If the number of columns is the same across the different Excel worksheets then you should be able to use the below code to merge the files together.

The code uses methods from the NamedRange interface from the Excel API.

Example Code: (Just remember to change the paths and file names to your environment)

# Create an instance of Excel
$Excel = New-Object -ComObject Excel.Application

# Find the files you want to process
$Files = Get-ChildItem -Path C:\Temp -Filter *.xlsx

# Create a target workbook and worksheet called 'Sheet1'
$TargetWorkbook = $Excel.Workbooks.add()
$TargetWorksheet = $TargetWorkbook.Sheets.Item("Sheet1")

# Loop through our Excel files
foreach($File in $Files) {
    # Open the workbook and get the first sheet
    $SourceWorkbook=$Excel.Workbooks.Open($File.FullName)
    $SourceWorksheet=$SourceWorkbook.Sheets.Item(1)

    # Calculate the end column letter
    $EndColumn = [char]([int][char]'A' + $SourceWorksheet.UsedRange.Columns.Count - 1)

    # Activate the source worksheet
    $SourceWorksheet.activate()

    # Get the total number of rows in the sheet
    $SourceLastRow = $SourceWorksheet.UsedRange.Rows.Count + 1

    # Calculate what our start row should be
    # A1 for the first worksheet only to include the headers
    $StartRow = (& { If ($TargetWorkSheet.UsedRange.rows.count -eq 1) { "A1" } Else { "A2" } } )

    # Get the range of data and copy it to the clipboard
    $SourceRange = $SourceWorksheet.Range("$($StartRow):$EndColumn$SourceLastRow")
    $SourceRange.copy()

    # Activate the target worksheet
    $TargetWorksheet.activate()

    # Get the total number of rows in the sheet
    $TargetLastRow = $TargetWorkSheet.UsedRange.Rows.Count
    if ($TargetWorkSheet.UsedRange.Rows.Count -ne 1) {
         # If this isn't the first sheet we've processed, add one additional row
        $TargetLastRow++
    }

    # Get the target range and paste the data
    $TargetRange = $TargetWorksheet.Range("A$($TargetLastRow):$EndColumn$($SourceRange.Rows.Count)")
    $TargetWorksheet.Paste($TargetRange)

    # Disable showing alerts, otherwise a notification about
    # large amounts of data on the clipboard will be shown
    $Excel.DisplayAlerts = $false

    # Close the source workbook
    $SourceWorkbook.Close()
}

# Re-enable showing alerts
$Excel.DisplayAlerts = $true

# Save the workbook to the desired path
$TargetWorkbook.SaveAs("C:\Temp\Merged.xlsx")

# Quit Excel
$Excel.Quit()

If your sheets have different numbers of columns, you could still use the above code, however you'll need to make some changes to the $SourceRange, $TargetRange and $EndColumn variables to account for this.