In Ubuntu 18.04 and newer it much more easier. In systemd is available a new mode suspend-then-hibernate. To start using this function you need to create a file /etc/systemd/sleep.conf with the next content:

[Sleep]
HibernateDelaySec=3600

Then you can test it by command:

sudo systemctl suspend-then-hibernate

you can edit HibernateDelaySec to reduce delay to hibernate.

If all works fine you can change Lid Close Action, to do it you need to edit the file /etc/systemd/logind.conf

You need to find option HandleLidSwitch=, uncomment it and change to HandleLidSwitch=suspend-then-hibernate. Then you need to restart systemd-logind service (warning! you user session will be restarted) by the next command:

sudo systemctl restart systemd-logind.service

That's all! Now you can use this nice function.

The solution to this is simple. First, upon suspend and resume, the pm-suspend program executes a series of scripts in /etc/pm/sleep.d and /usr/lib/pm-utils/sleep.d. So my solution is to add a script that does the following:

1. Upon suspend, record the current time and register a wakeup event using rtcwake.
   
2. Upon resume,check the current time against the recorded time from above. If enough time has elapsed, then we probably woke up due to the rtc timer event. Otherwise we woke up early due to a user event (such as opening the laptop screen).
   
3. If we woke up due to the rtc timer, then immediately issue a "pm-hibernate" command to go into hibernation.

Here is a script that does this. Name it 0000rtchibernate and place it in the /etc/pm/sleep.d directory (the 0000 is important, so that the script executes first on suspend, and last on resume).

#!/bin/bash
# Script name: /etc/pm/sleep.d/0000rtchibernate
# Purpose: Auto hibernates after a period of sleep
# Edit the "autohibernate" variable below to set the number of seconds to sleep.
curtime=$(date +%s)
autohibernate=7200
echo "$curtime $1" >>/tmp/autohibernate.log
if [ "$1" = "suspend" ]
then
    # Suspending.  Record current time, and set a wake up timer.
    echo "$curtime" >/var/run/pm-utils/locks/rtchibernate.lock
    rtcwake -m no -s $autohibernate
fi

if [ "$1" = "resume" ]
then
    # Coming out of sleep
    sustime=$(cat /var/run/pm-utils/locks/rtchibernate.lock)
    rm /var/run/pm-utils/locks/rtchibernate.lock
    # Did we wake up due to the rtc timer above?
    if [ $(($curtime - $sustime)) -ge $autohibernate ]
    then
        # Then hibernate
        rm /var/run/pm-utils/locks/pm-suspend.lock
        /usr/sbin/pm-hibernate
    else
        # Otherwise cancel the rtc timer and wake up normally.
        rtcwake -m no -s 1
    fi
fi

Hopefully this code comes through on this message board (this is my first post here).

Edit the timeout value autohibernate=7200 at the top, to however many seconds you which to sleep before going into hibernation. The current value above is 2 hours. Note, that you laptop WILL wake up at that time for a few seconds, while it is executing the hibernate function.

So if you plan on putting your laptop in a case, don't suspend, but hibernate instead. Otherwise your laptop could overheat in esp. if it is in a tight fitting slip case (although it will only be on for a few seconds to a minute).

I've been using this method for the past couple of days, so far it has been successful (and saved me from a dead battery this afternoon). Enjoy.

For other Linux distributions that use systemd and newer Ubuntu versions this should still work if you place the script in /usr/lib/systemd/system-sleep instead of /etc/pm/sleep.d. Also, replace the /usr/sbin/pm-hibernate command with systemctl hibernate.

To explain how this works (this is similar to Windows) in simple words: the machine doesn't wake up from standby when battery gets low to be able to save the machine state to the swap partition, it saves everything to the swap partition immediately on standby, and when the battery runs out, it will recover from that by loading the state from the swap partition (as it would do in case you hibernated).

AFAIK linux will/should use hybrid standby/hibernate instead of "normal" standby if it knows that it works for your hardware. It's also possible that this is disabled currently because of too many bugs or something... ;)

If you like experimenting, maybe you can see if you can get any good results with pm-suspend-hybrid.

