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models.py
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import numpy as np
import pandas as pd
from scipy.integrate import odeint
def dtok(temp):
"""Transform C.deg into K.deg"""
return temp + 273.15
def ktod(temp):
"""Transform K.deg into C.deg"""
return temp - 273.15
def vol_cst_model(y, time, m_dot_src, t_src, m_dot_snk, t_snk, ex_surf, mesh_h):
"""Define ODE for a 3 mesh constant volume stratified thermal buffer"""
t_top, t_mid, t_bot = y
mesh_vol = ex_surf * mesh_h
rho = 985 # kg.m-3
cp = 4185 # J.kg-1.K-1
e_cond = 0.62 # W.m-1.K-1
phi_port_top = m_dot_src * cp * t_src - m_dot_snk * cp * t_top
phi_port_low = m_dot_snk * cp * t_snk - m_dot_src * cp * t_bot
phi_cond_top_to_mid = e_cond * mesh_h * ex_surf * (t_top - t_mid)
phi_cond_mid_to_bot = e_cond * mesh_h * ex_surf * (t_mid - t_bot)
dydt = [
phi_port_top - phi_cond_top_to_mid,
phi_cond_top_to_mid - phi_cond_mid_to_bot,
phi_port_low + phi_cond_mid_to_bot
]
m_dot_mix = m_dot_snk - m_dot_src
if m_dot_mix > 0: # m_dot_mix UP
dydt[0] += m_dot_mix * cp * t_mid
dydt[1] += m_dot_mix * cp * (t_bot - t_mid)
dydt[2] -= m_dot_mix * cp * t_bot
if m_dot_mix < 0: # m_dot_mix DOWN
dydt[0] += m_dot_mix * cp * t_top
dydt[1] -= m_dot_mix * cp * (t_top - t_mid)
dydt[2] -= m_dot_mix * cp * t_mid
return np.array(dydt) / (mesh_vol * rho * cp)
def tau_model(y, t, io, tau, p_set):
"""Define ODE for a simplified dynamic heat pump model using time constant"""
dydt = (p_set * io - y) / tau
return dydt
class ThermalBuffer:
"""Model class of a 3 mesh constant volume stratified thermal buffer"""
UNIT = {"seconds": 1, "minutes": 60, "hours": 3600}
def __init__(self, ex_surf, mesh_h, temp_init=None, start='1/1/2000'):
if not temp_init:
temp_init = [dtok(80.0), dtok(60.0), dtok(40.0)]
assert len(temp_init) == 3
self.m_dot_src = 0 # kg/s
self.t_src = temp_init[0] # K.deg
self.m_dot_snk = 0 # kg/s
self.t_snk = temp_init[2] # K.deg
self.ex_surf = ex_surf
self.mesh_h = mesh_h
self.time = pd.to_datetime(start)
self.t_top = temp_init[0]
self.t_mid = temp_init[1]
self.t_bot = temp_init[2]
self.t_set_top = temp_init[0]
self.t_set_bop = temp_init[2]
self.soc = (np.mean([self.t_top, self.t_mid, self.t_bot]) - self.t_set_bop) / (self.t_set_top - self.t_set_bop)
def make_step(self, step, unit="seconds"):
end = self.time + pd.DateOffset(**{unit: step})
t = np.arange(start=0, stop=step * self.UNIT[unit], step=1.0)
y0 = [self.t_top, self.t_mid, self.t_bot]
res = odeint(vol_cst_model, y0, t, args=(
self.m_dot_src,
self.t_src,
self.m_dot_snk,
self.t_snk,
self.ex_surf,
self.mesh_h))
self.t_top, self.t_mid, self.t_bot = res[-1]
self.soc = (np.mean([self.t_top, self.t_mid, self.t_bot]) - self.t_set_bop) / (self.t_set_top - self.t_set_bop)
self.time += pd.DateOffset(**{unit: step})
class HeatPump:
"""Model class of a HP dynamic model based on a ratio of the theoretical COP of Carnot"""
UNIT = {"seconds": 1, "minutes": 60, "hours": 3600}
def __init__(self, p_max, t_cond, t_evap, n_th=0.4, tau=60.0, io_init=False, start='1/1/2000'):
assert t_cond > t_evap
self.p_max = p_max
self.t_cond = t_cond
self.t_evap = t_evap
self.n_th = n_th
self.tau = tau
self.time = pd.to_datetime(start)
self.io = io_init
self.cop = self.n_th * (self.t_cond / (self.t_cond - self.t_evap))
self.p_sink = self.io * self.p_max
self.p_elec = self.p_sink / self.cop
self.p_srce = self.p_sink - self.p_elec
def make_step(self, step, unit="seconds"):
end = self.time + pd.DateOffset(**{unit: step})
t = np.arange(start=0, stop=step * self.UNIT[unit], step=1.0)
res_p_sink = odeint(tau_model, self.p_sink, t, args=(self.io, self.tau, self.p_max))
self.cop = self.n_th * (self.t_cond / (self.t_cond - self.t_evap))
self.p_sink = round(res_p_sink[-1][0], 3)
self.p_elec = self.p_sink / self.cop
self.p_srce = self.p_sink - self.p_elec
self.time += pd.DateOffset(**{unit: step})
class Profile:
def __init__(self, data, method="nearest"):
self.series = data
self.time = pd.to_datetime(data.index[0])
self.value = data.iloc[0]
self.method = method
def make_step(self, step, unit="seconds"):
self.time += pd.DateOffset(**{unit: step})
self.value = self.series.iloc[self.series.index.get_loc(self.time, method=self.method)]
class Hysteresis:
def __init__(self, x_max=1.0, x_min=0.0, y_init=False):
self.x_max = x_max
self.x_min = x_min
self.x = None
self.y = y_init
def make_step(self):
if self.y and self.x >= self.x_max:
self.y = False
if not self.y and self.x <= self.x_min:
self.y = True
def t_out_from_m_dot_and_p(t_in, m_dot, p_kw):
cp = 4.18 # kJ/kg/K
return p_kw / m_dot / cp + t_in
def m_dot_from_p_and_t_in_and_t_set(p_kw, t_in, t_set):
cp = 4.18 # kJ/kg/K
return p_kw / cp / abs(t_in - t_set) # always >=0