Line Modeling Simulations

Originally Contributed by: Rodrigo Henriquez-Auba and José Daniel Lara

Introduction

This tutorial will introduce an example of considering dynamic lines in PowerSimulationsDynamics.

This tutorial presents a simulation of a three-bus system, with an infinite bus (represented as a voltage source behind an impedance) at bus 1, a one d- one q- machine on bus 2 and an inverter of 19 states, as a virtual synchronous machine at bus 3. The perturbation will be the trip of two of the three circuits (triplicating its resistance and impedance) of the line that connects bus 1 and bus 3. This case also consider a dynamic line model for connection between buses 2 and 3. We will compare it against a system without dynamic lines.

It is recommended to check the OMIB tutorial first, since that includes more details and explanations on all definitions and functions.

Step 1: Package Initialization

julia> using PowerSimulationsDynamics
julia> using PowerSystems
julia> using PowerNetworkMatrices
julia> using PowerSystemCaseBuilder
julia> using Sundials
julia> using Plots

Step 2: Data creation

Load the system using PowerSystemCaseBuilder.jl:

julia> threebus_sys = build_system(PSIDSystems, "Three Bus Dynamic data Example System")ERROR: UndefVarError: `build_system` not defined

In addition, we will create a new copy of the system on which we will simulate the same case, but will consider dynamic lines:

julia> threebus_sys_dyn = deepcopy(threebus_sys);ERROR: UndefVarError: `threebus_sys` not defined

Step 3: Create the fault and simulation on the Static Lines system

First, we construct the perturbation, by properly computing the new Ybus on the system:

julia> #Make a copy of the original system
       sys2 = deepcopy(threebus_sys)
       #Triplicates the impedance of the line named "BUS 1-BUS 3-i_1"ERROR: UndefVarError: `threebus_sys` not defined
julia> fault_branches = get_components(ACBranch, sys2)ERROR: UndefVarError: `sys2` not defined
julia> for br in fault_branches
           if get_name(br) == "BUS 1-BUS 3-i_1"
               br.r = 3 * br.r
               br.x = 3 * br.x
               b_new = (from = br.b.from / 3, to = br.b.to / 3)
               br.b = b_new
           end
       end
       #Obtain the new YbusERROR: UndefVarError: `fault_branches` not defined
julia> Ybus_fault = Ybus(sys2).data
       #Define Fault: Change of YBusERROR: UndefVarError: `sys2` not defined
julia> Ybus_change = NetworkSwitch(
           1.0, #change at t = 1.0
           Ybus_fault, #New YBus
       );ERROR: UndefVarError: `Ybus_fault` not defined

Now, we construct the simulation:

julia> #Time span of our simulation
       tspan = (0.0, 30.0)
       
       #Define Simulation(0.0, 30.0)
julia> sim = Simulation(
           ResidualModel, #Type of model used
           threebus_sys, #system
           pwd(), #folder to output results
           tspan, #time span
           Ybus_change, #Type of perturbation
       )ERROR: UndefVarError: `threebus_sys` not defined

We can obtain the initial conditions as:

julia> #Print the initial states. It also give the symbols used to describe those states.
       show_states_initial_value(sim)ERROR: UndefVarError: `sim` not defined

Step 4: Run the simulation of the Static Lines System

julia> #Run the simulation
       execute!(
           sim, #simulation structure
           IDA(), #Sundials DAE Solver
           dtmax = 0.02, #Maximum step size
       )ERROR: UndefVarError: `sim` not defined

Step 5: Store the solution

julia> results = read_results(sim)ERROR: UndefVarError: `sim` not defined
julia> series2 = get_voltage_magnitude_series(results, 102)ERROR: UndefVarError: `results` not defined
julia> zoom = [
           (series2[1][ix], series2[2][ix]) for
           (ix, s) in enumerate(series2[1]) if (s > 0.90 && s < 1.6)
       ];ERROR: UndefVarError: `series2` not defined

Step 3.1: Create the fault and simulation on the Dynamic Lines system

An important aspect to consider is that DynamicLines must not be considered in the computation of the Ybus. First we construct the Dynamic Line, by finding the Line named "BUS 2-BUS 3-i_1", and then adding it to the system.

