Merge c3c151b into 66d17e1

docs/absorption_chillers.rst

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+.. _absorption_chillers_label:
+
+
+~~~~~~~~~~~~~~~~~~~~~~~
+Absorption chillers
+~~~~~~~~~~~~~~~~~~~~~~~
+
+Calculations for absorption chillers based on the characteristic equation method.
+
+
+Scope
+_____
+
+This module was developed to provide cooling capacity and COP calculations
+based on temperatures for energy system optimizations with oemof.solph.
+
+
+Concept
+_______
+
+A characteristic equation model to describe the performance of
+absorption chillers.
+
+
+.. figure:: _pics/abs_chiller_col.png
+    :width: 40 %
+    :alt: abs_chiller_col.png
+    :align: center
+    :figclass: align-center
+
+    Fig.1: Absorption cooling (or heating) process.
+
+The cooling capacity (:math:`\dot{Q}_{E}`) is determined by a function of
+the characteristic
+temperature difference (:math:`\Delta\Delta t'`) that combines the external
+mean temperatures of the heat exchangers.
+
+Various approaches of the characteristic equation method exists.
+Here we use the approach described by Kühn and Ziegler [1]:
+
+.. math::
+  \Delta\Delta t = t_{G} - a \cdot t_{AC} + e \cdot t_{E}
+
+with the assumption
+
+.. math::
+  t_{A}  = t_{C} = t_{AC}
+
+where :math:`t` is the external mean fluid temperature of the heat exchangers
+(G: Generator, AC: Absorber and Condenser, E: Evaporator)
+and :math:`a` and :math:`e` are characteristic parameters.
+
+The cooling capacity (:math:`\dot{Q}_{E}`) and the driving
+heat (:math:`\dot{Q}_{G}`) can be expressed as linear functions of :math:`\Delta\Delta t'`:
+
+.. math::
+  \dot{Q}_{E} = s_{E} \cdot \Delta\Delta t' + r_{E}
+
+.. math::
+  \dot{Q}_{G} = s_{G} \cdot \Delta\Delta t' + r_{G}
+
+with the characteristic parameters :math:`s_{E}`, :math:`r_{E}`,
+:math:`s_{G}`, and :math:`r_{G}`.
+
+The COP can then be calculated from :math:`\dot{Q}_{E}` and :math:`\dot{Q}_{G}`:
+
+.. math::
+  COP = \frac{\dot{Q}_{E}}{\dot{Q}_{G}}
+
+
+These arguments are used in the formulas of the function:
+
+    ========================= =================================================== ===========
+    symbol                    argument                                            explanation
+    ========================= =================================================== ===========
+    :math:`\Delta\Delta t'`    :py:obj:`ddt`                                       Characteristic temperature difference
+
+    :math:`t_G`               :py:obj:`t_hot`                                     External mean fluid temperature of generator
+
+    :math:`t_{AC}`            :py:obj:`t_cool`                                    External mean fluid temperature of absorber and condenser
+
+    :math:`t_E`               :py:obj:`t_chill`                                   External mean fluid temperature of evaporator
+
+    :math:`a`                 :py:obj:`coef_a`                                    Characteristic parameter
+
+    :math:`e`                 :py:obj:`coef_e`                                    Characteristic parameter
+
+    :math:`s`                 :py:obj:`coef_s`                                    Characteristic parameter
+
+    :math:`r`                 :py:obj:`coef_r`                                    Characteristic parameter
+
+    :math:`\dot{Q}`           :py:obj:`Q_dots`                                    Heat flux
+
+    :math:`\dot{Q}_{E}`       :py:obj:`Q_dots_evap`                               Cooling capacity (heat flux at evaporator)
+
+    :math:`\dot{Q}_{G}`       :py:obj:`Q_dots_gen`                                Driving heat (heat flux at generator)
+
+    :math:`COP`               :py:obj:`COP`                                       Coefficient of performance
+    ========================= =================================================== ===========
+
+Usage
+_____
+
+The following example shows how to calculate the COP of a small absorption chiller.
+The characteristic coefficients used in this examples belong to a 10 kW absorption chiller developed and
+tested at the Technische Universität Berlin [1].
+
+.. code-block:: python
+
+    import oemof.thermal.absorption_heatpumps_and_chillers as abs_chiller
