From 5a994f16b8a8f6b7484cd2453d2fd8f1e720d8e4 Mon Sep 17 00:00:00 2001 From: Ossama Elshimy Date: Wed, 13 Nov 2024 14:26:23 +0100 Subject: [PATCH 1/8] added first version of sphinx docs --- docs/Makefile | 20 +++++++++ docs/make.bat | 35 ++++++++++++++++ docs/modules.rst | 8 ++++ docs/setup.rst | 7 ++++ docs/source/Figure_1.png | Bin 0 -> 130514 bytes docs/source/Figure_2.png | Bin 0 -> 60994 bytes docs/source/conf.py | 31 ++++++++++++++ docs/source/index.rst | 21 ++++++++++ docs/source/install.rst | 28 +++++++++++++ docs/source/overview.rst | 57 ++++++++++++++++++++++++++ docs/source/solver.rst | 19 +++++++++ docs/source/topotherm.rst | 84 ++++++++++++++++++++++++++++++++++++++ docs/source/usage.rst | 42 +++++++++++++++++++ 13 files changed, 352 insertions(+) create mode 100644 docs/Makefile create mode 100644 docs/make.bat create mode 100644 docs/modules.rst create mode 100644 docs/setup.rst create mode 100644 docs/source/Figure_1.png create mode 100644 docs/source/Figure_2.png create mode 100644 docs/source/conf.py create mode 100644 docs/source/index.rst create mode 100644 docs/source/install.rst create mode 100644 docs/source/overview.rst create mode 100644 docs/source/solver.rst create mode 100644 docs/source/topotherm.rst create mode 100644 docs/source/usage.rst diff --git a/docs/Makefile b/docs/Makefile new file mode 100644 index 0000000..d0c3cbf --- /dev/null +++ b/docs/Makefile @@ -0,0 +1,20 @@ +# Minimal makefile for Sphinx documentation +# + +# You can set these variables from the command line, and also +# from the environment for the first two. +SPHINXOPTS ?= +SPHINXBUILD ?= sphinx-build +SOURCEDIR = source +BUILDDIR = build + +# Put it first so that "make" without argument is like "make help". +help: + @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) + +.PHONY: help Makefile + +# Catch-all target: route all unknown targets to Sphinx using the new +# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). +%: Makefile + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) diff --git a/docs/make.bat b/docs/make.bat new file mode 100644 index 0000000..dc1312a --- /dev/null +++ b/docs/make.bat @@ -0,0 +1,35 @@ +@ECHO OFF + +pushd %~dp0 + +REM Command file for Sphinx documentation + +if "%SPHINXBUILD%" == "" ( + set SPHINXBUILD=sphinx-build +) +set SOURCEDIR=source +set BUILDDIR=build + +%SPHINXBUILD% >NUL 2>NUL +if errorlevel 9009 ( + echo. + echo.The 'sphinx-build' command was not found. Make sure you have Sphinx + echo.installed, then set the SPHINXBUILD environment variable to point + echo.to the full path of the 'sphinx-build' executable. Alternatively you + echo.may add the Sphinx directory to PATH. + echo. + echo.If you don't have Sphinx installed, grab it from + echo.https://www.sphinx-doc.org/ + exit /b 1 +) + +if "%1" == "" goto help + +%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% +goto end + +:help +%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O% + +:end +popd diff --git a/docs/modules.rst b/docs/modules.rst new file mode 100644 index 0000000..24e2d03 --- /dev/null +++ b/docs/modules.rst @@ -0,0 +1,8 @@ +topotherm-0.2.0 +=============== + +.. toctree:: + :maxdepth: 4 + + setup + topotherm diff --git a/docs/setup.rst b/docs/setup.rst new file mode 100644 index 0000000..552eb49 --- /dev/null +++ b/docs/setup.rst @@ -0,0 +1,7 @@ +setup module +============ + +.. automodule:: setup + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/Figure_1.png b/docs/source/Figure_1.png new file mode 100644 index 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https://www.sphinx-doc.org/en/master/usage/configuration.html#project-information + + +import sys + +project = 'Topotherm' +copyright = '2024, Amedeo' +author = 'Amedeo' +release = '0.2.0' + +# -- General configuration --------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#general-configuration + +extensions = ['sphinx.ext.autodoc'] + +templates_path = ['_templates'] +exclude_patterns = [] + + + +# -- Options for HTML output ------------------------------------------------- +# https://www.sphinx-doc.org/en/master/usage/configuration.html#options-for-html-output + +html_theme = 'sphinx_rtd_theme' +html_static_path = ['_static'] diff --git a/docs/source/index.rst b/docs/source/index.rst new file mode 100644 index 0000000..3b6f62b --- /dev/null +++ b/docs/source/index.rst @@ -0,0 +1,21 @@ +.. Topotherm documentation master file, created by + sphinx-quickstart on Wed Oct 9 10:16:32 2024. + You can adapt this file completely to your liking, but it should at least + contain the root `toctree` directive. + +Topotherm documentation +======================= + +**Topotherm** is a pyomo-based mixed-integer linear programming district heating +network design model which scales well into larger districts for single +and mulitple time steps. + +.. toctree:: + overview + install + solver + usage + topotherm + :maxdepth: 2 + :caption: Contents: + diff --git a/docs/source/install.rst b/docs/source/install.rst new file mode 100644 index 0000000..884d711 --- /dev/null +++ b/docs/source/install.rst @@ -0,0 +1,28 @@ +Install +========= + +Use git to clone this repository into your computer. Then, install topotherm +with a package manager such as Anaconda, or directly with Python. :: + + git + git clone https://github.com/jylambert/topotherm.git + +Python +--------- + +This can also be done with venv or equivalent. :: + + Python + cd topotherm + python setup.py install + +Anaconda or mamba +--------------------- + +We recommend to install the dependencies with anaconda or mamba: :: + + conda + cd topotherm + conda create -n topotherm python + conda activate topotherm + pip install -e . diff --git a/docs/source/overview.rst b/docs/source/overview.rst new file mode 100644 index 0000000..cc52f1a --- /dev/null +++ b/docs/source/overview.rst @@ -0,0 +1,57 @@ +Overview +=========== + +Intro +------ + +Topotherm is a pyomo-based mixed-integer linear programming district heating +network design model which scales well into larger districts for single +and mulitple time steps. +It has been benchmarked against multiple other open-source models in a +publication available at: + +> Lambert, Jerry and Ceruti, Amedeo and Spliethoff, Hartmut, Benchmark of Mixed-Integer Linear Programming Formulations for District Heating Network Design. Energy, Volume 308, 2024, 132885, ISSN 0360-5442, https://doi.org/10.1016/j.energy.2024.132885 + +Features +---------- + +* Single time-step topology and piping optimization. +* Multiple time-steps version additionally includes operation with variable heating demands. +* Greenfield optimization +* Existing network in development. +* Forced and economic expansion of the district heating network to consumers. +* Supports all solvers of pyomo, but the output helper functions in utils.py + * might have to be rewritten (utils.py) +* Plotting functions included + +Description +------------ + +To run the model, several incidence matrices have to be formulated. Then, the linear regression +parameters can be calculated for a given supply, ambient and return temperature of the network. +A pyomo model is then set up and solved with the solver of your choice. + +Why should I use this? +----------------------- + +Topotherm has the best scaling properties of multiple open-source models and +has been benchmarked and validated. + +How to cite +------------- + +> Lambert, Jerry and