Energy delivered from storage

What this step does

With AC coupling, the AC energy the battery delivers to the grid connection, metered after the discharge loss. It acts on the grid energy. With DC coupling the row is replaced by Change at the POI from storage.

The math

1. The row on the running total
2. Clip capture and daily full cycle, in a scheduled hour
3. Timed discharge, inside the window

$$E_{after} = E_{before} + \frac{E_{dis}}{P_{DC}},\qquad E_{dis} = \sum_i d_i\,\eta_d\,\Delta t \tag{1}$$ $$d_i = \min\!\left(P_{avail,i},\ \frac{P_{bat}}{\eta_d},\ \frac{P_{tgt} - p_i}{\eta_d}\right) \quad \text{when } p_i \le P_{tgt} \tag{2}$$ $$d_i = \min\!\left(P_{avail,i},\ \frac{P_{win}}{\eta_d}\right), \qquad P_{win} = \min\!\left(P_{bat},\ \frac{(S_{win} - S_{lo})\,\eta_d}{t_{win}}\right) \tag{3}$$

where

Symbol	Meaning	Unit
$E_{after}$	the running total after this row	kWh/kWp
$E_{before}$	the running total before this row	kWh/kWp
$E_{dis}$	the energy delivered	kWh
$P_{DC}$	the system DC nameplate	kWp
$d_i$	the power drawn from the cells at timestep $i$	kW
$\eta_d$	the discharge efficiency: one minus half of the round-trip loss, times the AC conversion efficiency	—
$\Delta t$	the length of one timestep	h
$P_{avail,i}$	the stored energy above the floor at timestep $i$ divided by $\Delta t$	kW
$P_{bat}$	the battery's power rating: it caps the power delivered on discharge and the power stored in the cells on charge	kW
$P_{tgt}$	the interconnect target (storage.interconnect_limit_kw): the grid injection above which clip capture charges and up to which the battery discharges	kW
$p_i$	the system's grid injection before the battery at timestep $i$	kW
$P_{win}$	the flat power of the window, fixed at its first hour	kW
$S_{win}$	the stored energy at the start of the window's first hour (the end of the hour before it)	kWh
$S_{lo}$	the floor of the state-of-charge window	kWh
$t_{win}$	the window length	h

Reading the number

A gain, positive. It is the charged energy less the conversion losses and the change in stored energy, about 87 % of Energy diverted to storage at the default 88 % round-trip efficiency and a 98 % AC conversion efficiency. Few discharge hours, or a target that leaves little room below it, make it small. Rooftop systems follow the same proportions.

References

1. DiOrio, Dobos & Janzou 2015, "Technoeconomic Modeling of Battery Energy Storage in SAM", NREL/TP-6A20-64641

API

storage.discharged

Symbols follow the symbol registry.