Depending on how granular you wanted to be, you could use seconds or milliseconds. So:
var time = 900; // 900 seconds = 15:00
Then in your JavaScript you could instantiate that time in todays date like so:
// get the current date and time
var date = new Date();
// reset the hours, mins, seconds, ms
date.setHours(0, 0, 0, 0);
// set according to the stored time
date.setSeconds(time);
In answer to a more standardised approach: most computers use the Unix Timestamp, which counts the number of milliseconds from 1 January 1970 UTC. But, as you've already stated, the date is not important to you.
Regardless of the importance of the day/month/year - using seconds or milliseconds is a good way of rehabilitating your data back into the common JavaScript Date object, which is a very useful thing at the application level.
For a mammoth amount of over-consideration and syntactic sugar, you may or may not find Moment useful.
var time = 900;
// get the current date and time
var date = new Date();
// reset the hours, mins, seconds, ms
date.setHours(0, 0, 0, 0);
// set according to the stored time
date.setSeconds(time);
document.body.innerHTML = date;