DAE_simulation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m environment at `/tank/home/ciaran/DCSideBatteryModeling/Project.toml`\n"
     ]
    }
   ],
   "source": [
    "] activate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Precompiling OrdinaryDiffEq [1dea7af3-3e70-54e6-95c3-0bf5283fa5ed]\n",
      "└ @ Base loading.jl:1260\n",
      "┌ Info: Precompiling Plots [91a5bcdd-55d7-5caf-9e0b-520d859cae80]\n",
      "└ @ Base loading.jl:1260\n",
      "┌ Info: For saving to png with the Plotly backend ORCA has to be installed.\n",
      "└ @ Plots /home/ciaran/.julia/packages/Plots/ViMfq/src/backends.jl:373\n",
      "┌ Info: Precompiling PowerSystems [bcd98974-b02a-5e2f-9ee0-a103f5c450dd]\n",
      "└ @ Base loading.jl:1260\n",
      "┌ Info: Precompiling ModelingToolkit [961ee093-0014-501f-94e3-6117800e7a78]\n",
      "└ @ Base loading.jl:1260\n"
     ]
    }
   ],
   "source": [
    "using LinearAlgebra\n",
    "using OrdinaryDiffEq #Gets the solvers\n",
    "using Plots\n",
    "plotly()\n",
    "using PowerSystems\n",
    "using DelimitedFiles\n",
    "\n",
    "include(joinpath(pwd(), \"DCSideBatteryModeling\", \"DCSideBatteryModeling.jl\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: The PSS(R)E parser currently supports buses, loads, shunts, generators, branches, transformers, and dc lines\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/parsers/pm_io/common.jl:26\n",
      "┌ Info: Constructing System from Power Models\n",
      "│   data[\"name\"] = omib\n",
      "│   data[\"source_type\"] = pti\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/parsers/power_models_data.jl:39\n",
      "┌ Info: Created InMemoryTimeSeriesStorage\n",
      "└ @ InfrastructureSystems /home/ciaran/.julia/packages/InfrastructureSystems/2F6Pq/src/in_memory_time_series_storage.jl:24\n",
      "┌ Info: Reading bus data\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/parsers/power_models_data.jl:140\n",
      "┌ Info: Reading generator data\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/parsers/power_models_data.jl:418\n",
      "┌ Info: Reading branch data\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/parsers/power_models_data.jl:575\n",
      "┌ Info: Reading branch data\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/parsers/power_models_data.jl:638\n",
      "┌ Info: Reading DC Line data\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/parsers/power_models_data.jl:609\n",
      "┌ Info: Unit System changed to SYSTEM_BASE\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/base.jl:353\n",
      "┌ Info: The System has no islands\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/utils/network_calculations/ybus_calculations.jl:139\n",
      "┌ Info: PowerFlow solve converged, the results have been stored in the system\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/utils/power_flow/power_flow.jl:307\n",
      "┌ Info: Unit System changed to SYSTEM_BASE\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/base.jl:359\n",
      "┌ Info: Serialized time series data to /tank/home/ciaran/DCSideBatteryModeling/data/OMIB_inverterDCside_time_series_storage.h5.\n",
      "└ @ InfrastructureSystems /home/ciaran/.julia/packages/InfrastructureSystems/2F6Pq/src/time_series_storage.jl:53\n",
      "┌ Info: Serialized System to /tank/home/ciaran/DCSideBatteryModeling/data/OMIB_inverterDCside.json\n",
      "└ @ InfrastructureSystems /home/ciaran/.julia/packages/InfrastructureSystems/2F6Pq/src/serialization.jl:8\n"
     ]
    }
   ],
   "source": [
