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A home automation system can detect if a device has been turned on in various ways:

1. Device Monitoring: Some systems directly monitor the device's power usage. They can track changes in power consumption to determine when a device has been turned on or off.

2. Smart Plugs/Switches: These devices can be integrated into the home automation system. They have the ability to track the on/off status of the devices connected to them. They often provide data logs that record when the connected device was powered on or off.

3. Communication Protocols: Devices in a home automation system often communicate using protocols like Zigbee, Z-Wave, or Wi-Fi. These protocols can transmit data regarding the device's status, allowing the system to track activity.

4. Motion or Occupancy Sensors: In some cases, motion sensors or occupancy sensors can indirectly indicate that a device has been turned on. For example, if a TV is on, it might trigger a motion sensor due to the movement on the screen.

5. Manual Input or Scheduled Actions: Users might also input information manually into the system, indicating when they turned a particular device on or off. Additionally, scheduled actions or timers set within the automation system can help track device usage.

These methods, individually or in combination, allow a home automation system to detect whether a device has been turned on within a specified timeframe, such as the past 24 hours.