Ceruti, Amedeo and Spliethoff, Hartmut, Benchmark of Mixed-Integer Linear Programming Formulations for District Heating Network Design. Energy, Volume 308, 2024, 132885, ISSN 0360-5442, https://doi.org/10.1016/j.energy.2024.132885 + +Getting Started +---------------- + +This repository needs a PC capable to run python and its standard libraries. + +Requirements +--------------- + +* Anaconda, mamba or venv + + + + diff --git a/docs/source/solver.rst b/docs/source/solver.rst new file mode 100644 index 0000000..948366a --- /dev/null +++ b/docs/source/solver.rst @@ -0,0 +1,19 @@ +Solver +======== + +Gurobi +--------- + +The results in the paper were obtained with the commercial solver gurobi. +A free academic license is available and can be installed by following +the documentation [here](https://support.gurobi.com/hc/en-us/articles/360044290292-How-do-I-install-Gurobi-for-Python-). + +Open-source Alternatives +-------------------------- + +You can try the code on smaller benchmarks with several open source solvers, +such as SCIP. Other popular open-source options are COIN-OR's cbc or HiGHS. :: + + conda + conda activate topotherm + conda install -c conda-forge pyscipopt diff --git a/docs/source/topotherm.rst b/docs/source/topotherm.rst new file mode 100644 index 0000000..ebc18f6 --- /dev/null +++ b/docs/source/topotherm.rst @@ -0,0 +1,84 @@ + +**Submodules** +============== + +topotherm.fileio module +----------------------- + +.. automodule:: topotherm.fileio + :members: + :undoc-members: + :show-inheritance: + +topotherm.model\_old module +--------------------------- + +.. automodule:: topotherm.model_old + :members: + :undoc-members: + :show-inheritance: + +topotherm.multiple\_timestep module +----------------------------------- + +.. automodule:: topotherm.multiple_timestep + :members: + :undoc-members: + :show-inheritance: + +topotherm.plotting module +------------------------- + +.. automodule:: topotherm.plotting + :members: + :undoc-members: + :show-inheritance: + +topotherm.postprocessing module +------------------------------- + +.. automodule:: topotherm.postprocessing + :members: + :undoc-members: + :show-inheritance: + +topotherm.precalculation\_hydraulic module +------------------------------------------ + +.. automodule:: topotherm.precalculation_hydraulic + :members: + :undoc-members: + :show-inheritance: + +topotherm.sets module +--------------------- + +.. automodule:: topotherm.sets + :members: + :undoc-members: + :show-inheritance: + +topotherm.settings module +------------------------- + +.. automodule:: topotherm.settings + :members: + :undoc-members: + :show-inheritance: + +topotherm.single\_timestep module +--------------------------------- + +.. automodule:: topotherm.single_timestep + :members: + :undoc-members: + :show-inheritance: + +topotherm.utils module +---------------------- + +.. automodule:: topotherm.utils + :members: + :undoc-members: + :show-inheritance: + diff --git a/docs/source/usage.rst b/docs/source/usage.rst new file mode 100644 index 0000000..b4b7995 --- /dev/null +++ b/docs/source/usage.rst @@ -0,0 +1,42 @@ +Usage +======== + +Generate the input incidence matrices for the district with .parquet format (see example). +Then, modify and run the either one of the three scripts in that folder. :: + + bash + cd example + python run_sts.py + + +Contribute +------------ + +Pull requests and any feedback regarding the code are very welcome. For major +changes, please open an issue first to discuss what you would like to change. + +Tests +------ + +To run the tests, use pytest. :: + + Python + pytest tests + + +Example of results +---------------------- +.. figure:: Figure_1.png + + Before Optimization + +.. figure:: Figure_2.png + + After Optimization + +License +---------- + +[MIT](https://en.wikipedia.org/wiki/MIT_License), see LICENSE file. + + From 7725fdd7831f9dfd8209df56fd855ef700c624d6 Mon Sep 17 00:00:00 2001 From: Ossama Elshimy Date: Fri, 22 Nov 2024 14:41:16 +0100 Subject: [PATCH 2/8] updated docs with documantion guide --- docs/source/documentation.rst | 27 +++++++++++++++++++++++++++ docs/source/index.rst | 1 + 2 files changed, 28 insertions(+) create mode 100644 docs/source/documentation.rst diff --git a/docs/source/documentation.rst b/docs/source/documentation.rst new file mode 100644 index 0000000..091557b --- /dev/null +++ b/docs/source/documentation.rst @@ -0,0 +1,27 @@ +Documentation +========= + +Activate the topotherm environment: :: + + conda activate topotherm + +Then, install the optional requirments if needed :: + + pip install sphinx sphinx-rtd-theme or pip install .[docs] + +In the topotherm root directory run: :: + + sphinx-apidoc -o docs/source/ . + +Then make the hmtl documentation files: :: + + make html + +The documentation is located under docs/build/html + +Adding New Pages +----------------- + +Create a new rts file under docs/source + +Add the name of the created page in index.rst \ No newline at end of file diff --git a/docs/source/index.rst b/docs/source/index.rst index 3b6f62b..fd62b7c 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -15,6 +15,7 @@ and mulitple time steps. install solver usage + documentation topotherm :maxdepth: 2 :caption: Contents: From ea0427815ffde564b3e1e7ff32e8d408901db09e Mon Sep 17 00:00:00 2001 From: Amedeo Ceruti Date: Wed, 27 Nov 2024 14:26:02 +0100 Subject: [PATCH 3/8] add description and bump topotherm version --- README.md | 21 +++++++++++++++++++++ docs/source/documentation.rst | 2 +- pyproject.toml | 2 +- 3 files changed, 23 insertions(+), 2 deletions(-) diff --git a/README.md b/README.md index 748cad9..4fc86bd 100644 --- a/README.md +++ b/README.md @@ -45,6 +45,7 @@ might have to be rewritten (utils.py) - [Usage](#usage) - [Contribute](#contribute) - [Tests](#tests) + - [Docs](#docs) - [License](#license) ## Description @@ -140,6 +141,26 @@ pip install .[dev] pytest tests ``` +## Docs + +Activate the topotherm environment: + +```conda activate topotherm``` + +Then, install the optional requirements: + +```pip install .[docs]``` + +In the topotherm root directory run: + +```sphinx-apidoc -o docs/source/ .``` + +Then make the hmtl documentation files: :: + +```make html``` + +The documentation is located under docs/build/html. + ## License [MIT](https://en.wikipedia.org/wiki/MIT_License), see LICENSE file. diff --git a/docs/source/documentation.rst b/docs/source/documentation.rst index 091557b..e71a511 100644 --- a/docs/source/documentation.rst +++ b/docs/source/documentation.rst @@ -5,7 +5,7 @@ Activate the topotherm environment: :: conda activate topotherm -Then, install the optional requirments if needed :: +Then, install the optional requirements if needed :: pip install sphinx sphinx-rtd-theme or pip install .[docs] diff --git a/pyproject.toml b/pyproject.toml index b960bb6..0f3cf75 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -5,7 +5,7 @@ build-backend = "setuptools.build_meta" [project] name = "topotherm" -version = "0.2.0" +version = "0.3.0" description = "A package to design district heating networks" readme = "README.md" From 84956f1d72c9889f07c1a4a45973e2c6cb7eaa3d Mon Sep 17 00:00:00 2001 From: Amedeo Ceruti Date: Wed, 27 Nov 2024 14:27:53 +0100 Subject: [PATCH 4/8] fix docs dependencies --- pyproject.toml | 2 -- 1 file changed, 2 deletions(-) diff --git a/pyproject.toml b/pyproject.toml index 0f3cf75..a4838ce 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -53,6 +53,4 @@ dev = [ docs = [ "sphinx", "sphinx-rtd-theme", - "sphinx-autodoc", - "sphinx-viewcode" ] \ No newline at end of file From 0b1b76083e85432968fdf6f0dd8703b49f8dba03 Mon Sep 17 00:00:00 2001 From: Ossama Elshimy Date: Wed, 27 Nov 2024 14:29:33 +0100 Subject: [PATCH 5/8] updated docs --- docs/source/annuitysts.png | Bin 0 -> 8142 bytes docs/source/bigmsts.png | Bin 0 -> 6606 bytes docs/source/connectedconsumersts.png | Bin 0 -> 3790 bytes docs/source/consumersmts.png | Bin 0 -> 10620 bytes docs/source/darcy.png | Bin 0 -> 6271 bytes docs/source/decisionmts.png | Bin 0 -> 7120 bytes docs/source/deltat.png | Bin 0 -> 8408 bytes docs/source/documentation.rst | 2 +- docs/source/edges.png | Bin 0 -> 2633 bytes docs/source/energyconmts.png | Bin 0 -> 13938 bytes docs/source/energyconsts.png | Bin 0 -> 10015 bytes docs/source/graph.png | Bin 0 -> 42971 bytes docs/source/haaland.png | Bin 0 -> 14315 bytes docs/source/heatbalanceeasy.png | Bin 0 -> 9948 bytes 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b/docs/source/methodology.rst @@ -0,0 +1,188 @@ +Methodology +============= + + + +Linearization of heat losses and pipe investment costs +-------------------------------------------------------- + The maximal mass flow 𝑚̇ with the corresponding velocities 𝑣 of each considered piping diameter 𝑑 must be determined to linearize the maximal thermal power flow in a district heating pipe with length l. Subsequently, the heat losses of the district heating network pipes can be determined for each diameter. The relationship between the investment costs and heat losses of a pipe with regard to the maximal thermal power flow is modeled with a linear regression. + +Initial Assumptions +^^^^^^^^^^^^^^^^^^^^ + + * The considered heat carrier medium is liquid water and, therefore, incompressible + * Temperature changes are assumed to be smaller than 𝛥𝑇=40◦C, therefore,temperature dependencies of the fluid properties (e.g.,density 𝜌,heat capacity cp and dynamic viscosity 𝜇) are neglected because the variations in the property values are small for the considered parameter range. + * The fluid properties of water are constant and determined at 70◦C. The feed line temperature is assumed to be at constant 90◦C, while the return temperature is assumed to be at constant 55◦C, and with an outdoor temperature of −20◦C + * The district heating pipes are buried at a depth of 1m and the pipe roughness is assumed to be 0.05mm + * The thermal conductivity of the ground is equal to 2.4W/(m⋅K) and the conductivity of the thermal insulation, formed by polyurethane, to 0.024W/(m⋅K) + +Calculations +^^^^^^^^^^^^^ + +.. figure:: darcy.png + + Calculating the pressure loss between the nodes i and j + +.. figure:: reynolds.png + + Calculating the Reynolds Number + +.. figure:: haaland.png + + Calculate the friction factor for a turbulent flow (Re > 2300) with pipe roughness 𝜀 + +.. figure:: vmax.png + + An iterative calculation (using SciPy) is performed to determine the maximum velocity in a pipe with a given inner diameter. The specific pressure drop per meter pipe length should range from 70Pa/m to 350Pa/m and the initial velocity is 0.5 m/s. After calculating the maximum speed the maximum flow rate can be calculated using (𝑚̇ = 𝜌 ⋅ 𝑣 ⋅ 𝑑² ⋅ 𝜋∕4) +.. figure:: deltat.png + + To model the thermal behavior of an insulated pipe buried underground the temperature difference 𝛩 between the water temperature in the pipe and the outside temperature is introduced +.. figure:: rij.png + + The combined thermal resistance 𝑅𝑖𝑗 of the pipe and soil per unit length is calculated with the ratio 𝑟 between outer and inner diameter. the buried depth of a pipe