The cluster DC voltage balancing control adopting zero-sequence voltage injection is appropriate for the star-connected cascaded H-bridge STATCOM because no zero-sequence currents are generated in the three-phase three-wire system. However

as the zero-sequence voltage is expressed in trigonometric form

traditional control methods involve many complicated operations

such as the square-root

trigonometric operations

and inverse tangent operations. To simplify cluster voltage balancing control

this paper converts the zero-sequence voltage to the

$dq$

frame in a DC representation by introducing a virtually orthogonal variable

and the DC components of the zero-sequence voltage in the

$dq$

frame are regulated linearly by proportional integral regulators

rather than being calculated from uneven active powers in traditional controls. This removes all complicated operations. Finally

this paper presents simulation and experimental results for a

$\mathbf{400}\ \mathbf{V}/ \pm \mathbf{7.5}$

kvar star-connected STATCOM

in balanced and unbalanced scenarios

thereby verifying the effectiveness of

the proposed control.