# -*- coding: utf-8
"""Module of class WaterElectrolyzer.
This file is part of project TESPy (github.com/oemof/tespy). It's copyrighted
by the contributors recorded in the version control history of the file,
available from its original location
tespy/components/reactors/water_electrolyzer.py
SPDX-License-Identifier: MIT
"""
import numpy as np
from tespy.components.component import Component
from tespy.tools import logger
from tespy.tools.data_containers import ComponentCharacteristics as dc_cc
from tespy.tools.data_containers import ComponentProperties as dc_cp
from tespy.tools.document_models import generate_latex_eq
from tespy.tools.fluid_properties import dT_mix_dph
from tespy.tools.fluid_properties import dT_mix_pdh
from tespy.tools.fluid_properties import h_mix_pT
[docs]
class WaterElectrolyzer(Component):
r"""
The water electrolyzer produces hydrogen and oxygen from water and power.
**Mandatory Equations**
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.fluid_func`
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.mass_flow_func`
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.reactor_pressure_func`
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.energy_balance_func`
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.gas_temperature_func`
**Optional Equations**
- cooling loop:
- :py:meth:`tespy.components.component.Component.zeta_func`
- :py:meth:`tespy.components.component.Component.pr_func`
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.eta_func`
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.eta_char_func`
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.heat_func`
- :py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.specific_energy_consumption_func`
Inlets/Outlets
- in1 (cooling inlet), in2 (feed water inlet)
- out1 (cooling outlet), out2 (oxygen outlet), out3 (hydrogen outlet)
Image
.. image:: /api/_images/WaterElectrolyzer.svg
:alt: flowsheet of the water electrolyzer
:align: center
:class: only-light
.. image:: /api/_images/WaterElectrolyzer_darkmode.svg
:alt: flowsheet of the water electrolyzer
:align: center
:class: only-dark
Parameters
----------
label : str
The label of the component.
design : list
List containing design parameters (stated as String).
offdesign : list
List containing offdesign parameters (stated as String).
design_path : str
Path to the components design case.
local_offdesign : boolean
Treat this component in offdesign mode in a design calculation.
local_design : boolean
Treat this component in design mode in an offdesign calculation.
char_warnings : boolean
Ignore warnings on default characteristics usage for this component.
printout : boolean
Include this component in the network's results printout.
P : float, dict, :code:`"var"`
Power input, :math:`P/\text{W}`.
Q : float, dict
Heat output of cooling, :math:`Q/\text{W}`
e : float, dict, :code:`"var"`
Electrolysis specific energy consumption,
:math:`e/(\text{J}/\text{m}^3)`.
eta : float, dict
Electrolysis efficiency (referring to H2 higher heating value),
:math:`\eta/1`.
eta_char : tespy.tools.characteristics.CharLine, dict
Electrolysis efficiency characteristic line.
pr : float, dict, :code:`"var"`
Cooling loop pressure ratio, :math:`pr/1`.
zeta : float, dict, :code:`"var"`
Geometry independent friction coefficient for cooling loop pressure
drop, :math:`\frac{\zeta}{D^4}/\frac{1}{\text{m}^4}`.
Note
----
Other than usual components, the water electrolyzer has the fluid
composition built into its equations for the feed water inlet and the
hydrogen and oxygen outlet. Thus, the user must not specify the fluid
composition at these connections!
Example
-------
Create a water electrolyzer and compress the hydrogen, e.g. for a hydrogen
storage.
>>> from tespy.components import (Sink, Source, Compressor,
... WaterElectrolyzer)
>>> from tespy.connections import Connection
>>> from tespy.networks import Network
>>> import shutil
>>> nw = Network(T_unit='C', p_unit='bar', v_unit='l / s', iterinfo=False)
>>> fw = Source('feed water')
>>> oxy = Sink('oxygen sink')
>>> hydro = Sink('hydrogen sink')
>>> cw_cold = Source('cooling water source')
>>> cw_hot = Sink('cooling water sink')
>>> comp = Compressor('compressor', eta_s=0.9)
>>> el = WaterElectrolyzer('electrolyzer')
>>> el.component()
'water electrolyzer'
The electrolyzer should produce 100 l/s of hydrogen at an operating
pressure of 10 bars and an outlet temperature of 50 °C. The fluid
composition needs to be specified for the cooling liquid only. The storage
pressure is 25 bars. The electrolysis efficiency is at 80 % and the
compressor isentropic efficiency at 85 %. After designing the plant the
offdesign electrolysis efficiency is predicted by the characteristic line.