ℎ, as well as the thermal conductivities of the ground (𝑘ᵍ) and of the pipe’s insulation (𝑘ⁱⁿˢᶸˡ) are used to calculate the combined thermal resistance. + +Linear regression +^^^^^^^^^^^^^^^^^^ + +The previous equations form a full nonlinear thermohydraulic model of a district heating pipe. To represent the considered diameter range in a MILP, the nonlinear dependencies have to be represented as continuous and linear within the optimization problem. The linearization in this study is performed with a simple linear regression 𝑦 = a ⋅ 𝑥 + b, where 𝑦 is the dependent variable, 𝑥 is the independent variable, and the factors a and b are the regression coefficients. This approach is adopted to formulate an optimization problem that can be solved within a feasible computing time, consistent with the methodologies of previous works. + +For pipes ranging from DN 20 to DN 400, the thermal losses are calculated through the temperature difference between the water and the pipe calculated earlier using the maximal mass flow rate, while the total investment costs for piping are adapted from `Nussbaumer & Thalmann (2016) `_ + +.. figure:: regression.png + + + + +Mixed-integer formulations for district heating network design +--------------------------------------------------------------- + +Graphical representation +^^^^^^^^^^^^^^^^^^^^^^^^^ + +A graph representation of a district heating network has to be introduced to mathematically represent pipes, junctions, producers, and consumers. The district heating systems’ pipes correspond to the graph’s edges and the network’s junctions to the nodes. The district heating network consists of a feed and return network with edges of opposite directions. This superstructure contains all possible connections and pathways from the heat source to the consumers. + +.. figure:: nodes.png + + Thi set of all nodes is subdivided into three different subsets: int denotes all nodes without a consumer or a producer, the subscript p describes all nodes connected to at least one producer, and the subscript c all nodes connected to at least one consumer. + +.. figure:: edges.png + + This set 𝐴 representing all edges of the network is subdivided into three different subsets: int represents the geometrical pipe connection between two different internal nodes. p and c denote the state transition between the district heating system and a producer or a consumer, respectively. + + +A certain network node will be referred to as 𝑛, whereas a directed edge going from node 𝑖 to node 𝑗 as 𝑖𝑗 ∈ A. + +.. figure:: graph.png + +Single Time Step Formulation +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +The bidirectionality of the network (two edges per pipe) is explicitly considered and modeled in the single time step formulation of topotherm. In order to allow flows in the opposite direction, every potential pipe 𝑖𝑗 is also modeled in the direction 𝑗𝑖. + +The constraints of the sts solution are as follows: + +.. figure:: heatbalancests.png + + The heat balance of the pipe, which contains the heat outflow of each pipe Qout, the heat inflow Qin and the thermal losses over the length l𝑖𝑗.The thermal losses are determined by the linear regression coefficients aₜₕₑᵣₘ and bₜₕₑᵣₘ while the binary variable 𝜆𝑖𝑗 represents the flow direction of the considered pipe. + +.. figure:: bigmsts.png + + A big-M constraint is formulated to enforce zero thermal power flow if the direction 𝑖𝑗 is not used. ̇ 𝑄max is modeled as a sufficiently large constant power flow. + +.. figure:: energyconsts.png + + Each consumer connection to the district heating grid is modeled as unidirectional, and thus no heat feed-in from a consumer is possible. Moreover,energy