    "include(joinpath(pwd(), \"data\",\"make_data.jl\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "┌ Info: Created InMemoryTimeSeriesStorage\n",
      "└ @ InfrastructureSystems /home/ciaran/.julia/packages/InfrastructureSystems/2F6Pq/src/in_memory_time_series_storage.jl:24\n",
      "┌ Warning: There are no Generator Components in the System\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/utils/IO/system_checks.jl:56\n",
      "┌ Warning: System peak load (50.0) exceeds total capacity capability (0).\n",
      "└ @ PowerSystems /home/ciaran/.julia/packages/PowerSystems/cvPQ9/src/utils/IO/system_checks.jl:72\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<h1>System</h1>\n",
       "<p><b>Base Power</b>: 100.0</p>\n",
       "<h2>Components</h2>\n",
       "<p><b>Num components</b>: 8</p>\n",
       "<table class=\"data-frame\"><thead><tr><th></th><th>ConcreteType</th><th>SuperTypes</th></tr><tr><th></th><th>String</th><th>String</th></tr></thead><tbody><p>7 rows × 3 columns (omitted printing of 1 columns)</p><tr><th>1</th><td>Area</td><td>AggregationTopology &lt;: Topology &lt;: Component &lt;: PowerSystemType &lt;: InfrastructureSystemsType &lt;: Any</td></tr><tr><th>2</th><td>Bus</td><td>Topology &lt;: Component &lt;: PowerSystemType &lt;: InfrastructureSystemsType &lt;: Any</td></tr><tr><th>3</th><td>DynamicInverter{AverageConverter,OuterControl{VirtualInertia,ReactivePowerDroop},CurrentControl,FixedDCSource,KauraPLL,LCLFilter}</td><td>DynamicInjection &lt;: Device &lt;: Component &lt;: PowerSystemType &lt;: InfrastructureSystemsType &lt;: Any</td></tr><tr><th>4</th><td>GenericBattery</td><td>Storage &lt;: StaticInjection &lt;: Device &lt;: Component &lt;: PowerSystemType &lt;: InfrastructureSystemsType &lt;: Any</td></tr><tr><th>5</th><td>Line</td><td>ACBranch &lt;: Branch &lt;: Device &lt;: Component &lt;: PowerSystemType &lt;: InfrastructureSystemsType &lt;: Any</td></tr><tr><th>6</th><td>LoadZone</td><td>AggregationTopology &lt;: Topology &lt;: Component &lt;: PowerSystemType &lt;: InfrastructureSystemsType &lt;: Any</td></tr><tr><th>7</th><td>PowerLoad</td><td>StaticLoad &lt;: ElectricLoad &lt;: StaticInjection &lt;: Device &lt;: Component &lt;: PowerSystemType &lt;: InfrastructureSystemsType &lt;: Any</td></tr></tbody></table>\n",
       "\n",
       "<h2>Forecasts</h2>\n",
       "<p><b>Resolution</b>: 0 seconds</p>\n",
       "<p><b>Horizon</b>: 0</p>\n",
       "<p><b>Initial Times</b>: </p>\n",
       "<p><b>Interval</b>: 0 seconds</p>\n",
       "<p><b>Components with Forecasts</b>: 0</p>\n",
       "<p><b>Total Forecasts</b>: 0</p>\n"
      ],
      "text/plain": [
       "System\n",
       "======\n",
       "System Units Base: SYSTEM_BASE\n",
       "Base Power: 100.0\n",
       "Base Frequency: 60.0\n",
       "\n",
       "Components\n",
       "==========\n",
       "Num components: 8\n",
       "\n",
       "7×3 DataFrame. Omitted printing of 3 columns\n",
       "│ Row │ │     │ ├─────┼\n",
       "│ 1   │ │ 2   │ │ 3   │ │ 4   │ │ 5   │ │ 6   │ │ 7   │ \n",
       "\n",
       "Forecasts\n",
       "=========\n",
       "Resolution: 0 seconds\n",
       "Horizon: 0\n",
       "Initial Times: \n",
       "Interval: 0 seconds\n",
       "Components with Forecasts: 0\n",
       "Total Forecasts: 0\n"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "omib_sys = System(joinpath(pwd(), \"data\", \"OMIB_inverterDCside.json\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Experiment Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0:0.25:5.0"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "InitialLoad = 0.2 # Initial value of the active power demand\n",
