In this article, we use a spectral and statistical analysis of load fluctuations to calculate plausible conditions that an electricity mix of power sources must satisfy to fulfill a variable power demand on a territory. These criteria can be applied to electricity mixes with a variable composition in controlled (dispatchable) and mandatory (non-dispatchable) sources in order to derive the maximum amount of mandatory fluctuating sources that can be tolerated in the mix if frequent power cuts are to be avoided. These criteria take into account the intermittent nature of the production of the mandatory renewable sources. Incorporated in the MIXOPTIM software, the three criteria can be used to assess the respective merits of the controllable power sources (e.g., coal, gas, nuclear, ... according to their agility, and what would be gained if this agility could be improved. These criteria take into account the influence of interconnection between the considered territory and its neighbors, and allows one to calculate to what extent an increase of the interconnection capacity increases the physically allowable proportion of renewable power sources in the mix. They also make it possible to evaluate the beneficial influence of demand smoothing, and of electricity storage facilities, and to calculate to what extent the introduction of demand smoothing or storage facilities move the physical limits of introduction of renewable mandatory fluctuating sources in the mix. We also investigate how these physical limits evolve if the renewable fluctuating sources are no longer considered as mandatory, and become controlled sources, with curtailment of their excess output when this excess power is not needed. This paper is devoted to the description of this methodological toolbox, a separate paper is devoted to its application to the French mix.