Despite its name, the past participle is a non-finite verb form, which means that it has no tense. The past participle is used:
- in forming the present perfect ("I have written")
- in forming the past perfect ("I had written")
- in forming the perfect infinitive ("(to) have written", as in "I must have written")
- in forming passives ("it was written")
- attributively as a descriptor ("a quickly written poem").
In many cases, the simple past is identical in form to the past participle ("I said", "I have said"). In other cases, they are different ("I did", "I have done").
Once you know what the past participle is, you can combine it with forms of "have" to form the present perfect and past perfect - hence there is no need for a table of irregular verb forms to include the past perfect: it just needs to include the past participle.