diff --git a/.gitignore b/.gitignore index 9fc0ff3..e3d55f7 100644 --- a/.gitignore +++ b/.gitignore @@ -2,4 +2,5 @@ *__pycache__/ .vscode/settings.json *.pyc -Messing Around/ \ No newline at end of file +Messing Around/ +Messing Around/messy_nb.ipynb diff --git a/Druckrohrleitung/Druckrohrleitung_class_file.py b/Druckrohrleitung/Druckrohrleitung_class_file.py index c6ce967..d5f3737 100644 --- a/Druckrohrleitung/Druckrohrleitung_class_file.py +++ b/Druckrohrleitung/Druckrohrleitung_class_file.py @@ -240,7 +240,7 @@ class Druckrohrleitung_class: self.v[i] = 0.5*(self.v_old[i+1]+self.v_old[i-1])-0.5/(rho*c)*(self.p_old[i+1]-self.p_old[i-1]) \ +dt*g*np.sin(alpha)-f_D*dt/(4*D)*(abs(self.v_old[i+1])*self.v_old[i+1]+abs(self.v_old[i-1])*self.v_old[i-1]) - self.p[i] = 0.5*(self.p_old[i+1]+self.p_old[i-1]) - 0.5*rho*c*(self.v_old[i+1]-self.v_old[i-1]) \ + self.p[i] = 0.5*(self.p_old[i+1]+self.p_old[i-1])-0.5*rho*c*(self.v_old[i+1]-self.v_old[i-1]) \ +f_D*rho*c*dt/(4*D)*(abs(self.v_old[i+1])*self.v_old[i+1]-abs(self.v_old[i-1])*self.v_old[i-1]) # update overall min and max values for pressure and velocity per node @@ -254,3 +254,35 @@ class Druckrohrleitung_class: # else one can overwrite data by accidient and change two variables at once without noticing self.p_old = self.p.copy() self.v_old = self.v.copy() + + def timestep_characteristic_method_vectorized(self): + # use the method of characteristics to calculate the pressure and velocities at all nodes except the boundary ones + # they are set with the .set_boundary_conditions_next_timestep() method beforehand + + # constants for cleaner formula + rho = self.density # density of liquid + c = self.c # pressure propagation velocity + f_D = self.f_D # Darcy friction coefficient + dt = self.dt # timestep + D = self.dia # pipeline diameter + g = self.g # graviational acceleration + alpha = self.angle # pipeline angle + + # Vectorized loop + self.v[1:-1] = 0.5*(self.v_old[2:]+self.v_old[:-2])-0.5/(rho*c)*(self.p_old[2:]-self.p_old[:-2]) \ + +dt*g*np.sin(alpha)-f_D*dt/(4*D)*(np.abs(self.v_old[2:])*self.v_old[2:]+np.abs(self.v_old[:-2])*self.v_old[:-2]) + + self.p[1:-1] = 0.5*(self.p_old[2:]+self.p_old[:-2])-0.5*rho*c*(self.v_old[2:]-self.v_old[:-2]) \ + +f_D*rho*c*dt/(4*D)*(np.abs(self.v_old[2:])*self.v_old[2:]-np.abs(self.v_old[:-2])*self.v_old[:-2]) + + # update overall min and max values for pressure and velocity per node + self.p_min = np.minimum(self.p_min,self.p) + self.p_max = np.maximum(self.p_max,self.p) + self.v_min = np.minimum(self.v_min,self.v) + self.v_max = np.maximum(self.v_max,self.v) + + # prepare for next call + # use .copy() to write data to another memory location and avoid the usual python reference pointer + # else one can overwrite data by accidient and change two variables at once without noticing + self.p_old = self.p.copy() + self.v_old = self.v.copy() diff --git a/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb b/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb index 5e73d33..86d90d3 100644 --- a/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb +++ b/Druckrohrleitung/Druckrohrleitung_test_steady_state.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -22,7 +22,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -80,48 +80,9 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The pipeline has the following attributes: \n", - "----------------------------- \n", - "Length = 1013.0 m \n", - "Diameter = 0.9 m \n", - "Hydraulic head = 105.0 m \n", - "Number of segments = 50 \n", - "Number of nodes = 51 \n", - "Length per segments = 20.26 m \n", - "Pipeline angle = 0.104 rad \n", - "Pipeline angle = 5.95° \n", - "Darcy friction factor = 0.014 \n", - "Density of liquid = 1000.0 kg/m³ \n", - "Pressure wave vel. = 500.0 m/s \n", - "Simulation timestep = 0.04052 s \n", - "----------------------------- \n", - "Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n", - "The pipeline has the following attributes: \n", - "----------------------------- \n", - "Length = 1013.0 m \n", - "Diameter = 0.9 m \n", - "Hydraulic head = 105.0 m \n", - "Number of segments = 50 \n", - "Number of nodes = 51 \n", - "Length per segments = 20.26 m \n", - "Pipeline angle = 0.104 rad \n", - "Pipeline angle = 5.95° \n", - "Darcy friction factor = 0.014 \n", - "Density of liquid = 1000.0 kg/m³ \n", - "Pressure wave vel. = 500.0 m/s \n", - "Simulation timestep = 0.04052 s \n", - "----------------------------- \n", - "Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n" - ] - } - ], + "outputs": [], "source": [ "# create objects\n", "\n", @@ -137,7 +98,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -168,7 +129,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -193,48 +154,9 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The cuboid reservoir has the following attributes: \n", - "----------------------------- \n", - "Base area = 74.0 m² \n", - "Outflux area = 0.636 m² \n", - "Current level = 8.0 m\n", - "Critical level low = 0.0 m \n", - "Critical level high = inf m \n", - "Volume in reservoir = 592.0 m³ \n", - "Current influx = 0.773 m³/s \n", - "Current outflux = 0.773 m³/s \n", - "Current outflux vel = 1.215 m/s \n", - "Current pipe pressure = 7.854 mWS \n", - "Simulation timestep = 0.001013 s \n", - "Density of liquid = 1000.0 kg/m³ \n", - "----------------------------- \n", - "\n", - "The pipeline has the following attributes: \n", - "----------------------------- \n", - "Length = 1013.0 m \n", - "Diameter = 0.9 m \n", - "Hydraulic head = 105.0 m \n", - "Number of segments = 50 \n", - "Number of nodes = 51 \n", - "Length per segments = 20.26 m \n", - "Pipeline angle = 0.104 rad \n", - "Pipeline angle = 5.95° \n", - "Darcy friction factor = 0.014 \n", - "Density of liquid = 1000.0 kg/m³ \n", - "Pressure wave vel. = 500.0 m/s \n", - "Simulation timestep = 0.04052 s \n", - "----------------------------- \n", - "Velocity and pressure distribution are vectors and are accessible by the .v and .p attribute of the pipeline object\n" - ] - } - ], + "outputs": [], "source": [ "for it_pipe in range(1,nt+1):\n", "# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n", @@ -257,7 +179,7 @@ " 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", + " pipe.timestep_characteristic_method_vectorized()\n", "\n", " # prepare for next loop\n", " p_old = pipe.get_current_pressure_distribution()\n", @@ -283,7 +205,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ diff --git a/Kraftwerk/Kraftwerk_class_file.py b/Kraftwerk/Kraftwerk_class_file.py new file mode 100644 index 0000000..afce927 --- /dev/null +++ b/Kraftwerk/Kraftwerk_class_file.py @@ -0,0 +1,114 @@ +import numpy as np +#importing Druckrohrleitung +import sys +import os +current = os.path.dirname(os.path.realpath('Main_Programm.ipynb')) +parent = os.path.dirname(current) +sys.path.append(parent) +from functions.pressure_conversion import pressure_conversion +from Turbinen.Turbinen_class_file import Francis_Turbine + +class Kraftwerk_class: + g = 9.81 + + def __init__(self): + self.turbines = [] + self.n_turbines = 0 + +# setter + def set_LAs(self,LA_vec,display_warning=True): + for i in range(self.n_turbines): + self.turbines[i].set_LA(LA_vec[i],display_warning) + + def set_pressure(self,pressure): + for i in range(self.n_turbines): + self.turbines[i].set_pressure(pressure) + + def set_steady_state(self,ss_flux,ss_pressure): + self.identify_Q_proportion() + for i in range(self.n_turbines): + self.turbines[i].set_steady_state(ss_flux*self.Q_prop[i],ss_pressure) + +# getter + def get_current_Q(self): + Q = 0 + for i in range(self.n_turbines): + Q += self.turbines[i].get_current_Q() + return Q + + def get_current_LAs(self): + LAs = [] + for i in range(self.n_turbines): + LAs.append(self.turbines[i].get_current_LA()) + return np.array(LAs) + + def get_current_pressure(self): + pressures = [] + for i in range(self.n_turbines): + pressures.append(self.turbines[i].get_current_pressure()) + return np.array(pressures) # consider taking the average, after evaluating how the converge() method affects the result + + def get_n_turbines(self): + return self.n_turbines + + def get_info(self): + for turbine in self.turbines: + turbine.get_info(full=True) + +# methods + def identify_Q_proportion(self): + Q_n_vec = np.zeros(self.n_turbines) + for i in range(self.n_turbines): + Q_n_vec[i] = self.turbines[i].get_Q_n() + self.Q_prop = Q_n_vec/np.sum(Q_n_vec) + + def add_turbine(self,turbine): + self.turbines.append(turbine) + self.n_turbines += 1 + + def update_LAs(self,LA_soll_vec): + for i in range(self.n_turbines): + self.turbines[i].update_LA(LA_soll_vec[i]) + + def converge(self,convergence_parameters): + # small numerical disturbances (~1e-12 m/s) in the velocity can get amplified at the turbine node, because the new velocity of the turbine and the + # new pressure from the forward characteristic are not perfectly compatible. + # Therefore, iterate the flux and the pressure so long, until they converge + + eps = 1e-12 # convergence criterion: iteration change < eps + iteration_change = 1. # change in Q from one iteration to the next + i = 0 # safety variable. break loop if it exceeds 1e6 iterations + g = self.g # gravitational acceleration + p = convergence_parameters[0] # pressure at second to last node (see method of characterisctics - boundary condidtions) + v = convergence_parameters[1] # velocity at second to last node (see method of characterisctics - boundary condidtions) + D = convergence_parameters[2] # diameter of the pipeline + area_pipe = convergence_parameters[3] # area of the pipeline + alpha = convergence_parameters[4] # elevation angle of the pipeline + f_D = convergence_parameters[5] # Darcy friction coefficient + c = convergence_parameters[6] # pressure wave propagtation velocity + rho = convergence_parameters[7] # density of the liquid + dt = convergence_parameters[8] # timestep of the characteristic method + + Q_old = self.get_current_Q() + v_old = Q_old/area_pipe + + + while iteration_change > eps: + p_new = p-rho*c*(v_old-v)+rho*c*dt*g*np.sin(alpha)-f_D*rho*c*dt/(2*D)*abs(v)*v + self.set_pressure(p_new) + Q_new = self.get_current_Q() + v_new = Q_new/area_pipe + + iteration_change = abs(Q_old-Q_new) + Q_old = Q_new.copy() + v_old = v_new.copy() + i = i+1 + if i == 1e6: + print('did not converge') + break + # print(i) + + + + + diff --git a/Untertweng_mit_Pegelregler.ipynb b/Kraftwerk/Kraftwerk_test_steady_state.ipynb similarity index 54% rename from Untertweng_mit_Pegelregler.ipynb rename to Kraftwerk/Kraftwerk_test_steady_state.ipynb index 64e9204..a79a8a2 100644 --- a/Untertweng_mit_Pegelregler.ipynb +++ b/Kraftwerk/Kraftwerk_test_steady_state.ipynb @@ -2,13 +2,19 @@ "cells": [ { "cell_type": "code", - "execution_count": 4, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", + "from Kraftwerk_class_file import Kraftwerk_class\n", "\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 Druckrohrleitung.Druckrohrleitung_class_file import Druckrohrleitung_class\n", @@ -18,7 +24,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -30,10 +36,23 @@ "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", - " # 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", + " # for KW OL \n", + "OL_T1_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n", + "OL_T1_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "OL_T1_closingTime = 90. # [s] closing time of turbine\n", + "\n", + "OL_T2_Q_nenn = 0.85/2 # [m³/s] nominal flux of turbine \n", + "OL_T2_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "OL_T2_closingTime = 90. # [s] closing time of turbine\n", + "\n", + " # for KW UL\n", + "UL_T1_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n", + "UL_T1_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "UL_T1_closingTime = 90. # [s] closing time of turbine\n", + "\n", + "UL_T2_Q_nenn = 0.85/2 # [m³/s] nominal flux of turbine \n", + "UL_T2_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "UL_T2_closingTime = 90. # [s] closing time of turbine\n", "\n", " # for PI controller\n", "Con_targetLevel = 8. # [m]\n", @@ -67,16 +86,16 @@ "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", + "flux_init = (OL_T1_Q_nenn+OL_T2_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 = 100. