Economic Dispatch and Frequency Control

There is no grid-scale storage, so any surplus or deficit flows into or out of the kinetic energy of the rotating machines — which changes their speed. Frequency is therefore a direct readout of the supply-demand balance, identical everywhere on a synchronised system.

That broadcasts the balance to every machine with no communication at all. A governor watching its own shaft speed is watching the state of the entire grid, which is what makes a synchronous system coordinate itself.

A governor reduces its speed setpoint as output rises — droop, typically 4%. Without it, two machines each trying to hold exact frequency would fight for the whole load. Droop makes them share proportionally.

It is proportional control, so it leaves a deliberate steady-state error: after a disturbance the frequency settles slightly off nominal, and something else must restore it.

Primary plus secondary is a PI controller operating across an entire country. Each layer also restores the reserve the layer before it consumed, which is why the third exists at all.

Frequency control keeps the balance; it says nothing about which generators supply it. Marginal costs vary by a factor of five across a fleet, and the obvious rule — fill the cheapest unit before starting the next — is wrong.

Each unit's incremental cost dC/dP rises with its own output, so beyond some point the next megawatt is cheaper elsewhere. The optimum equalises dC/dP across every running unit: if one were lower, shifting output to it would save money.

Equal incremental cost, not equal average cost, and not cheapest-first. That distinction is the entire content of the classical dispatch problem.

Transmission losses depend on where power is generated relative to where it is consumed, so a distant cheap unit's delivered cost exceeds its generation cost. Penalty factors weight each unit's incremental cost accordingly, equalising cost at the load rather than at the terminals.

That is the physical basis of locational marginal pricing in electricity markets — the location of a generator genuinely changes what its output is worth.

Deciding which units run at all is a harder, separate problem: start-up costs and times, minimum up and down times, and a spinning-reserve requirement sized for the largest single credible loss.

It is a day-ahead integer optimisation, within which economic dispatch is the easy continuous part. Renewable forecast error has made commitment considerably harder than demand uncertainty ever did — the uncertainty is now larger and less predictable.