# Add PowerShell Snapin
 $snapin = Get-PSSnapin | Where-Object {$_.Name -eq 'Microsoft.SharePoint.Powershell'}
 if ($snapin -eq $null)
 {
     Add-PSSnapin "Microsoft.SharePoint.Powershell"
 }

 # Get the Site URL
 $SiteUrl = "https://MySiteCollectionURL/"

 # Get the Web URL
 $WebUrl = "https://MyWebSiteURL"

 # Get the Page on which WE are going to Add the WebPart
 $PageName = "Test.aspx"

 # The location of the WEbPart Definition File
 $localWebpartPath = "C:WebPartsMyWebPart.webpart"

 # Error Message which is required as a Reference Parameter while Importing the WEbPart
 $errorMsg = "Test Error Message"

 # Initializing the SPSite Object
 $Site = Get-SPSite($SiteUrl)

 # Get an instance for Publishing Site based on SPSite
 $PubSite = New-Object Microsoft.SharePoint.Publishing.PublishingSite($Site)

 # Get the SPWEb Object
 $Web = Get-SPWeb $WebUrl

 # Get the Publishing Web Based on the SPWeb Object
 $PubWeb = [Microsoft.SharePoint.Publishing.PublishingWeb]::GetPublishingWeb($Web)

 # The below commented line is to get all the Pages
 #$PubWeb.GetPublishingPages($PageName);

 # Get only our Page
 $PublishingPage = $PubWeb.GetPublishingPage("https://MyWebURL/Pages/Test.aspx");

 # Make the Web as AllowUnSafeUpdates as true
 $Web.AllowUnsafeUpdates = $true

 # Checkout the Publishing Page
 $PublishingPage.CheckOut();

 # Get the LimitedWEbPartManager
 $limitedWebPartManager = $PublishingPage.ListItem.File.GetLimitedWebPartManager([System.Web.UI.WebControls.WebParts.PersonalizationScope]::Shared);

 # Initialize the XmlReaderSettings Object which is required for the XmlReader Object
 $xmlReaderSettings = New-Object System.Xml.XmlReaderSettings

 # Create the XmlReader Object by using the WebPart Definition file and the ReaderSettings Object
 $xmlReader = [System.Xml.XmlReader]::Create($localWebpartPath,$xmlReaderSettings);

 #Add Web Part to catalogs folder and Get the WebPart Definition Object based on the webpart definition xml file
 $oWebPartDefinition = $limitedWebPartManager.ImportWebPart($xmlReader,[ref]$errorMsg);

 # Add the WebPart to the WebPartManager by specifing the Zone and the Index.
 $limitedWebPartManager.AddWebPart($oWebPartDefinition,"RightZone",1);

 # Checkin the Publishing Page
 $PublishingPage.CheckIn("Checkin");

 # Publish the Page
 $PublishingPage.ListItem.File.Publish("Publish");

 # Revert the AllowUnsafeUpdates to False once we are done.
 $Web.AllowUnsafeUpdates = $false

 # I was trying to Approve the Page.  But, if the Approve is enabled on the Pages Library level,
 # then only we can do that.  Otherwise we cannot.  But the Syntax is correct as below.

 # $PageListItem.File.Approve("Page approved automatically by PowerShell script")

- See more at: http://www.sharepointpals.com/post/How-to-Add-WebPart-to-the-Publishing-Page-using-PowerShell-in-SharePoint-2013#sthash.xcdNmxZv.dpuf