Hibernate/suspend on critical battery level - where should I set it from MATE GUI?

GUI method

From: Change Critical Battery Level and Action in Linux Mint 18 Cinnamon you can install dconf-editor using:

$ sudo apt-get install dconf-editor

Then go to org -> cinnamon -> settings-daemon -> plugins -> power

• Default settings are (in %):
• Critical battery action: hibernate
• Critical: 2
• Action: 2
• Low: 10

Exercise caution and tweak to your heart’s content 🙂

Original Answer and edits below

Review your current settings with:

$ gsettings list-recursively | grep critical
org.gnome.settings-daemon.plugins.power critical-battery-action 'shutdown'
org.gnome.settings-daemon.plugins.power percentage-critical 3
org.gnome.settings-daemon.plugins.power time-critical 300

Change your critical-battery-action

$ gsettings set org.gnome.settings-daemon.plugins.power critical-battery-action 'suspend'

Linux Mate differences

When using Linux Mate you need to substitute org.gnome with org.mate and possibly change your keys. From ArchWiki:

Battery discharge

To disable the notification on battery discharge, run:

$ gsettings set org.mate.power-manager.notify-discharging false

However in Ubuntu there is no equivalent.

Find all Mate power settings

To find all Mate power settings use:

$ gsettings list-recursively | grep power-manager

In Ubuntu you would use:

$ gsettings list-recursively | grep plugins.power

I still can't find GUI solution for my problem. So I switched to semi-GUI solution.

I fixed this issue by using other battery level indicator - it is named fdpowermon:

Description-en: simple battery power monitor for laptops with ACPI

fdpowermon is a simple perl script that installs an icon in a system tray compatible with the freedesktop.org specification.
Every three seconds, fdpowermon calls acpi to find out what the current battery level is. It will set the output of the acpi command as a tooltip text, and will update the used icon as appropriate.
In addition, fdpowermon can optionally call perl subroutines when the power reaches a given level. No such subroutines are provided or enabled by default, however.

So I have installed it

sudo apt-get install fdpowermon

and created configuration folder for this application with:

mkdir -p ~/.config/fdpowermon/

and placed here two files:

1. file with my modified theme (in discharging array note the 3rd element 20:battery-low.png, it will be used to suspend in Perl script):

cat << \EOF > ~/.config/fdpowermon/theme.cfg 
[mytheme]
steps = 8
dir = /usr/share/icons/oxygen/22x22/status
# The below line makes fdpowermon not show an icon when the power is
# connected and the battery is completely full. This is by design,
# because that's how the author likes to use the software, and he is of
# the opinion that it's easier to ship software configured just the way
# he likes it rather than to have to reconfigure things.
#
# Requests are often made to change this default. This will not happen,
# but it's an easy change: just change the last entry in this "charging"
# configuration so that it says "100:battery-charging.png" rather than
# "99:battery-charging.png", and you're done!
charging = 0:battery-charging-low.png, 10:battery-charging-low.png, 20:battery-charging-caution.png, 30:battery-charging-caution.png, 50:battery-charging-040.png, 70:battery-charging-060.png, 90:battery-charging-080.png,100:battery-charging.png
discharging = 2:battery-missing.png:battery-low.png,10:battery-low.png, 20:battery-low.png,30:battery-caution.png,50:battery-040.png,70:battery-060.png,90:battery-080.png,100:battery-100.png
EOF

2. Perl script file with dbus suspend action:

cat << \EOF > ~/.config/fdpowermon/theme.pl
# Copy this file to ~/.config/fdpowermon/theme.pl.
#
# If you don't like the 'default' theme, define a new one by copying
# /etc/fdpowermon/theme.cfg to ~/.config/fdpowermon/theme.cfg and
# renaming/adjusting the 'default' theme there to something new.
# Don't forget to replace "default" below with your new theme name.
#
# See the manpage fdpowermon(1) for full details on what you can do
# here.

# define a suspend action
sub suspend {
    system("dbus-send --print-reply --system --dest=org.freedesktop.login1 /org/freedesktop/login1 org.freedesktop.login1.Manager.Suspend boolean:true");
}

# initialize our theme, from /etc/fdpowermon/theme.cfg or
# ~/.config/fdpowermon/theme.cfg
my $theme = fdpowermon::theme::get_theme("mytheme");

# on the discharge event for the lowest element in the list of steps (0 = first
# in the index, "d" for discharge), call the "suspend" sub defined above
$theme->set_event( 2, \&suspend, 'd' );
EOF

(the DBus suspend command came from this great answer).

And finally I have disabled MATE Power Manager battery indicator with

gsettings set org.mate.power-manager icon-policy 'never'

and created auto-start desktop file to have fdpowermon shown in the tray instead:

mkdir -p ~/.config/autostart

cat << EOF > ~/.config/autostart/fdpowermon.desktop 
[Desktop Entry]
Type=Application
Exec=fdpowermon
Hidden=false
X-MATE-Autostart-enabled=true
Name[en_US]=fdpowermon
Name=fdpowermon
Comment[en_US]=
Comment=
EOF

As the result I have nice-looking battery icon in the tray from to and and system automatically suspends on 20% battery level (the level is configurable, but my new battery seems to report low values wrongly).