Passive virtual synchronous machine with bounded frequency and virtual flux

A controller to operate a power electronic converter as a virtual synchronous machine, the power electronic converter having an LC filter consisting of a converter-side inductor and a capacitor, the controller comprising:

• a real power-frequency channel that generates a frequency signal based on a real power set-point, a negative real power feedback signal, a frequency offset signal, and a frequency reference;
• a reactive power-flux channel that generates a flux signal based on a reactive power set-point, a negative reactive power feedback signal, a flux offset signal, and a flux reference;
• an interconnection block that:
• generates sinusoidal and cosinusoidal signals with their frequency being the same as the frequency signal,
• expands the sinusoidal and cosinusoidal signals into sinusoidal and cosinusoidal vectors consisting of equally spaced sinusoidal and cosinusoidal signals corresponding to a number of phases of the power electronic converter, and
• generates a VSM voltage, a signal {tilde over (T)} and a signal {tilde over (Γ)} based on the frequency signal, the flux signal, the sinusoidal and cosinusoidal vectors, and an input current, wherein the signal {tilde over (T)} and signal {tilde over (Γ)} are fed through a conversion block and through respective passive filters to generate the negative real power feedback signal and the negative reactive power feedback signal;
• and
• a virtual damper that generates an output voltage that is used as a control signal for the power electronic converter after Pulse-Width-Modulation (PWM) based on the VSM voltage and a measured voltage;
• wherein the real power-frequency channel includes a first block that converts a sum of the real power set-point and the negative real power feedback signal into a frequency command, after adding the frequency offset signal to it, for an inner frequency tracking loop that tracks the frequency command and generates a frequency addition signal to be added to the frequency reference to form the frequency signal, and
• wherein the reactive power-flux channel includes a second block that converts a sum of the reactive power set-point and the negative reactive power feedback signal into a flux command, after adding the flux offset signal to it, for an inner flux tracking loop that tracks the flux command and generates a flux addition signal to be added to the flux reference to form the flux signal.