Notebook

Using PowerSystems to calculate network matrices¶

Originally Contributed by: Clayton Barrows

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: 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 4 does not match the value at bus 4
[ Info: the voltage setpoint on generator 1 does not match the value at bus 1
[ Info: the voltage setpoint on generator 5 does not match the value at bus 10
[ Info: the voltage setpoint on generator 2 does not match the value at bus 1
[ Info: the voltage setpoint on generator 3 does not match the value at bus 3
[ 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
┌ Warning: Rate 1200.0 MW for bus2-bus3-i_4 is larger than the max expected in the range of (min = 134.0, max = 145.0).
└ @ PowerSystems ~/.julia/packages/PowerSystems/N2l8o/src/utils/IO/branchdata_checks.jl:148
┌ Warning: Rate 200.0 MW for bus1-bus2-i_1 is larger than the max expected in the range of (min = 134.0, max = 145.0).
└ @ PowerSystems ~/.julia/packages/PowerSystems/N2l8o/src/utils/IO/branchdata_checks.jl:148
┌ Warning: Rate 200.0 MW for bus1-bus4-i_2 is larger than the max expected in the range of (min = 134.0, max = 145.0).
└ @ PowerSystems ~/.julia/packages/PowerSystems/N2l8o/src/utils/IO/branchdata_checks.jl:148
┌ Warning: Rate 200.0 MW for bus4-bus5-i_7 is larger than the max expected in the range of (min = 134.0, max = 145.0).
└ @ PowerSystems ~/.julia/packages/PowerSystems/N2l8o/src/utils/IO/branchdata_checks.jl:148
┌ Warning: Rate 1000.0 MW for bus1-bus5-i_3 is larger than the max expected in the range of (min = 134.0, max = 145.0).
└ @ PowerSystems ~/.julia/packages/PowerSystems/N2l8o/src/utils/IO/branchdata_checks.jl:148
[ Info: Reading branch data
[ Info: Reading DC Line data
[ Info: Reading storage data

Out[1]:

System

Base Power: 100.0

Components

Num components: 30

9 rows × 3 columns

	ConcreteType	SuperTypes	Count
	String	String	Int64
1	Arc	Topology <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	6
2	Area	AggregationTopology <: Topology <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	1
3	Bus	Topology <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	5
4	Line	ACBranch <: Branch <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	5
5	LoadZone	AggregationTopology <: Topology <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	1
6	PhaseShiftingTransformer	ACBranch <: Branch <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	2
7	PowerLoad	StaticLoad <: ElectricLoad <: StaticInjection <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	3
8	RenewableDispatch	RenewableGen <: Generator <: StaticInjection <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	2
9	ThermalStandard	ThermalGen <: Generator <: StaticInjection <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any	5

TimeSeriesContainer

Components with time series data: 0

Total StaticTimeSeries: 0

Total Forecasts: 0

Resolution: 0 seconds

Ybus¶

In [2]:

ybus = Ybus(sys)

[ 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          0.0+0.0im
      0.0+0.0im      -9.16758+91.6758im          0.0+0.0im
  -3.2569+32.569im        0.0+0.0im         -3.33367+33.3367im
 -15.4703+154.703im       0.0+0.0im           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.