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The drive to net zero energy requires high renewable penetration but most renewables are either affordable or dispatchable but not both. Thermochemical energy storage integrated into concentrating solar power plants can enhance dispatchability and solar-to-electricity efficiency. Combining these technologies with lower cost photovoltaic plants exploits synergies related to dispatchability and costs. However, this combination leads to complex interactions between the different power plant components and requires sophisticated design guidelines to simultaneously achieve low costs and high dispatchability. Here, we develop multi-objective optimisations and guidelines for the design of hybrid solar power plants with a calcium-looping thermochemical energy storage system. The presented tools focus on the optimisation of the design and operation of hybrid power plants with respect to competing technical and financial performance metrics. First, the design optimisation stage evaluates ten design variables and three objectives. Then, the operational optimisation stage, which is nested inside the design stage, finds the best one-year hourly operational strategy for each configuration considered in the first stage. We evaluated three case studies with different solar resource: Seville (Spain), Tonopah (United States), and the Atacama Desert (Chile). The best dispatchable hybrid solar power plant with Levelised cost of electricity of 123 USD ⋅ MWh−1 and a capacity factor of 73% is reached for the Atacama Desert, which has the best solar resource. The optimisation results are used to develop guidelines for the optimal design of dispatchable hybrid solar power plants with calcium-looping based on the given solar resource and required dispatchability. These guidelines provide an initial design for affordable and dispatchable hybrid solar power plants and can enable their widespread deployment. • Developed a multi-objective optimisation framework for the design and operation of hybrid solar power plants with thermochemical energy storage based on calcium-looping process. • Multi-objective design optimisation is crucial to achieving low cost and high dispatchability of solar energy technologies. • Optimal dispatchable designs in the Atacama Desert reach capacity factors of 73%. • Developed guidelines for the optimal design of hybrid solar power plants based on the solar resource and required dispatchability. • Provided tools to exploit synergies in technology integration to support the transition to a clean energy system. [ABSTRACT FROM AUTHOR]