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\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": 6, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -90,27 +109,40 @@ "pipe = Druckrohrleitung_class(Pip_length,Pip_dia,Pip_head,Pip_n_seg,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n", "pipe.set_steady_state(flux_init,reservoir.get_current_pressure())\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,pipe.get_current_pressure_distribution()[-1])\n", + "# influx setting turbines\n", + "OL_T1 = Francis_Turbine(OL_T1_Q_nenn,OL_T1_p_nenn,OL_T1_closingTime,Pip_dt,pUnit_conv)\n", + "OL_T2 = Francis_Turbine(OL_T2_Q_nenn,OL_T2_p_nenn,OL_T2_closingTime,Pip_dt,pUnit_conv)\n", "\n", - "# influx setting turbine\n", - "turbine_in = Francis_Turbine(Tur_Q_nenn,Tur_p_nenn,Tur_closingTime,Pip_dt,pUnit_conv)\n", - "turbine_in.set_steady_state(flux_init,Tur_p_nenn)\n", + "KW_OL = Kraftwerk_class()\n", + "KW_OL.add_turbine(OL_T1)\n", + "KW_OL.add_turbine(OL_T2)\n", "\n", - "# level controll\n", + "KW_OL.set_steady_state(flux_init,OL_T1_p_nenn)\n", + "\n", + "# downstream turbines\n", + "UL_T1 = Francis_Turbine(UL_T1_Q_nenn,UL_T1_p_nenn,UL_T1_closingTime,Pip_dt,pUnit_conv)\n", + "UL_T2 = Francis_Turbine(UL_T2_Q_nenn,UL_T2_p_nenn,UL_T2_closingTime,Pip_dt,pUnit_conv)\n", + "\n", + "KW_UL = Kraftwerk_class()\n", + "KW_UL.add_turbine(UL_T1)\n", + "KW_UL.add_turbine(UL_T2)\n", + "\n", + "KW_UL.set_steady_state(flux_init,pipe.get_current_pressure_distribution()[-1])\n", + "\n", + "# level controller\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" + "level_control.set_control_variable(UL_T1.get_current_LA(),display_warning=False)\n" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# initialization for Timeloop\n", "\n", + "# pipeline\n", "v_old = pipe.get_current_velocity_distribution()\n", "v_min = pipe.get_current_velocity_distribution()\n", "v_max = pipe.get_current_velocity_distribution()\n", @@ -121,9 +153,6 @@ "p_min = pipe.get_current_pressure_distribution()\n", "p_max = pipe.get_current_pressure_distribution()\n", "\n", - "Q_in_vec = np.zeros_like(t_vec)\n", - "Q_in_vec[0] = flux_init\n", - "\n", "v_boundary_res = np.zeros_like(t_vec)\n", "v_boundary_tur = np.zeros_like(t_vec)\n", "Q_boundary_res = np.zeros_like(t_vec)\n", @@ -131,30 +160,55 @@ "p_boundary_res = np.zeros_like(t_vec)\n", "p_boundary_tur = np.zeros_like(t_vec)\n", "\n", - "level_vec = np.full_like(t_vec,level_init) # level at the end of each pipeline timestep\n", - "volume_vec = np.full_like(t_vec,reservoir.get_current_volume()) # volume at the end of each pipeline timestep\n", + "v_boundary_res[0] = v_old[0]\n", + "v_boundary_tur[0] = v_old[-1] \n", + "Q_boundary_res[0] = Q_old[0]\n", + "Q_boundary_tur[0] = Q_old[-1]\n", + "p_boundary_res[0] = p_old[0]\n", + "p_boundary_tur[0] = p_old[-1]\n", "\n", - "v_boundary_res[0] = v_old[0]\n", - "v_boundary_tur[0] = v_old[-1] \n", - "Q_boundary_res[0] = Q_old[0]\n", - "Q_boundary_tur[0] = Q_old[-1]\n", - "p_boundary_res[0] = p_old[0]\n", - "p_boundary_tur[0] = p_old[-1]\n", + "# reservoir\n", + "Q_in_vec = np.zeros_like(t_vec)\n", + "Q_in_vec[0] = flux_init\n", + "# Outflux from reservoir is stored in Q_boundary_res\n", + "level_vec = np.zeros_like(t_vec) # level at the end of each pipeline timestep\n", + "level_vec[0] = level_init\n", + "volume_vec = np.zeros_like(t_vec) # volume at the end of each pipeline timestep\n", + "volume_vec[0] = reservoir.get_current_volume()\n", "\n", - "LA_soll_vec = np.full_like(t_vec,turbine.get_current_LA())\n", - "LA_ist_vec = np.full_like(t_vec,turbine.get_current_LA())\n", + "# controller\n", + "UL_T1_LA_soll_vec = np.zeros_like(t_vec)\n", + "UL_T1_LA_soll_vec[0] = UL_T1.get_current_LA()\n", "\n", - "LA_soll_vec2 = np.full_like(t_vec,turbine_in.get_current_LA())\n", - "LA_soll_vec2[500:] = 0\n", - "# LA_soll_vec2[500:1000] = 0.\n", - "# LA_soll_vec2[1000:1500] = 1. \n", - "# LA_soll_vec2[1500:2000] = 0.\n", - "# LA_soll_vec2[2000:2500] = 0.5 \n" + "# OL KW\n", + "OL_T1_LA_soll_vec = np.full_like(t_vec,OL_T1.get_current_LA())\n", + "# OL_T1_LA_soll_vec[2000:] = 0.\n", + "# OL_T1_LA_soll_vec[2000:4000] = 0.\n", + "# OL_T1_LA_soll_vec[4000:6000] = 1. \n", + "# OL_T1_LA_soll_vec[6000:8000] = 0.\n", + "# OL_T1_LA_soll_vec[8000:1000] = 0.5 \n", + "\n", + "OL_T2_LA_soll_vec = np.full_like(t_vec,OL_T2.get_current_LA())\n", + "\n", + "OL_T1_LA_ist_vec = np.zeros_like(t_vec)\n", + "OL_T1_LA_ist_vec[0] = OL_T1.get_current_LA()\n", + "\n", + "OL_T2_LA_ist_vec = np.zeros_like(t_vec)\n", + "OL_T2_LA_ist_vec[0] = OL_T2.get_current_LA()\n", + "\n", + "# UL KW\n", + "UL_T2_LA_soll_vec = np.full_like(t_vec,UL_T2.get_current_LA())\n", + "\n", + "UL_T1_LA_ist_vec = np.zeros_like(t_vec)\n", + "UL_T1_LA_ist_vec[0] = UL_T1.get_current_LA()\n", + "\n", + "UL_T2_LA_ist_vec = np.zeros_like(t_vec)\n", + "UL_T2_LA_ist_vec[0] = UL_T2.get_current_LA()\n" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -187,7 +241,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -196,9 +250,9 @@ "# loop through Con_T_ime steps of the pipeline\n", "for it_pipe in range(1,nt+1):\n", "\n", - " turbine_in.update_LA(LA_soll_vec2[it_pipe])\n", - " turbine_in.set_pressure(Tur_p_nenn)\n", - " Q_in_vec[it_pipe] = turbine_in.get_current_Q()\n", + " KW_OL.update_LAs([OL_T1_LA_soll_vec[it_pipe],OL_T2_LA_soll_vec[it_pipe]])\n", + " KW_OL.set_pressure(OL_T1_p_nenn)\n", + " Q_in_vec[it_pipe] = KW_OL.get_current_Q()\n", " reservoir.set_influx(Q_in_vec[it_pipe])\n", "\n", "# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n", @@ -208,25 +262,26 @@ " # calculate the Con_T_ime evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n", " for it_res in range(Res_nt):\n", " reservoir.timestep_reservoir_evolution() \n", - " level_vec[it_pipe] = reservoir.get_current_level() \n", + " level_vec[it_pipe] = reservoir.get_current_level() \n", " volume_vec[it_pipe] = reservoir.get_current_volume() \n", "\n", " # get the control variable\n", " level_control.update_control_variable(level_vec[it_pipe])\n", - " LA_soll_vec[it_pipe] = level_control.get_current_control_variable()\n", + " UL_T1_LA_soll_vec[it_pipe] = level_control.get_current_control_variable()\n", " \n", " # change the Leitapparatöffnung based on the target value\n", - " turbine.update_LA(LA_soll_vec[it_pipe])\n", - " LA_ist_vec[it_pipe] = turbine.get_current_LA()\n", + " KW_UL.update_LAs([UL_T1_LA_soll_vec[it_pipe],UL_T2_LA_soll_vec[it_pipe]])\n", + " OL_T1_LA_ist_vec[it_pipe], OL_T2_LA_ist_vec[it_pipe] = KW_OL.get_current_LAs()\n", + " UL_T1_LA_ist_vec[it_pipe], UL_T2_LA_ist_vec[it_pipe] = KW_UL.get_current_LAs()\n", "\n", " # set boundary condition for the next timestep of the characterisCon_T_ic method\n", - " turbine.set_pressure(p_old[-1])\n", + " KW_UL.set_pressure(p_old[-1])\n", " convergence_parameters[0] = p_old[-2]\n", " convergence_parameters[1] = v_old[-2]\n", - " turbine.converge(convergence_parameters)\n", + " KW_UL.converge(convergence_parameters)\n", " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n", - " v_boundary_tur[it_pipe] = 1/Pip_area*turbine.get_current_Q()\n", - " Q_boundary_tur[it_pipe] = turbine.get_current_Q()\n", + " v_boundary_tur[it_pipe] = 1/Pip_area*KW_UL.get_current_Q()\n", + " Q_boundary_tur[it_pipe] = KW_UL.get_current_Q()\n", "\n", " # the the boundary condition 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", @@ -236,7 +291,7 @@ " Q_boundary_res[it_pipe] = pipe.get_current_flux_distribution()[0]\n", "\n", " # perform the next timestep via the characterisCon_T_ic method\n", - " pipe.timestep_characteristic_method()\n", + " pipe.timestep_characteristic_method_vectorized()\n", "\n", " # prepare for next loop\n", " p_old = pipe.get_current_pressure_distribution()\n", @@ -245,24 +300,25 @@ "\n", " # plot some stuff\n", " # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n", - " lo_p.remove()\n", - " lo_pmin.remove()\n", - " lo_pmax.remove()\n", - " lo_q.remove()\n", - " lo_qmin.remove()\n", - " lo_qmax.remove()\n", - " # plot new pressure and velocity distribution in the pipeline\n", - " lo_p, = axs1[0].plot(Pip_x_vec,pipe.get_current_pressure_distribution(disp_flag=True),marker='.',c='blue')\n", - " lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", - " lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", - " lo_q, = axs1[1].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n", - " lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", - " lo_qmax, = axs1[1].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\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) " + " if it_pipe%50 == 0:\n", + " lo_p.remove()\n", + " lo_pmin.remove()\n", + " lo_pmax.remove()\n", + " lo_q.remove()\n", + " lo_qmin.remove()\n", + " lo_qmax.remove()\n", + " # plot new pressure and velocity distribution in the pipeline\n", + " lo_p, = axs1[0].plot(Pip_x_vec,pipe.get_current_pressure_distribution(disp_flag=True),marker='.',c='blue')\n", + " lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", + " lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", + " lo_q, = axs1[1].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n", + " lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + " lo_qmax, = axs1[1].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\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(0.000001) " ] }, { @@ -271,8 +327,6 @@ "metadata": {}, "outputs": [], "source": [ - "# plot Con_T_ime evolution of boundary pressure and velocity as well as the reservoir level\n", - "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('Level and Volume reservoir')\n", "axs2.plot(t_vec,level_vec,label='level')\n", @@ -285,54 +339,108 @@ "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('LA')\n", - "axs2.plot(t_vec,100*LA_soll_vec,label='Target')\n", - "axs2.plot(t_vec,100*LA_ist_vec,label='Actual')\n", + "axs2.plot(t_vec,100*OL_T1_LA_soll_vec,label='OL_T1 Target',c='b')\n", + "axs2.scatter(t_vec[::200],100*OL_T1_LA_ist_vec[::200],label='OL_T1 Actual',c='b',marker='+')\n", + "axs2.plot(t_vec,100*OL_T2_LA_soll_vec,label='OL_T2 Target',c='g')\n", + "axs2.scatter(t_vec[::200],100*OL_T2_LA_ist_vec[::200],label='OL_T2 Actual',c='g',marker='+')\n", + "axs2.plot(t_vec,100*UL_T1_LA_soll_vec,label='UL_T1 Target',c='r')\n", + "axs2.scatter(t_vec[::200],100*UL_T1_LA_ist_vec[::200],label='UL_T1 Actual',c='r',marker='+')\n", + "axs2.plot(t_vec,100*UL_T2_LA_soll_vec,label='UL_T2 Target',c='k')\n", + "axs2.scatter(t_vec[::200],100*UL_T2_LA_ist_vec[::200],label='UL_T2 Actual',c='k',marker='+')\n", "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2.set_ylabel(r'$LA$ [%]')\n", "axs2.legend()\n", "\n", "fig2,axs2 = plt.subplots(1,1)\n", - "axs2.set_title('Pressure reservoir and turbine')\n", - "axs2.plot(t_vec,pressure_conversion(p_boundary_res,pUnit_calc, pUnit_conv),label='Reservoir')\n", - "axs2.plot(t_vec,pressure_conversion(p_boundary_tur,pUnit_calc, pUnit_conv),label='Turbine')\n", + "axs2.set_title('Pressure change vs t=0 at reservoir and turbine')\n", + "axs2.plot(t_vec,pressure_conversion(p_boundary_res-p_boundary_res[0],pUnit_calc, pUnit_conv),label='Reservoir')\n", + "axs2.plot(t_vec,pressure_conversion(p_boundary_tur-p_boundary_tur[0],pUnit_calc, pUnit_conv),label='Turbine')\n", "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", "axs2.legend()\n", "\n", "fig2,axs2 = plt.subplots(1,1)\n", "axs2.set_title('Fluxes')\n", - "axs2.plot(t_vec,Q_boundary_res,label='Outflux')\n", "axs2.plot(t_vec,Q_in_vec,label='Influx')\n", - "axs2.plot(t_vec,Q_boundary_tur,label='Flux Turbine')\n", - "axs2.set_ylim(-2*Tur_Q_nenn,+2*Tur_Q_nenn)\n", + "axs2.plot(t_vec,Q_boundary_res,label='Outflux')\n", + "axs2.scatter(t_vec[::200],Q_boundary_tur[::200],label='Flux Turbine',c='g',marker='+')\n", "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", "axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", "axs2.legend()\n", "\n", - "fig2,axs2 = plt.subplots(1,1)\n", - "axs2.set_title('Min and Max Pressure')\n", - "axs2.plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", - "axs2.plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", - "axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", - "axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "# fig2,axs2 = plt.subplots(1,1)\n", + "# axs2.set_title('Min and Max Pressure')\n", + "# axs2.plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", + "# axs2.plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", + "# axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "# axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", "\n", - "fig2,axs2 = plt.subplots(1,1)\n", - "axs2.set_title('Min and Max Fluxes')\n", - "axs2.plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", - "axs2.plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", - "axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", - "axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", - "\n", - "# axs2[0,1].legend()\n", - "# axs2[1,0].legend()\n", - "# axs2[1,1].legend()\n", - "# # axs2[2,0].legend()\n", - "# # axs2[2,1].legend()\n", + "# fig2,axs2 = plt.subplots(1,1)\n", + "# axs2.set_title('Min and Max Fluxes')\n", + "# axs2.plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + "# axs2.plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", + "# axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "# axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", "\n", "\n", "fig2.tight_layout()\n", "plt.show()" ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "fig3,axs3 = plt.subplots(2,2)\n", + "axs3[0,0].set_title('Level and Volume reservoir')\n", + "axs3[0,0].plot(t_vec,level_vec,label='level')\n", + "axs3[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[0,0].set_ylabel(r'$h$ [m]')\n", + "x_twin_00 = axs3[0,0].twinx()\n", + "x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n", + "x_twin_00.plot(t_vec,volume_vec)\n", + "axs3[0,0].legend()\n", + "\n", + "axs3[0,1].set_title('LA')\n", + "axs3[0,1].plot(t_vec,100*OL_T1_LA_soll_vec,label='OL_T1 Target',c='b')\n", + "axs3[0,1].scatter(t_vec[::200],100*OL_T1_LA_ist_vec[::200],label='OL_T1 Actual',c='b',marker='+')\n", + "axs3[0,1].plot(t_vec,100*OL_T2_LA_soll_vec,label='OL_T2 Target',c='g')\n", + "axs3[0,1].scatter(t_vec[::200],100*OL_T2_LA_ist_vec[::200],label='OL_T2 Actual',c='g',marker='+')\n", + "axs3[0,1].plot(t_vec,100*UL_T1_LA_soll_vec,label='UL_T1 Target',c='r')\n", + "axs3[0,1].scatter(t_vec[::200],100*UL_T1_LA_ist_vec[::200],label='UL_T1 Actual',c='r',marker='+')\n", + "axs3[0,1].plot(t_vec,100*UL_T2_LA_soll_vec,label='UL_T2 Target',c='k')\n", + "axs3[0,1].scatter(t_vec[::200],100*UL_T2_LA_ist_vec[::200],label='UL_T2 Actual',c='k',marker='+')\n", + "axs3[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[0,1].set_ylabel(r'$LA$ [%]')\n", + "axs3[0,1].legend()\n", + "\n", + "axs3[1,0].set_title('Fluxes')\n", + "axs3[1,0].plot(t_vec,Q_in_vec,label='Influx')\n", + "axs3[1,0].plot(t_vec,Q_boundary_res,label='Outflux')\n", + "axs3[1,0].scatter(t_vec[::200],Q_boundary_tur[::200],label='Flux Turbine',c='g',marker='+')\n", + "axs3[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[1,0].set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", + "axs3[1,0].legend()\n", + "\n", + "axs3[1,1].set_title('Pressure change vs t=0 at reservoir and turbine')\n", + "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_res-p_boundary_res[0],pUnit_calc, pUnit_conv),label='Reservoir')\n", + "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_tur-p_boundary_tur[0],pUnit_calc, pUnit_conv),label='Turbine')\n", + "axs3[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[1,1].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs3[1,1].legend()\n", + "\n", + "fig3.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] } ], "metadata": { diff --git a/Turbinen/Turbinen_class_file.py b/Turbinen/Turbinen_class_file.py index d8fbf41..628e9a6 100644 --- a/Turbinen/Turbinen_class_file.py +++ b/Turbinen/Turbinen_class_file.py @@ -78,6 +78,8 @@ class Francis_Turbine: if ss_LA < 0 or ss_LA > 1: raise Exception('LA out of range [0;1]') self.set_LA(ss_LA,display_warning=False) + self.set_pressure(ss_pressure) + self.get_current_Q() #getter - get attributes def get_current_Q(self): @@ -113,22 +115,26 @@ class Francis_Turbine: f"Nominal pressure = {round(p_n,3):<10} {self.pressure_unit_disp}{new_line}" f"Nominal LA = {self.LA_n*100:<10} {self.LA_unit_disp} {new_line}" f"Closing time = {self.t_c:<10} {self.time_unit_disp} {new_line}" - f"Current flux = {self.Q:<10} {self.flux_unit_disp} {new_line}" + f"Current flux = {round(self.Q,3):<10} {self.flux_unit_disp} {new_line}" f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_disp} {new_line}" - f"Current LA = {self.LA*100:<10} {self.LA_unit_disp} {new_line}" + f"Current LA = {round(self.LA,4)*100:<10} {self.LA_unit_disp} {new_line}" f"Simulation timestep = {self.dt:<10} {self.time_unit_disp} {new_line}" f"----------------------------- {new_line}") else: # :<10 pads the self.value to be 10 characters wide print_str = (f"The current attributes are: {new_line}" f"----------------------------- {new_line}" - f"Current