PTDF (Power Transmission Distribution Factors)¶

GridCal features a PTDF simulation of the branches sensitivity to the generation variations. This classic method is implemented in GridCal using two variants:

Vary power by generator by generator.
Vary power by generator technology group.
Vary power by node (this is the most general case).

The simulation consists in:

Simulate a base power flow and collect the results.
Compute all the power variation vectors ( $Svaried$ ) either by generator or by group. These vector will have the same length as the number of nodes.
For every variation:

C.1. run a power flow simulation with the varied power injections $Sbus = Sbus_0 - Svaried$

C.2. Collect the power flow results.

C.3. Compute the branch sensitivity ( $PTDF_{i,j}$ ) as the power flow variation divided by the power generation variation.

$PTDF_{i,j} = \frac{Sbranch_{0j} - Sbranch_j}{power\_variation_i}$

This renders a simple method to identify how much power flow changed in a branch given the successive generation diminishings.

PTDF results for the Pegase 1354-bus grid.

VTDF (Voltage Transmission Distribution Factors)¶

We can extend the PTDF simple concept to the capture of other magnitudes’ variation. In this case we can capture the voltage module variation.

$VTDF_{i,j} = \frac{V_{0j} - V_j}{power\_variation_i}$

PTDF and VTDF times series¶

To know the sensitivity is alright, but the real use of the PTDF and VTDF is to get estimations of the flows and voltages in far less time than performing a normal time series simulation.

The formulation for the flows is:

$Sbranch_{t,j} = Sbranch_{0, j} + PTDF_{i, j} \cdot power\_variation_{t,i} \quad \forall j \in Branches, i \in Variations, t \in Time$

Which in matrix form turns into:

$Sbranch_t = Sbranch_{0} + PTDF \times power\_variation_t \quad \forall t \in Time$

The voltage form is the same equation, replacing the magnitude of interest:

$V_{t,j} = V_{0, j} + VTDF_{i, j} \cdot power\_variation_{t,i} \quad \forall j \in Branches, i \in Variations, t \in Time$

Which in matrix form turns into:

$V_t = V_{0} + VTDF \times power\_variation_t \quad \forall t \in Time$

The results of branch flow and voltage module for the IEEE39 with the weekly profiles provided by GridCal is:

PTDF results for the IEEE39 with a week’s profile

VTDF results for the IEEE39 with a week’s profile