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In a deregulated power industry, power producing companies bid in the hour-ahead and day-ahead power markets in an attempt to maximize their profit. For a successful bidding strategy, each power-producing company has to generate bidding curves derived from an optimal self-schedule. This self-schedule is commonly obtained from a profit-maximizing optimal power flow model based on predicted locational marginal prices (LMPs). However, at the time of self-scheduling, the predicted values of the LMPs are largely uncertain. Therefore, it is desired to produce robust self-schedules that can be used to lessen the risk resulting from exposure to fluctuating prices. In portfolio optimization theory, methods of risk management include Value-at-Risk (VaR) and conditional Value-at-Risk (CVaR). CVaR is known to be a more consistent measure of risk than VaR. In fact, whilst CVaR is the mean excess loss, the VaR provides no indication on the extent of losses that might be suffered beyond the amount indicated by this measure. This research proposes a method for robust self-scheduling based on CVaR. It will be shown that polynomial interior-point methods can be used to obtain the robust self-schedules from a second-order cone program. The obtained schedules provide a compromise solution between maximum profit and minimum risk. Simulation results on a standard IEEE bus test system will be used to demonstrate the scheduling model based on CVaR.