Virtual synchronous machines with improved voltage and frequency control

Electrical apparatus (20) includes an inverter (24) having input terminals for receiving DC input power and output terminals for coupling to an AC power grid. A pulse-width modulation (PWM) generator and drivers (26) drive the switches so as to control respective amplitudes, frequencies, and phases of the output current waveforms of the inverter. Control circuitry (28) receives measurements of respective time-varying voltages and currents on the input and output terminals, computes a model (40) that includes three virtual currents flowing in a synchronous machine that is emulated by the apparatus, wherein the three virtual currents are associated respectively with the three output current waveforms, and controls the PWM generator and drivers responsively to the three virtual currents so as to synchronize the amplitudes, frequencies, and phases of the three output current waveforms of the inverter with the three phases of the AC power grid.