If the following says you're lucky, then in theory hybrid suspend is supported on your system:

pm-is-supported --suspend-hybrid && echo "you're lucky"

You may be interested in s2both. It is provided by the package uswsusp in Ubuntu 10.10. It suspends to disk, but instead of shutting down the system instead puts it in S3, which is the power mode usually associated with the "Suspend" option in Ubuntu. pm-suspend-hybrid is another tool that purports to do the same thing.

To make this automated on lid close, take a look at the following guide which allows you to run an arbitrary script when a lid event is caught:

http://ubuntuforums.org/showthread.php?t=1076486

If you happen to have a ThinkPad, the manpage for tpctl makes reference to an argument, --pm-sedation-hibernate-from-suspend-timer, which seems to provide the feature you're looking for. I would caution you against trying this on non-ThinkPad hardware.

For reference, I looked through the manpage for hibernate.conf; it didn't seem to have any relevant options but might be worth a second reading.

Ubuntu 16.04 - from suspend/sleep into hibernate after a pre-determined time

It seems that on Ubuntu 16.04 things are a little different, so steps I took to make it work were:

1. Make sure hibernate is working as expected when running

   systemctl hibernate
   

2. Copy the original suspend.target file:

   sudo cp /lib/systemd/system/suspend.target /etc/systemd/system/suspend.target
   

   Then edit the file /etc/systemd/system/suspend.target and add the line:

   Requires=delayed-hibernation.service
   

   to the [Unit] section of that file.

3. Create the file /etc/systemd/system/delayed-hibernation.service with the following content:

[Unit]
Description=Delayed hibernation trigger
Before=suspend.target
Conflicts=hibernate.target hybrid-suspend.target
StopWhenUnneeded=true

[Service]
Type=oneshot
RemainAfterExit=yes
ExecStart=/usr/local/bin/delayed-hibernation.sh pre suspend
ExecStop=/usr/local/bin/delayed-hibernation.sh post suspend

[Install]
WantedBy=sleep.target

4. Create the configuration file /etc/delayed-hibernation.conf for the script with the following content:

# Configuration file for 'delayed-hibernation.sh' script

# Specify the time in seconds to spend in sleep mode before the computer hibernates
TIMEOUT=1200  #in seconds, gives 20 minutes

5. Create the script which will actually does the hard work.

   Create file /usr/local/bin/delayed-hibernation.sh with the content:

#!/bin/bash
# Script name: delayed-hibernation.sh
# Purpose: Auto hibernates after a period of sleep
# Edit the `TIMEOUT` variable in the `$hibernation_conf` file to set the number of seconds to sleep.

hibernation_lock='/var/run/delayed-hibernation.lock'
hibernation_fail='/var/run/delayed-hibernation.fail'
hibernation_conf='/etc/delayed-hibernation.conf'

# Checking the configuration file
if [ ! -f $hibernation_conf ]; then
    echo "Missing configuration file ('$hibernation_conf'), aborting."
    exit 1
fi
hibernation_timeout=$(grep "^[^#]" $hibernation_conf | grep "TIMEOUT=" | awk -F'=' '{ print $2 }' | awk -F'#' '{print $1}' | tr -d '[[ \t]]')
if [ "$hibernation_timeout" = "" ]; then
    echo "Missing 'TIMEOUT' parameter from configuration file ('$hibernation_conf'), aborting."
    exit 1
elif [[ ! "$hibernation_timeout" =~ ^[0-9]+$ ]]; then
    echo "Bad 'TIMEOUT' parameter ('$hibernation_timeout') in configuration file ('$hibernation_conf'), expected number of seconds, aborting."
    exit 1
fi

