Virtual circuit control for active damping of LCL resonance in grid-connected voltage source converters

A comparison of virtual circuit-based control designs for half-bridge converters with LCL output filters

“…The latter type of relation can also be shown to hold for the average system behaviour over the control interval [13], i.e.…”

“…whereby x k = x(kT s ), the filter state as sampled at the end of each control interval. These discrete-time models can be derived from continuous-time descriptions [13]. Moreover, it is assumed that any measurement y can be written as the linear combination of the state and the input vectors, i.e.…”

“…of which the corresponding matrices for the control law in (9) are shown in Table I. The virtual inductance and resistance can be designed from [13]…”

Systematic control design for half-bridge converters with LCL output filters through virtual circuit similarity transformations

“…3, v conv,vc or i r,vc are selected respectively. In the condition above, it can be shown that a solution to (18) is found by solvinḡ…”

“…Converter-Side Inductor (Circuit B) 1) Control law: The controller in (18) aims to control i 1 to behave closely to i r,vc in circuit B, which can be written as…”