    "LoadStep = 0.5 # Active power step change\n",
    "CapSize = 2000e-6 # DC-link capacitor size\n",
    "StartTime=0 # Start time of time-domain simulation \n",
    "EndTime=0.05 # End time of time-domain simulation\n",
    "TimeStep= 0.0001 # Timestep of saved time series\n",
    "\n",
    "cap_range = 2000e-6:500e-6:7000e-6 # DC-link capacitor sizing\n",
    "kpred_range = 0:0.25:5 # Range of predictive gain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9-element Array{String,1}:\n",
       " \"Cb_dc\"\n",
       " \"cdc\"\n",
       " \"pl\"\n",
       " \"kpvb\"\n",
       " \"kivb\"\n",
       " \"kpib\"\n",
       " \"kiib\"\n",
       " \"kpred\"\n",
       " \"vdcʳ\""
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exp_params = [\"Cb_dc\", \"cdc\", \"pl\", \"kpvb\", \"kivb\", \"kpib\", \"kiib\", \"kpred\", \"vdcʳ\"] #This is a list of parameters that we will adjust during experiment "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Instantiate ODE Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ModelOperatingPoint\n"
      ]
     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameter_mapping = instantiate_parameters(omib_sys)\n",
    "M_4th= instantiate_4th_order_model(omib_sys)\n",
    "M_2nd= instantiate_2nd_order_model(omib_sys)\n",
    "M_0th= instantiate_0th_order_model(omib_sys)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "_parameter_names = [string(x.first) for x in parameter_mapping]; # Extract list of parameter values\n",
    "_parameter_values = [x.second for x in parameter_mapping]; # Extract list of parameter values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [],
   "source": [
    "params_indx = Dict{String,Integer}()\n",
    "for p in exp_params\n",
    "    params_indx[p] = findfirst(isequal(p), _parameter_names) # Dict mapping exp_parms to index corresponfing index in model\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_parameter_values[params_indx[\"cdc\"]]=CapSize/_parameter_values[params_indx[\"Cb_dc\"]]\n",
    "_parameter_values[params_indx[\"pl\"]]=InitialLoad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make copy of parameters and change value of load at t=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disturbance=deepcopy(_parameter_values)\n",
    "disturbance[params_indx[\"pl\"]]=InitialLoad+LoadStep # Load step change from 0.2 p.u. to 0.7 p.u."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Instantiate and simualte 4$^{th}$-, 2$^{nd}$- and 0$^{th}$-order model for non-optimized gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_4th_nonopt = instantiate_4th_order_dae(disturbance, M_4th; tspan = (StartTime, EndTime))\n",
    "sol_4th_nonopt = solve(sim_4th_nonopt, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_2nd_nonopt = instantiate_2nd_order_dae(disturbance, M_2nd; tspan = (StartTime, EndTime))\n",
    "sol_2nd_nonopt = solve(sim_2nd_nonopt, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_0th_nonopt = instantiate_0th_order_dae(disturbance, M_0th; tspan = (StartTime, EndTime))\n",
    "sol_0th_nonopt = solve(sim_0th_nonopt, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting DC-voltage for all three models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sol_4th_nonopt, vars=(0,13), label=\"4th-order\", ylabel=\"DC-link Voltage (p.u.)\")\n",
    "plot!(sol_2nd_nonopt, vars=(0,13), label=\"2nd-order\")\n",
    "plot!(sol_0th_nonopt, vars=(0,13), label=\"0th-order\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save results to array and write to .csv file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "untuned_4th = [sol_4th_nonopt.t transpose(Array(sol_4th_nonopt))]\n",