The default characteristic line can be found here: :py:mod:`tespy.data`.
>>> fw_el = Connection(fw, 'out1', el, 'in2')
>>> el_o = Connection(el, 'out2', oxy, 'in1')
>>> el_cmp = Connection(el, 'out3', comp, 'in1')
>>> cmp_h = Connection(comp, 'out1', hydro, 'in1')
>>> cw_el = Connection(cw_cold, 'out1', el, 'in1')
>>> el_cw = Connection(el, 'out1', cw_hot, 'in1')
>>> nw.add_conns(fw_el, el_o, el_cmp, cmp_h, cw_el, el_cw)
>>> fw_el.set_attr(p=10, T=15)
>>> cw_el.set_attr(p=5, T=15, fluid={'H2O': 1})
>>> el_cw.set_attr(T=45)
>>> cmp_h.set_attr(p=25)
>>> el_cmp.set_attr(v=100, T=50)
>>> el.set_attr(eta=0.8, pr=0.99, design=['eta', 'pr'],
... offdesign=['eta_char', 'zeta'])
>>> comp.set_attr(eta_s=0.85)
>>> nw.solve('design')
>>> nw.save('tmp')
>>> round(el.e0 / el.P.val * el_cmp.m.val_SI, 1)
0.8
>>> P_design = el.P.val / 1e6
>>> round(P_design, 1)
13.2
>>> nw.solve('offdesign', design_path='tmp')
>>> round(el.eta.val, 1)
0.8
>>> el_cmp.set_attr(v=None)
>>> el.set_attr(P=P_design * 0.66)
>>> nw.solve('offdesign', design_path='tmp')
>>> round(el.eta.val, 2)
0.88
>>> shutil.rmtree('./tmp', ignore_errors=True)
"""
[docs]
@staticmethod
def component():
return 'water electrolyzer'
[docs]
def get_parameters(self):
return {
'P': dc_cp(min_val=0),
'Q': dc_cp(
max_val=0, num_eq=1,
deriv=self.heat_deriv, func=self.heat_func,
latex=self.heat_func_doc),
'pr': dc_cp(
max_val=1, num_eq=1,
deriv=self.pr_deriv, func=self.pr_func,
func_params={'pr': 'pr'}, latex=self.pr_func_doc),
'zeta': dc_cp(
min_val=0, num_eq=1,
deriv=self.zeta_deriv, func=self.zeta_func,
func_params={'zeta': 'zeta'}, latex=self.zeta_func_doc),
'eta': dc_cp(
min_val=0, max_val=1, num_eq=1, latex=self.eta_func_doc,
deriv=self.eta_deriv, func=self.eta_func),
'eta_char': dc_cc(
deriv=self.eta_char_deriv, func=self.eta_char_func,
latex=self.eta_char_func_doc, num_eq=1,
param='m_out', char_params={
'type': 'rel', 'outconn': 2}),
'e': dc_cp(
min_val=0, num_eq=1,
deriv=self.specific_energy_consumption_deriv,
func=self.specific_energy_consumption_func,
latex=self.specific_energy_consumption_func_doc)
}
[docs]
def get_mandatory_constraints(self):
num_mass_eq = (
(self.inl[1].m.is_var or self.outl[1].m.is_var)
+ (self.inl[1].m.is_var or self.outl[2].m.is_var)
)
return {
'mass_flow_constraints': {
'func': self.mass_flow_func, 'deriv': self.mass_flow_deriv,
'constant_deriv': True, 'latex': self.mass_flow_func_doc,
'num_eq': num_mass_eq},
'energy_balance_constraints': {
'func': self.energy_balance_func,
'deriv': self.energy_balance_deriv,
'constant_deriv': False, 'latex': self.energy_balance_func_doc,
'num_eq': 1},
'reactor_pressure_constraints': {
'func': self.reactor_pressure_func,
'deriv': self.reactor_pressure_deriv,
'constant_deriv': True,
'latex': self.reactor_pressure_func_doc,
'num_eq': 2},
'gas_temperature_constraints': {
'func': self.gas_temperature_func,
'deriv': self.gas_temperature_deriv,
'constant_deriv': False,
'latex': self.gas_temperature_func_doc,
'num_eq': 1}
}
[docs]
@staticmethod
def inlets():
return ['in1', 'in2']
[docs]
@staticmethod
def outlets():
return ['out1', 'out2', 'out3']
[docs]
def preprocess(self, num_nw_vars):
if not self.P.is_set:
self.set_attr(P='var')
msg = ('The power input of a water electrolyzer must be set! '
'We are adding the power input of component ' +
self.label + ' as custom variable of the system.')
logger.info(msg)
self.o2 = "O2"
self.h2 = "H2"
self.h2o = "H2O"
self.e0 = self.calc_e0()
super().preprocess(num_nw_vars)
[docs]
def calc_e0(self):
r"""
Calculate the minimum specific energy required for electrolysis.
