First of all, every system has a permanent Morale Modifier (MM). This is the sum of all building morale modifiers that apply to this system.
Note that buildings that have an output type of "Morale" (Hex value 14; e.g. Holo Cinema) or "Morale empire-wide" (Hex value 28; e.g. Great Hall) need to be powered in order to produce that output.
In contrast, Morals bonuses/penalties (not outputs) that are connected to buildings (e.g. Mining Prison, Utopia Planitia) will still be constantly applied even if the buildings would need energy and are switched off.
At the beginning of each turn, first the non-permanent Morale changes are applied (e.g. you declare war, you make peace, you colonize a system, you win a battle). After that, the MM will be applied, but the result depends on the system's Moral level.
On all difficulty levels except "Impossible", there are 6 different Morale levels for a (self-colonized or starting) system:
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LV0: 1 - 99 Morale Points
LV1: 100 - 119 MPs
LV2: 120 - 138 MPs
LV3: 139 - 157 MPs
LV4: 158 - 176 MPs
LV5: 177 - 195 MPs
If your system is at a certain LV, then you need at least the according MM to maintain your current Moral value. If your MM is higher/lower, then you gain/lose Morale points equal to the difference. If your system's LV would change by this, the higher LV counts (exception: you can get from 99 MPs to 100 MPs with a MM of +1).
Example: Your system currently has 117 MPs. Nothing happened during this turn. Now if your MM is 0, your Morale will drop by 1 point. If the MM is 1, it (the Morale) will remain the same. If the MM is 2, it will increase by 1. If the MM is 4, it will only increase by 2, because the "normal" increase of 3 points would bring you into the higher LV, where your MM has a lower effect.
This also means that if your system has 100 MPs and a MM of +1 (for example, the Great Hall and nothing else), it will stay at 100.
Such a system has a base value of 100 MPs. The value is capped at 195. (however, I once had 200 MPs on Romulus, it was either a bug or a special event, the latter would mean that special events can bypass the cap. Btw I couldn't maintain the value of 200 back then, it dropped back to 195)
Although the highest LV number is 5, a MM of, say, +8 will still have its effect, bringing you to 195 MPs fast, where the value will remain.
On "Impossible", your starting systems will have a base value of 80 and the following levels:
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LV0: 1 - 79 Morale Points
LV1: 80 - 99 MPs
LV2: 100 - 118 MPs
LV3: 119 - 137 MPs
LV4: 138 - 156 MPs
LV5: 157 - 175 MPs
LV6: 176 - 194 MPs
The cap is 194 here.
Your other systems will still have the same LVs as on the lower difficulties, since they start with 100 MPs.
Now I tested a few minor race systems, playing as Cardassians and acquiring them as members. The resulting base values (they did not depend on the difficulty level or the Minor Race's attitude towards me):
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100 for the Ktarians
100 for the Mintakans
100 for the Nausicaans
80 for the Tamarians
85 for the Trill
100 for the Ullians
100 for the Zakdorn
Conclusions:
(1) The values are always 20 points higher than on the table. Perhaps that's because they're happy members.