# Processing given parameters
if [ "$2" = "suspend" ]; then
    curtime=$(date +%s)
    if [ "$1" = "pre" ]; then
        if [ -f $hibernation_fail ]; then
            echo "Failed hibernation detected, skipping setting RTC wakeup timer."
        else
            echo "Suspend detected. Recording time, set RTC timer"
            echo "$curtime" > $hibernation_lock
            rtcwake -m no -s $hibernation_timeout
        fi
    elif [ "$1" = "post" ]; then
        if [ -f $hibernation_fail ]; then
            rm $hibernation_fail
        fi
        if [ -f $hibernation_lock ]; then
            sustime=$(cat $hibernation_lock)
            rm $hibernation_lock
            if [ $(($curtime - $sustime)) -ge $hibernation_timeout ]; then
                echo "Automatic resume from suspend detected. Hibernating..."
                systemctl hibernate
                if [ $? -ne 0 ]; then
                    echo "Automatic hibernation failed. Trying to suspend instead."
                    touch $hibernation_fail
                    systemctl suspend
                    if [ $? -ne 0 ]; then
                        echo "Automatic hibernation and suspend failover failed. Nothing else to try."
                    fi
                fi
            else
                echo "Manual resume from suspend detected. Clearing RTC timer"
                rtcwake -m disable
            fi
        else
            echo "File '$hibernation_lock' was not found, nothing to do"
        fi
    else
        echo "Unrecognised first parameter: '$1', expected 'pre' or 'post'"
    fi
else
    echo "This script is intended to be run by systemctl delayed-hibernation.service (expected second parameter: 'suspend')"
fi

6. Make the script executable:

chmod 755 /usr/local/bin/delayed-hibernation.sh

It took me quite a lot until writing this script based on other replies in this thread, things I found on the internet like https://bbs.archlinux.org/viewtopic.php?pid=1554259

My version of the script tries to deal with many problems like go into suspend again if hibernate was not successful but do not wake again after the pre-determined time over and over.

7. Final step I assume would be to just execute

   sudo systemctl daemon-reload
   sudo systemctl enable delayed-hibernation.service 
   

   to make sure new service/configurations are being used.

To check the service log, you can use:

sudo systemctl status delayed-hibernation.service

or for a complete log of the service use:

sudo journalctl -u delayed-hibernation.service

A normal log I get from the running service is:

mile@mile-ThinkPad:~$ sudo systemctl status delayed-hibernation.service 
● delayed-hibernation.service - Delayed hibernation trigger
   Loaded: loaded (/etc/systemd/system/delayed-hibernation.service; enabled; vendor preset: enabled)
   Active: inactive (dead)

Jun 09 20:35:42 mile-ThinkPad systemd[1]: Starting Delayed hibernation trigger...
Jun 09 20:35:42 mile-ThinkPad delayed-hibernation.sh[2933]: Suspend detected. Recording time, set RTC timer
Jun 09 20:35:42 mile-ThinkPad delayed-hibernation.sh[2933]: rtcwake: assuming RTC uses UTC ...
Jun 09 20:35:42 mile-ThinkPad delayed-hibernation.sh[2933]: rtcwake: wakeup using /dev/rtc0 at Thu Jun  9 18:55:43 2016
Jun 09 20:55:44 mile-ThinkPad systemd[1]: Started Delayed hibernation trigger.
Jun 09 20:55:44 mile-ThinkPad systemd[1]: delayed-hibernation.service: Unit not needed anymore. Stopping.
Jun 09 20:55:44 mile-ThinkPad systemd[1]: Stopping Delayed hibernation trigger...
Jun 09 20:55:44 mile-ThinkPad delayed-hibernation.sh[3093]: Automatic resume from suspend detected. Hibernating...
Jun 09 20:55:44 mile-ThinkPad systemd[1]: Stopped Delayed hibernation trigger.
mile@mile-ThinkPad:~$ 

So This would be it, I hope it really helps someone since I spent days trying to figure out the right combination of configurations and script versions to make this handy feature work.

Just in case something goes wrong during pm-hibernate i'd rather put the computer to suspend than let it run. So you can use:

   ...
/usr/sbin/pm-hibernate || /usr/sbin/pm-suspend
   ...