Returns
-------
float
Minimum specific energy.
.. math::
e0 = -\frac{\sum_i {\Delta H_f^0}_i -
\sum_j {\Delta H_f^0}_j }
{M_{H_2}}\\
\forall i \in \text{reation products},\\
\forall j \in \text{reation educts},\\
\Delta H_f^0: \text{molar formation enthalpy}
"""
hf = {}
hf['H2O'] = -286000
hf['H2'] = 0
hf['O2'] = 0
M = self.outl[2].fluid.wrapper[self.h2]._molar_mass
e0 = -(2 * hf['H2O'] - 2 * hf['H2'] - hf['O2']) / (2 * M)
return e0
[docs]
def gas_temperature_func(self):
r"""
Equation for temperature equality of product gases.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = T_\mathrm{out,2} - T_\mathrm{out,3}
"""
return self.outl[1].calc_T() - self.outl[2].calc_T()
[docs]
def gas_temperature_func_doc(self, label):
r"""
Equation for temperature equality of product gases.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0 = T_\mathrm{out,2} - T_\mathrm{out,3}'
return generate_latex_eq(self, latex, label)
[docs]
def gas_temperature_deriv(self, increment_filter, k):
r"""
Partial derivatives for product gas temperature function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
# derivatives for outlet 1
o = self.outl[1]
if self.is_variable(o.p, increment_filter):
self.jacobian[k, o.p.J_col] = dT_mix_dph(o.p.val_SI, o.h.val_SI, o.fluid_data, o.mixing_rule)
if self.is_variable(o.h, increment_filter):
self.jacobian[k, o.h.J_col] = dT_mix_pdh(o.p.val_SI, o.h.val_SI, o.fluid_data, o.mixing_rule)
# derivatives for outlet 2
o = self.outl[2]
if self.is_variable(o.p, increment_filter):
self.jacobian[k, o.p.J_col] = -dT_mix_dph(o.p.val_SI, o.h.val_SI, o.fluid_data, o.mixing_rule)
if self.is_variable(o.h, increment_filter):
self.jacobian[k, o.h.J_col] = -dT_mix_pdh(o.p.val_SI, o.h.val_SI, o.fluid_data, o.mixing_rule)
[docs]
def eta_func(self):
r"""
Equation for electrolysis efficiency.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = P \cdot \eta - \dot{m}_{H_2,out,3} \cdot e_0
"""
return self.P.val * self.eta.val - self.outl[2].m.val_SI * self.e0
[docs]
def eta_func_doc(self, label):
r"""
Equation for electrolysis efficiency.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0 = P \cdot \eta - \dot{m}_\mathrm{H_2,out,3} \cdot e_0'
return generate_latex_eq(self, latex, label)
[docs]
def eta_deriv(self, increment_filter, k):
r"""
Partial derivatives for efficiency function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
if self.outl[2].m.is_var:
self.jacobian[k, self.outl[2].m.J_col] = -self.e0
# derivatives for variable P
if self.P.is_var:
self.jacobian[k, self.P.J_col] = self.eta.val
[docs]
def heat_func(self):
r"""
Equation for heat output.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = \dot{Q}-\dot{m}_{in,1}\cdot \left(h_{in,1}-h_{out,1}\right)
"""
return self.Q.val - self.inl[0].m.val_SI * (
self.inl[0].h.val_SI - self.outl[0].h.val_SI)
[docs]
def heat_func_doc(self, label):
r"""
Equation for heat output.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'0=\dot{Q}-\dot{m}_\mathrm{in,1}\cdot\left(h_\mathrm{in,1}-'
r'h_\mathrm{out,1}\right)')
return generate_latex_eq(self, latex, label)
[docs]
def heat_deriv(self, increment_filter, k):
r"""
Partial derivatives for heat output function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
i = self.inl[0]
o = self.outl[0]
if i.m.is_var:
self.jacobian[k, i.m.J_col] = o.h.val_SI - i.h.val_SI
if i.h.is_var:
self.jacobian[k, i.h.J_col] = -i.m.val_SI
if o.h.is_var:
self.jacobian[k, o.h.J_col] = i.m.val_SI
[docs]
def specific_energy_consumption_func(self):
r"""
Equation for specific energy consumption.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = P - \dot{m}_{H_2,out3} \cdot e