+
+    # Characteristic temperature difference
+    ddt = abs_chiller.calc_characteristic_temp(
+        t_hot=[85],  # in °C
+        t_cool=[26],  # in °C
+        t_chill=[15],  # in °C
+        coef_a=10,
+        coef_e=2.5,
+        method='kuehn_and_ziegler')
+
+    # Cooling capacity
+    Q_dots_evap = abs_chiller.calc_heat_flux(
+        ddts=ddt,
+        coef_s=0.42,
+        coef_r=0.9,
+        method='kuehn_and_ziegler')
+
+    # Driving heat
+    Q_dots_gen = abs_chiller.calc_heat_flux(
+        ddts=ddt,
+        coef_s=0.51,
+        coef_r=2,
+        method='kuehn_and_ziegler')
+
+    COPs = Q_dots_evap / Q_dots_gen
+
+Fig.2 illustrates how the cooling capacity and the COP of an absorption
+chiller (here the 10 kW absorption chiller mentioned above) depend on the
+cooling water temperature, i.e. the mean external fluid temperature at
+absorber and condenser.
+
+.. figure:: _pics/cooling_capacity_over_cooling_water_temperature_Kuehn.png
+    :width: 80 %
+    :alt: cooling_capacity_over_cooling_water_temperature_Kuehn.png
+    :align: center
+    :figclass: align-center
+
+    Fig.2: Dependency of the cooling capacity and the COP of a 10 kW absorption
+    chiller on the cooling water temperature.
+
+You find the code that is behind Fig.2 in our examples:
+https://github.com/oemof/oemof-thermal/tree/master/examples
+
+You can run the calculations for any other absorption heat pump or chiller by
+entering the specific parameters (a, e, s, r) belonging to that specific machine.
+The specific parameters are determined by a numerical fit of the
+four parameters with testing data or data from the fact sheet (technical
+specifications from the manufacturer) if temperatures for at least two
+points of operation are given.
+You find detailed information in the referenced papers.
+
+This package comes with characteristic parameters for five absorption chillers.
+Four published by Puig-Arnavat et al. [3]: 'Rotartica', 'Safarik', 'Broad_01' and 'Broad_02'
+and one published by Kühn and Ziegler [1]: 'Kuehn'.
+If you like to contribute parameters for other machines,
+please feel free to contact us or to contribute directly via github.
+
+To model one of the machines provided by this package you can adapt the code
+above in the following way.
+
+.. code-block:: python
+
+    import oemof.thermal.absorption_heatpumps_and_chillers as abs_chiller
+    import pandas as pd
+    import os
+
+    filename_charpara = os.path.join(os.path.dirname(__file__), 'data/characteristic_parameters.csv')
+    charpara = pd.read_csv(filename_charpara)
+
+    chiller_name = 'Kuehn'  # 'Rotartica', 'Safarik', 'Broad_01', 'Broad_02'
+
+     # Characteristic temperature difference
+    ddt = abs_chiller.calc_characteristic_temp(
+        t_hot=[85],  # in °C
+        t_cool=[26],  # in °C
+        t_chill=[15],  # in °C
+        coef_a=charpara[(charpara['name'] == chiller_name)]['a'].values[0],
+        coef_e=charpara[(charpara['name'] == chiller_name)]['e'].values[0],
+        method='kuehn_and_ziegler')
+
+    # Cooling capacity
+    Q_dots_evap = abs_chiller.calc_heat_flux(
+        ddts=ddt,
+        coef_s=charpara[(charpara['name'] == chiller_name)]['s_E'].values[0],
+        coef_r=charpara[(charpara['name'] == chiller_name)]['r_E'].values[0],
+        method='kuehn_and_ziegler')
+
+    # Driving heat
+    Q_dots_gen = abs_chiller.calc_heat_flux(
+        ddts=ddt,
+        coef_s=charpara[(charpara['name'] == chiller_name)]['s_G'].values[0],
+        coef_r=charpara[(charpara['name'] == chiller_name)]['r_G'].values[0],
+        method='kuehn_and_ziegler')
+
+    COPs = [Qevap / Qgen for Qgen, Qevap in zip(Q_dots_gen, Q_dots_evap)]
+
+You find information on the machines in [1], [2] and [3].
+Please be aware that [2] introduces a slightly different approach
+(using an improved characteristic equation with :math:`\Delta\Delta t''`
+instead of :math:`\Delta\Delta t'`).
+The characteristic parameters that we use are derived from [2] and therefore differ from those in [1].
+
+References
+__________
+
+
+.. include:: ../src/oemof/thermal/absorption_heatpumps_and_chillers.py
+  :start-after: Reference**
+  :end-before: """

