Notebook

One Machine against Infinite Bus (OMIB) simulation with PowerSimulationsDynamics.jl

Originally Contributed by: Rodrigo Henriquez and José Daniel Lara

Introduction¶

This tutorial will introduce you to the functionality of PowerSimulationsDynamics for running power system dynamic simulations.

This tutorial presents a simulation of a two-bus system with an infinite bus (represented as a voltage source behind an impedance) at bus 1, and a classic machine on bus 2. The perturbation will be the trip of one of the two circuits (doubling its resistance and impedance) of the line that connects both buses.

Dependencies¶

In [1]:

using SIIPExamples #hide
using PowerSimulationsDynamics
PSID = PowerSimulationsDynamics
using PowerSystems
using Sundials
using Plots
gr()

[ Info: Precompiling PowerSimulationsDynamics [398b2ede-47ed-4edc-b52e-69e4a48b4336]
[ Info: Precompiling Sundials [c3572dad-4567-51f8-b174-8c6c989267f4]

Out[1]:

Plots.GRBackend()

PowerSystems (abbreviated with PSY) is used to properly define the data structure and establish an equilibrium point initial condition with a power flow routine, while Sundials is used to solve the problem defined in PowerSimulationsDynamics.

Load the system¶

The following command requires that you have executed the dynamic systems data example previously to generate the json file.

In [2]:

file_dir = joinpath(
    dirname(dirname(pathof(SIIPExamples))),
    "script",
    "4_PowerSimulationsDynamics_examples",
    "Data",
)
omib_sys = System(joinpath(file_dir, "omib_sys.json"))

[ Info: Loaded time series from storage file existing=omib_sys_time_series_storage.h5 new=/var/folders/27/2jr8c7gn4j72fvrg4qt81zrw8w_711/T/jl_CJpTN1
┌ Warning: struct DynamicGenerator does not exist in validation configuration file, validation skipped
└ @ InfrastructureSystems ~/.julia/packages/InfrastructureSystems/v75Hd/src/validation.jl:51
┌ Warning: struct DynamicGenerator does not exist in validation configuration file, validation skipped
└ @ InfrastructureSystems ~/.julia/packages/InfrastructureSystems/v75Hd/src/validation.jl:51
┌ Warning: There are no ElectricLoad Components in the System
└ @ PowerSystems ~/.julia/packages/PowerSystems/4kGrw/src/utils/IO/system_checks.jl:56

Out[2]:

System

Base Power: 100.0

Components

Num components: 10

8 rows × 3 columns (omitted printing of 1 columns)

	ConcreteType	SuperTypes
	String	String
1	Arc	Topology <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any
2	Area	AggregationTopology <: Topology <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any
3	Bus	Topology <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any
4	DynamicGenerator{BaseMachine,SingleMass,AVRFixed,TGFixed,PSSFixed}	DynamicInjection <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any
5	Line	ACBranch <: Branch <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any
6	LoadZone	AggregationTopology <: Topology <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any
7	Source	StaticInjection <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any
8	ThermalStandard	ThermalGen <: Generator <: StaticInjection <: Device <: Component <: InfrastructureSystemsComponent <: InfrastructureSystemsType <: Any

TimeSeriesContainer

Components with time series data: 0

Total StaticTimeSeries: 0

Total Forecasts: 0

Resolution: 0 seconds

Build the simulation and initialize the problem¶

The next step is to create the simulation structure. This will create the indexing of our system that will be used to formulate the differential-algebraic system of equations. To do so, it is required to specify the perturbation that will occur in the system. PowerSimulationsDynamics supports three types of perturbations:

Network Switch: Change in the Y-bus values.
Branch Trip: Disconnects a line from the system.
Change in Reference Parameter

Here, we will use a Branch Trip perturbation, that is modeled by modifying the specifying which line we want to trip. In this case we disconnect one of the lines that connects BUS 1 and BUS 2, named "BUS 1-BUS 2-i_1".

With this, we are ready to create our simulation structure:

In [3]:

time_span = (0.0, 30.0)
perturbation_trip = BranchTrip(1.0, "BUS 1-BUS 2-i_1")
sim = PSID.Simulation(pwd(), omib_sys, time_span, perturbation_trip)

[ Info: Serialized time series data to /var/folders/27/2jr8c7gn4j72fvrg4qt81zrw8w_711/T/jl_rz4W6B/sys_time_series_storage.h5.
[ Info: Serialized System to /var/folders/27/2jr8c7gn4j72fvrg4qt81zrw8w_711/T/jl_rz4W6B/sys.json
[ Info: Loaded time series from storage file existing=sys_time_series_storage.h5 new=/var/folders/27/2jr8c7gn4j72fvrg4qt81zrw8w_711/T/jl_5pYqF2
┌ Warning: struct DynamicGenerator does not exist in validation configuration file, validation skipped
└ @ InfrastructureSystems ~/.julia/packages/InfrastructureSystems/v75Hd/src/validation.jl:51
┌ Warning: struct DynamicGenerator does not exist in validation configuration file, validation skipped
└ @ InfrastructureSystems ~/.julia/packages/InfrastructureSystems/v75Hd/src/validation.jl:51
┌ Warning: There are no ElectricLoad Components in the System
└ @ PowerSystems ~/.julia/packages/PowerSystems/4kGrw/src/utils/IO/system_checks.jl:56

