Network Matrices

PowerSystems.jl is able to build classic power systems modeling network matrices such as Ybus, PTDF and LODF

Check section Network Matrices for more details

Overview

Network matrices are implemented in PowerSystems.jl as arrays that enable using Branch or Bus names as indexes to facilitate exploration and analysis. Ybus is stored as an SparseMatrix and the PTDF and LODF are stored as dense matrices. **Note*** Ybus is converted to a dense matrix for printing in the REPL, The network matrices code implements the Goderya algorithm to find islands.

using PowerSystems
const PSY = PowerSystems
system_data = System(joinpath(DATA_DIR, "matpower/case14.m"))

System

Base Power: 100.0

Components

Num components: 73

9 rows × 3 columns

TimeSeriesContainer

Components with time series data: 0

Total StaticTimeSeries: 0

Total Forecasts: 0

Resolution: 0 seconds

Ybus

The ybus can be calculated as follows:

ybus = Ybus(system_data)

The matrix can be indexed using directly the bus numbers. In this example buses are numbered 1-14. However, in large systems buses don't usually follow sequential numbering. You can access the entries of the Ybus with direct indexing or using the buses.

ybus_entry = ybus[3,3]

bus3 = get_component(Bus, system_data, "Bus 3     HV")
ybus_entry = ybus[bus3, bus3]

We recognize that many models require matrix operations. For those cases, you can access the sparse data as follows:

sparse_array = get_data(ybus)

PTDF

The PTDF matrix can be calculated as follows:

ptdf = PTDF(system_data)

The entries of the matrix can also be indexed using the devices directly:

line = get_component(Line, system_data, "Bus 1     HV-Bus 2     HV-i_1")
bus = get_component(Bus, system_data, "Bus 3     HV")

ptdf_entry = ptdf[line, bus]

Alternatively, the branch name and bus number can be used. For instance, for the same PTDF entry we can do:

ptdf_entry = ptdf["Bus 1     HV-Bus 2     HV-i_1", 3]

PTDF also takes a vector of distributed slacks, for now this feature requires passing a vector of weights with the same number of elements are buses in the system. For more details check the API entry for PTDF.

In the same fashion as in the case of the Ybus, we recognize many models use matrix operations when using the PTDF matrix. The raw data is available using get_data and the lookup table between (names,numbers) and (i,j) matrix entries is available using get_lookup

branch_lookup, bus_lookup = get_lookup(ptdf);
nothing #hide

Branch lookup:

branch_lookup

Bus Look up

bus_lookup

LODF

LODF and PTDF share the same characteristics in terms of indexing and calculation:

lodf = LODF(system_data)