How do I create a private ppa server?

A ppa repository is simply (approximately) a APT repository that is managed by launchpad server.

As an alternative, if you don't want to set up a launchpad server (that isn't easy), you could simply make an apt repository, that is more easy and permit you to distribute your packages privately.

You can see other questions about that in askubuntu - How to set up an apt repository.

And from that question, you can follow this guide on how to make a repository. See that you have two options, a simple (easy to follow but no so automatic for users) and an advanced (complex but easy to use for users).

This is not going to be easy.

As far as I can tell the usage of PPA's is launchpad.net only. So there is no PPA server.

From: https://launchpad.net/ubuntu/+ppas

Personal Package Archives (PPA) allow you to upload Ubuntu source packages to be built and published as an apt repository by Launchpad. You can find out more about PPAs and how to use them in our help page.

So to answer your question: you will need to run your own Launchpad instance. Lucky for your there is a very lengthy article on this here.

From the link some important notes:

Building and running Launchpad requires a computer running Ubuntu. The production Launchpad.net site runs on Ubuntu 10.04 LTS. Developers mostly run 10.04 LTS, 11.10 or 12.04 LTS, but others may work.

The recommended development configuration is Ubuntu 12.04 LTS or later running Launchpad in an LXC container to minimise its impact on the wider system.

Note: the changes introduced by the install script may break your current web development setup, so it is advisable to try Launchpad in a virtual machine or an LXC container, as described above.

Also have a look at Does anyone have experience with a private Launchpad instance?