{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from functions.pressure_conversion import pressure_conversion\n",
    "from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class\n",
    "from Druckrohrleitung.Druckrohrleitung_class_file import Druckrohrleitung_class\n",
    "from Turbinen.Turbinen_class_file import Francis_Turbine\n",
    "from Regler.Regler_class_file import PI_controller_class"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "#define constants\n",
    "\n",
    "#Turbine\n",
    "Q_nenn          = 0.85  # m³/s\n",
    "p_nenn          = pressure_conversion(10.6,'bar','Pa')\n",
    "closing_time    = 70    #s\n",
    "\n",
    "# physics\n",
    "g               = 9.81                          # gravitational acceleration [m/s²]\n",
    "rho             = 1000.                         # density of water [kg/m³]\n",
    "\n",
    "\n",
    "# define controller constants\n",
    "target_level = 8.  # m\n",
    "Kp = 0.1\n",
    "Ti = 10.\n",
    "deadband_range = 0.05 # m\n",
    "\n",
    "\n",
    "# pipeline\n",
    "L               = 535.+478.                     # length of pipeline [m]\n",
    "D               = 0.9                           # pipe diameter [m]\n",
    "A_pipe          = D**2/4*np.pi                  # pipeline area\n",
    "h_pipe          = 105                           # hydraulic head without reservoir [m] \n",
    "alpha           = np.arcsin(h_pipe/L)           # Höhenwinkel der Druckrohrleitung \n",
    "n               = 50                            # number of pipe segments in discretization\n",
    "f_D             = 0.014                           # Darcy friction factor\n",
    "c               = 500.                          # propagation velocity of the pressure wave [m/s]\n",
    "# consider prescribing a total simulation time and deducting the number of timesteps from that\n",
    "nt              = 1000                          # number of time steps after initial conditions\n",
    "\n",
    "# derivatives of the pipeline constants\n",
    "dx              = L/n                           # length of each pipe segment\n",
    "dt              = dx/c                          # timestep according to method of characterisitics\n",
    "nn              = n+1                           # number of nodes\n",
    "initial_level   = target_level                  # water level in upstream reservoir [m]\n",
    "pl_vec          = np.arange(0,nn,1)*dx          # pl = pipe-length. position of the nodes on the pipeline\n",
    "t_vec           = np.arange(0,nt+1)*dt          # time vector\n",
    "h_vec           = np.arange(0,nn,1)*h_pipe/n    # hydraulic head of pipeline at each node \n",
    "\n",
    "\n",
    "\n",
    "# reservoir\n",
    "# replace influx by vector\n",
    "initial_flux                = Q_nenn/1.1        # initial influx  of volume to the reservoir [m³/s]\n",
    "initial_pressure_unit       = 'Pa'      # DO NOT CHANGE! for pressure conversion in print statements and plot labels \n",
    "conversion_pressure_unit    = 'bar'     # for pressure conversion in print statements and plot labels\n",
    "area_base                   = 74.       # total base are of the cuboid reservoir [m²]   \n",
    "area_outflux                = A_pipe    # outlfux area of the reservoir, given by pipeline area [m²]\n",
    "critical_level_low          = 0.        # for yet-to-be-implemented warnings[m]\n",
    "critical_level_high         = np.inf    # for yet-to-be-implemented warnings[m]\n",
    "\n",
    "# make sure e-RK4 method of reservoir has a small enough timestep to avoid runaway numerical error\n",
    "nt_eRK4                     = 1000      # number of simulation steps of reservoir in between timesteps of pipeline              \n",
    "simulation_timestep         = dt/nt_eRK4\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# create objects\n",
    "\n",
    "V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,simulation_timestep)\n",
    "V.set_steady_state(initial_flux,initial_level,conversion_pressure_unit)\n",
    "\n",
    "\n",
