Automatic TeamCity backup with Powershell

Automatic TeamCity backup is not configurable in UI, but you can use provided REST API and schedule powershell script launch on TeamCity machine or remote machine, which has access to TeamCity server.

You should make POST request, providing parameters in request string not in post data.
Get request to the same URL will return current backup status. See documenatation:

Data Backup

Start backup: POST http://teamcity:8111/httpAuth/app/rest/server/backup?includeConfigs=true&includeDatabase=true&includeBuildLogs=true&fileName=<fileName&gt; where <fileName> is the prefix of the file to save backup to. The file will be created in the default backup directory (see more).
Get current backup status (idle/running): GET http://teamcity:8111/httpAuth/app/rest/server/backup

Here is my code for scheduled task:

function Execute-HTTPPostCommand() {
    param(
        [string] $url,
		[string] $username,
		[string] $password
    )

	$authInfo = $username + ":" + $password
	$authInfo = [System.Convert]::ToBase64String([System.Text.Encoding]::Default.GetBytes($authInfo))

    $webRequest = [System.Net.WebRequest]::Create($url)
    $webRequest.ContentType = "text/html"
    $PostStr = [System.Text.Encoding]::Default.GetBytes("")
    $webrequest.ContentLength = $PostStr.Length
	$webRequest.Headers["Authorization"] = "Basic " + $authInfo
    $webRequest.PreAuthenticate = $true
    $webRequest.Method = "POST"

    $requestStream = $webRequest.GetRequestStream()
    $requestStream.Write($PostStr, 0, $PostStr.length)
    $requestStream.Close()

    [System.Net.WebResponse] $resp = $webRequest.GetResponse();
    $rs = $resp.GetResponseStream();
    [System.IO.StreamReader] $sr = New-Object System.IO.StreamReader -argumentList $rs;
    [string] $results = $sr.ReadToEnd();

    return $results;
}

function Execute-TeamCityBackup() {
    param(
        [string] $server,
		[string] $addTimestamp,
		[string] $includeConfigs,
		[string] $includeDatabase,
		[string] $includeBuildLogs,
		[string] $includePersonalChanges,
		[string] $fileName
    )
	$TeamCityURL = [System.String]::Format("{0}/httpAuth/app/rest/server/backup?addTimestamp={1}&includeConfigs={2}&includeDatabase={3}&includeBuildLogs={4}&includePersonalChanges={5}&fileName={6}",
											$server,
											$addTimestamp,
											$includeConfigs,
											$includeDatabase,
											$includeBuildLogs,
											$includePersonalChanges,
											$fileName);

	Execute-HTTPPostCommand $TeamCityURL "USER" "PASSWORD"
}

$server = "http://YOUR_SERVER"
$addTimestamp = $true
$includeConfigs = $true
$includeDatabase = $true
$includeBuildLogs = $true
$includePersonalChanges = $true
$fileName = "TeamCity_Backup_"

Execute-TeamCityBackup $server $addTimestamp $includeConfigs $includeDatabase $includeBuildLogs $includePersonalChanges $fileName

I’m using TeamCity 7.1, but previous versions also provide REST API.