    "untuned_2nd = [sol_2nd_nonopt.t transpose(Array(sol_2nd_nonopt))]\n",
    "untuned_0th = [sol_0th_nonopt.t transpose(Array(sol_0th_nonopt))];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [],
   "source": [
    "fileName=string(\"results/dae_sim/untuned_4th_\", Int(floor(CapSize/1e-6)), \"uF.csv\")\n",
    "writedlm( fileName,  untuned_4th, ',')\n",
    "fileName=string(\"results/dae_sim/untuned_2nd_\", Int(floor(CapSize/1e-6)), \"uF.csv\")\n",
    "writedlm( fileName,  untuned_2nd, ',')\n",
    "fileName=string(\"results/dae_sim/untuned_0th_\", Int(floor(CapSize/1e-6)), \"uF.csv\")\n",
    "writedlm( fileName,  untuned_0th, ',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load optimal gains from parameter_search.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×1 Array{Float64,2}:\n",
       " 4443.0\n",
       "    0.06802762588059204"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fileName=string(\"results/stable_gains/capSize_\", Int(floor(CapSize/1e-6)), \"uF.csv\") \n",
    "gains = readdlm(fileName, ',') # Loading set of stable gains \n",
    "fileName=string(\"results/optimal_gains/capSize_\", Int(floor(CapSize/1e-6)), \"uF.csv\")\n",
    "optIndex = readdlm( fileName, ',') # Loading index of optimal set of gains"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set controller gains to optimal values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.0"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_parameter_values[params_indx[\"kpvb\"]]=gains[Int(optIndex[1]),1] #K_p^v\n",
    "_parameter_values[params_indx[\"kivb\"]]=gains[Int(optIndex[1]),2] #K_i^v\n",
    "_parameter_values[params_indx[\"kpib\"]]=gains[Int(optIndex[1]),3] #K_p^i\n",
    "_parameter_values[params_indx[\"kiib\"]]=gains[Int(optIndex[1]),4] #K_i^i"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Re-calculate initial conditons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "21-element Array{Float64,1}:\n",
       "  1.0067935237422023\n",
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       "  0.2023199540292933\n",
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       "  0.0002721717227920591\n",
       " -2.1729269003940933e-5\n",
       "  0.07044778826693796\n",
       " -0.002789251686115313\n",
       "  1.084409521544636\n",
       "  0.4294351687452164\n",
       " -7.084994987786322e-19\n",
       "  0.0706567181744013\n",
       "  2.5036080038079005e-38\n",
       "  4.600046756145387e-9\n",
       " -4.3790577010150533e-47\n",
       "  0.0\n",
       "  1.4375146112954338e-13"
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     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "M_4th(_parameter_values)\n",
    "M_2nd(_parameter_values)\n",
    "M_0th(_parameter_values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Make copy of parameters and change value of load at t=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "disturbance=deepcopy(_parameter_values)\n",
    "disturbance[params_indx[\"pl\"]]=InitialLoad+LoadStep # Load step change from 0.2 p.u. to 0.7 p.u."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Instantiate and simulate 4$^{th}$-, 2$^{nd}$- and 0$^{th}$-order model with optimized gains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_4th_opt = instantiate_4th_order_dae(disturbance, M_4th; tspan = (StartTime, EndTime))\n",
    "sol_4th_opt = solve(sim_4th_opt, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_2nd_opt = instantiate_2nd_order_dae(disturbance, M_2nd; tspan = (StartTime, EndTime))\n",
