This script adds a user or group to the Site Collection Administrators Group of every Site Collection of a Web Application. Define your parameters in line 1 and line 2.

addUserOrGroupToAllSiteCollectionAdministratorsPerWebApplication.ps1

$AccountList = @("Domain\UserOrGroup")
$webapp = Get-SPWebApplication -Identity https://webapplicationurl/

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
		}
	}     
}