y=|x1-x2| for binary variable is the same as y = x1 xor x2. This can be written as:

y <= x1+x2 
y >= x1-x2 
y >= x2-x1 
y <= 2-x1-x2

(see here).

When x1,x2 are continuous variables between 0 and U you can write:

y1-y2 = x1-x2
y = y1+y2
y1 <= delta*U
y2 <= (1-delta)*U
y1>=0
y2>=0
delta in {0,1}

In many cases this can be simplified.

The arguments to Model.addGenConstrAbs() must be variables (Var), not linear expressions (LinExpr). Try this:

for t in range(0,Period):
    z = m.addVar(lb=-GRB.INFINITY)
    m.addConstr(z == EG[t]+STG[t]-XXX)
    m.addGenConstrAbs(PEN[t], z, "PEN Constraint") 

Hi I think what you are trying to do is not supported by gurobi yet. Not at least as a quadratic programming.

First you have your variables in the denominator which is not advised / supported directly Second what you are defining is not a quadratic problem. It is a polynomial problem. As far as I know gurobi currently supports only quadratic programs with expressions such as y*y

This is unconstrained problem so I wonder why you need gurobi. Scientific solvers deal with these problem pretty well using gradient decent, Newton and so on methods

I hope this helps