One elapsed second == 1 simulator minute is a fairly common value in life simulators. You'll find that value in major games like The Sims. One simulated day lasts just under a half hour, giving enough time for players to control their characters.
But be very, very careful about figuring out real life time. DO NOT USE THE CURRENT CLOCK TIME, the OS provides elapsed time stopwatch values you should use instead.
Real life time skips around. It is not always consecutive, sometimes jumping a few seconds or microseconds, sometimes jumping hours or even days. Sometimes it moves backwards. The most obvious examples are things like daylight saving time and leap seconds to adjust the clock. Slightly less obvious are the usually minor clock adjustments on your system clock when it re-synchronizes with time servers. A user could alt-tab out of their game, adjust their system clock forward or back several years, and resume playing the game.
So be careful in converting real life time into simulator elapsed time. A person playing at 2:00 AM on daylight saving adjustment day may be upset when their clock switches, either because now they need to wait for two simulator days for the real life clock to catch up, or because the game suddenly launched forward two simulator days.
But assuming you correctly compute the elapsed real word time, keeping the simulator time is straightforward.
Use a simple counter preserved at the simulation. The epoch, the beginning of time, is zero. Every minimum time unit is +1. Do not tie that to real life time. Simulator time 0 could be midnight starting the Sunday of the week 0 of the game, but you could start a new game as 7:30 AM on Tuesday of week 1, a simulator clock time of 691650. A player might speed up time making a simulator minute take one second or two seconds or ten seconds, a player might slow down time by making a simulator minute take twenty seconds, or even making a simulator minute take one clock minute.
Make sure animations and effects and motion and other elements are based on simulator time, not real-life clock time. If the player fast-forwards the game you want animations to play completely but quickly, if they slow down time you want them to move correspondingly slow. Always remember to base game content like animations and effects and potentially even sound on game simulator time rather than player update clocks time.
So if you were building a life simulator and decided a simulator tick equals one second, all it takes is a bit of division to get time of day and other factors. You've got:
CurrentSecondOfDay = SimTime % 86400;
CurrentHour = CurrentSecondOfDay / 3600;
CurrentMinute = (CurrentSecondOfDay % 3600)/60;
etc.
You can build a bunch of similar functions to get the current day of the week or the current year of the calendar. I strongly recommend you also simplify time to a 28 day month for easy calculation, but you can make it as complex as you want.
Then you can work with whatever time-related simulation values you need. Light of the sky may change based on the current second of the day, certain triggered events may happen at certain minutes, in-game events can happen on computed days of the week or computed weeks of the year.