flux = {self.Q:<10} {self.flux_unit_disp} {new_line}" + f"Current flux = {round(self.Q,3):<10} {self.flux_unit_disp} {new_line}" f"Current pipe pressure = {round(p,3):<10} {self.pressure_unit_disp} {new_line}" - f"Current LA = {self.LA*100:<10} {self.LA_unit_disp} {new_line}" + f"Current LA = {round(self.LA,4)*100:<10} {self.LA_unit_disp} {new_line}" f"----------------------------- {new_line}") print(print_str) + def get_Q_n(self): + # needed for Kraftwerk_class + return self.Q_n + # update methods def update_LA(self,LA_soll): # update the Leitappartöffnung and consider the restrictions of the closing time of the turbine @@ -182,4 +188,4 @@ class Francis_Turbine: print('did not converge') break # print(i) - self.Q = Q_new \ No newline at end of file + # self.get_current_Q() \ No newline at end of file diff --git a/Turbinen/Turbinen_test_steady_state.ipynb b/Turbinen/Turbinen_test_steady_state.ipynb index 2891587..acc9658 100644 --- a/Turbinen/Turbinen_test_steady_state.ipynb +++ b/Turbinen/Turbinen_test_steady_state.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -23,7 +23,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -74,14 +74,14 @@ " # 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 = 100. # [s] target for total simulation time (will vary slightly to fit with Pip_dt)\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": null, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -110,7 +110,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -149,12 +149,13 @@ "LA_soll_vec = np.full_like(t_vec,turbine.get_current_LA())\n", "LA_ist_vec = np.full_like(t_vec,turbine.get_current_LA())\n", "\n", - "LA_soll_vec2 = np.full_like(t_vec,turbine_in.get_current_LA())\n" + "LA_soll_vec2 = np.full_like(t_vec,turbine_in.get_current_LA())\n", + "# LA_soll_vec2[100:] = 0\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -187,7 +188,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -267,7 +268,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ diff --git a/Untertweng.ipynb b/Untertweng.ipynb new file mode 100644 index 0000000..3473550 --- /dev/null +++ b/Untertweng.ipynb @@ -0,0 +1,473 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\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 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\n", + "from Kraftwerk.Kraftwerk_class_file import Kraftwerk_class" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "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", + " # for KW OL \n", + "OL_T1_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n", + "OL_T1_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "OL_T1_closingTime = 90. # [s] closing time of turbine\n", + "\n", + "OL_T2_Q_nenn = 0.85/2 # [m³/s] nominal flux of turbine \n", + "OL_T2_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "OL_T2_closingTime = 90. # [s] closing time of turbine\n", + "\n", + " # for KW UL\n", + "UL_T1_Q_nenn = 0.85 # [m³/s] nominal flux of turbine \n", + "UL_T1_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "UL_T1_closingTime = 90. # [s] closing time of turbine\n", + "\n", + "UL_T2_Q_nenn = 0.85/2 # [m³/s] nominal flux of turbine \n", + "UL_T2_p_nenn = pressure_conversion(10.6,'bar',pUnit_calc) # [Pa] nominal pressure of turbine \n", + "UL_T2_closingTime = 90. # [s] closing time of turbine\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 = 1000. # [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", + " # 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", + " # for reservoir\n", + "Res_area_base = 74. # [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 = (OL_T1_Q_nenn+OL_T2_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": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# create objects\n", + "\n", + "# Upstream reservoir\n", + "reservoir = Ausgleichsbecken_class(Res_area_base,Res_area_out,Res_dt,pUnit_conv,Res_level_crit_lo,Res_level_crit_hi,rho)\n", + "reservoir.set_steady_state(flux_init,level_init)\n", + "\n", + "# pipeline\n", + "pipe = Druckrohrleitung_class(Pip_length,Pip_dia,Pip_head,Pip_n_seg,Pip_f_D,Pip_pw_vel,Pip_dt,pUnit_conv,rho)\n", + "pipe.set_steady_state(flux_init,reservoir.get_current_pressure())\n", + "\n", + "# influx setting turbines\n", + "OL_T1 = Francis_Turbine(OL_T1_Q_nenn,OL_T1_p_nenn,OL_T1_closingTime,Pip_dt,pUnit_conv)\n", + "OL_T2 = Francis_Turbine(OL_T2_Q_nenn,OL_T2_p_nenn,OL_T2_closingTime,Pip_dt,pUnit_conv)\n", + "\n", + "KW_OL = Kraftwerk_class()\n", + "KW_OL.add_turbine(OL_T1)\n", + "KW_OL.add_turbine(OL_T2)\n", + "\n", + "KW_OL.set_steady_state(flux_init,OL_T1_p_nenn)\n", + "\n", + "# downstream turbines\n", + "UL_T1 = Francis_Turbine(UL_T1_Q_nenn,UL_T1_p_nenn,UL_T1_closingTime,Pip_dt,pUnit_conv)\n", + "UL_T2 = Francis_Turbine(UL_T2_Q_nenn,UL_T2_p_nenn,UL_T2_closingTime,Pip_dt,pUnit_conv)\n", + "\n", + "KW_UL = Kraftwerk_class()\n", + "KW_UL.add_turbine(UL_T1)\n", + "KW_UL.add_turbine(UL_T2)\n", + "\n", + "KW_UL.set_steady_state(flux_init,pipe.get_current_pressure_distribution()[-1])\n", + "\n", + "# level controller\n", + "level_control = PI_controller_class(Con_targetLevel,Con_deadbandRange,Con_K_p,Con_T_i,Pip_dt)\n", + "level_control.set_control_variable(UL_T1.get_current_LA(),display_warning=False)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "# initialization for Timeloop\n", + "\n", + "# pipeline\n", + "v_old = pipe.get_current_velocity_distribution()\n", + "v_min = pipe.get_current_velocity_distribution()\n", + "v_max = pipe.get_current_velocity_distribution()\n", + "Q_old = pipe.get_current_flux_distribution()\n", + "Q_min = pipe.get_current_flux_distribution()\n", + "Q_max = pipe.get_current_flux_distribution()\n", + "p_old = pipe.get_current_pressure_distribution()\n", + "p_min = pipe.get_current_pressure_distribution()\n", + "p_max = pipe.get_current_pressure_distribution()\n", + "\n", + "v_boundary_res = np.zeros_like(t_vec)\n", + "v_boundary_tur = np.zeros_like(t_vec)\n", + "Q_boundary_res = np.zeros_like(t_vec)\n", + "Q_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", + "v_boundary_res[0] = v_old[0]\n", + "v_boundary_tur[0] = v_old[-1] \n", + "Q_boundary_res[0] = Q_old[0]\n", + "Q_boundary_tur[0] = Q_old[-1]\n", + "p_boundary_res[0] = p_old[0]\n", + "p_boundary_tur[0] = p_old[-1]\n", + "\n", + "# reservoir\n", + "Q_in_vec = np.zeros_like(t_vec)\n", + "Q_in_vec[0] = flux_init\n", + "# Outflux from reservoir is stored in Q_boundary_res\n", + "level_vec = np.zeros_like(t_vec) # level at the end of each pipeline timestep\n", + "level_vec[0] = level_init\n", + "volume_vec = np.zeros_like(t_vec) # volume at the end of each pipeline timestep\n", + "volume_vec[0] = reservoir.get_current_volume()\n", + "\n", + "# controller\n", + "UL_T1_LA_soll_vec = np.zeros_like(t_vec)\n", + "UL_T1_LA_soll_vec[0] = UL_T1.get_current_LA()\n", + "\n", + "# OL KW\n", + "OL_T1_LA_soll_vec = np.full_like(t_vec,OL_T1.get_current_LA())\n", + "OL_T1_LA_soll_vec[2000:] = 0.\n", + "OL_T1_LA_soll_vec[2000:4000] = 0.\n", + "OL_T1_LA_soll_vec[4000:6000] = 1. \n", + "OL_T1_LA_soll_vec[6000:8000] = 0.\n", + "OL_T1_LA_soll_vec[8000:1000] = 0.5 \n", + "\n", + "OL_T2_LA_soll_vec = np.full_like(t_vec,OL_T2.get_current_LA())\n", + "\n", + "OL_T1_LA_ist_vec = np.zeros_like(t_vec)\n", + "OL_T1_LA_ist_vec[0] = OL_T1.get_current_LA()\n", + "\n", + "OL_T2_LA_ist_vec = np.zeros_like(t_vec)\n", + "OL_T2_LA_ist_vec[0] = OL_T2.get_current_LA()\n", + "\n", + "# UL KW\n", + "UL_T2_LA_soll_vec = np.full_like(t_vec,UL_T2.get_current_LA())\n", + "\n", + "UL_T1_LA_ist_vec = np.zeros_like(t_vec)\n", + "UL_T1_LA_ist_vec[0] = UL_T1.get_current_LA()\n", + "\n", + "UL_T2_LA_ist_vec = np.zeros_like(t_vec)\n", + "UL_T2_LA_ist_vec[0] = UL_T2.get_current_LA()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "%matplotlib qt5\n", + "# Con_T_ime 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[0].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs1[0].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs1[1].set_title('Flux distribution in pipeline')\n", + "axs1[1].set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "axs1[1].set_ylabel(r'$Q$ [$\\mathrm{m}^3 / \\mathrm{s}$]')\n", + "lo_p, = axs1[0].plot(Pip_x_vec,pressure_conversion(p_old,pUnit_calc, pUnit_conv),marker='.')\n", + "lo_q, = axs1[1].plot(Pip_x_vec,Q_old,marker='.')\n", + "lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", + "lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", + "lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + "lo_qmax, = axs1[1].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", + "\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": 15, + "metadata": {}, + "outputs": [], + "source": [ + "convergence_parameters = [p_old[-2],v_old[-2],Pip_dia,Pip_area,Pip_angle,Pip_f_D,Pip_pw_vel,rho,Pip_dt]\n", + "\n", + "# loop through Con_T_ime steps of the pipeline\n", + "for it_pipe in range(1,nt+1):\n", + "\n", + " KW_OL.update_LAs([OL_T1_LA_soll_vec[it_pipe],OL_T2_LA_soll_vec[it_pipe]])\n", + " KW_OL.set_pressure(OL_T1_p_nenn)\n", + " Q_in_vec[it_pipe] = KW_OL.get_current_Q()\n", + " reservoir.set_influx(Q_in_vec[it_pipe])\n", + "\n", + "# for each pipeline timestep, execute nt_eRK4 timesteps of the reservoir code\n", + " # set initial condition for the reservoir Con_T_ime evolution calculted with e-RK4\n", + " reservoir.set_pressure(p_old[0],display_warning=False)\n", + " reservoir.set_outflux(Q_old[0],display_warning=False)\n", + " # calculate the Con_T_ime evolution of the reservoir level within each pipeline timestep to avoid runaway numerical error\n", + " for it_res in range(Res_nt):\n", + " reservoir.timestep_reservoir_evolution() \n", + " level_vec[it_pipe] = reservoir.get_current_level() \n", + " volume_vec[it_pipe] = reservoir.get_current_volume() \n", + "\n", + " # get the control variable\n", + " level_control.update_control_variable(level_vec[it_pipe])\n", + " UL_T1_LA_soll_vec[it_pipe] = level_control.get_current_control_variable()\n", + " \n", + " # change the Leitapparatöffnung based on the target value\n", + " KW_UL.update_LAs([UL_T1_LA_soll_vec[it_pipe],UL_T2_LA_soll_vec[it_pipe]])\n", + " OL_T1_LA_ist_vec[it_pipe], OL_T2_LA_ist_vec[it_pipe] = KW_OL.get_current_LAs()\n", + " UL_T1_LA_ist_vec[it_pipe], UL_T2_LA_ist_vec[it_pipe] = KW_UL.get_current_LAs()\n", + "\n", + " # set boundary condition for the next timestep of the characterisCon_T_ic method\n", + " KW_UL.set_pressure(p_old[-1])\n", + " convergence_parameters[0] = p_old[-2]\n", + " convergence_parameters[1] = v_old[-2]\n", + " KW_UL.converge(convergence_parameters)\n", + " p_boundary_res[it_pipe] = reservoir.get_current_pressure()\n", + " v_boundary_tur[it_pipe] = 1/Pip_area*KW_UL.get_current_Q()\n", + " Q_boundary_tur[it_pipe] = KW_UL.get_current_Q()\n", + "\n", + " # the the boundary condition 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", + " pipe.v[0] = (0.8*pipe.v[0]+0.2*reservoir.get_current_outflux()/Res_area_out)\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", + " Q_boundary_res[it_pipe] = pipe.get_current_flux_distribution()[0]\n", + "\n", + " # perform the next timestep via the characterisCon_T_ic method\n", + " pipe.timestep_characteristic_method_vectorized()\n", + "\n", + " # prepare for next loop\n", + " p_old = pipe.get_current_pressure_distribution()\n", + " v_old = pipe.get_current_velocity_distribution()\n", + " Q_old = pipe.get_current_flux_distribution()\n", + "\n", + " # plot some stuff\n", + " # remove line-objects to autoscale axes (there is definetly a better way, but this works ¯\\_(ツ)_/¯ )\n", + " if it_pipe%10 == 0:\n", + " lo_p.remove()\n", + " lo_pmin.remove()\n", + " lo_pmax.remove()\n", + " lo_q.remove()\n", + " lo_qmin.remove()\n", + " lo_qmax.remove()\n", + " # plot new