    "pipe = Druckrohrleitung_class(L,D,n,alpha,f_D)\n",
    "pipe.set_pressure_propagation_velocity(c)\n",
    "pipe.set_number_of_timesteps(nt)\n",
    "pipe.set_steady_state(initial_flux,initial_level,pl_vec,h_vec)\n",
    "\n",
    "initial_pressure_turbine = pipe.get_current_pressure_distribution()[-1]\n",
    "\n",
    "T1 = Francis_Turbine(Q_nenn,p_nenn,closing_time,timestep = dt)\n",
    "T1.set_steady_state(initial_flux,initial_pressure_turbine)\n",
    "\n",
    "Pegelregler = PI_controller_class(target_level,deadband_range,Kp,Ti,dt)\n",
    "Pegelregler.control_variable = T1.get_current_LA()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialization for timeloop\n",
    "\n",
    "# prepare the vectors in which the pressure and velocity distribution in the pipeline from the previous timestep are stored\n",
    "v_old = pipe.get_current_velocity_distribution()\n",
    "p_old = pipe.get_current_pressure_distribution()\n",
    "\n",
    "# prepare the vectors in which the temporal evolution of the boundary conditions are stored\n",
    "    # keep in mind, that the velocity at the turbine and the pressure at the reservoir follow from boundary conditions\n",
    "        # reservoir level and flow through turbine\n",
    "    # the pressure at the turbine and the velocity at the reservoir are calculated from the method of characteristics\n",
    "v_boundary_res  = np.zeros_like(t_vec)\n",
    "v_boundary_tur  = np.zeros_like(t_vec)\n",
    "p_boundary_res  = np.zeros_like(t_vec)\n",
    "p_boundary_tur  = np.zeros_like(t_vec)\n",
    "\n",
    "# prepare the vectors that store the temporal evolution of the level in the reservoir\n",
    "level_vec       = np.full(nt+1,initial_level)  # level at the end of each pipeline timestep\n",
    "\n",
    "# set the boundary conditions for the first timestep\n",
    "v_boundary_res[0]   = v_old[0]\n",
    "v_boundary_tur[0]   = v_old[-1] \n",
    "p_boundary_res[0]   = p_old[0]\n",
    "p_boundary_tur[0]   = p_old[-1]\n",
    "\n",
    "LA_soll_vec = np.full_like(t_vec,T1.LA)\n",
    "LA_ist_vec  = np.full_like(t_vec,T1.LA)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib qt5\n",
    "# time loop\n",
    "\n",
    "# create a figure and subplots to display the velocity and pressure distribution across the pipeline in each pipeline step\n",
    "fig1,axs1 = plt.subplots(2,1)\n",
    "fig1.suptitle(str(0) +' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
    "axs1[0].set_title('Pressure distribution in pipeline')\n",
    "axs1[1].set_title('Velocity distribution in pipeline')\n",
    "axs1[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
    "axs1[0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
    "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n",
    "axs1[1].set_ylabel(r'$v$ [$\\mathrm{m} / \\mathrm{s}$]')\n",
    "lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.')\n",
    "lo_01, = axs1[1].plot(pl_vec,v_old,marker='.')\n",
    "axs1[0].autoscale()\n",
    "axs1[1].autoscale()\n",
    "\n",
    "fig1.tight_layout()\n",
    "fig1.show()\n",
    "plt.pause(1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2146505196687856\n"
     ]
    }
   ],
   "source": [
    "print(initial_flux/area_outflux)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# loop through time steps of the pipeline\n",
    "for it_pipe in range(1,pipe.nt+1):\n",
    "\n",
    "\n",
    "    if it_pipe > 0.015*(nt+1):\n",
    "        if V.get_current_influx() > 0:\n",
    "            V.set_influx(np.max([V.get_current_influx()-initial_flux*5*1e-3,0.]))\n",
    "# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n",
    "    # set initial conditions for the reservoir time evolution calculted with e-RK4\n",
    "    V.set_pressure      = p_old[0]\n",
    "    V.set_outflux       = v_old[0]\n",
    "    # calculate the time evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n",
    "    for it_res in range(nt_eRK4):\n",
    "        V.timestep_reservoir_evolution()                                                             \n",
