In most cases Spotify streams that show $0.00 actually do represent payments of a small fraction of a cent that have been rounded to $0.00. To see the actual amount of the payment past the second decimal place, please click the "Details" link to the right of the payable column.
If the payable amount for your Spotify streams is actually zero, and shows only zeros in the "Details" page, this means that Spotify has determined that these are Artificial Streams. For more information please read What happens if I use a service that promises more streams, or I play my own music on repeat?
We can not appeal this determination on your behalf, but this determination by Spotify does not mean you can't earn money for your legitimate streams in the future.