"""
return self.P.val - self.outl[2].m.val_SI * self.e.val
[docs]
def specific_energy_consumption_func_doc(self, label):
r"""
Equation for specific energy consumption.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = r'0=P - \dot{m}_\mathrm{H_2,out3} \cdot e'
return generate_latex_eq(self, latex, label)
[docs]
def specific_energy_consumption_deriv(self, increment_filter, k):
r"""
Partial derivatives for specific energy consumption function.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
if self.outl[2].m.is_var:
self.jacobian[k, self.outl[2].m.J_col] = -self.e.val
# derivatives for variable P
if self.P.is_var:
self.jacobian[k, self.P.J_col] = 1
# derivatives for variable e
if self.e.is_var:
self.jacobian[k, self.e.J_col] = -self.outl[2].m.val_SI
[docs]
def energy_balance_func(self):
r"""
Calculate the residual in energy balance.
Returns
-------
residual : float
Residual value of energy balance equation.
.. math::
\begin{split}
0=&P + \dot{m}_\mathrm{in,2}\cdot\left(h_\mathrm{in,2}-
h_\mathrm{in,2,ref}\right)\\
&-\dot{m}_\mathrm{in,1}\cdot\left( h_\mathrm{out,1} -
h_\mathrm{in,1} \right)\\
& -\dot{m}_\mathrm{out,2} \cdot \left( h_\mathrm{out,2} -
h_\mathrm{out,2,ref} \right)\\
& +\dot{m}_\mathrm{out,3} \cdot \left( h_\mathrm{out,3} -
h_\mathrm{out,3,ref} + e_0\right)\\
\end{split}
- Reference temperature: 298.15 K.
- Reference pressure: 1 bar.
"""
return self.P.val - self.calc_P()
[docs]
def energy_balance_func_doc(self, label):
r"""
Calculate the residual in energy balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0=&P + \dot{m}_\mathrm{in,2}\cdot\left(h_\mathrm{in,2}-'
r'h_\mathrm{in,2,ref}\right)\\' + '\n'
r'&-\dot{m}_\mathrm{in,1}\cdot\left( h_\mathrm{out,1} -'
r'h_\mathrm{in,1} \right)\\' + '\n'
r'& - \dot{m}_\mathrm{out,2} \cdot \left( h_\mathrm{out,2} -'
r'h_\mathrm{out,2,ref} \right)\\' + '\n'
r'& + \dot{m}_\mathrm{out,3} \cdot \left( h_\mathrm{out,3} -'
r'h_\mathrm{out,3,ref} + e_0\right)\\' + '\n'
r'&p_\mathrm{ref}=\unit[1]{bar},'
r'\;T_\mathrm{ref}=\unit[25]{^\circ C}\\' + '\n'
r'\end{split}'
)
return generate_latex_eq(self, latex, label)
[docs]
def energy_balance_deriv(self, increment_filter, k):
r"""
Partial derivatives for reactor energy balance.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
# derivatives determined from calc_P function
T_ref = 298.15
p_ref = 1e5
h_refh2o = h_mix_pT(p_ref, T_ref, self.inl[1].fluid_data, self.inl[1].mixing_rule)
h_refo2 = h_mix_pT(p_ref, T_ref, self.outl[1].fluid_data, self.outl[1].mixing_rule)
h_refh2 = h_mix_pT(p_ref, T_ref, self.outl[2].fluid_data, self.outl[2].mixing_rule)
# derivatives cooling water inlet
i = self.inl[0]
if i.m.is_var:
self.jacobian[k, i.m.J_col] = i.h.val_SI - self.outl[0].h.val_SI
if i.h.is_var:
self.jacobian[k, i.h.J_col] = i.m.val_SI
# derivatives feed water inlet
i = self.inl[1]
if i.m.is_var:
self.jacobian[k, i.m.J_col] = i.h.val_SI - h_refh2o
if i.h.is_var:
self.jacobian[k, i.h.J_col] = i.m.val_SI
# derivative cooling water outlet
o = self.outl[0]
if o.h.is_var:
self.jacobian[k, o.h.J_col] = -self.inl[0].m.val_SI
# derivatives oxygen outlet
o = self.outl[1]
if o.m.is_var:
self.jacobian[k, o.m.J_col] = -(o.h.val_SI - h_refo2)
if o.h.is_var:
self.jacobian[k, o.h.J_col] = -o.m.val_SI
# derivatives hydrogen outlet
o = self.outl[2]
if o.m.is_var:
self.jacobian[k, o.m.J_col] = -(o.h.val_SI - h_refh2 + self.e0)
if o.h.is_var:
self.jacobian[k, o.h.J_col] = -o.m.val_SI
# derivatives for variable P
if self.P.is_var:
self.jacobian[k, self.P.J_col] = 1
[docs]
def eta_char_func(self):
r"""
Equation for given efficiency characteristic of a water electrolyzer.
