{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# PTDF with [PowerSimulations.jl](https://github.com/NREL-SIIP/PowerSimulations.jl)"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "**Originally Contributed by**: Sourabh Dalvi"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Introduction"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "PowerSimulations.jl supports linear PTDF optimal power flow formulation. This example shows a\n",
    "single multi-period optimization of economic dispatch with a linearized DC-OPF representation of\n",
    "using PTDF power flow and how to extract duals values or locational marginal prices for energy."
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Dependencies"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using SIIPExamples\n",
    "using PowerSystems\n",
    "using PowerSimulations\n",
    "const PSI = PowerSimulations\n",
    "using PowerSystemCaseBuilder\n",
    "using DataFrames"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Since we'll be retrieving duals, we need a solver that returns duals values\n",
    "here we use HiGHS."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using HiGHS # mip solver\n",
    "solver = optimizer_with_attributes(HiGHS.Optimizer, \"mip_rel_gap\" => 0.05)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can use the same RTS data and some of the initialization as in\n",
    "[OperationsProblem example](https://nbviewer.jupyter.org/github/NREL-SIIP/SIIPExamples.jl/blob/master/notebook/3_PowerSimulations_examples/01_operations_problems.ipynb)"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "sys = build_system(PSITestSystems, \"modified_RTS_GMLC_DA_sys\")"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Here, we want do define an economic dispatch (linear generation decisions) with\n",
    "linear DC-OPF using PTDF network representation.\n",
    "So, starting with the network, we can select from _almost_ any of the endpoints on this\n",
    "tree:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "print_tree(PowerSimulations.PM.AbstractPowerModel)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Calculate the PTDF matrix."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "PTDF_matrix = PTDF(sys)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "For now, let's just choose a standard PTDF formulation."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "template = template_unit_commitment(\n",
    "    network = NetworkModel(\n",
    "        StandardPTDFModel,\n",
    "        PTDF = PTDF_matrix,\n",
    "        duals = [CopperPlateBalanceConstraint],\n",
    "        use_slacks = false,\n",
    "    ),\n",
    "    use_slacks = true,\n",
    ")\n",
    "for (k, v) in template.branches\n",
    "    v.duals = [NetworkFlowConstraint]\n",
    "end"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we can build a 4-hour economic dispatch / OPF problem with the RTS data.\n",
    "Here, we have to pass the keyword argument `constraint_duals` to OperationsProblem\n",
    "with the name of the constraint for which duals are required for them to be returned in the results."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "problem = DecisionModel(template, sys, horizon = 24, optimizer = solver)\n",
    "build!(problem, output_dir = mktempdir())"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "And solve the problem and collect the results"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "solve!(problem)"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Here we collect the dual values from the results for the `:CopperPlateBalance` and `:network_flow`\n",
    "constraints. In the case of PTDF network formulation we need to compute the final LMP for each bus in the system by\n",
    "subtracting the duals (μ) of `:network_flow` constraints multiplied by the PTDF matrix\n",
    "from the  dual (λ) of `:CopperPlateBalance` constraint."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "res = ProblemResults(problem)\n",
    "duals = read_duals(\n",
    "    res,\n",
    "    [k for k in list_dual_keys(res) if PSI.get_entry_type(k) == NetworkFlowConstraint],\n",
    ")\n",
    "λ = read_dual(res, \"CopperPlateBalanceConstraint__System\")[:, 2]\n",
    "flow_duals = outerjoin(values(duals)..., on = :DateTime)\n",
    "μ = Matrix(flow_duals[:, PTDF_matrix.axes[1]])"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Here we calculate LMP as λ + congestion component of the LMP which is a product of μ and the PTDF matrix."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "LMP = flow_duals[:, [:DateTime]]\n",
    "for bus in get_components(Bus, sys)\n",
    "    LMP[:, get_name(bus)] = λ .+ μ * PTDF_matrix[:, get_number(bus)]\n",
    "end"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "Finally here we have the LMPs"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "LMP"
   ],
   "metadata": {},
   "execution_count": null
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
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