You can get project converted document id by project document revision Id from here

api/ProjectDocumentConverted/GetConvDocByRevId

Query String

Parameter	Required	Value
docRevisionId	Mandatory	User Input
convFileType	Mandatory	User Input

Request Header

Parameter	Required	Value
TokenKey	Mandatory	User Input
PINProjectID	Mandatory	User Input

Request Body

Response

DocumentRevisionID:1234

Cache-Control →no-cache
Connection →Close
Content-Length →5
Content-Type →application/json; charset=utf-8
Date →Fri, 27 Jan 2017 12:59:10 GMT
Expires →-1
Pragma →no-cache
Server →ASP.NET Development Server/11.0.0.0
X-AspNet-Version →4.0.30319