Returns
-------
residual : float
Residual value of equation.
.. math::
0 = P - \dot{m}_{H_2,out,3} \cdot \frac{e_0}{\eta_{design}\cdot
f\left(expr \right)}
"""
p = self.eta_char.param
expr = self.get_char_expr(p, **self.eta_char.char_params)
if not expr:
msg = ('Please choose a valid parameter, you want to link the '
'efficiency to at component ' + self.label + '.')
logger.error(msg)
raise ValueError(msg)
return (
self.P.val - self.outl[2].m.val_SI * self.e0 /
(self.eta.design * self.eta_char.char_func.evaluate(expr)))
[docs]
def eta_char_func_doc(self, label):
r"""
Equation for given efficiency characteristic of a water electrolyzer.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
p = self.eta_char.param
expr = self.get_char_expr_doc(p, **self.eta_char.char_params)
if not expr:
msg = ('Please choose a valid parameter, you want to link the '
'efficiency to at component ' + self.label + '.')
logger.error(msg)
raise ValueError(msg)
latex = (
r'0=P-\dot{m}_\mathrm{H_2,out,3}\cdot\frac{e_0}'
r'{\eta_\mathrm{design}\cdot f\left(X\right)}')
return generate_latex_eq(self, latex, label)
[docs]
def eta_char_deriv(self, increment_filter, k):
r"""
Partial derivatives electrolysis efficiency characteristic.
Parameters
----------
increment_filter : ndarray
Matrix for filtering non-changing variables.
k : int
Position of derivatives in Jacobian matrix (k-th equation).
"""
o = self.outl[2]
if o.m.is_var:
f = self.eta_char_func
self.jacobian[k, o.m.J_col] = self.numeric_deriv(f, 'm', o)
if self.P.is_var:
self.jacobian[k, self.P.J_col] = 1
[docs]
def mass_flow_func(self):
r"""
Equations for mass conservation.
Returns
-------
residual : list
Residual values of equation.
.. math::
O_2 = \frac{M_{O_2}}{M_{O_2} + 2 \cdot M_{H_2}}\\
0 =\dot{m}_\mathrm{in,1}-\dot{m}_\mathrm{out,1}\\
0=O_2\cdot\dot{m}_\mathrm{H_{2}O,in,2}-
\dot{m}_\mathrm{O_2,out,2}\\
0 = \left(1 - O_2\right) \cdot \dot{m}_\mathrm{H_{2}O,in,2} -
\dot{m}_\mathrm{H_2,out,3}
"""
# calculate the ratio of o2 in water
M_o2 = self.outl[1].fluid.wrapper[self.o2]._molar_mass
M_h2 = self.outl[2].fluid.wrapper[self.h2]._molar_mass
o2 = M_o2 / (M_o2 + 2 * M_h2)
# equations for mass flow balance electrolyzer
residual = []
if self.inl[1].m.is_var or self.outl[1].m.is_var:
residual += [o2 * self.inl[1].m.val_SI - self.outl[1].m.val_SI]
if self.inl[1].m.is_var or self.outl[2].m.is_var:
residual += [(1 - o2) * self.inl[1].m.val_SI - self.outl[2].m.val_SI]
return residual
[docs]
def mass_flow_func_doc(self, label):
r"""
Equations for mass conservation.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'O_2 = &\frac{M_{O_2}}{M_{O_2} + 2 \cdot M_{H_2}}\\' + '\n'
r'0 =&\dot{m}_\mathrm{in,1}-\dot{m}_\mathrm{out,1}\\' + '\n'
r'0=&O_2\cdot\dot{m}_\mathrm{H_{2}O,in,2}-'
r'\dot{m}_\mathrm{O_2,out,2}\\' + '\n'
r'0 =&\left(1 - O_2\right) \cdot \dot{m}_\mathrm{H_{2}O,in,2}-'
r'\dot{m}_\mathrm{H_2,out,3}\\' + '\n'
r'\end{split}'
)
return generate_latex_eq(self, latex, label)
[docs]
def mass_flow_deriv(self, k):
r"""
Calculate the partial derivatives for all mass flow balance equations.
