PW-E1 · Renewables and the grid

Connecting solar and wind: an inverter has no inertia

The power system so far has assumed large synchronous generators doing the turning. Solar produces DC and wind produces AC whose frequency follows the wind, so both are connected to the grid through inverters, and an inverter has almost none of the inertia that a synchronous machine's rotating mass provided. Drag the renewable share yourself and you can confirm that the less inertia there is, the faster and deeper the frequency falls after the same disturbance.

Drag the renewable share and read the frequency

The curve shows how the grid frequency changes over time right after one generator trips off. Drag the handle on the lower bar to raise the renewable share: synchronous machines drop out, the system inertia shrinks, and even for a disturbance of the same size the frequency falls more steeply and its lowest point goes deeper. When that lowest point drops below the green dashed line, the underfrequency load-shedding threshold of 59.43 Hz, the curve turns red and load shedding is triggered. In this figure that happens once the renewable share passes about 46%.

Drag the lower handle left and right to change the renewable share.

Frequency right after the disturbance (60 Hz system)

nadir ≈ 59.50 Hz   RoCoF ≈ 0.39 Hz/s

Within range

r ≈ 20%   H ≈ 4.6 s

The inverter stands in between

A synchronous generator is connected directly to the grid, so its rotor turns as one with the grid frequency. Solar, however, produces DC, and many wind turbines produce AC whose frequency changes with the wind, so neither can be connected as is to a 60 Hz grid. An inverter, a power-electronic device, therefore sits in between and rebuilds that output to match the grid's frequency, voltage and phase before pushing it in. An inverter is a smart device that measures the grid and keeps itself synchronized, but the very property of separating the energy source from the grid is what makes the inertia disappear.

Inertia holds the frequency up

The grid frequency is the needle that shows the balance between generation and load. When generation suddenly falls short the frequency drops, and its initial rate of fall, RoCoF = ΔP/2H, is inversely proportional to the system's inertia constant H. The heavy spinning rotor of a synchronous generator holds kinetic energy ½Jω², and at the moment of a disturbance it releases that energy automatically, holding the frequency up so it falls slowly. An inverter electronically decouples its energy source (sun, wind or battery) from the grid frequency, so unless extra control is added it does not deliver this inertia.

ObserveH_inv ≈ 0

An inverter's own inertia is nearly 0.

ChooseRoCoF = ΔP / ?

The rate of frequency change is inverse to inertia.

Fill inr ↑ → H ↓ → RoCoF ?

More renewables means less inertia and a larger RoCoF.

On your ownH ↓ → nadir ?

The lower the inertia, the lower the frequency nadir.

What low inertia costs

As the renewable share rises and displaces synchronous machines, the system inertia shrinks, and the same generation loss makes the frequency fall faster (RoCoF↑) and deeper (nadir↓). In the figure, raising the share from 0% to 90% cuts the inertia constant H from 5.6 s to 1.1 s, makes RoCoF grow about fivefold from 0.32 to 1.64 Hz/s, and lowers the nadir from 59.53 Hz to 59.13 Hz. If the frequency falls too far, underfrequency load shedding must deliberately cut load to prevent collapse, and if even that is not enough, the result is a wide-area blackout. The remedies are to add synthetic (virtual) inertia control to inverters so they imitate inertia, to add the fast frequency response of batteries, and to keep synchronous condensers on the grid. This shortage of inertia is the central engineering challenge of the renewable transition.

Back to the first screen

The disturbance stayed the same size, yet as the renewable share went up the frequency curve fell more steeply and its lowest point went deeper, and at about half the curve dropped below the green dashed line and turned red. What changed was not the disturbance but the amount of rotating inertia available to absorb the shock. An inverter synchronizes smartly with the grid, but it has no heavy rotor like a synchronous machine, so it cannot supply the inertia that holds the frequency up. Moving to renewables brings clean energy but leaves the task of restoring this inertia, and that task leads into the stability story of the next unit.

Solar and wind grid connection: renewables connect to the grid through inverters (power electronics), not synchronous generators, and actively synchronize their output to the grid's frequency and phase. The key difference is inertia. The rotating mass of a synchronous machine slows frequency changes with its kinetic energy (RoCoF = ΔP/2H), but an inverter's inertia is ≈0. The higher the renewable share, the less inertia, so the same disturbance gives RoCoF↑ · nadir↓, and synthetic inertia and fast frequency response are the remedies.

The next step

Having opened the topic of inertia and frequency, the final unit (PW-E2) brings system stability and frequency together. The supply-demand balance sets the frequency, and after a disturbance inertia first slows the fall, then the governor stops it and automatic generation control returns the frequency to 60 Hz. In this figure, too, the curve does not come all the way back to 60 Hz but settles a little below, because only the governor acts. The unit also covers transient stability, where on the power-angle curve from D1 an angle widened by a fault that passes the equal-area condition makes a generator lose synchronism, and every piece so far fits into one picture called stability.