Set-PublishingWebDefaultPage.ps

# variables
$siteUrl = "http://www.example.ma"
$defaultPageFileName = "Home.aspx"

Add-PSSnapin Microsoft.SharePoint.PowerShell -EA SilentlyContinue
$web = GetSPWeb -Identity $siteUrl
if([Microsoft.SharePoint.Publishing.PublishingWeb]::IsPublishingWeb($web)) {
    $publishingWeb = [Microsoft.SharePoint.Publishing.PublishingWeb]::GetPublishingWeb($web)
    $publishingWeb.DefaultPage = ($publishingWeb.PagesList.Items | Where-Object { $_.File.Name -eq $defaultPageFileName }).File
    $publishingWeb.Update()
} else {
    Write-Error "this site doesn't use publishing site template"
}