What is the role of inertia in the future grid?

This is a great question; I think of the Hornsea use case. Although the power transferred through renewables to the system is through power electronics, power electronics typically do not provide an inertial response to the grid. An example of this was August 9^, 2019, from the Hornsea Windfarm in the UK.

The Hornsea Project is an offshore wind farm located off the Yorkshire coast within the Hornsea Zone in the southern North Sea. During the evening rush hour, London and surrounding areas suffered a widespread power outage Friday, August 9, 2019. During the blackout, renewable generation was a significant portion of the overall contribution to the transmission system. Unfortunately, the lack of inertia coupled with improper settings on the wind farm did not correctly respond to the dip in frequency from the transient event. As a result, a cascading blackout occurred that dropped power to hundreds of thousands of people.

With renewables that have transient power output and power electronic sources, becoming the primary source of generation to the grid, grid flexibility is key to not simply having an after-action review after a blackout but to prevent outages in the first place. Dynamic controls coupled with a state estimator and real-time power flow tool will allow the grid to maintain a two-way power flow while assuring the generation matches the demand.

Paul, the relatively slow responding mechanical systems to which your refer are an asset, not a liability. The steady output of large power plants provides a stable basis for frequency and voltage that is unavailable from renewable sources of energy.

The much-anticipated "energy transition" to solar and wind is already accompanied by a corresponding transition to unreliability, and it will only get worse.

Building on the comments from Doug Houseman and Roger Arnold, there is definitely some consideration, and action, given to this issue, especially on smaller grids where inverter-based resources can make up a significant percentage of total generation at times.  I recalled hearing about a project in the UK, just in the last few years, that will specifically target the addition of inertia to the grid.  Here are a few links with more info: 

Giant flywheel project in Scotland could prevent UK blackouts

National Grid ESO - ’Cheaper and greener’ – the project that’s changing how we keep the grid stable

Additionally, there are also efforts to install equipment to monitor, and measure, grid inertia for decision making on dispatch/curtailment of inverter-based generation:

UK installs 5 MW ultracapacitor as ‘sonar’ to detect power grid inertia

Synchronous condensers (the generators at large retired power plants are a good example) can also help maintain far more than inertia. As the plants the transmission grid were designed around, the ability of the transmission grid to move power decreases, so leaving the generator in place as a synchronous condenser provides both ancillary services and increased transmission capacity (In the docket for DTE's IRP filling is a wonderful filing from ITC on this topic, please read that if you need more background).

I am not worried about how, I am worried about if people will pay enough attention to inertia. Pharma, computer chip making, some chemical processes, spot welding, and food manufacturing of some sorts are all sensitive to power quality, if we don't make it a priority in the transition, much of that manufacturing will be forced to go elsewhere, at a time where we are already struggling with supply chain issues and high quality jobs. 

Full sine-wave inverters can be designed to provide a degree of "synthetic inertia". In fact they can simulate infinite rotational inertia in their response to transients, if the transients are small. To do so, their DC inputs need to be buffered with enough capacitance to sustain bursts of power well above the steady-state rated power of the inverter. The inverter circuits must also be able to tolerate bursts of over-current without blowing out.

What an inverter can't do -- economically -- is to keep up its simulation of high rotational inertia for very long in the face of the kinds of transients that arise when re-making the connection to a black sub-grid. Synchronous condensers are probably a better option for that. A synchronous condenser is a free-spinning synchronous motor-generator. It provides true rotational inertia.