    "sol_2nd_opt = solve(sim_2nd_opt, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim_0th_opt = instantiate_0th_order_dae(disturbance, M_0th; tspan = (StartTime, EndTime))\n",
    "sol_0th_opt = solve(sim_0th_opt, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting DC-voltage for all three models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sol_4th_opt, vars=(0,13), label=\"4th-order\", ylabel=\"DC-link Voltage (p.u.)\")\n",
    "plot!(sol_2nd_opt, vars=(0,13), label=\"2nd-order\")\n",
    "plot!(sol_0th_opt, vars=(0,13), label=\"0th-order\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save results to array and write to .csv file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [],
   "source": [
    "tuned_4th = [sol_4th_opt.t transpose(Array(sol_4th_opt))]\n",
    "tuned_2nd = [sol_2nd_opt.t transpose(Array(sol_2nd_opt))]\n",
    "tuned_0th = [sol_0th_opt.t transpose(Array(sol_0th_opt))];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "fileName=string(\"results/dae_sim/tuned_4th_\", Int(floor(CapSize/1e-6)), \"uF.csv\")\n",
    "writedlm( fileName,  tuned_4th, ',')\n",
    "fileName=string(\"results/dae_sim/tuned_2nd_\", Int(floor(CapSize/1e-6)), \"uF.csv\")\n",
    "writedlm( fileName,  tuned_2nd, ',')\n",
    "fileName=string(\"results/dae_sim/tuned_0th_\", Int(floor(CapSize/1e-6)), \"uF.csv\")\n",
    "writedlm( fileName,  tuned_0th, ',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Performance imporvement from increasing predictive gain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [],
   "source": [
    "_parameter_values[params_indx[\"kpred\"]]=0 #K_pred\n",
    "M_0th(_parameter_values) # Recalcualte initial conditons \n",
    "\n",
    "disturbance=deepcopy(_parameter_values)\n",
    "disturbance[params_indx[\"pl\"]]=InitialLoad+LoadStep # Load step change from 0.2 p.u. to 0.7 p.u.\n",
    "\n",
    "sim_k0 = instantiate_0th_order_dae(disturbance, M_0th; tspan = (StartTime, EndTime))\n",
    "sol_k0 = solve(sim_k0, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [],
   "source": [
    "_parameter_values[params_indx[\"kpred\"]]=1 #K_pred\n",
    "M_0th(_parameter_values) # Recalcualte initial conditons \n",
    "\n",
    "disturbance=deepcopy(_parameter_values)\n",
    "disturbance[params_indx[\"pl\"]]=InitialLoad+LoadStep # Load step change from 0.2 p.u. to 0.7 p.u.\n",
    "\n",
    "sim_k1 = instantiate_0th_order_dae(disturbance, M_0th; tspan = (StartTime, EndTime))\n",
    "sol_k1 = solve(sim_k1, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [],
   "source": [
    "_parameter_values[params_indx[\"kpred\"]]=2 #K_pred\n",
    "M_0th(_parameter_values) # Recalcualte initial conditons \n",
    "\n",
    "disturbance=deepcopy(_parameter_values)\n",
    "disturbance[params_indx[\"pl\"]]=InitialLoad+LoadStep # Load step change from 0.2 p.u. to 0.7 p.u.\n",
    "\n",
    "sim_k2 = instantiate_0th_order_dae(disturbance, M_0th; tspan = (StartTime, EndTime))\n",
    "sol_k2 = solve(sim_k2, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [],
   "source": [
    "_parameter_values[params_indx[\"kpred\"]]=5 #K_pred\n",
    "M_0th(_parameter_values) # Recalcualte initial conditons \n",
    "\n",
    "disturbance=deepcopy(_parameter_values)\n",
    "disturbance[params_indx[\"pl\"]]=InitialLoad+LoadStep # Load step change from 0.2 p.u. to 0.7 p.u.\n",
    "\n",
    "sim_k5 = instantiate_0th_order_dae(disturbance, M_0th; tspan = (StartTime, EndTime))\n",
    "sol_k5 = solve(sim_k5, Rodas5(), saveat = TimeStep);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting DC-voltage for various predictive gain"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(sol_k0, vars=(0,13), xlims = (0,0.025), label=\"k_pred=0\", ylabel=\"DC-link Voltage (p.u.)\")\n",
