Introduction¶

PowerSystems.jl supports the calculation of several different matrix representations of power system networks. This example demonstrates how to use PowerSystems.jl to calculate:

Y bus
Power transfer distribution factor (PTDF)
Line outage distribution factor (LODF)

Dependencies¶

Let's use a dataset from the tabular data parsing example

In [1]:

using SIIPExamples

pkgpath = dirname(dirname(pathof(SIIPExamples)))
include(joinpath(pkgpath, "test", "2_PowerSystems_examples", "02_parse_matpower.jl"))

[ Info: Correcting vm in bus 1 to 1.07762 to match generator set-point
[ Info: Correcting vm in bus 3 to 1.1 to match generator set-point
[ Info: Correcting vm in bus 4 to 1.06414 to match generator set-point
[ Info: Correcting vm in bus 10 to 1.06907 to match generator set-point
[ Info: Correcting vm in bus 3 to 1.0 to match generator set-point
┌ Error: Generator voltage set-points for bus 3 are inconsistent. This can lead to unexpected results
└ @ PowerSystems ~/.julia/packages/PowerSystems/gGFFl/src/parsers/pm_io/matpower.jl:245
[ Info: Correcting vm in bus 10 to 1.0 to match generator set-point
┌ Error: Generator voltage set-points for bus 10 are inconsistent. This can lead to unexpected results
└ @ PowerSystems ~/.julia/packages/PowerSystems/gGFFl/src/parsers/pm_io/matpower.jl:245
[ Info: extending matpower format with data: areas 1x3
[ Info: extending matpower format with data: gen_name 7x4
[ Info: extending matpower format by appending matrix "gen_name" in to "gen"
[ Info: reversing the orientation of branch 6 (4, 3) to be consistent with other parallel branches
[ Info: the voltage setpoint on generator 6 does not match the value at bus 3
[ Info: the voltage setpoint on generator 7 does not match the value at bus 10
[ Info: removing 1 cost terms from generator 4: [4000.0, 0.0]
[ Info: removing 1 cost terms from generator 1: [1400.0, 0.0]
[ Info: removing 1 cost terms from generator 5: [1000.0, 0.0]
[ Info: removing 1 cost terms from generator 2: [1500.0, 0.0]
[ Info: removing 3 cost terms from generator 6: Float64[]
[ Info: removing 3 cost terms from generator 7: Float64[]
[ Info: removing 1 cost terms from generator 3: [3000.0, 0.0]
┌ Info: Constructing System from Power Models
│   data["name"] = "nesta_case5_pjm"
└   data["source_type"] = "matpower"
[ Info: Reading bus data
[ Info: Reading generator data
[ Info: Reading branch data
[ Info: Reading branch data
[ Info: Reading DC Line data
[ Info: Reading storage data

Out[1]:

System
Property	Value
System Units Base	SYSTEM_BASE
Base Power	100.0
Base Frequency	60.0
Num Components	30

Static Components
Type	Count	Has Static Time Series	Has Forecasts
Arc	6	false	false
Area	1	false	false
Bus	5	false	false
Line	5	false	false
LoadZone	1	false	false
PhaseShiftingTransformer	2	false	false
PowerLoad	3	false	false
RenewableDispatch	2	false	false
ThermalStandard	5	false	false

Ybus¶

In [2]:

ybus = Ybus(sys)

[ Info: Validating connectivity with Goderya algorithm
[ Info: The System has no islands

Out[2]:

PowerNetworkMatrix
:
  22.2507-222.484im  -3.52348+35.2348im  …  -15.4703+154.703im
 -3.52348+35.2348im   12.6911-126.898im              ⋅    
          ⋅          -9.16758+91.6758im              ⋅    
  -3.2569+32.569im            ⋅             -3.33367+33.3367im
 -15.4703+154.703im           ⋅               18.804-188.021im

PTDF¶

In [3]:

ptdf = PTDF(sys)

Out[3]:

PowerNetworkMatrix
:
  0.23245   -0.37175   -0.219627  0.0   0.19124
  0.41667    0.201807   0.119226  0.0   0.342801
  0.35088    0.169943   0.100401  0.0  -0.53404
  0.23245    0.62825   -0.219627  0.0   0.19124
  0.116225   0.314125   0.390186  0.0   0.0956199
  0.116225   0.314125   0.390186  0.0   0.0956199
 -0.35088   -0.169943  -0.100401  0.0  -0.46596

LODF¶

In [4]:

lodf = LODF(sys)

Out[4]:

PowerNetworkMatrix
:
 -1.0        0.398488   0.3581   -1.0       -0.360154  -0.360154  -0.3581
  0.542857  -1.0        0.6419    0.542857   0.195512   0.195512  -0.6419
  0.457143   0.601512  -1.0       0.457143   0.164642   0.164642   1.0
 -1.0        0.398488   0.3581   -1.0       -0.360154  -0.360154  -0.3581
 -0.5        0.199244   0.17905  -0.5       -1.0        0.639846  -0.17905
 -0.5        0.199244   0.17905  -0.5        0.639846  -1.0       -0.17905
 -0.457143  -0.601512   1.0      -0.457143  -0.164642  -0.164642  -1.0

Indexing¶

Note that the axes of these matrices that correspond to buses are indexed by bus number (::Int64) while the branch axes are indexed by branch name (::String). You can access specific elements of the matrices as follows:

In [5]:

ptdf["bus3-bus4-i_6", 3]

Out[5]:

0.39018648100730935

Additionally, PowerSystems provides accessors to the network matrices that take Componets as arguments so that you can pass references to the components themselves rather than the name or number. For example:

In [6]:

buses = collect(get_components(Bus, sys))
ybus[buses[1], buses[2]]

Out[6]:

-3.2569046378322044 + 32.56904637832204im

If you would instead like to index by bus name, something like the following should work:

In [7]:

busname2num = get_components(Bus, sys) |> (c -> Dict(zip(get_name.(c), get_number.(c))))
ptdf["bus3-bus4-i_6", busname2num["bus3"]]

Out[7]:

0.39018648100730935

This notebook was generated using Literate.jl.