This paper addresses the short-term operation planning of a concentrated solar power (CSP) plant equipped with a backup fuel boiler and operating in the Spanish day-ahead electricity market. The problem is formulated as a mixed-integer linear programming model. Forecasted values of electricity prices and direct sun irradiation are considered. The main concern in the problem is to set an optimal use of the backup system in order to increase power generation and maximize the profits. Interaction between the solar and fuel heated systems is considered through heat balance constraints while parameters referring to the boiler are independent from the rest of the system allowing various types of boilers to be tested. A realistic case study provides results of a CSP plant operating a) without boiler, b) with a natural gas boiler and c) with a biomass boiler. Results demonstrate the advantages of the proposed model.