docs/index.rst

@@ -19,6 +19,7 @@ Welcome to oemof.thermal's documentation!
    :maxdepth: 1
    :caption: User's guide
 
+   absorption_chillers
    cogeneration
    compression_heat_pumps_and_chillers
    concentrating_solar_power

examples/absorption_heatpumps_and_chiller/absorption_chiller.py

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+
+# import absorption_heatpumps_and_chillers as abs_hp_chiller
+import oemof.thermal.absorption_heatpumps_and_chillers as abs_hp_chiller
+import oemof.solph as solph
+import oemof.outputlib as outputlib
+import pandas as pd
+import os
+import matplotlib.pyplot as plt
+
+solver = 'cbc'
+debug = False
+number_of_time_steps = 48
+solver_verbose = False
+
+date_time_index = pd.date_range('1/1/2012', periods=number_of_time_steps,
+                                freq='H')
+energysystem = solph.EnergySystem(timeindex=date_time_index)
+
+# Read data file
+filename_data = os.path.join(os.path.dirname(__file__), 'data/AC_example.csv')
+data = pd.read_csv(filename_data)
+
+filename_charpara = os.path.join(os.path.dirname(__file__),
+                                 'data/characteristic_parameters.csv')
+charpara = pd.read_csv(filename_charpara)
+chiller_name = 'Kuehn'
+
+# Buses with three different temperature levels
+b_th_high = solph.Bus(label="hot")
+# b_th_medium = solph.Bus(label="cool")
+b_th_low = solph.Bus(label="chilled")
+energysystem.add(b_th_high, b_th_low)
+
+energysystem.add(solph.Source(
+    label='driving_heat',
+    outputs={b_th_high: solph.Flow(variable_costs=0)}))
+energysystem.add(solph.Source(
+    label='cooling_shortage',
+    outputs={b_th_low: solph.Flow(variable_costs=20)}))
+# energysystem.add(solph.Sink(
+#     label='dry_cooling_tower',
+#     inputs={b_th_medium: solph.Flow(variable_costs=0)}))
+energysystem.add(solph.Sink(
+    label='cooling_demand',
+    inputs={b_th_low: solph.Flow(actual_value=1,
+                                 fixed=True,
+                                 nominal_value=35)}))
+
+# Mean cooling water temperature in degC (dry cooling tower)
+temp_difference = 4
+t_cooling = [t + temp_difference for t in data['air_temperature']]
+n = len(t_cooling)
+
+# Pre-Calculations
+ddt = abs_hp_chiller.calc_characteristic_temp(
+    t_hot=[85],
+    t_cool=t_cooling,
+    t_chill=[15] * n,
+    coef_a=charpara[(charpara['name'] == chiller_name)]['a'].values[0],
+    coef_e=charpara[(charpara['name'] == chiller_name)]['e'].values[0],
+    method='kuehn_and_ziegler')
+Q_dots_evap = abs_hp_chiller.calc_heat_flux(
+    ddts=ddt,
+    coef_s=charpara[(charpara['name'] == chiller_name)]['s_E'].values[0],
+    coef_r=charpara[(charpara['name'] == chiller_name)]['r_E'].values[0],
+    method='kuehn_and_ziegler')
+Q_dots_gen = abs_hp_chiller.calc_heat_flux(
+    ddts=ddt,
+    coef_s=charpara[(charpara['name'] == chiller_name)]['s_G'].values[0],
+    coef_r=charpara[(charpara['name'] == chiller_name)]['r_G'].values[0],
+    method='kuehn_and_ziegler')
+COPs = [Qevap / Qgen for Qgen, Qevap in zip(Q_dots_gen, Q_dots_evap)]
+nominal_Q_dots_evap = 10
+actual_value = [Q_e / nominal_Q_dots_evap for Q_e in Q_dots_evap]
+actual_value_df = pd.DataFrame(actual_value).clip(0)
+
+# Absorption Chiller
+energysystem.add(solph.Transformer(
+    label="AC",
+    inputs={b_th_high: solph.Flow()},
+    outputs={b_th_low: solph.Flow(nominal_value=nominal_Q_dots_evap,
+                                  max=actual_value_df.values,
+                                  variable_costs=5)},
+    conversion_factors={b_th_low: COPs}))
+
+model = solph.Model(energysystem)
+
+model.solve(solver=solver, solve_kwargs={'tee': solver_verbose})
+
+energysystem.results['main'] = outputlib.processing.results(model)
+energysystem.results['meta'] = outputlib.processing.meta_results(model)
+
+energysystem.dump(dpath=None, filename=None)
+
+
+# ****************************************************************************
+# ********** PART 2 - Processing the results *********************************
+# ****************************************************************************
+
+energysystem = solph.EnergySystem()
+energysystem.restore(dpath=None, filename=None)
+
+results = energysystem.results['main']
+
+high_temp_bus = outputlib.views.node(results, 'hot')
+low_temp_bus = outputlib.views.node(results, 'chilled')
+
+string_results = outputlib.views.convert_keys_to_strings(
+    energysystem.results['main'])
+AC_output = string_results[
+    'AC', 'chilled']['sequences'].values
+demand_cooling = string_results[
+    'chilled', 'cooling_demand']['sequences'].values
+ASHP_input = string_results[
+    'hot', 'AC']['sequences'].values
+
+
+fig2, axs = plt.subplots(3, 1, figsize=(8, 5), sharex=True)
+axs[0].plot(AC_output, label='cooling output')
+axs[0].plot(demand_cooling, linestyle='--', label='cooling demand')
+axs[1].plot(COPs, linestyle='-.')
+axs[2].plot(data['air_temperature'])
+axs[0].set_title('Cooling capacity and demand')
+axs[1].set_title('Coefficient of Performance')
+axs[2].set_title('Air Temperature')
+axs[0].legend()
+
+axs[0].grid()
+axs[1].grid()
+axs[2].grid()
+axs[0].set_ylabel('Cooling capacity in kW')
+axs[1].set_ylabel('COP')
+axs[2].set_ylabel('Temperature in $°$C')
+axs[2].set_xlabel('Time in h')
+plt.tight_layout()
+plt.show()
+
+print('********* Main results *********')
+print(high_temp_bus['sequences'].sum(axis=0))
+print(low_temp_bus['sequences'].sum(axis=0))