Marginal value (which is the relevant measure) of Hydro is not zero, because the used water has a potential value in the future when it could have been used instead. Hydro plants calculate a monetary value of the water based on a guess on future prices where the water could have been used, in addition to all kind of other smaller factors (like increased maintenance cost of shutting of, and legal requirements for minimal water in the rivers, etc). And then they bid based on this.
Any power-source which can move its production has this feature, independently of renewability.
But if you have some points in time where all the energy is delivered by intermittent power-sources, and there is insufficient power lines to transport this power elsewhere, prices can to 0, and if too much power is offered, the price becomes negative, and power producers has to pay to push in power. This is not just theoretical, it has happened in the European power market. But the equilibrium still exists. And because there are some costs associated with turning them off, it does not actually drop immediately to 0 production at negative prices.
Any power-source which can move its production has this feature, independently of renewability.
But if you have some points in time where all the energy is delivered by intermittent power-sources, and there is insufficient power lines to transport this power elsewhere, prices can to 0, and if too much power is offered, the price becomes negative, and power producers has to pay to push in power. This is not just theoretical, it has happened in the European power market. But the equilibrium still exists. And because there are some costs associated with turning them off, it does not actually drop immediately to 0 production at negative prices.