julia> # get component return the Branch on threebus_sys_dyn named "BUS 2-BUS 3-i_1"
       dyn_branch = DynamicBranch(get_component(Line, threebus_sys_dyn,"BUS 2-BUS 3-i_1"))
       # Adding a dynamic line will immediately remove the static line from the system.ERROR: UndefVarError: `threebus_sys_dyn` not defined
julia> add_component!(threebus_sys_dyn, dyn_branch)ERROR: UndefVarError: `threebus_sys_dyn` not defined

Similarly, we construct the Ybus fault by creating a copy of the original system, but removing the Line "BUS 2-BUS 3-i_1" to avoid considering it in the Ybus:

julia> #Make a copy of the original system
       sys3 = deepcopy(threebus_sys);
       #Remove Line "BUS 2-BUS 3-i_1"ERROR: UndefVarError: `threebus_sys` not defined
julia> remove_component!(Line, sys3, "BUS 2-BUS 3-i_1")
       #Triplicates the impedance of the line named "BUS 1-BUS 2-i_1"ERROR: UndefVarError: `sys3` not defined
julia> fault_branches2 = get_components(Line, sys3)ERROR: UndefVarError: `sys3` not defined
julia> for br in fault_branches2
           if get_name(br) == "BUS 1-BUS 3-i_1"
               br.r = 3 * br.r
               br.x = 3 * br.x
               b_new = (from = br.b.from / 3, to = br.b.to / 3)
               br.b = b_new
           end
       end
       #Obtain the new YbusERROR: UndefVarError: `fault_branches2` not defined
julia> Ybus_fault_dyn = Ybus(sys3).data
       #Define Fault: Change of YBusERROR: UndefVarError: `sys3` not defined
julia> Ybus_change_dyn = NetworkSwitch(
           1.0, #change at t = 1.0
           Ybus_fault_dyn, #New YBus
       )ERROR: UndefVarError: `Ybus_fault_dyn` not defined

Step 4.1: Run the simulation of the Dynamic Lines System

Now, we construct the simulation:

julia> # Define Simulation
       sim_dyn = Simulation(
           ResidualModel, #Type of model used
           threebus_sys_dyn, #system
           pwd(), #folder to output results
           (0.0, 30.0), #time span
           Ybus_change_dyn, #Type of perturbation
       )ERROR: UndefVarError: `threebus_sys_dyn` not defined

julia> # Run the simulation
       execute!(
           sim_dyn, #simulation structure
           IDA(), #Sundials DAE Solver
           dtmax = 0.02, #Maximum step size
       )ERROR: UndefVarError: `sim_dyn` not defined

We can obtain the initial conditions as:

julia> #Print the initial states. It also give the symbols used to describe those states.
       show_states_initial_value(sim_dyn)ERROR: UndefVarError: `sim_dyn` not defined

Step 5.1: Store the solution

julia> results_dyn = read_results(sim_dyn)ERROR: UndefVarError: `sim_dyn` not defined
julia> series2_dyn = get_voltage_magnitude_series(results_dyn, 102);ERROR: UndefVarError: `results_dyn` not defined
julia> zoom_dyn = [
           (series2_dyn[1][ix], series2_dyn[2][ix]) for
           (ix, s) in enumerate(series2_dyn[1]) if (s > 0.90 && s < 1.6)
       ];ERROR: UndefVarError: `series2_dyn` not defined

Step 6.1: Compare the solutions:

We can observe the effect of Dynamic Lines

julia> plot(series2_dyn, label = "V_gen_dyn");ERROR: UndefVarError: `series2_dyn` not defined
julia> plot!(series2, label = "V_gen_st", xlabel = "Time [s]", ylabel = "Voltage [pu]");ERROR: UndefVarError: `series2` not defined

that looks quite similar. The differences can be observed in the zoom plot:

julia> plot(zoom_dyn, label = "V_gen_dyn");ERROR: UndefVarError: `zoom_dyn` not defined
julia> plot!(zoom, label = "V_gen_st", xlabel = "Time [s]", ylabel = "Voltage [pu]");ERROR: UndefVarError: `zoom` not defined