Help me identify the type of Knapack Problem I am dealing with
There's no special "name" for this problem that I'm aware of. Don't assume that problem specifications this specific will necessarily have a "name" or "type".

Instead, it's simply one of many problems that can be solved straightforwardly with dynamic programming.  You fill in an array $A[1..n]$, defined as follows: $A[i]$ is the minimum number of power supplies needed to provide power to sections $1,2,3,\dots,i$.  Then there is a simple recurrence for $A[i]$ that allows you to fill in the entire array in $O(n)$ time, namely,

$$A[i] = 1 + \min \{ A[j] : 10-i  \le j &lt; i \text{ and } P(j,i-1)\}$$

where $P(j,i-1)$ is true if a single power supply can power sections $j,j+1,\dots,i-1$ simultaneously.

This allows you to compute the minimal number of power supplies needed.

Then, once you know this number, you can know optimize things to find the most equal distribution of power.  Let $k$ denote the number of power supplies, and $\mu$ denote the average power per supply when using $k$ supplies.  Given a constant threshold $t$, you can determine whether there exists a way to power all sections using $k$ power supplies such that every power supply's power consumption falls in the range $\mu-t \dots \mu+t$, using similar methods.  Now use binary search on $t$ to find the minimal $t$ such that this is possible.  This will give you the solution to your problem.

In general, computer science provides many techniques that can be combined in creative ways to solve problems.  When you have a new problem with multiple specific requirements, you might have to look for how to apply those techniques in a way specific to your particular situation; there's no guarantee that it will fall cleanly into some existing "category" or "type".