Out[3]:

Simulation()

This will automatically initialize the system by running a power flow and update V_ref, P_ref and hence eq_p (the internal voltage) to match the solution of the power flow. It will also initialize the states in the equilibrium, which can be printed with:

In [4]:

print_device_states(sim)

Voltage Variables
====================
BUS 1
====================
Vm 1.05
θ -0.0
====================
BUS 2
====================
Vm 1.04
θ 0.0229
====================
====================
Differential States
generator-102-1
====================
δ 0.1685
ω 1.0
====================

To examine the calculated initial conditions, we can export them into a dictionary:

In [5]:

x0_init = PSID.get_initial_conditions(sim)

Out[5]:

Dict{String,Any} with 5 entries:
  "generator-102-1" => Dict(:ω=>1.0,:δ=>0.168525)
  "V_R"             => Dict(102=>1.03973,101=>1.05)
  "Vm"              => Dict(102=>1.04,101=>1.05)
  "θ"               => Dict(102=>0.0228958,101=>-1.27016e-19)
  "V_I"             => Dict(102=>0.0238095,101=>-1.33367e-19)

Run the Simulation¶

Finally, to run the simulation we simply use:

In [6]:

PSID.execute!(
    sim, #simulation structure
    IDA(), #Sundials DAE Solver
    dtmax = 0.02,
); #Arguments: Maximum timestep allowed

In some cases, the dynamic time step used for the simulation may fail. In such case, the keyword argument dtmax can be used to limit the maximum time step allowed for the simulation.

Exploring the solution¶

PowerSimulationsDynamics has two functions to obtain different states of the solution:

get_state_series(sim, ("generator-102-1", :δ)): can be used to obtain the solution as

a tuple of time and the required state. In this case, we are obtaining the rotor angle :δ of the generator named "generator-102-1".

In [7]:

angle = get_state_series(sim, ("generator-102-1", :δ));
Plots.plot(angle, xlabel = "time", ylabel = "rotor angle [rad]", label = "rotor angle")

Out[7]:

get_voltagemag_series(sim, 102): can be used to obtain the voltage magnitude as a

tuple of time and voltage. In this case, we are obtaining the voltage magnitude at bus 102 (where the generator is located).

In [8]:

volt = get_voltagemag_series(sim, 102);
Plots.plot(volt, xlabel = "time", ylabel = "Voltage [pu]", label = "V_2")

Out[8]:

Optional: Small Signal Analysis¶

PowerSimulationsDynamics uses automatic differentiation to compute the reduced Jacobian of the system for the differential states. This can be used to analyze the local stability of the linearized system. We need to re-initialize our simulation:

In [9]:

sim2 = PSID.Simulation(pwd(), omib_sys, time_span, perturbation_trip)

small_sig = small_signal_analysis(sim2)

[ Info: Serialized time series data to /var/folders/27/2jr8c7gn4j72fvrg4qt81zrw8w_711/T/jl_ItVYcx/sys_time_series_storage.h5.
[ Info: Serialized System to /var/folders/27/2jr8c7gn4j72fvrg4qt81zrw8w_711/T/jl_ItVYcx/sys.json
[ Info: Loaded time series from storage file existing=sys_time_series_storage.h5 new=/var/folders/27/2jr8c7gn4j72fvrg4qt81zrw8w_711/T/jl_uOiNgv
┌ Warning: struct DynamicGenerator does not exist in validation configuration file, validation skipped
└ @ InfrastructureSystems ~/.julia/packages/InfrastructureSystems/v75Hd/src/validation.jl:51
┌ Warning: struct DynamicGenerator does not exist in validation configuration file, validation skipped
└ @ InfrastructureSystems ~/.julia/packages/InfrastructureSystems/v75Hd/src/validation.jl:51
┌ Warning: There are no ElectricLoad Components in the System
└ @ PowerSystems ~/.julia/packages/PowerSystems/4kGrw/src/utils/IO/system_checks.jl:56

Out[9]:

The system is small signal stable

The small_sig result can report the reduced jacobian for \delta and \omega,

In [10]:

small_sig.reduced_jacobian

Out[10]:

2×2 Array{Float64,2}:
  0.0       376.991
 -0.466763   -0.317662

and can also be used to report the eigenvalues of the reduced linearized system:

In [11]:

small_sig.eigenvalues

Out[11]:

2-element Array{Complex{Float64},1}:
 -0.15883100381194412 - 13.264252860693972im
 -0.15883100381194412 + 13.264252860693972im

This notebook was generated using Literate.jl.