1. Model DescriptionΒΆ
val-tab shows all the details for the used variables.
{table} Variables used for mathematical description :name: val-tab
symbols of variables |
unit |
definition |
description |
|---|---|---|---|
\( x_{{th}_{j,t}} \) |
non -negative real |
thermal energy fed into the grid |
|
\( Cap_{j} \) |
non -negative real |
capacity |
|
\( Cap_{{nom}_{j}} \) |
non -negative real |
normative capacity |
|
\( x_{{el}_{j,t}} \) |
non -negative real |
electrical energy fed into the grid |
|
\( P_{{el}_{max}} \) |
non -negative real |
maximum electrical power |
|
\( x_{{load}_{hs,t}} \) |
real |
optimization variable depending on the load of heat storages, time-dependent |
|
\( Cap_{hs} \) |
non -negative real |
capacity of heat storage |
|
\( storelevel_{{hs}_{t}} \) |
non -negative real |
storage level of heat storage, time-dependent |
|
\( ramp_{{j}_{chp,t}} \) |
non -negative real |
ramp function, chp (combined heat and power) and time-dependent |
|
\( ramp_{{j}_{waste,t}} \) |
non -negative real |
ramp function, waste and time-dependent |
|
\( coldstart_{j,t} \) |
boolean |
cold start, time-dependent |
|
\( Activate_{j,t} \) |
boolean |
||
\( Activate_{{2}_{j,t}} \) |
binary |
||
\( Activate_{{3}_{j,t}} \) |
binary |
In param-tab, the parameters are mentioned and described.
{table} Parameters used for mathematical description :name: param-tab
symbols of parameters |
unit |
definition |
description |
|---|---|---|---|
\( demand_{{th}_{t}} \) |
thermal demand, time-dependent |
||
\( temp_{river} \) |
temperature of river water |
||
\( temp_{ww} \) |
temperature of waste water |
||
\( temp_{flow} \) |
flow temperature |
||
\( temp_{return} \) |
return temperature |
||
\( temp_{ambient} \) |
ambient temperature |
||
\( radiation \) |
solar radiation |
||
\( max_{demand} \) |
maximum demand |
||
\( potential_{j} \) |
potential of the heat generator j |
||
\( pow_{{cap}_{j}} \) |
|||
\( radiation_{t} \) |
radiation, time-dependent |
||
\( IK_{j} \) |
|||
\( OP_{{fix}_{j}} \) |
|||
\( n_{{el}_{j}} \) |
electrical efficiency of heat generator j |
||
\( elPrice_{jt} \) |
electricity price for heat generator j , time-dependent |
||
\( P_{{min,el}_{chp}} \) |
minimum electrical power of chp |
||
\( Q_{{min,th}_{chp}} \) |
minimum thermal energy of chp |
||
\( ratio_{{P,max}_{FW}} \) |
ratio of maximum power for FW |
||
\( ratio_{P,max} \) |
ratio of maximum power |
||
\( mc_{jt} \) |
|||
\( n_{{th}_{jt}} \) |
thermal efficiency of heat generator j, time-dependent |
||
\( hp_{{restrictionfactor}_{jt}} \) |
restriction factor of heat pump of heat generator j, time-dependent |
||
\( nom_{{p}_{th,j}} \) |
|||
\( min_{{p}_{th,j}} \) |
|||
\( x_{{th}_{cap,j}} \) |
|||
\( lt_{j} \) |
|||
\( ec_{j} \) |
|||
\( ir \) |
|||
\( \alpha_{j} \) |
|||
\( load_{{cap}_{hs}} \) |
load capacity of heat storage |
||
\( unload_{{cap}_{hs}} \) |
unload capacity of heat storage |
||
\( n_{hs} \) |
efficiency of heat storage |
||
\( loss_{hs} \) |
losses of heat storage |
||
\( IK_{hs} \) |
IK of heat storage |
||
\( cap_{hs} \) |
capacity of heat storage |
||
\( c_{{ramp}_{chp}} \) |
|||
\( c_{{ramp}_{waste}} \) |
|||
\( c_{{coldstart}_{j}} \) |
|||
\( \alpha_{hs} \) |
|||
\( rf_{j} \) |
|||
\( rf_{tot} \) |
|||
\( OP_{{var}_{j}} \) |
|||
\( temperature_{t} \) |
time-dependent temperature |
||
\( sale_{{electricityprice}_{jt}} \) |
|||
\( OP_{{fix}_{hs}} \) |
|||
\( mr_{j} \) |
|||
\( em_{j} \) |
|||
\( pco2 \) |
\(CO_2\) price |
||
\( cap_{{losse}_{hs}} \) |
capacity losses of heat storages |
||
\( n_{{th}_{nom,jt}} \) |
thermal, normative efficiency of heat generator j, time-dependent |
||
\( restricitionfactor_{th} \) |
thermal restriction factor |
||
\( min_{{out}_{factor,j}} \) |
minimum output factor of heat generator j |