m of year y (kW)

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