{ "cells": [ { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from Regler_class_file import PI_controller_class\n", "\n", "#importing Druckrohrleitung\n", "import sys\n", "import os\n", "current = os.path.dirname(os.path.realpath('Main_Programm.ipynb'))\n", "parent = os.path.dirname(current)\n", "sys.path.append(parent)\n", "from functions.pressure_conversion import pressure_conversion\n", "from Ausgleichsbecken.Ausgleichsbecken_class_file import Ausgleichsbecken_class\n", "from Turbinen.Turbinen_class_file import Francis_Turbine" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "# define constants\n", "\n", " # for physics\n", "g = 9.81 # [m/s²] gravitational acceleration \n", "rho = 1000. # [kg/m³] density of water \n", "pUnit_calc = 'Pa' # [text] DO NOT CHANGE! for pressure conversion in print statements and plot labels \n", "pUnit_conv = 'mWS' # [text] for pressure conversion in print statements and plot labels\n", "\n", "\n", " # for Turbine\n", "Tur_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n", "Tur_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", "Tur_closingTime = 90. # [s] closing time of turbine\n", "\n", "\n", " # for PI controller\n", "Con_targetLevel = 8. # [m]\n", "Con_K_p = 0.1 # [-] proportional constant of PI controller\n", "Con_T_i = 10. # [s] timespan in which a steady state error is corrected by the intergal term\n", "Con_deadbandRange = 0.05 # [m] Deadband range around targetLevel for which the controller does NOT intervene\n", "\n", "\n", " # for pipeline\n", "Pip_length = (535.+478.) # [m] length of pipeline\n", "Pip_dia = 0.9 # [m] diameter of pipeline\n", "Pip_area = Pip_dia**2/4*np.pi # [m²] crossectional area of pipeline\n", "Pip_head = 105. # [m] hydraulic head of pipeline without reservoir\n", "Pip_angle = np.arcsin(Pip_head/Pip_length) # [rad] elevation angle of pipeline \n", "Pip_n_seg = 50 # [-] number of pipe segments in discretization\n", "Pip_f_D = 0.014 # [-] Darcy friction factor\n", "Pip_pw_vel = 500. # [m/s] propagation velocity of the pressure wave (pw) in the given pipeline\n", " # derivatives of the pipeline constants\n", "Pip_dx = Pip_length/Pip_n_seg # [m] length of each pipe segment\n", "Pip_dt = Pip_dx/Pip_pw_vel # [s] timestep according to method of characteristics\n", "Pip_nn = Pip_n_seg+1 # [1] number of nodes\n", "Pip_x_vec = np.arange(0,Pip_nn,1)*Pip_dx # [m] vector holding the distance of each node from the upstream reservoir along the pipeline\n", "Pip_h_vec = np.arange(0,Pip_nn,1)*Pip_head/Pip_n_seg # [m] vector holding the vertival distance of each node from the upstream reservoir\n", "\n", "\n", " # for reservoir\n", "Res_area_base = 10. # [m²] total base are of the cuboid reservoir \n", "Res_area_out = Pip_area # [m²] outflux area of the reservoir, given by pipeline area\n", "Res_level_crit_lo = 0. # [m] for yet-to-be-implemented warnings\n", "Res_level_crit_hi = np.inf # [m] for yet-to-be-implemented warnings\n", "Res_dt_approx = 1e-3 # [s] approx. timestep of reservoir time evolution to ensure numerical stability (see Res_nt why approx.)\n", "Res_nt = max(1,int(Pip_dt//Res_dt_approx)) # [1] number of timesteps of the reservoir time evolution within one timestep of the pipeline\n", "Res_dt = Pip_dt/Res_nt # [s] harmonised timestep of reservoir time evolution\n", "\n", " # for general simulation\n", "flux_init = Tur_Q_nenn/1.1 # [m³/s] initial flux through whole system for steady state initialization \n", "level_init = Con_targetLevel # [m] initial water level in upstream reservoir for steady state initialization\n", "simTime_target = 600. