A converter assembly has a converter with multiple converter valves, each with a plurality of semiconductor switches, and with a stored energy source branch which is connected in parallel with at least one of the converter valves. The stored energy source branch has voltage converter modules and stored energy source modules. The voltage converter modules are connected to one another in a series circuit on the input side and to the respectively associated stored energy source module on the output side. There is also described an assembly having the stored energy source branch and a method for stabilizing an alternating current system by way of the converter assembly.