Returns
-------
deriv : ndarray
Matrix with partial derivatives for the mass flow equations.
"""
M_o2 = self.outl[1].fluid.wrapper[self.o2]._molar_mass
M_h2 = self.outl[2].fluid.wrapper[self.h2]._molar_mass
o2 = M_o2 / (M_o2 + 2 * M_h2)
# number of equations may vary here
if self.inl[1].m.is_var or self.outl[1].m.is_var:
if self.inl[1].m.is_var:
self.jacobian[k, self.inl[1].m.J_col] = o2
if self.outl[1].m.is_var:
self.jacobian[k, self.outl[1].m.J_col] = -1
k += 1
# derivatives for mass flow balance for hydrogen output
if self.inl[1].m.is_var:
self.jacobian[k, self.inl[1].m.J_col] = (1 - o2)
if self.outl[2].m.is_var:
self.jacobian[k, self.outl[2].m.J_col] = -1
[docs]
def reactor_pressure_func(self):
r"""
Equations for reactor pressure balance.
Returns
-------
residual : list
Residual values of equation.
.. math::
0 = p_\mathrm{in,2} - p_\mathrm{out,2}\\
0 = p_\mathrm{in,2} - p_\mathrm{out,3}
"""
return [
self.inl[1].p.val_SI - self.outl[1].p.val_SI,
self.inl[1].p.val_SI - self.outl[2].p.val_SI
]
[docs]
def reactor_pressure_func_doc(self, label):
r"""
Equations for reactor pressure balance.
Parameters
----------
label : str
Label for equation.
Returns
-------
latex : str
LaTeX code of equations applied.
"""
latex = (
r'\begin{split}' + '\n'
r'0 = & p_\mathrm{in,2} - p_\mathrm{out,2}\\' + '\n'
r'0 = & p_\mathrm{in,2} - p_\mathrm{out,3}\\' + '\n'
r'\end{split}')
return generate_latex_eq(self, latex, label)
[docs]
def reactor_pressure_deriv(self, k):
r"""
Calculate the partial derivatives for combustion pressure equations.
Returns
-------
deriv : ndarray
Matrix with partial derivatives for the pressure equations.
"""
i = self.inl[1]
for o in self.outl[1:]:
if i.p.is_var:
self.jacobian[k, i.p.J_col] = 1
if o.p.is_var:
self.jacobian[k, o.p.J_col] = -1
k += 1
[docs]
def calc_P(self):
r"""
Calculate water electrolyzer power input.
Returns
-------
P : float
Value of power input.
.. math::
\begin{split}
P = & -\dot{m}_{in,2} \cdot \left( h_{in,2} - h_{in,2,ref}
\right)\\
& + \dot{m}_{in,1} \cdot \left( h_{out,1} - h_{in,1} \right)\\
& + \dot{m}_{out,2} \cdot \left( h_{out,2} - h_{out,2,ref}
\right)\\
& - \dot{m}_{out,3} \cdot \left( h_{out,3} - h_{out,3,ref}
+ e_0\right)\\
\end{split}
Note
----
The temperature for the reference state is set to 25 °C, thus
the feed water must be liquid as proposed in the calculation of
the minimum specific energy consumption for electrolysis:
:py:meth:`tespy.components.reactors.water_electrolyzer.WaterElectrolyzer.calc_e0`.
The part of the equation regarding the cooling water is implemented
with negative sign as the energy for cooling is extracted from the
reactor.
- Reference temperature: 298.15 K.
- Reference pressure: 1 bar.
