= Power inverter
A <power inverter> converts electrical <power> from a <direct current> input to an <alternating current> output. Its switches reverse or modulate the connection to the DC supply, while its control and filtering determine the output waveform. It transfers <energy> from its input; the switching operation itself is not an energy source. The DOE overview explains the switching-and-filtering principle and distinguishes equipment designed for independent operation from equipment relying on a grid reference.<Solar Integration: Inverters and Grid Services Basics by the U.S. Department of Energy>[What are Inverters?; Grid Services and Inverters]{ref}
An ideal <H-bridge> uses four controlled switches around a two-terminal load. One diagonal pair applies $+V_d$ across the load, and the opposite pair applies $-V_d$. In a stipulated square-wave mode with equal half-periods,
$$
v_o(t)=V_d\operatorname{sgn}(\sin\omega t).
$$
Its <root mean square> magnitude is $V_d$, but it is not sinusoidal. Its <Fourier series> is
$$
v_o(t)=\frac{4V_d}{\pi}\left(\sin\omega t+\frac13\sin3\omega t+\frac15\sin5\omega t+\cdots\right).
$$
The fundamental RMS magnitude is $2\sqrt2V_d/\pi$. Thus a $48\,\mathrm V$ input gives a $48\,\mathrm V$ RMS ideal square-wave output, but only about $43.22\,\mathrm V$ RMS in the fundamental. Equal total RMS does not imply equal waveform or equal response of every <electrical load>.
For a $12\,\Omega$ purely resistive load directly across this ideal square-wave output, mean <active power> is $V_d^2/R=192\,\mathrm W$. The fundamental contributes $8V_d^2/(\pi^2R)\approx155.63\,\mathrm W$ and the other <harmonic components> supply the remainder. The <harmonic active power sum> accounts for that difference. Adding a filter changes the circuit; the directly connected resistor calculation should not then be reused unchanged.
Rapid switching also permits averaged control. If a short switching interval applies $+V_d$ for fraction $d$ and $-V_d$ for the rest, its average output is $(2d-1)V_d$. Choosing $d(t)=(1+m\sin\omega t)/2$, with $0\le m\le1$, makes that local average sinusoidal. The actual waveform still contains switching components that the load and filter must handle.
A proposed low-voltage demonstration records DC input <electric potential difference> and <electric current>, output waveform and load <electric current>, comparing average input and output <power>. Output <frequency>, total RMS, fundamental RMS and waveform distortion answer different questions. For <islanded microgrid operation>, control of a usable local supply is an additional capability, not a consequence of DC-to-AC conversion alone.
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