    "plot!(sol_k1, vars=(0,13), xlims = (0,0.025), label=\"k_pred=1\")\n",
    "plot!(sol_k2, vars=(0,13), xlims = (0,0.025), label=\"k_pred=2\")\n",
    "plot!(sol_k5, vars=(0,13), xlims = (0,0.025), label=\"k_pred=5\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Save results to array and write to .csv file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "kpred_0 = [sol_k0.t transpose(Array(sol_k0))]\n",
    "kpred_1 = [sol_k1.t transpose(Array(sol_k1))]\n",
    "kpred_2 = [sol_k2.t transpose(Array(sol_k2))];\n",
    "kpred_5 = [sol_k5.t transpose(Array(sol_k5))];"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [],
   "source": [
    "writedlm( \"results/dae_sim/kpred_0.csv\",  kpred_0, ',')\n",
    "writedlm( \"results/dae_sim/kpred_1.csv\",  kpred_1, ',')\n",
    "writedlm( \"results/dae_sim/kpred_2.csv\",  kpred_2, ',')\n",
    "writedlm( \"results/dae_sim/kpred_5.csv\",  kpred_5, ',')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculating reduction in voltage nadir"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "19.395725180396084"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nadir_reduction = 100*(minimum(kpred_5[:,14])-minimum(kpred_0[:,14]))/(_parameter_values[params_indx[\"vdcʳ\"]]-minimum(kpred_0[:,14]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sweeping DC_link Capacitor size and predictive gain to generate heatmap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [],
   "source": [
    "heat_map_values=reshape([],0,3);\n",
    "for cap in cap_range\n",
    "    for k in kpred_range\n",
    "        _parameter_values[params_indx[\"cdc\"]]=cap/_parameter_values[params_indx[\"Cb_dc\"]] # Adjusting DC-link capacitor size\n",
    "        fileName=string(\"results/stable_gains/capSize_\", Int(floor(cap/1e-6)), \"uF.csv\")\n",
    "        gains = readdlm(fileName, ',', Float64) # Loading set of stable gains\n",
    "        fileName=string(\"results/optimal_gains/capSize_\", Int(floor(cap/1e-6)), \"uF.csv\")\n",
    "        optIndex = readdlm(fileName, ',', Float64) # Loading index of optimal gain\n",
    "        _parameter_values[params_indx[\"kpvb\"]]=gains[Int(optIndex[1]),1] #K_p^v\n",
    "        _parameter_values[params_indx[\"kivb\"]]=gains[Int(optIndex[1]),2] #K_i^v\n",
    "        _parameter_values[params_indx[\"kpib\"]]=gains[Int(optIndex[1]),3] #K_p^i\n",
    "        _parameter_values[params_indx[\"kiib\"]]=gains[Int(optIndex[1]),4] #K_i^i\n",
    "        _parameter_values[params_indx[\"kpred\"]]=k #K_pred\n",
    "        M_0th(_parameter_values) #Initializing 0th order model\n",
    "\n",
    "        disturbance=deepcopy(_parameter_values)\n",
    "        disturbance[params_indx[\"pl\"]]=InitialLoad+LoadStep # Step change in load from 0.2 p.u. to 0.7 p.u.\n",
    "\n",
    "        sim = instantiate_0th_order_dae(disturbance, M_0th; tspan = (StartTime, EndTime))\n",
    "        sol = solve(sim, Rodas5(), saveat = TimeStep);\n",
    "        solArray = Array(sol)\n",
    "        nadir=100*maximum(_parameter_values[params_indx[\"vdcʳ\"]].-solArray[13,:]) # Calculating nadir drop in % of Base Votlage \n",
    "        \n",
    "        heat_map_values = [heat_map_values; [floor(cap/1e-3) k round(nadir, digits=3)]] # Concatenating results\n",
    "    end\n",
    "end\n",
    "writedlm( \"results/dae_sim/heat_map_matrix.csv\",  heat_map_values, ',') # Writing array to .csv file"
   ]
  }
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