You should think of a DFIG as a synchronous motor and not an induction generator. The difference between an DFIG and conventional synchronous generator is that unlike a conventional synchronous generator, the field of a DFIG has AC instead of DC exciting it. The name Doubly Fed Induction Generator is a bit misleading.
The machine itself is a wound rotor induction motor. In an induction motor (or generator), the rotor currents are induced by the stator. The rotor circuit is passive in the sense that it is only reacting to the stator flux and the slip. The rotor circuit is absorbing energy, either with a resistor or a energy recovery inverter. In an induction motor there is slip. It can only be a motor below synchronous or a generator above synchronous.
To make a DFIG out of a wound motor, the rotor is instead actively fed by a stiff voltage from the inverter. The flux produced by the applied rotor voltage summed with the rotor speed will always be at synchronous speed. So in your example of 850 RPM on a 1500 RPM DFIG, the inverter would produce 21 2/3 Hz so the 850 RPM rotor is summed with a 650 RPM rotor flux to get a air gap speed of 1500 RPM to match the stator flux. There is no "slip" because the to fluxes are locked into synchronism.
Whenever the speed is below synchronous the inverter is actually supplying energy to the rotor to sum with the speed of the rotor. That extra power required flows out the stator and is looped back through the inverter. At synchronous the inverter is only feeding DC, the energy is very low. Above synchronous the rotor is absorbing power and the inverter exports power to the grid.
As I alluded before, the inverter is very expensive so there is an attempt to make it as economical as possible. The way to do this is to minimize the current the inverter has to handle, and the way the current is minimized is to have as many turns on the rotor as the possible which means the same rotor flux can be produced by a lower inverter current.
I don't know what the voltages are on the machine of your example, but I'll throw out a hypothetical example. Let's say the stator voltage is 3.3kV, and the inverter runs at 690V on your 2MW machine. And further let's use the number of 1950 RPM as the maximum speed. At 1950 RPM, the machine exports 77% (1500/1950) of the power through the stator and 23% through the rotor and inverter. Now the lowest possible rotor and inverter current in that scenario is to have 690V at the rotor terminals at 1.3 times base speed. This is done by giving a rotor with 69.7% of the turns of the stator (690V/(1.3-1)=2400V; 2400V/3300V=0.697). Less turns on the rotor would mean more current and less than 690V at 1950 RPM. Above 1.3 times base speed the voltage would rise above 690V and the machine would have to shut down for over-voltage on the inverter.
Below the 1500 RPM base speed, the same limit would apply. Right at 1500 RPM, there is no (AC) rotor voltage (just the DC for the IR drop in the rotor). As the speed drops, the rotor voltage rises until at 0.7 of base speed or at 1050 RPM the inverter voltage is back at 690V again. Going any slower increases the voltage, until stall the full 2400V would be at the rotor. Since the inverter can only take 690V, operation below 1050 RPM isn't allowed. To prevent catastrophic failure of the inverter, line voltage must not be applied until the rotor is spinning at 1050 RPM.
Below the 1050 RPM point, the stator is disconnected from the line and shorted. In this configuration, the generator is now an induction machine, connected through the inverter to the line. Normally this is only used for startup to motor the turbine up to cut-in speed or to brake the turbine on shutdown.
The 'trick' of switching from delta to star extends the minimum speed lower. When the stator is in star connection, only 1/sqrt(3) or 57% of line voltage is applied to the each stator winding. The flux drops by 57%, and the matching rotor voltage drops by 57%. The rotor can slow down more until the inverter would hit rated voltage. In the hypothetical design, the stator would have 1905V per winding; at 1050 RPM the rotor voltage drops from 690V to 400V. The speed is no longer constrained at 1050 RPM for power operation. The speed can be further reduced to 0.4 of base speed or 606 RPM.