    "    level_vec[it_pipe] = V.get_current_level()                                                 \n",
    "\n",
    "    # get the control variable\n",
    "    Pegelregler.update_control_variable(level_vec[it_pipe])\n",
    "    LA_soll_vec[it_pipe] = Pegelregler.get_current_control_variable()\n",
    "    \n",
    "    # change the Leitapparatöffnung  based on the target value\n",
    "    T1.update_LA(LA_soll_vec[it_pipe])\n",
    "    T1.set_pressure(p_old[-1])\n",
    "\n",
    "    LA_ist_vec[it_pipe] = T1.LA\n",
    "\n",
    "    # set boundary conditions for the next timestep of the characteristic method\n",
    "    p_boundary_res[it_pipe] = V.get_current_pressure()\n",
    "    v_boundary_tur[it_pipe] = 1/A_pipe*T1.get_current_Q()\n",
    "\n",
    "    # the the boundary conditions in the pipe.object and thereby calculate boundary pressure at turbine\n",
    "    pipe.set_boundary_conditions_next_timestep(p_boundary_res[it_pipe],v_boundary_tur[it_pipe])\n",
    "    p_boundary_tur[it_pipe] = pipe.get_current_pressure_distribution()[-1]\n",
    "    v_boundary_res[it_pipe] = pipe.get_current_velocity_distribution()[0]\n",
    "\n",
    "    # perform the next timestep via the characteristic method\n",
    "    pipe.timestep_characteristic_method()\n",
    "\n",
    "    # prepare for next loop\n",
    "    p_old = pipe.get_current_pressure_distribution()\n",
    "    v_old = pipe.get_current_velocity_distribution()\n",
    "\n",
    "    # plot some stuff\n",
    "        # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n",
    "    lo_00.remove()\n",
    "    lo_01.remove()\n",
    "    # lo_02.remove()\n",
    "        # plot new pressure and velocity distribution in the pipeline\n",
    "    lo_00, = axs1[0].plot(pl_vec,pressure_conversion(p_old,initial_pressure_unit, conversion_pressure_unit),marker='.',c='blue')\n",
    "    lo_01, = axs1[1].plot(pl_vec,v_old,marker='.',c='blue')\n",
    "    # lo_02, = axs1[2].plot(level_vec_2,c='blue')\n",
    "    fig1.suptitle(str(round(t_vec[it_pipe],2))+ ' s / '+str(round(t_vec[-1],2)) + ' s' )\n",
    "    fig1.canvas.draw()\n",
    "    fig1.tight_layout()\n",
    "    fig1.show()\n",
    "    plt.pause(0.001)    \n",
    "\n",
    "        \n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# plot time evolution of boundary pressure and velocity as well as the reservoir level\n",
    "\n",
    "fig2,axs2 = plt.subplots(3,2)\n",
    "axs2[0,0].set_title('Pressure reservoir')\n",
    "axs2[0,0].plot(t_vec,pressure_conversion(p_boundary_res,initial_pressure_unit, conversion_pressure_unit))\n",
    "axs2[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[0,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
    "\n",
    "axs2[0,1].set_title('Velocity reservoir')\n",
    "axs2[0,1].plot(t_vec,v_boundary_res)\n",
    "axs2[0,1].set_ylim(-2*Q_nenn,+2*Q_nenn)\n",
    "axs2[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[0,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
    "\n",
    "axs2[1,0].set_title('Pressure turbine')\n",
    "axs2[1,0].plot(t_vec,pressure_conversion(p_boundary_tur,initial_pressure_unit, conversion_pressure_unit))\n",
    "axs2[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[1,0].set_ylabel(r'$p$ ['+conversion_pressure_unit+']')\n",
    "\n",
    "axs2[1,1].set_title('Velocity turbine')\n",
    "axs2[1,1].plot(t_vec,v_boundary_tur)\n",
    "axs2[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[1,1].set_ylabel(r'$v$ [$\\mathrm{m}/\\mathrm{s}$]')\n",
    "\n",
    "axs2[2,0].set_title('Level reservoir')\n",
    "axs2[2,0].plot(t_vec,level_vec)\n",
    "axs2[2,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[2,0].set_ylabel(r'$h$ [m]')\n",
    "\n",
    "axs2[2,1].set_title('LA')\n",
    "axs2[2,1].plot(t_vec,100*LA_soll_vec)\n",
    "axs2[2,1].plot(t_vec,100*LA_ist_vec)\n",
    "axs2[2,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n",
    "axs2[2,1].set_ylabel(r'$LA$ [%]')\n",
    "fig2.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "print(np.sum(v_boundary_res[2500:])*area_outflux)"
   ]
  }
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