Thank you for your quick reply. Based on your answer, the competent authorities are the Danish ones, and the applicable law is also Danish. Your wife's Swedish citizenship does not count.
Under Danish law, because you have lived separated for more than 2 years you can obtain right away a divorce, even if she does not agree. Before filing for a divorce, I strongly suggest contacting her to see whether she agrees, because if there is agreement, the State Administration will simply grant you the divorce without further discussion. If you do not agree, there may be a need for mediation (which is organized by the state and costs 1000,- DKR) or even a court order.
To file for a divorce you need to fill a form and pay a fee of DKR 900,-. The form is available in English (link) and Danish (link). Information on paying the fee can be found here (link) (Danish). She will be sent the form and may also agree afterwards, even if you do not speak in advance. But it is also possible to make the form together, which is even better.
If you have what is called a 'NemID' you should go to this page: https://www.borger.dk/Sider/Separation-og-skilsmisse.aspx (link). Click on the link entitled 'Ansøg om skilsmisse uden forudgående separation', log in with your NemID and you may file for the divorce on-line.
I hope this helps you and remain available for any further questions. I also look forward to your rating.
Dr Ioan-Luca Vlad