Potassium Metavanadate Synthesis
Potassium Vanadate can be prepared by any of the three process:



  Potassium Metavanadate, $\ce{KVO3}$, is obtained as white or colourless crystals by dissolving vanadium pentoxide in hot, strong
  caustic potash solution. By varying the concentrations several
  hydrates have also been prepared: $\ce{2KVO3.3H2O}$;
  $\ce{KVO3.2H2O}$; $\ce{2KVO3.5H2O}$; $\ce{KVO3.3H2O}$. On being
  heated, all these hydrates lose their water and leave a white,
  nacreous mass of the anhydrous salt, which melts at 495° C. Two
  other hydrates were prepared by Rammelsberg: $\ce{KVO3.H2O}$ and
  $\ce{KVO3.7H2O}$. (source)


  [...] the reaction of vanadium(V)
  oxide from waste catalyst with potassium chloride in the presence of
  steam.
  $$\ce{2KCl + V2O5 + H2O(g) → 2KVO3 + 2HCl↑}$$
  (source)


  Ammonium metavanadate react with potassium carbonate to produce 
   potassium metavanadate, ammonia, carbon dioxide and water. Potassium
   carbonate - concentrated solution. The reaction takes place in a
   boiling solution.
  
  $$\ce{2NH4VO3 + K2CO3 → 2KVO3 + 2NH3 + CO2 + H2O}$$ (source)