conservation is assumed in every node under consideration of the consumer’s heat demand and the heat source’s feed-in + +.. figure:: unidirecionalsts.png + + To ensure a unidirectional use of a pipe and to reduce the solution space during the Branch-and-Bound, this constraint prevents the simultaneous use of the direction 𝑖𝑗 and 𝑗𝑖. + +.. figure:: connectedconsumersts.png + + In this study, all consumers must be connected to the district heating system grid therefore, the direction 𝜆𝑖𝑗 of pipe 𝑖𝑗 to a consumer node 𝑗 is set to 1, forcing the edge to be used and heating to be supplied. + +.. figure:: thermalcapacitysts.png + + The thermal power output ̇ 𝑄𝑝 is constrained by the installed thermal capacity of the source ̇ 𝑄inst𝑝 + +.. figure:: annuitysts.png + + The annuity method distributes investment costs of pipes or heat sources over the defined life span 𝑛years with an interest rate w. + +.. figure:: supconstraint.png + + Additional constraints with redundant information can help to tighten further the Branch-and-Bound during the optimization. To that end, a supplementary constraint is formulated to ensure the total system energy conservation. + +Finally, the objective function minimizes the district heating network’s total investment and operational costs. + +.. figure:: objectivefunctionsts.png + + The investment costs are determined by the linear regression factors aᶜᴼˢᵗ and bᶜᴼˢᵗ. By introducing full load hours flh, the investment and operational costs are weighted. + + +Multiple Time Step Formulation +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +In order to optimize district heating systems with multiple time steps and changing flow directions with topotherm_mts, the previous formulation needs to be expanded. Not only the bidirectional operation of the pipe has to be modeled, but also a binary variable has to be incorporated to model the decision if a pipe is built independent of the flow direction. As with the sts formulation, only equations in direction 𝑖𝑗 are provided in exemplary fashion below. Moreover, 𝑡 refers to the set of all considered hourly timesteps defined in the set T. + +The constraints of the mts solution are as follows: + +.. figure:: heatbalancemts.png + + The heating power balance of each pipe is enforced. 𝑄out𝑖𝑗,𝑡 is the mean power outflow of each pipe, ̇ 𝑄in𝑖𝑗,𝑡 the inflow and ̇ 𝑄loss𝑖𝑗,𝑡 the thermal losses during time step 𝑡.These equations can be adapted for different time steps durations by changing from a power flow to an energy flow with 𝑄𝑡= ̇ 𝑄𝑡 ⋅𝛥𝑇𝑡. + +The thermal losses for pipe 𝑖𝑗 need to be modeled as an independent variable and cannot be incorporated into the equation directly. This is due to the thermal losses along a pipe being nearly independent of the inflowing mass flow rate and depending mostly on the installed diameter + +.. figure:: thermallossesmts.png + + l𝑖𝑗 is the pipe length, atherm and btherm are linear regression coefficients calculated previously, and 𝜆𝑖𝑗,𝑡 is the binary decision to operate direction 𝑖𝑗 in time step t. + +If the direction 𝑖𝑗 is not used,the first equation ensures that the heat losses equal 0. The second equation enforces the heat loss calculation with the maximal built thermal capacity ̇ 𝑄max according to the flow direction in the pipe. + +.. figure:: thermalflowmts.png + + This constraint enforces zero thermal flow if the direction 𝑖𝑗 of a pipe is not used. + +.. figure:: qcapmts.png + + Additionally, the maximal thermal power inflow ̇ 𝑄in𝑖𝑗,𝑡 at each time step 𝑡∈T is limited to the maximal thermal capacity of a pipe and maximal thermal capacity to the binary decision 𝜆built𝑖𝑗 if a pipe is built or not. + +.. figure:: decisionmts.png + + The decision