Here's an updated version of Derek Pressnall's answer that works with systemd and includes Eliah Kagan's suggestion, just drop it in /usr/lib/systemd/system-sleep/delayed_hibernation.sh and make it executable:

#!/bin/bash

hibernation_timeout=1800  #30 minutes

if [ "$2" = "suspend" ]; then
    curtime=$(date +%s)
    if [ "$1" = "pre" ]; then
        echo -e "[($curtime) $@]\nExecuting pre-suspend hook..." >> /tmp/delayed_hibernation.log
        echo "$curtime" > /var/run/delayed_hibernation.lock
        rtcwake -m no -s $hibernation_timeout
    elif [ "$1" = "post" ]; then
        echo -e "[($curtime) $@]\nExecuting post-suspend hook..." >> /tmp/delayed_hibernation.log
        sustime=$(cat /var/run/delayed_hibernation.lock)
        if [ $(($curtime - $sustime)) -ge $hibernation_timeout ]; then
            echo -e "Automatic resume detected, hibernating.\n" >> /tmp/delayed_hibernation.log
            systemctl hibernate || systemctl suspend
        else
            echo -e "Manual resume detected, clearing RTC alarm.\n" >> /tmp/delayed_hibernation.log
            rtcwake -m no -s 1
        fi
        rm /var/run/delayed_hibernation.lock
    fi
fi

Here is my recipe (tested it on two notebooks Ubuntu 16.04):

Put this script whereever you like (I put it to root, /syspend.sh) and make it executable (chmod +x /suspend.sh)

TIMELOG=/tmp/autohibernate.log
ALARM=$(tail -n 1 $TIMELOG)
SLEEPTIME=5000 #edit this line to change timer, e.g. 2 hours "$((2*60*60))"
if [[ $1 == "resume" ]]
then
    if [[ $(date +%s) -ge $(( $ALARM + $SLEEPTIME )) ]]
    then
        echo "hibernate triggered $(date +%H:%M:%S)">>$TIMELOG
        systemctl hibernate 2>> $TIMELOG
    else
        echo "normal wakeup $(date +%H:%M:%S)">>$TIMELOG
    fi
elif [[ $1 == "suspend" ]]
then
    echo "$(date +%s)" >> $TIMELOG
    rtcwake -m no -s $SLEEPTIME
fi

Then create systemd target: # touch /etc/systemd/system/suspend-to-sleep.target Paste this content:

#/etc/systemd/system/suspend-to-hibernate.service
[Unit]
Description=Delayed hibernation trigger
Before=suspend.target
Conflicts=hibernate.target hybrid-suspend.target
StopWhenUnneeded=true

[Service]
Type=oneshot
RemainAfterExit=yes
ExecStart=/bin/bash /suspend.sh suspend
ExecStop=/bin/bash /suspend.sh wakeup

[Install]
WantedBy=sleep.target
RequiredBy=suspend.target

Then enable it # systemctl enable suspend-to-sleep.target.

I've faced an issue on the one of notebooks: closing lid didn't trigger this target. This was due to xfce4-power-manager. There are two ways to workaround this problem. The first one is to edit /etc/systemd/logind.conf file and replace HandleLidSwitch=ignore with HandleLidSwitch=suspend. But it will be systemwide, so I just added symlink to my script # ln -s /suspend.sh /etc/pm/sleep.d/0000rtchibernate

Another more common workaround you can use hybrid-sleep (like the Mac OS does). If your computer supports hibernation, you can use this feature:

systemctl hybrid-sleep

That command should suspend and send to disk (hibernate) the computer. After some time the computer will turn off (when turning on, it will use the hibernation files to wake up).

p.s.: I know it's not exactly what the OP posted, but it's fairly close

Don't forget to chmod +x that file, make it executable.

There's another solution without rtcwake, using wakealarm in /sys/class/rtc/rtc0. Make use obsolete code in pm-functions (/usr/lib/pm-utils) after the comments #since the kernel does not directly support ... , ('cos the current kernel (after 3.6 something) does directly support). Revert that code and put in do_suspend() part instead of do_suspend_hybrid().