"""
T_ref = 298.15
p_ref = 1e5
# equations to set a reference point for each h2o, h2 and o2
h_refh2o = h_mix_pT(p_ref, T_ref, self.inl[1].fluid_data, self.inl[1].mixing_rule)
h_refo2 = h_mix_pT(p_ref, T_ref, self.outl[1].fluid_data, self.outl[1].mixing_rule)
h_refh2 = h_mix_pT(p_ref, T_ref, self.outl[2].fluid_data, self.outl[2].mixing_rule)
val = (
-self.inl[1].m.val_SI * (self.inl[1].h.val_SI - h_refh2o)
+ self.inl[0].m.val_SI * (self.outl[0].h.val_SI - self.inl[0].h.val_SI)
+ self.outl[1].m.val_SI * (self.outl[1].h.val_SI - h_refo2)
+ self.outl[2].m.val_SI * (self.outl[2].h.val_SI - h_refh2 + self.e0)
)
return val
[docs]
def bus_func(self, bus):
r"""
Calculate the value of the bus function.
Parameters
----------
bus : tespy.connections.bus.Bus
TESPy bus object.
Returns
-------
val : float
Value of energy transfer :math:`\dot{E}`. This value is passed to
:py:meth:`tespy.components.component.Component.calc_bus_value`
for value manipulation according to the specified characteristic
line of the bus.
.. math::
\dot{E} = \begin{cases}
P & \text{key = 'P'}\\
- \dot{m}_{in,1} \cdot \left(h_{out,1} - h_{in,1} \right) &
\text{key = 'Q'}\\
\end{cases}
"""
######################################################################
# equations for power on bus
if bus['param'] == 'P':
val = self.calc_P()
######################################################################
# equations for heat on bus
elif bus['param'] == 'Q':
val = -self.inl[0].m.val_SI * (
self.outl[0].h.val_SI - self.inl[0].h.val_SI
)
######################################################################
# missing/invalid bus parameter
else:
msg = ('The parameter ' + str(bus['param']) + ' is not a valid '
'parameter for a component of type ' + self.component() +
'. Please specify a bus parameter (P/Q) for component ' +
self.label + '.')
logger.error(msg)
raise ValueError(msg)
return val
[docs]
def bus_func_doc(self, bus):
r"""
Return LaTeX string of the bus function.
Parameters
----------
bus : tespy.connections.bus.Bus
TESPy bus object.
Returns
-------
latex : str
LaTeX string of bus function.
"""
if bus['param'] == 'P':
return r'P_\mathrm{el}'
elif bus['param'] == 'Q':
return (
r'-\dot{m}_\mathrm{in,1} \cdot \left(h_\mathrm{out,1} - '
r'h_\mathrm{in,1} \right)')
[docs]
def bus_deriv(self, bus):
r"""
Calculate partial derivatives of the bus function.
Parameters
----------
bus : tespy.connections.bus.Bus
TESPy bus object.
Returns
-------
deriv : ndarray
Matrix of partial derivatives.
"""
f = self.calc_bus_value
b = bus.comps.loc[self]
######################################################################
# derivatives for power on bus
if b['param'] == 'P':
for c in self.inl + self.outl:
if c.m.is_var and c != self.outl[0]:
if c.m.J_col not in bus.jacobian:
bus.jacobian[c.m.J_col] = 0
bus.jacobian[c.m.J_col] -= self.numeric_deriv(f, 'm', c, bus=bus)
if c.h.is_var:
if c.h.J_col not in bus.jacobian:
bus.jacobian[c.h.J_col] = 0
bus.jacobian[c.h.J_col] -= self.numeric_deriv(f, 'h', c, bus=bus)
# variable power
if self.P.is_var:
if self.P.J_col not in bus.jacobian:
bus.jacobian[self.P.J_col] = 0
bus.jacobian[self.P.J_col] -= self.numeric_deriv(f, 'P', None, bus=bus)
######################################################################
# derivatives for heat on bus
elif b['param'] == 'Q':
i = self.inl[0]
o = self.outl[0]
if i.m.is_var:
if i.m.J_col not in bus.jacobian:
bus.jacobian[i.m.J_col] = 0
bus.jacobian[i.m.J_col] -= self.numeric_deriv(f, 'm', i, bus=bus)
if o.h.is_var:
if o.h.J_col not in bus.jacobian:
bus.jacobian[o.h.J_col] = 0
bus.jacobian[o.h.J_col] -= self.numeric_deriv(f, 'h', o, bus=bus)
if o.h.is_var:
if o.h.J_col not in bus.jacobian:
bus.jacobian[o.h.J_col] = 0
bus.jacobian[o.h.J_col] -= self.numeric_deriv(f, 'h', o, bus=bus)
######################################################################
# missing/invalid bus parameter
else:
msg = ('The parameter ' + str(b['param']) + ' is not a valid '
'parameter for a component of type ' + self.component() +
'. Please specify a bus parameter (P/Q) for component ' +
self.label + '.')
