Table 1 Abbreviations and nomenclature...

Table 1

Abbreviations and nomenclature

Symbols	Acronyms	Symbols	Acronyms
A. Indices		$E^{l}$	Stand-by losses of the battery
$y$	Index of year	bd	Battery yearly degradation rate
$d$	Index of day	$π_{y, d, t}^{'}$	Price of electricity in hour $t$ of day $d$ of year y
$t$	Index of hour	$π_{y, d, t}$	Cost of electricity in hour $t$ of day $d$ of year y
B. Sets		$P_{\max}^{h} / P_{\min}^{h}$	Maximum/minimum capacity of the inverter unit
$Ξ^{T}$	Set of hours at each day of the scheduling horizon	$P_{\max}^{i n}$	Maximum allowable power import from the grid
$Ξ^{D}$	Set of days in each year	$P_{\max}^{e n}$	Maximum allowable power export to the grid
$Ξ^{Y}$	Set of years	$P_{\max}^{ch} / P_{\min}^{ch}$	Maximum/minimum charging rate for battery
C. Parameters		$η^{inv} η^{b}$	Efficiency of inverter/battery
$i$	Yearly interest rate	D. Variables
$A_{\max}$	Maximum allowable number of PV panels	A	Number of PV panels with power generation ${\overset{̅}{P}}_{y, d, t}$
$B_{\max}$	Maximum allowable number of batteries	$B_{y}$	Number of batteries with the capacity of $E^{'}$ in year y
$L T T^{p v}$	Lifetime of PV panels	${T B}_{y}$	Total usable storage capacity of the batteries in year y
${LT}_{n}^{b}$	Lifetime of battery	${S O C}_{y, d, t}$	Battery state of charge at each time
$C^{pv}$	Price of PV panel with power generation ${\overset{̅}{P}}_{y, d, t}$	$P_{y, d, t}^{i n}$	Import electricity from the grid in hour $t$ of day $d$ of year y
$C_{y}^{b}$	Price of battery with the capacity of $E^{'}$ in year y	$P_{y, d, t}^{e n}$	Export electricity to the grid in hour $t$ of day $d$ of year y
$C_{y}^{m P V}$	Annual maintenance cost per kilowatt of PV.	$P_{y, d, t}^{dmp}$	Dumped power in hour $t$ of day $d$ of year y
$C_{y}^{m B}$	Annual maintenance cost per kilowatt of Battery	$P_{y, d, t}^{ch}$	Battery Charging in hour $t$ of day d of year y
${\overset{̅}{P}}_{y, d, t}$	Forecasted power generation by each PV unit	$P_{y, d, t}^{v}$	Total PV generation in hour $t$ of day $d$ of year y
${\overset{̅}{L}}_{y, d, t}$	Forecast electric load in hour $t$ of day $d$ of year y	$P_{y, d, t}^{dt}$	Inverter input in hour $t$ of day $d$ of year y
$E^{'}$	Capacity of battery	$P_{y, d, t}^{h}$	Inverter output in hour $t$ of day $d$ of year y
$E_{\min}^{'}$	Minimum energy level of battery	$P_{y, d, t}^{ch}$	Battery charging in hour $t$ of day d of year y
$E^{int}$	Initial energy level of battery in $y = d = t = 0$	$P_{y, d, t}^{dch}$	Battery discharging in hour $t$ of day d of year y

Symbols	Acronyms	Symbols	Acronyms
A. Indices		$E^{l}$	Stand-by losses of the battery
$y$	Index of year	bd	Battery yearly degradation rate
$d$	Index of day	$π_{y, d, t}^{'}$	Price of electricity in hour $t$ of day $d$ of year y
$t$	Index of hour	$π_{y, d, t}$	Cost of electricity in hour $t$ of day $d$ of year y
B. Sets		$P_{\max}^{h} / P_{\min}^{h}$	Maximum/minimum capacity of the inverter unit
$Ξ^{T}$	Set of hours at each day of the scheduling horizon	$P_{\max}^{i n}$	Maximum allowable power import from the grid
$Ξ^{D}$	Set of days in each year	$P_{\max}^{e n}$	Maximum allowable power export to the grid
$Ξ^{Y}$	Set of years	$P_{\max}^{ch} / P_{\min}^{ch}$	Maximum/minimum charging rate for battery
C. Parameters		$η^{inv} η^{b}$	Efficiency of inverter/battery
$i$	Yearly interest rate	D. Variables
$A_{\max}$	Maximum allowable number of PV panels	A	Number of PV panels with power generation ${\overset{̅}{P}}_{y, d, t}$
$B_{\max}$	Maximum allowable number of batteries	$B_{y}$	Number of batteries with the capacity of $E^{'}$ in year y
$L T T^{p v}$	Lifetime of PV panels	${T B}_{y}$	Total usable storage capacity of the batteries in year y
${LT}_{n}^{b}$	Lifetime of battery	${S O C}_{y, d, t}$	Battery state of charge at each time
$C^{pv}$	Price of PV panel with power generation ${\overset{̅}{P}}_{y, d, t}$	$P_{y, d, t}^{i n}$	Import electricity from the grid in hour $t$ of day $d$ of year y
$C_{y}^{b}$	Price of battery with the capacity of $E^{'}$ in year y	$P_{y, d, t}^{e n}$	Export electricity to the grid in hour $t$ of day $d$ of year y
$C_{y}^{m P V}$	Annual maintenance cost per kilowatt of PV.	$P_{y, d, t}^{dmp}$	Dumped power in hour $t$ of day $d$ of year y
$C_{y}^{m B}$	Annual maintenance cost per kilowatt of Battery	$P_{y, d, t}^{ch}$	Battery Charging in hour $t$ of day d of year y
${\overset{̅}{P}}_{y, d, t}$	Forecasted power generation by each PV unit	$P_{y, d, t}^{v}$	Total PV generation in hour $t$ of day $d$ of year y
${\overset{̅}{L}}_{y, d, t}$	Forecast electric load in hour $t$ of day $d$ of year y	$P_{y, d, t}^{dt}$	Inverter input in hour $t$ of day $d$ of year y
$E^{'}$	Capacity of battery	$P_{y, d, t}^{h}$	Inverter output in hour $t$ of day $d$ of year y
$E_{\min}^{'}$	Minimum energy level of battery	$P_{y, d, t}^{ch}$	Battery charging in hour $t$ of day d of year y
$E^{int}$	Initial energy level of battery in $y = d = t = 0$	$P_{y, d, t}^{dch}$	Battery discharging in hour $t$ of day d of year y

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