Log failure in a SQL Agent PowerShell job step

I wanted to have a template for a SQL Server Agent PowerShell job step. A key feature of the template is to make the job step fail controlled with a customized and informative error message.
The job step is defined in a script file (.ps1) called by the SQL Server PowerShell job step. If an error occurs in the script file, this is caught, described and handled. The script exits and the job step presents the error in the job step history and fail. By failure I also want that the value of “run_status” in the table msdb.dbo.sysjobhistory is set to “0” (zero).
The output from the script and the job step is streamed to a log file defined in the job step. The log file should hold all output and messages of the job step execution. That is both customized output and standard output from components.

The name of the logfile is defined with other job step parameters in a script configuration file for the job step.
$LogName = 'JobStepFailure'
$LogFileFolder = 'D:\MSSQL\MSSQL10_50.MSSQLSERVER\MSSQL\Log'
In the script file the log file is implemented and initialized
$ScriptStartTime = [System.DateTime]::Now
$LogFileName = "$LogFileFolder\$LogName.{0:yyyyddMMTHHmmss}.log" -f $ScriptStartTime

After the script and the logfile is initialized, I move on to reset the error array. Just in case...
$Error.Clear()
and the script execution can start for real
"{0:s}  Begin." -f $([System.DateTime]::Now) > $LogFileName

If a error occurs in the script execution, I usually handle the basics like this
try {$rowsSource = $DataAdpt.Fill($DataSet) }
catch {
  "{0:s}  Exeption: $_" -f $([System.DateTime]::Now) >> $LogFileName
  throw "Error in script. Check logfile '$LogFileName' for details."
}
finally { $CnnSource.Close() }

At the end of the script
"{0:s}  End." -f $([System.DateTime]::Now) >> $LogFileName
I check one more time for errors and exit the script
if ($Error) {
  throw "One or more error in script execution.`nCheck logfile '$LogFileName' for details."
}
else {
  "Script executed with success.`nCheck logfile '$LogFileName' for details." | Write-Output
}

One major argument to create the log file from the script file instead of using the parameter @output_file_name to the procedure msdb.dbo.sp_add_jobstep is that if the PowerShell script throws an exception, the content of the logfile is only the exception.
I do believe that this template can be used as a general solution.