logger.error(msg)
raise ValueError(msg)
[docs]
@staticmethod
def is_branch_source():
return True
[docs]
def start_branch(self):
branches = {}
for outconn in self.outl[1:]:
if outconn == self.outl[1] and "O2" not in outconn.fluid.val:
outconn.fluid.val["O2"] = 1
if outconn == self.outl[2] and "H2" not in outconn.fluid.val:
outconn.fluid.val["H2"] = 1
branch = {
"connections": [outconn],
"components": [self, outconn.target],
"subbranches": {}
}
outconn.target.propagate_to_target(branch)
branches.update({outconn.label: branch})
return branches
[docs]
def start_fluid_wrapper_branch(self):
branches = {}
for outconn in self.outl[1:]:
branch = {
"connections": [outconn],
"components": [self]
}
outconn.target.propagate_wrapper_to_target(branch)
branches.update({outconn.label: branch})
return branches
[docs]
def propagate_to_target(self, branch):
inconn = branch["connections"][-1]
if inconn == self.inl[0]:
conn_idx = self.inl.index(inconn)
outconn = self.outl[conn_idx]
branch["connections"] += [outconn]
branch["components"] += [outconn.target]
outconn.target.propagate_to_target(branch)
else:
if "H2O" not in inconn.fluid.val:
inconn.fluid.val["H2O"] = 1
return
[docs]
def propagate_wrapper_to_target(self, branch):
inconn = branch["connections"][-1]
if inconn == self.inl[0]:
conn_idx = self.inl.index(inconn)
outconn = self.outl[conn_idx]
branch["connections"] += [outconn]
branch["components"] += [self]
outconn.target.propagate_wrapper_to_target(branch)
else:
branch["components"] += [self]
return
[docs]
def initialise_source(self, c, key):
r"""
Return a starting value for pressure and enthalpy at outlet.
Parameters
----------
c : tespy.connections.connection.Connection
Connection to perform initialisation on.
key : str
Fluid property to retrieve.
Returns
-------
val : float
Starting value for pressure/enthalpy in SI units.
.. math::
val = \begin{cases}
5 \cdot 10^5 & \text{key = 'p'}\\
h\left(T=323.15, p=5 \cdot 10^5\right) & \text{key = 'h'}
\end{cases}
"""
if key == 'p':
return 5e5
elif key == 'h':
T = 50 + 273.15
return h_mix_pT(c.p.val_SI, T, c.fluid_data, c.mixing_rule)
[docs]
def initialise_target(self, c, key):
r"""
Return a starting value for pressure and enthalpy at inlet.
Parameters
----------
c : tespy.connections.connection.Connection
Connection to perform initialisation on.
key : str
Fluid property to retrieve.
Returns
-------
val : float
Starting value for pressure/enthalpy in SI units.
.. math::
val = \begin{cases}
5 \cdot 10^5 & \text{key = 'p'}\\
h\left(T=293.15, p=5 \cdot 10^5\right) & \text{key = 'h'}
\end{cases}
"""
if key == 'p':
return 5e5
elif key == 'h':
T = 20 + 273.15
return h_mix_pT(c.p.val_SI, T, c.fluid_data, c.mixing_rule)
[docs]
def calc_parameters(self):
r"""Postprocessing parameter calculation."""
self.Q.val = -self.inl[0].m.val_SI * (
self.outl[0].h.val_SI - self.inl[0].h.val_SI
)
self.pr.val = self.outl[0].p.val_SI / self.inl[0].p.val_SI
self.e.val = self.P.val / self.outl[2].m.val_SI
self.eta.val = self.e0 / self.e.val
i = self.inl[0]
o = self.outl[0]
self.zeta.val = self.calc_zeta(i, o)
[docs]
def exergy_balance(self, T0):
self.E_P = (
self.outl[1].Ex_chemical + self.outl[2].Ex_chemical
- self.inl[1].Ex_chemical + self.outl[0].Ex_physical
+ self.inl[0].Ex_physical
)
self.E_F = self.P.val
self.E_D = self.E_F - self.E_P
self.epsilon = self._calc_epsilon()
self.E_bus = self.P.val