Georg_Brantegger/Python-DT_Slot_3
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

fix for numerical runaway of rounding errors

Browse Source 
due to turbine-pipeline interatction
via a convergence method in the turbine
and a "damping" trick on the reservoir velocity
plus: code cleanup with consistent naming of variables
This commit is contained in:
Brantegger Georg
2022-08-03 15:56:56 +02:00
parent 84631ee4cc
commit ba696444bb
13 changed files with 1257 additions and 1198 deletions
Download Patch File Download Diff File Expand all files Collapse all files

285
Regler/Pegelregler_test.ipynb
View File

@@ -2,7 +2,7 @@
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
@@ -23,85 +23,108 @@
},
{
"cell_type": "code",
"execution_count": 2,
"execution_count": 28,
"metadata": {},
"outputs": [],
"source": [
"#define constants\n",
"# define constants\n",
"\n",
"#Turbine\n",
"Q_nenn = 0.85 # m³/s\n",
"p_nenn = pressure_conversion(10.6,'bar','Pa')\n",
"closing_time = 480. #s\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",
"# physics\n",
"g = 9.81 # gravitational acceleration [m/s²]\n",
"rho = 1000. # density of water [kg/m³]\n",
"\n",
"# define controller constants\n",
"target_level = 8. # m\n",
"Kp = 0.01\n",
"Ti = 3600.\n",
"deadband_range = 0.05 # m\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",
"# reservoir\n",
"initial_level = target_level\n",
"initial_influx = Q_nenn/2 # 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 = 1. # outflux 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",
"p0 = rho*g*initial_level-0.5*rho*(initial_influx/area_outflux)**2\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",
"# offset the pressure in front of the turbine to get realisitc fluxes\n",
"h_fict = 100\n",
"offset_pressure = rho*g*h_fict\n",
"\n",
"t_max = 1e4 #s\n",
"dt = 1e-2 # simulation timestep\n",
"nt = int(t_max//dt) # number of simulation steps of reservoir in between timesteps of pipeline \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",
"t_vec = np.arange(0,nt+1,1)*dt\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": 3,
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"# create objects\n",
"offset_pressure = pressure_conversion(Pip_head,'mws',pUnit_calc)\n",
"\n",
"V = Ausgleichsbecken_class(area_base,area_outflux,critical_level_low,critical_level_high,dt)\n",
"V.set_steady_state(initial_influx,initial_level,conversion_pressure_unit)\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",
"T1 = Francis_Turbine(Q_nenn,p_nenn,closing_time,dt)\n",
"T1.set_steady_state(initial_influx,p0+offset_pressure)\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",
"Pegelregler = PI_controller_class(target_level,deadband_range,Kp,Ti,dt)"
"\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": 4,
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"level_vec = np.full(nt+1,V.level)\n",
"LA_ist_vec = np.full(nt+1,T1.LA)\n",
"LA_soll_vec = np.full(nt+1,T1.LA)\n",
"Q_vec = np.full(nt+1,initial_influx)\n",
"\n",
"Pegelregler.control_variable = T1.get_current_LA()"
"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": 5,
"execution_count": 31,
"metadata": {},
"outputs": [
{
@@ -109,105 +132,20 @@
"output_type": "stream",
"text": [
"0.0\n",
"100.0\n",
"200.0\n",
"300.0\n",
"400.0\n",
"500.0\n",
"600.0\n",
"700.0\n",
"800.0\n",
"900.0\n",
"1000.0\n",
"1100.0\n",
"1200.0\n",