pressure and velocity distribution in the pipeline\n", + " lo_p, = axs1[0].plot(Pip_x_vec,pipe.get_current_pressure_distribution(disp_flag=True),marker='.',c='blue')\n", + " lo_pmin, = axs1[0].plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", + " lo_pmax, = axs1[0].plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", + " lo_q, = axs1[1].plot(Pip_x_vec,pipe.get_current_flux_distribution(),marker='.',c='blue')\n", + " lo_qmin, = axs1[1].plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + " lo_qmax, = axs1[1].plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\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(0.000001) " + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('Level and Volume reservoir')\n", + "axs2.plot(t_vec,level_vec,label='level')\n", + "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2.set_ylabel(r'$h$ [m]')\n", + "x_twin_00 = axs2.twinx()\n", + "x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n", + "x_twin_00.plot(t_vec,volume_vec)\n", + "axs2.legend()\n", + "\n", + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('LA')\n", + "axs2.plot(t_vec,100*OL_T1_LA_soll_vec,label='OL_T1 Target',c='b')\n", + "axs2.scatter(t_vec[::200],100*OL_T1_LA_ist_vec[::200],label='OL_T1 Actual',c='b',marker='+')\n", + "axs2.plot(t_vec,100*OL_T2_LA_soll_vec,label='OL_T2 Target',c='g')\n", + "axs2.scatter(t_vec[::200],100*OL_T2_LA_ist_vec[::200],label='OL_T2 Actual',c='g',marker='+')\n", + "axs2.plot(t_vec,100*UL_T1_LA_soll_vec,label='UL_T1 Target',c='r')\n", + "axs2.scatter(t_vec[::200],100*UL_T1_LA_ist_vec[::200],label='UL_T1 Actual',c='r',marker='+')\n", + "axs2.plot(t_vec,100*UL_T2_LA_soll_vec,label='UL_T2 Target',c='k')\n", + "axs2.scatter(t_vec[::200],100*UL_T2_LA_ist_vec[::200],label='UL_T2 Actual',c='k',marker='+')\n", + "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2.set_ylabel(r'$LA$ [%]')\n", + "axs2.legend()\n", + "\n", + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('Pressure change vs t=0 at reservoir and turbine')\n", + "axs2.plot(t_vec,pressure_conversion(p_boundary_res-p_boundary_res[0],pUnit_calc, pUnit_conv),label='Reservoir')\n", + "axs2.plot(t_vec,pressure_conversion(p_boundary_tur-p_boundary_tur[0],pUnit_calc, pUnit_conv),label='Turbine')\n", + "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs2.legend()\n", + "\n", + "fig2,axs2 = plt.subplots(1,1)\n", + "axs2.set_title('Fluxes')\n", + "axs2.plot(t_vec,Q_in_vec,label='Influx')\n", + "axs2.plot(t_vec,Q_boundary_res,label='Outflux')\n", + "axs2.scatter(t_vec[::200],Q_boundary_tur[::200],label='Flux Turbine',c='g',marker='+')\n", + "axs2.set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", + "axs2.legend()\n", + "\n", + "# fig2,axs2 = plt.subplots(1,1)\n", + "# axs2.set_title('Min and Max Pressure')\n", + "# axs2.plot(Pip_x_vec,pipe.get_lowest_pressure_per_node(disp_flag=True),c='red')\n", + "# axs2.plot(Pip_x_vec,pipe.get_highest_pressure_per_node(disp_flag=True),c='red')\n", + "# axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "# axs2.set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "\n", + "# fig2,axs2 = plt.subplots(1,1)\n", + "# axs2.set_title('Min and Max Fluxes')\n", + "# axs2.plot(Pip_x_vec,pipe.get_lowest_flux_per_node(),c='red')\n", + "# axs2.plot(Pip_x_vec,pipe.get_highest_flux_per_node(),c='red')\n", + "# axs2.set_xlabel(r'$x$ [$\\mathrm{m}$]')\n", + "# axs2.set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", + "\n", + "\n", + "fig2.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "fig3,axs3 = plt.subplots(2,2)\n", + "axs3[0,0].set_title('Level and Volume reservoir')\n", + "axs3[0,0].plot(t_vec,level_vec,label='level')\n", + "axs3[0,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[0,0].set_ylabel(r'$h$ [m]')\n", + "x_twin_00 = axs3[0,0].twinx()\n", + "x_twin_00.set_ylabel(r'$V$ [$\\mathrm{m}^3$]')\n", + "x_twin_00.plot(t_vec,volume_vec)\n", + "axs3[0,0].legend()\n", + "\n", + "axs3[0,1].set_title('LA')\n", + "axs3[0,1].plot(t_vec,100*OL_T1_LA_soll_vec,label='OL_T1 Target',c='b')\n", + "axs3[0,1].scatter(t_vec[::200],100*OL_T1_LA_ist_vec[::200],label='OL_T1 Actual',c='b',marker='+')\n", + "axs3[0,1].plot(t_vec,100*OL_T2_LA_soll_vec,label='OL_T2 Target',c='g')\n", + "axs3[0,1].scatter(t_vec[::200],100*OL_T2_LA_ist_vec[::200],label='OL_T2 Actual',c='g',marker='+')\n", + "axs3[0,1].plot(t_vec,100*UL_T1_LA_soll_vec,label='UL_T1 Target',c='r')\n", + "axs3[0,1].scatter(t_vec[::200],100*UL_T1_LA_ist_vec[::200],label='UL_T1 Actual',c='r',marker='+')\n", + "axs3[0,1].plot(t_vec,100*UL_T2_LA_soll_vec,label='UL_T2 Target',c='k')\n", + "axs3[0,1].scatter(t_vec[::200],100*UL_T2_LA_ist_vec[::200],label='UL_T2 Actual',c='k',marker='+')\n", + "axs3[0,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[0,1].set_ylabel(r'$LA$ [%]')\n", + "axs3[0,1].legend()\n", + "\n", + "axs3[1,0].set_title('Fluxes')\n", + "axs3[1,0].plot(t_vec,Q_in_vec,label='Influx')\n", + "axs3[1,0].plot(t_vec,Q_boundary_res,label='Outflux')\n", + "axs3[1,0].scatter(t_vec[::200],Q_boundary_tur[::200],label='Flux Turbine',c='g',marker='+')\n", + "axs3[1,0].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[1,0].set_ylabel(r'$Q$ [$\\mathrm{m}^3/\\mathrm{s}$]')\n", + "axs3[1,0].legend()\n", + "\n", + "axs3[1,1].set_title('Pressure change vs t=0 at reservoir and turbine')\n", + "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_res-p_boundary_res[0],pUnit_calc, pUnit_conv),label='Reservoir')\n", + "axs3[1,1].plot(t_vec,pressure_conversion(p_boundary_tur-p_boundary_tur[0],pUnit_calc, pUnit_conv),label='Turbine')\n", + "axs3[1,1].set_xlabel(r'$t$ [$\\mathrm{s}$]')\n", + "axs3[1,1].set_ylabel(r'$p$ ['+pUnit_conv+']')\n", + "axs3[1,1].legend()\n", + "\n", + "fig3.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "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": { + 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