A Dual Method for Computing Power Transfer Distribution Factors

Abstract

Abstract-Power Transfer Distribution Factors (PTDFs) play a crucial role in power grid security analysis, planning, and redispatch. Fast calculation of the PTDFs is therefore of great importance. In this paper, we present a non-approximative dual method of computing PTDFs. It uses power flows along topological cycles of the network but still relies on simple matrix algebra. At the core, our method changes the size of the matrix that needs to be inverted to calculate the PTDFs from N × N , where N is the number of buses, towhere L is the number of lines and L − N + 1 is the number of independent cycles (closed loops) in the network while remaining mathematically fully equivalent. For power grids containing a relatively small number of cycles, the method can offer a speedup of numerical calculations.

A new restructuring of centralized congestion management focusing on flow-gate and locational price impacts

“…Now, an increase in the active power injection at bus s and a corresponding decrease at node r is assumed. The amount of changes is assumed equal to P. The new vector of active power injections can therefore be expressed as follows 21 :…”

“…To decrease the notational clutter, the dependence of P′ on s and r is removed. The voltage angles of buses can be rearranged as follows 21 :…”

“…where X = B −1 is the Moore-Penrose pseudoinverse of the nodal susceptance matrix. Eventually, PTDFs are given as follows 21 :…”

“…where F ij = b ij (θ i − θ j ) and b ij indicate the susceptance between 2 buses of i and j. 21 It is clear that q sr is a matrix that only includes 0, +1, and −1. Considering +1 and −1 for the beginning and end nodes means that the PTDFs of each line have the largest positive and negative values at their own beginning and end nodes.…”

“…The operation of electric power systems is mainly denoted by the equilibrium of active and reactive power on all buses of the network (ie, Tellegen's theorem). 21 The active power balance at one node is defined as follows 21 :…”