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Modern power systems are facing the tremendous challenge of integrating vast amounts of variable (non-dispatchable) renewable generation capacity, such as solar photovoltaic or wind power. In this context, the required power system flexibility needs to be allocated in other units that can include energy storage, demand management or providing reserve from renewables curtailing the output power. The present paper proposes the new concept of grid-forming load, which can be considered a totally flexible concept of demand. The concept is not only ensuring the load is supporting the grid stability by adapting the load to the overall system balancing, but also ensures that the load is actually contributing to form the grid and to provide synchronization power to the overall system. In this sense, the new concept allows running a system powered only by renewables operating at maximum power (or operator defined set-point) in grid-following mode, while the overall system control is ubicated in the demand side. This is an important change of paradigm as it considers that all the flexibility, synchronism and stability provision is on the demand side. This concept can applied either to isolated systems or also to future power systems, where millions of loads steer the power system while the renewables are operating at full power. The paper proposes the concept, suggests possible control implementations of the grid-forming load and analyses the concept in four simulation case studies.