The solution from the blog Prevent desktop lock or screensaver with PowerShell is working for me. Here is the relevant script, which simply sends a single period to the shell:
param($minutes = 60)
$myshell = New-Object -com "Wscript.Shell"
for ($i = 0; $i -lt $minutes; $i++) {
Start-Sleep -Seconds 60
$myshell.sendkeys(".")
}
and an alternative from the comments, which moves the mouse a single pixel:
$Pos = [System.Windows.Forms.Cursor]::Position
[System.Windows.Forms.Cursor]::Position = New-Object System.Drawing.Point((($Pos.X) + 1) , $Pos.Y)
$Pos = [System.Windows.Forms.Cursor]::Position
[System.Windows.Forms.Cursor]::Position = New-Object System.Drawing.Point((($Pos.X) - 1) , $Pos.Y)