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\n", "nt = int(simTime_target//Pip_dt) # [1] Number of timesteps of the whole system\n", "t_vec = np.arange(0,nt+1,1)*Pip_dt # [s] time vector. At each step of t_vec the system parameters are stored\n" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "# create objects\n", "offset_pressure = pressure_conversion(Pip_head,'mws',pUnit_calc)\n", "\n", "# Upstream reservoir\n", "reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,Res_level_crit_lo,Res_level_crit_hi,rho)\n", "reservoir.set_steady_state(flux_init,level_init)\n", "\n", "# downstream turbine\n", "turbine = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime,Pip_dt,pUnit_conv)\n", "turbine.set_steady_state(flux_init,reservoir.get_current_pressure()+offset_pressure)\n", "\n", "\n", "# level controll\n", "level_control = PI_controller_class(Con_targetLevel,Con_deadbandRange,Con_K_p,Con_T_i,Pip_dt)\n", "level_control.set_control_variable(turbine.get_current_LA(),display_warning=False)\n" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [ "level_vec = np.zeros_like(t_vec)\n", "level_vec[0] = level_init\n", "LA_ist_vec = np.zeros_like(t_vec)\n", "LA_ist_vec[0] = turbine.get_current_LA()\n", "LA_soll_vec = np.zeros_like(t_vec)\n", "LA_soll_vec[0] = turbine.get_current_LA()\n", "Q_vec = np.zeros_like(t_vec)\n", "Q_vec[0] = turbine.get_current_Q()" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0\n", "40.52\n", "81.04\n", "121.56\n", "162.08\n", "202.6\n", "243.12\n", "283.64\n", "324.16\n", "364.68\n", "405.2\n", "445.72\n", "486.24\n", "526.76\n", "567.28\n" ] } ], "source": [ "# time loop\n", "\n", "for i in range(nt+1):\n", "\n", " if np.mod(i,1e3) == 0:\n", " print(t_vec[i])\n", "\n", " if i > 0.1*(nt+1):\n", " reservoir.set_influx(0.)\n", "\n", " p = reservoir.get_current_pressure()\n", " level_control.update_control_variable(reservoir.level)\n", " LA_soll = level_control.get_current_control_variable()\n", " turbine.update_LA(LA_soll)\n", " turbine.set_pressure(p+offset_pressure)\n", " LA_soll_vec[i] = LA_soll\n", " LA_ist_vec[i] = turbine.get_current_LA()\n", " Q_vec[i] = turbine.get_current_Q()\n", "\n", " \n", " reservoir.set_outflux(Q_vec[i],display_warning=False)\n", "\n", " for it_res in range(Res_nt):\n", " reservoir.timestep_reservoir_evolution() \n", " level_vec[i] = reservoir.get_current_level()\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 32, "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(3,1)\n", "axs1[0].set_title('Level')\n", "axs1[0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs1[0].set_ylabel(r'$h$ [$\\mathrm{m}$]')\n", "axs1[0].plot(t_vec,level_vec)\n", "axs1[0].set_ylim([0*level_init,1.5*level_init])\n", "axs1[1].set_title('Flux')\n", "axs1[1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs1[1].set_ylabel(r'$Q$ [$\\mathrm{m} / \\mathrm{s}^3$]')\n", "axs1[1].plot(t_vec,Q_vec)\n", "axs1[1].set_ylim([0,2*flux_init])\n", "axs1[2].set_title('LA')\n", "axs1[2].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs1[2].set_ylabel(r'$LA$ [%]')\n", "axs1[2].plot(t_vec,LA_soll_vec)\n", "axs1[2].plot(t_vec,LA_ist_vec)\n", "axs1[2].set_ylim([0,1])\n", "fig1.tight_layout()\n", "fig1.show()\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.8.13 ('Georg_DT_Slot3')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.13" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "84fb123bdc47ab647d3782661abcbe80fbb79236dd2f8adf4cef30e8755eb2cd" } } }, "nbformat": 4, "nbformat_minor": 2 }