= Power-rating limit versus energy autonomy in a microgrid
<Power-rating limit versus energy autonomy in a microgrid> distinguishes how much electrical <power> can be delivered at an instant from how long a specified demand can be sustained. A storage output rating has units of <watts>; available output <energy> has units such as <joules> or watt-hours. Their quotient is a duration only when the output boundary and discharge assumptions agree.
For an original constant-deficit model, let $P_d$ be the remaining <electrical load> plus losses after other generation, and let $E_o$ be usable storage <energy> measured at the output. A necessary operating condition and the corresponding duration are
$$
0<P_d\le P_{\max},\qquad T=\frac{E_o}{P_d}.
$$
A store with $P_{\max}=40\,\mathrm{kW}$ and $E_o=70\,\mathrm{kWh}$ supports a $35\,\mathrm{kW}$ deficit for two hours under these assumptions. A $65\,\mathrm{kW}$ deficit is infeasible immediately, even though dividing $70$ by $65$ gives a positive duration. That quotient cannot override the output constraint.
Variable demand adds a cumulative constraint. For discharge-only output $P_d(t)\ge0$, the conditions become
$$
P_d(t)\le P_{\max}(t),\qquad
\int_0^T P_d(t)\,dt\le E_o.
$$
Suppose $P_{\max}=40\,\mathrm{kW}$ and $E_o=20\,\mathrm{kWh}$. A demand of $30\,\mathrm{kW}$ for ten minutes followed by $10\,\mathrm{kW}$ for ninety minutes consumes exactly $20\,\mathrm{kWh}$ and respects the rating. Replacing the first interval by $60\,\mathrm{kW}$ for five minutes leaves the same <energy> demand but violates the rating. Equal energy budgets need not imply equal feasibility.
If storage <energy> $E_s$ is specified before conversion and a constant discharge fraction $\eta$ reaches the output, then $E_o=\eta E_s$; do not apply that factor again when $E_o$ is already an output quantity. Charging, temperature, state-dependent ratings and reserve requirements require a more detailed model.
The DOE overview's controller and component diagram supplies the physical context: generation, storage and connected <electrical loads> must operate together.<Microgrid Overview by the U.S. Department of Energy>[Printed pp.1–2, key components and Figure 1; printed p.4, peak-load design considerations]{ref} A proposed <islanded microgrid operation> test therefore includes both a short high-demand interval and a sustained demand interval. Record unmet demand as well as discharged <energy>, so a long runtime obtained by disconnected loads is not mistaken for delivery of the originally requested service.
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