We show that the negative demand shock due to the COVID-19 lock-down has reduced net-demand system demand less the amount of energy produced by intermittent renewables and net imports that must be served by controllable generation units. Introducing additional intermittent renewable generation capacity will also reduce the net-demand, which implies the lock-down can provide insights about how electricity markets will perform with a large share of renewable generation capacity. We find that the lock-down induced demand shock in the Italian electricity market has reduced day-ahead market prices by 23 EUR/MWh (-45%) but re-dispatch cost have increased by 9 EUR/MWh (+103%) per MWh of load, both relative to the average to the same magnitude for the same time period in previous years. Relating the actual re-dispatch cost to a non-COVID-19 re-dispatch cost counter-factual derived from a deep-learning model estimated using pre-COVID-19 data yields an increase of 40%. We argue that the difference between these two re-dispatch cost increases can be attributed to the increased opportunities for suppliers with controllable units to exercise market power in the re-dispatch market in these low net-demand conditions. These results imply that an increased intermittent renewable energy share is likely to increase significantly the costs of maintaining a reliable grid because of the low levels of net-demand.