At design point the air angles are all matched. But at off design (say low compressor speed) the pressure falls at the discharge of the compressor causing the velocity in discharge (HP ) stages to increase,  which can choke these stages. This causes the front or LP stage of the compressor to increase in loading and can stall these stage causing compressor surge (a violent aerodynamic compressor instability) at such low speed.  Closing variable stator vanes in the front stages will unload these stages thus preventing the compressor from stalling

You can see that effect that Rasak mention in the following Flow Ilustrator.

https://www.youtube.com/watch?v=MulWTBx3szc

https://www.youtube.com/watch?v=kYSfLXAjLzE

I hope this can help you

The issue is that compressors are unstable at low massflows. They tend to stall as the incidence on to the aerofoils increases. This can lead to a phenomenon called rotating stall and if the pressure rise is high enough surge of the engine. This forces the shutting down of the engine if it occurs and can cause the plane to crash. Variable stators can be altered whilst the engin is running this allows control of the flow angle and can ameliorate the effects of incidence making the compressor more stable and adding to its "surge magin" the distance the compresor is away from the surge line (can be delta massflow or delta pressure).

Thanks Razak, Jimenez, & Martin.

Yours answers have been very helpful in my current research.

Cheers

Earlier comments of course are right and proper. It can only be completed with more  comment:

- Outside the nominal operating conditions, high incidence angles result in a sharp increase in profile profile (flow separation), hence adjustable vane blades fit the direction of the flow to actual working conditions

- A similar effect is achieved by use of a two-shaft rotor design having different speeds or the boundary layer control (aspirated compressor concept)

- Compressor bleed is less effective in this case and typical for older machines or centrifugal stages

- A lot of useful information can be found in two excellent books:

Kerrebrock, J .: Aircraft Engines and Gas Turbines, 2nd Ed.

Dixon, S.L. .; Hall, C.:Fluid Mechanics andThermodynamics of Turbomachinery, 7th Ed.

I wish you success, Jan Gorski, AGH University

The VSVs protect the compressor from surging hence improve the stabiltity of operation. In addition, if you compare a variable geometry gas turbine with a fixed geometry gas turbine, the one with VSVs can reach a higher/lower power setting faster than the fixed gometry one. The reason lies in the fact that shaft inertia is proportional to the response time of the engine, and the VSVs enable the engine to increase/decrease its air mass flow rate faster.