Obsolete code (suspend then hibernate when suspend_hybrid is called):

# since the kernel does not directly support hybrid sleep, we do
# something else -- suspend and schedule an alarm to go into
# hibernate if we have slept long enough.
# Only do this if we do not need to do any special video hackery on resume
# from hibernate, though.
if [ -z "$SUSPEND_HYBRID_MODULE" -a -w "$PM_RTC/wakealarm" ] && \
    check_suspend && check_hibernate && ! is_set $HIBERNATE_RESUME_POST_VIDEO; \
    then
    SUSPEND_HYBRID_MODULE="kernel"
    do_suspend_hybrid() {
    WAKETIME=$(( $(cat "$PM_RTC/since_epoch") + PM_HIBERNATE_DELAY))
    echo >"$PM_RTC/wakealarm"
    echo $WAKETIME > "$PM_RTC/wakealarm"
    if do_suspend; then
        NOW=$(cat "$PM_RTC/since_epoch")
        if [ "$NOW" -ge "$WAKETIME" -a "$NOW" -lt $((WAKETIME + 30)) ]; then
        log "Woken by RTC alarm, hibernating."
        # if hibernate fails for any reason, go back to suspend.
        do_hibernate || do_suspend
        else
        echo > "$PM_RTC/wakealarm"
        fi
    else
        # if we cannot suspend, just try to hibernate.
        do_hibernate
    fi
    }
fi

Recommended. Even easier to use uswsusp while the same time maximize the benefit of s2both i.e. s2both when suspend. Put the reverted code in do_suspend() part of uswsusp module (/usr/lib/pm-utils/module.d).

Reverted code (suspend_hybrid when suspend is called):

WAKETIME=$(( $(cat "$PM_RTC/since_epoch") + PM_HIBERNATE_DELAY))
echo >"$PM_RTC/wakealarm"
echo $WAKETIME > "$PM_RTC/wakealarm"
if do_suspend_hybrid; then
    NOW=$(cat "$PM_RTC/since_epoch")
    if [ "$NOW" -ge "$WAKETIME" -a "$NOW" -lt $((WAKETIME + 30)) ];             then
    log "Woken by RTC alarm, hibernating."
    # if hibernate fails for any reason, go back to suspend_hybrid.
    do_hibernate || do_suspend_hybrid
    else
    echo > "$PM_RTC/wakealarm"
    fi
else
    # when do_suspend is being called, convert to suspend_hybrid.
    do_suspend_hybrid
fi      

With uswsusp, we can see the progress of suspend/hibernate and the reverse process displayed in text, even we can abort it by pressing backspace. Without uswsusp, suspend/hibernate just appear-disappear annoyingly, especially when wakealarm is triggered and execute hibernate (s2disk in uswsusp). Set the period of sleep before hibernate in the usual place on pm-functions file.

# variables to handle hibernate after suspend support
PM_HIBERNATE_DELAY=900  # 15 minutes
PM_RTC=/sys/class/rtc/rtc0

Here's the uswsusp mod: (remember, this module is called from pm-functions so the inserted variables are the same)

#!/bin/sh

# disable processing of 90chvt and 99video.
# s2ram and s2disk handle all this stuff internally.
uswsusp_hooks()
{
    disablehook 99video "disabled by uswsusp"
}

