4.2 DC Power Flow

For the DC power flow problem [20], the vector x  consists of the set of voltage angles at non-reference buses

    [    ]
x =  𝜃{i} ,  ∀i ∕∈ ℐref

and (4.1) takes the form

Bdcx − Pdc = 0

where Bdc  is the (nb − 1) × (nb − 1)  matrix obtained by simply eliminating from Bbus   the row and column corresponding to the slack bus and reference angle, respectively. Given that the generator injections Pg  are specified at all but the slack bus, Pdc  can be formed directly from the non-slack rows of the last four terms of (3.32).

The voltage angles in x  are computed by a direct solution of the set of linear equations. The branch flows and slack bus generator injection are then calculated directly from the bus voltage angles via (3.29) and the appropriate row in (3.32), respectively.