Albo goes to Cairns, page-63

Payments vary depending on what state you live in.
For most an eligible recipient is someone already getting payments or have a specific type of concession card as listed on the Federal site.
https://www.energy.gov.au/energy-bill-relief-fund/energy-bill-relief-fund-households

The WA state Government generously gave every household a rebate.

For Vic the next part payment is due next year.
https://www.energy.vic.gov.au/households/help-paying-your-bills
has schedules for various types of eligible households.

For example:
Existing concessions recipients
First instalment
If you already receive a concession, your energy retailer will automatically apply the first instalment of $125 to your account in August 2023; you do not need to provide any further information. You should receive this payment on your electricity bill from September 2023 onwards.
Second instalment
A second and final instalment of $125 will be applied to your account in February 2024. You should receive this payment on your electricity bill from March 2024 onwards.