There are three issues that are being described.
EST SIGA-CT1 Fire Alarm System Input Module
The SIGA-CT1 is an input module for the building's fire alarm system. It is wired so it will look at, or monitor, the trouble contacts of the EST BPS (Booster Power Supply).
When something is not normal for the BPS, like a problem with one of the Notification Appliance Circuits (NACs), ground fault, battery trouble, internal problem with the BPS, or loss of power, a relay inside the BPS relaxes and closes contacts; the BPS's relay is sending a trouble signal.
The SIGA-CT1 senses the trouble signal, and sends that trouble signal to the control panel as a supervisory trouble. The SIGA-CT1 has its own way of saying that something is not normal; the control panel receives a trouble (not a supervisory) to indicate that the SIGA-CT1 is not normal.
In other words, it is doing its job.
EST BPS Power Supply
The BPS Power Supply is there to power some of the horns and strobes, and it has several indicator lights to show its status. A green light turned on, and no other light means that everything about the power supply is in the normal, working condition.
If no other light is lit on the power supply, the BPS power supply is saying that the battery tests OK, the circuits powered by the BPS aren't ground faulted, and all four NAC power circuits are normal.
The green power-on light says that AC power is applied, and also that there isn't any internal problem with the power supply.
AC power is provided to the BPS power supply at the AC power input. However, a turned-off Green Power-On LED is kinda dumb; if it is off, it doesn't show why there is a problem, only that there is a problem. The problem could be on a different circuit breaker somewhere else in the building, or the problem could be inside the BPS.
This is a time sensitive issue. When the AC Power LED is not lit, the BPS is running on the battery backup. The size of the backup batteries has been designed to keep the system working for at least 24 hours, and at the end of the 24 hours, be able to sound the alarms for 5 minutes.
The BPS will probably last longer than 24 hours from the time the green light turned off, but I wouldn't count on that.
Call your fire alarm service company. They are familiar with this kind of problem, and can help.