Does zero instantaneous reactive power guarantee zero reactive power under asymmetric voltage condition?

The instantaneous reactive power concept has attracted much attention since its proposal. It has been claimed that reactive powers can be compensated instantly without energy storage system under asymmetric voltage condition, which received doubts from some authors. However, theoretical criticism has not been given clearly. In this paper, theoretical criticism and example are given to show that zero instantaneous reactive power does not mean zero reactive power under asymmetric voltage condition.