Recent research has shown that generation self-scheduling in electricity markets can be approached using conditional value-at-risk (CVaR). This study considers a worst-case CVaR methodology applicable to cases where only partial information on the underlying probability distribution of prices is given. In particular, the probability distribution is considered under box and ellipsoidal uncertainty structures. It is shown that both structures result in self-scheduling problems that can be formulated as a quadratic cone program. The cone program can be used to (i) compute the worst-case conditional robust profit with probability level ?? and (ii) optimise the self-schedule for a pre-specified probability ?? of the corresponding worst-case conditional robust profit. Simulation results are used to demonstrate the self-scheduling model based on the worst-case CVaR. The usefulness of the proposed model is established by contrasting it with the CVaR approach.