6.2 Standard DC OPF

When using DC network modeling assumptions and limiting polynomial costs to second order, the standard OPF problem above can be simplified to a quadratic program, with linear constraints and a quadratic cost function. In this case, the voltage magnitudes and reactive powers are eliminated from the problem completely and real power flows are modeled as linear functions of the voltage angles. The optimization variable is

     [    ]
x =

and the overall problem reduces to the following form.

min     fiP(pig)

subject to

gP(Θ, Pg) = BbusΘ  + Pbus,shift + Pd + Gsh − CgPg =  0

  𝜃rief≤ 𝜃i ≤ 𝜃rief,      i ∈ ℐref                     (6.32)
 i,min    i    i,max
pg    ≤ pg ≤ pg   ,    i = 1...ng                  (6.33)