What is a doubly-fed induction generator (DFIG)?
Working principle
A doubly-fed induction generator is a wound-rotor induction machine whose stator is connected straight to the grid while the rotor is fed through slip rings by a back-to-back converter. The converter injects a voltage at the slip frequency, so the stator always sees the grid frequency, whatever the speed. Per phase, V_r/s = (R_r/s + jX_r)·I_r − E: the rotor voltage is proportional to the slip s, which is why the converter can be small.
Sub- and super-synchronous operation
With slip s = (n_s − n)/n_s, the rotor power is P_r ≈ −s·P_s and the total power to the grid is P ≈ (1 − s)·P_s. Below synchronous speed (s > 0) the rotor absorbs power from the grid through the converter; above it (s < 0) the rotor delivers power too, so the machine can put out more than its stator rating. At synchronous speed the rotor current is DC and the rotor power is zero. A converter of 25–30 % of the machine rating covers about ±30 % speed.
Wind turbine control
The turbine power is P = ½·ρ·A·v³·Cp(λ, β), with the tip-speed ratio λ = ω·R/v. Below rated wind the blades are flat (β = 0) and the maximum-power-point tracker sets the speed that keeps λ at its optimum, near 8, so the speed rises with the wind. Once the speed limit and the rated power are reached, the blades pitch out of the wind to cap the power. Between the cut-in and cut-out wind speeds the turbine runs; outside that window it is parked.
Reactive power and grid support
The rotor current has to supply the magnetising current the stator does not, so the converter controls the stator reactive power (and active power) through the rotor d- and q-currents. The machine can deliver or absorb reactive power to hold the grid voltage, within the converter’s voltage and current limits. When the set-point asks for more than the converter allows, the reactive power is limited first and then an overload is flagged. The grid-side converter usually runs at unity power factor.
Frequently asked questions
- Why can the converter be rated at only about 30 % of the machine?
- Because it only carries the slip power. The rotor voltage is proportional to the slip and the rotor active power is about s times the stator power, so over a ±30 % speed range the converter handles at most about 30 % of the rated power. A full-power converter, as in a synchronous-generator turbine, must handle all of it, which makes it larger, costlier and lossier.
- What happens at synchronous speed?
- The slip is zero, so the rotor voltage is almost zero and the rotor current is DC, like the excitation of a synchronous machine. The rotor power is zero and changes sign there: the rotor absorbs power below it and delivers power above it. Staying long at this point heats the converter unevenly, because one phase carries most of the DC current, so turbines usually pass through quickly.
- Why does the turbine pitch its blades above rated wind?
- Wind power rises with the cube of wind speed, but the generator and converter have a fixed rating. Pitching the blades lowers the power coefficient Cp, so the turbine captures only the rated power while the speed is held at its limit. Below rated wind the blades stay flat and the tracker maximises Cp instead.