The DC grid operation will have no effect on the condition. An inverter will be used to convert DC to AC. The inverter will be looking it as a unbalanced loading condition and will adjust the current flow. eventually you will not observe much difference. the worst case condition inverter will isolate or disconnect the circuit depending on the under voltage protection which you have utilized for synchronization.  

Hope this many help you..

I can suggest to read the following paper. It can be helpfull.

http://orbit.dtu.dk/fedora/objects/orbit:130710/datastreams/file_f8c3b27f-a184-48e0-9e44-b001d53f9538/content

i think that the AC fault will not have any effect on the operation of the DC grid, because one of the most advantages of the VSC are the isolation and the elimination of cascaded faults

Thanks for your valuable answers

The DC grid may be affected by a fault condition at the AC  system dedepending on the selected topology of power inverter. If for example the power inverter is based on LCC or CSC mode which uses the thyristor as switches. The commutation of thyristor depends on the AC system, if the AC side is weak, then the control of parameters in the AC/DC junction becomes vulnerable. Unless you design an AC/DC link with a very high short circuit ratio. The VSC-PWM based power Inverter topology may be the better choice to use in the AC/DC junction, because the commutation of IGBT or IGCT switches does not depends on the AC system.

Dear Musasa, Thanks for your valuable answers