The heat that would have been required in each slot to keep the tank at
least at its comfort floor, for any compressor schedule: the static
schedule's counterpart of attr(result, "unmet_heat_kw") of
add_tank_optimization(), which uses this same function. Per slot of dt
hours, with the level S following get_tank_level() (it stops at 0, the
inlet temperature), Smin = Tcap * SOCmin / 100, k = (1 - loss/100)^dt
and S~[t] = k * S[t-1] + (cop[t] * power[t] + backup[t] - heat_demand[t]) * dt the level the balance asks for:
Usage
get_tank_unmet_heat(
power,
heat_demand,
cop,
init,
Tcap,
SOCmin,
loss = 0,
time_resolution = 60,
backup = 0
)Arguments
- power
numeric vector, compressor electric power (kW), such as the result of
add_tank_optimization()- heat_demand
numeric vector, heat demand (kW thermal)
- cop
numeric vector, coefficient of performance (heat per electric kWh)
- init
numeric, level before the first slot (in kWh, not %)
- Tcap
numeric, tank capacity (kWh thermal, > 0), as in
add_tank_optimization(): the heat between the inlet water temperature and the top of the tank- SOCmin
numeric, comfort floor (%, between 0 and 100)
- loss
numeric, standing loss of the level (% per hour)
- time_resolution
numeric, time resolution of the time-series (in minutes)
- backup
numeric, backup heater power (kW electric = kW thermal):
attr(result, "backup_kw")ofadd_tank_optimization(), or 0 without a backup heater
Details
unmet[t] * dt = max(0, min(Smin, k * S[t-1]) - S~[t])
that is the heat the tank gives from below its comfort floor, plus the
demand it cannot serve at all at the inlet temperature. It is positive
while the level falls below the floor, and 0 while the level stays at or
above it or rises back towards it; standing losses below the floor are not
counted, and neither is a slot whose gap is within half a rounding step of
the power (0.005 * max(cop, 1) * dt kWh).