This script adds a user or group to the Site Collection Administrators Group of every Site Collection Farm-wide. Define your User or Group in line 2.

addUserOrGroupToAllSiteCollectionAdministratorsFarmwide.ps1

#example: $AccountList = @("DOMAIN\User" , "DOMAIN\Group")
$AccountList = @("DOMAIN\User")

$wapps = Get-SPWebApplication
Foreach($webapp in $wapps)
{
  foreach ($SiteCollection in $webapp.Sites)
  {
       write-host $SiteCollection.url
       $spweb = Get-SPWeb $SiteCollection.url
 
       foreach ($Account in $AccountList)
       {
           $user = Get-SPUSER -identity $Account -web $SiteCollection.url -ErrorAction SilentlyContinue
           if ($user -eq $null)
           {
               $SPWeb.ALLUsers.ADD($Account, "", "", "Added by SiteCollectionAdminScript")
               $user = Get-SPUSER -identity $Account -web $SiteCollection.url
               Write-host "Added user $Account to URL $SPWeb.URL" -Foregroundcolor green
           }
            else
           {
                Write-host "user $Account was already in URL " $SPWeb.URL -Foregroundcolor red
           }
           if ($user.IsSiteAdmin -ne $true)
           {
             $user.IsSiteAdmin = $true
             $user.Update()
             Write-host "$account has been made an admin on $SPWeb.URL" -Foregroundcolor green
           }
           else
           {
             Write-host "$account was already an admin on $SPWeb.URL" -Foregroundcolor red
           }
       }     
  }
 }