# Since we disabled 99video, we need to take responsibility for proper
# quirk handling.  s2ram handles all common video quirks internally,
# so all we have to do is translate the HAL standard options to s2ram options.
uswsusp_get_quirks()
{
    OPTS=""
    ACPI_SLEEP=0
    for opt in $PM_CMDLINE; do
        case "${opt##--quirk-}" in # just quirks, please
            dpms-on)       ;; # no-op
            dpms-suspend)      ;; # no-op
            radeon-off)        OPTS="$OPTS --radeontool" ;;
            reset-brightness)  ;; # no-op
            s3-bios)       ACPI_SLEEP=$(($ACPI_SLEEP + 1)) ;;
            s3-mode)       ACPI_SLEEP=$(($ACPI_SLEEP + 2)) ;;
            vbe-post)      OPTS="$OPTS --vbe_post" ;;
            vbemode-restore)   OPTS="$OPTS --vbe_mode" ;;
            vbestate-restore)  OPTS="$OPTS --vbe_save" ;;
            vga-mode-3)        ;; # no-op
            save-pci)          OPTS="$OPTS --pci_save" ;;
            none)          QUIRK_NONE="true" ;;
            *) continue ;;
        esac
    done
    [ $ACPI_SLEEP -ne 0 ] && OPTS="$OPTS --acpi_sleep $ACPI_SLEEP"
    # if we were told to ignore quirks, do so.
    # This is arguably not the best way to do things, but...
    [ "$QUIRK_NONE" = "true" ] && OPTS=""
}

# Since we disabled 99video, we also need to handle displaying
# help info for the quirks we handle.
uswsusp_help()
{
    echo  # first echo makes it look nicer.
    echo "s2ram video quirk handler options:"
    echo
    echo "  --quirk-radeon-off"
    echo "  --quirk-s3-bios"
    echo "  --quirk-s3-mode"
    echo "  --quirk-vbe-post"
    echo "  --quirk-vbemode-restore"
    echo "  --quirk-vbestate-restore"
    echo "  --quirk-save-pci"
    echo "  --quirk-none"
}

# This idiom is used for all sleep methods.  Only declare the actual
# do_ method if:
# 1: some other sleep module has not already done so, and
# 2: this sleep method can actually work on this system.
#
# For suspend, if SUSPEND_MODULE is set then something else has already
# implemented do_suspend.  We could just check to see of do_suspend was
# already declared using command_exists, but using a dedicated environment
# variable makes it easier to debug when we have to know what sleep module
# ended up claiming ownership of a given sleep method.
if [ -z "$SUSPEND_MODULE" ] && command_exists s2ram && \
    ( grep -q mem /sys/power/state || \
        ( [ -c /dev/pmu ] && check_suspend_pmu; ); ); then
    SUSPEND_MODULE="uswsusp"
    do_suspend()
    {
        WAKETIME=$(( $(cat "$PM_RTC/since_epoch") + PM_HIBERNATE_DELAY))
        echo >"$PM_RTC/wakealarm"
        echo $WAKETIME > "$PM_RTC/wakealarm"
        if do_suspend_hybrid; then
            NOW=$(cat "$PM_RTC/since_epoch")
            if [ "$NOW" -ge "$WAKETIME" -a "$NOW" -lt $((WAKETIME + 30)) ];             then
            log "Woken by RTC alarm, hibernating."
            # if hibernate fails for any reason, go back to suspend_hybrid.
            do_hibernate || do_suspend_hybrid
            else
            echo > "$PM_RTC/wakealarm"
            fi
        else
            # when do_suspend is being called, convert to suspend_hybrid.
            do_suspend_hybrid
        fi      
    }
fi

if [ -z "$HIBERNATE_MODULE" ] && \
    [ -f /sys/power/disk ] && \
    grep -q disk /sys/power/state && \
    [ -c /dev/snapshot ] &&
    command_exists s2disk; then
    HIBERNATE_MODULE="uswsusp"
    do_hibernate()
    {
        s2disk
    }
fi

if [ -z "$SUSPEND_HYBRID_MODULE" ] && 
    grep -q mem /sys/power/state && \
    command_exists s2both && \
    check_hibernate; then
    SUSPEND_HYBRID_MODULE="uswsusp"
    do_suspend_hybrid()
    {   
        uswsusp_get_quirks
        s2both --force $OPTS 
    }
    if [ "$METHOD" = "suspend_hybrid" ]; then
        add_before_hooks uswsusp_hooks
        add_module_help uswsusp_help
    fi
fi