"1300.0\n",
"1400.0\n",
"1500.0\n",
"1600.0\n",
"1700.0\n",
"1800.0\n",
"1900.0\n",
"2000.0\n",
"2100.0\n",
"2200.0\n",
"2300.0\n",
"2400.0\n",
"2500.0\n",
"2600.0\n",
"2700.0\n",
"2800.0\n",
"2900.0\n",
"3000.0\n",
"3100.0\n",
"3200.0\n",
"3300.0\n",
"3400.0\n",
"3500.0\n",
"3600.0\n",
"3700.0\n",
"3800.0\n",
"3900.0\n",
"4000.0\n",
"4100.0\n",
"4200.0\n",
"4300.0\n",
"4400.0\n",
"4500.0\n",
"4600.0\n",
"4700.0\n",
"4800.0\n",
"4900.0\n",
"5000.0\n",
"5100.0\n",
"5200.0\n",
"5300.0\n",
"5400.0\n",
"5500.0\n",
"5600.0\n",
"5700.0\n",
"5800.0\n",
"5900.0\n",
"6000.0\n",
"6100.0\n",
"6200.0\n",
"6300.0\n",
"6400.0\n",
"6500.0\n",
"6600.0\n",
"6700.0\n",
"6800.0\n",
"6900.0\n",
"7000.0\n",
"7100.0\n",
"7200.0\n",
"7300.0\n",
"7400.0\n",
"7500.0\n",
"7600.0\n",
"7700.0\n",
"7800.0\n",
"7900.0\n",
"8000.0\n",
"8100.0\n",
"8200.0\n",
"8300.0\n",
"8400.0\n",
"8500.0\n",
"8600.0\n",
"8700.0\n",
"8800.0\n",
"8900.0\n",
"9000.0\n",
"9100.0\n",
"9200.0\n",
"9300.0\n",
"9400.0\n",
"9500.0\n",
"9600.0\n",
"9700.0\n",
"9800.0\n",
"9900.0\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"
]
}
],
@@ -216,34 +154,34 @@
"\n",
"for i in range(nt+1):\n",
"\n",
" if np.mod(i,1e4) == 0:\n",
" if np.mod(i,1e3) == 0:\n",
" print(t_vec[i])\n",
"\n",
" if i == 0.4*(nt+1):\n",
" V.set_influx(0.)\n",
" if i > 0.1*(nt+1):\n",
" reservoir.set_influx(0.)\n",
"\n",
" p = V.get_current_pressure()\n",
" Pegelregler.update_control_variable(V.level)\n",
" LA_soll = Pegelregler.get_current_control_variable()\n",
" T1.update_LA(LA_soll)\n",
" T1.set_pressure(p+offset_pressure)\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] = T1.get_current_LA()\n",
" Q_vec[i] = T1.get_current_Q()\n",
" LA_ist_vec[i] = turbine.get_current_LA()\n",
" Q_vec[i] = turbine.get_current_Q()\n",
"\n",
" \n",
" V.set_outflux(Q_vec[i])\n",
" reservoir.set_outflux(Q_vec[i],display_warning=False)\n",
"\n",
" V.timestep_reservoir_evolution() \n",
" \n",
" level_vec[i] = V.get_current_level()\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": 6,
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
@@ -256,12 +194,12 @@
"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*initial_level,1.5*initial_level])\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*initial_influx])\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",
@@ -271,27 +209,6 @@
"fig1.tight_layout()\n",
"fig1.show()\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x1caf15caca0>]"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"fig2 = plt.figure()\n",
"plt.plot(t_vec,Pegelregler.get_error_history())"
]
}
],
"metadata": {

6
Regler/Regler_class_file.py
View File

@@ -84,17 +84,17 @@ class PI_controller_class:
# use a list to be able to append more easily - will get converted to np.array when needed
self.error_history = [0]
self.control_variable = -99
self.cv_lower_limit = lower_limit # limits for the controll variable
self.cv_upper_limit = upper_limit # limits for the controll variable
# setter
def set_setpoint(self,setpoint):
self.SP = setpoint
def set_control_variable(self,control_variable, display_warning=True):
if display_warning == True and self.control_variable != -99:
if display_warning == True:
print('WARNING! You are setting the control variable of the PI controller manually \
and are not using the .update_controll_variable() method')
self.control_variable = control_variable