to build a pipe has to be linked with the possibility to use a certain direction of the pipe. + +.. figure:: unidirectionalmts.png + + The simultaneous use of the direction 𝑖𝑗 and 𝑗𝑖 is prevented using this constraint. + +.. figure:: consumersmts.png + + In this study, all consumers must be connected to the district heating system grid.Therefore at a node 𝑗 with a consumer,the binary direction 𝑖𝑗 pipe and the binary building decision of that pipe is set to 1 + +.. figure:: energyconmts.png + + Additional constraint for energy conservation + +.. figure:: qoptimalmts.png + + The thermal power of the source ̇ 𝑄𝑝,𝑡 is limited by the optimal installed thermal power ̇ 𝑄inst𝑝. + + +.. figure::objectivemts.png + + The objective function of the sts case is adapted to depict multiple time steps and flow directions. The full load hours are scaled according to the simulated time period and adjust the considered heat demand to the yearly heat demand. + +The forced expansion assumed can be easily modified for a planned expansion by eliminating the constraints connecting all consumers and modifying the objective function to economic indicators, such as revenue maximization. + +Simplified Multiple Time Step Formulation +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +As previously mentioned, the thermal losses in a pipe do not depend on the thermal power flow into the pipe but rather on the installed capacity of the pipe.As the consideration of the installed capacity of the pipe earlier is computationally expensive, an alternative formulation named topothermmts_easy is formulated, where the thermal losses do not depend on the maximal thermal pipe capacity but rather on the thermal power inflow at each time step. + +.. figure:: heatbalanceeasy.png + + Modified heat balance constraint + +.. figure:: objectiveeasy.png + + Modified objective function \ No newline at end of file diff --git a/docs/source/nodes.png b/docs/source/nodes.png new file mode 100644 index 0000000000000000000000000000000000000000..d791a97d8dc1e3601ed49728b4823172bf89e5aa GIT binary patch literal 3038 zcmXw5cRU=*6F==l3#Ys2hlmzLFUOtJB6mmrAFsZpam2@x$wqK0TEPA5Xt zQ=&(A+Uecz^4|OXu{%5a*`1l4`OeP77#V2OQG=-g005n?4#ETgATcJcrLF;qGwR@N z36YR^nrOoTWj{IBhz$8Nm_7^us7$0ex1k{NRPH*Ko&W%=;GaRFYa*}%0MK~qB4GD@ ztv28J=`dS!Hd{Z%_VkFQ7~Cb>G^q+-r%${d&U;tCK_D+>gi-lYI5tOE7}UUEESZPTb7Q1}K}Yc8Ls7IZ!r8XBs_28rnHy;sR% zBl@3&k_ts!OrFDbX$0YYAN1R9iq^`c6@a2m%pI|C{DIZ#Z!smGhW;!E|wrBgV z&bHMWB~2B5wm97;Ys9aP3HeDf&$nk(FAq17$^5;cJ=%dfU89=#Q@MJj;FX_ThkGlA zH9p%`e94ASp9*Cvc<}G-?lQjC3JVLf=+9QwjFqJP&#qGZq#fkt(bnU0eM3Xa+pG)E zj}P!{!}W^_B_T%i{~hYXBYjN148CLb@$u<8B)|6TXBJ3N-1A`FZ03`h=;hY5G9RB9 zU0UL4QbOq~)zwJ>!|J-ajKGs!%>s5kJw2w%^icWMV&i;^L~d1ddyt~nD#IRuU}IWj zz`}Ua=(h(viZC)W6D&w?N$!dAx(7JSaZ8C4uGVLNzPqT~XtU)0yPZmt9?g1kdLSx# z>y}M}d{$C-QBxE5Q3L=-r}tZDNkd5p;6G5St0kkR_I_;&mF##PCjx z?nL&zxf4~7!Mx(^G%+zjY#54&icZAekS_-3|1oAkM=4!tON=Gwmy5%O=Iobv;X0hU zySpTQyb_YB>?2VaO2Z~mkty#Mn<^!F!0gP!$jC2%1{<9eCqmXN*6XV715nTYxw*m= z9~09ePuAN(sS+gdN?t^4B}?R=!fLM#>0&X zCbcPfyXD?D?y{$V*?h1G68S^fd%fM84I)tJalB&#MRn2!tqlqC4FVk;9DKhuP(IRG z%=dS~AAIm{ju=sKHiJ6Cm0q}R=+1tLTiu+jC7{c#u@VCDt1}E!9UYp%u))DW{-Wfn zXZ_C~Ja}M51ct!w$@$5hEt;+a0s&;=!mBz5(TZbWJSirGOy&iQM0#yZji)sI^);py z@PPe*o~|*H7AzCpm#vB{U{`*z!Hx+y`JyAc#RdlVsHmu*5l~lG*VEf{IrG1U)EBCT zLdS_#bj`ZWHqDpcVh;)&%+;U--JwUOCjLrFcy|LcR4Z9{W!Ig=ry?O?P!M-ZL}bW6 zjv*j0(9hdjcG=J0e~(M~#gj)=+q2k}u0)=dhA6m>7?})xbA9V;lDpk~eH|AzP--0kM~}n`dIr9LaIsBGVOq=va`E za6z#XVG5~v-IWZ{-ajj|##-rQQql&gs{>rO*VY_Nm?B1dC_|#2p6o7J1csqnUWxMa zw-yiblg5DeewDJOP*%-kZna?U_k#k$wcQ7VNr;4s4cpp;xD&)xIxO_EKcmX?-Ay}ufUW_ zZDdFInQxe;*dk{4wRww3t^2kcBcTt)c|L|;hYue(&UKK_@GgcXfWcry zf`dX;0*~s;0&H2~0$+Wb3|$S<0~-TWAokQrO0c&y?%^8~RoWYWfr*MVAg8s23|(E_(*Vy;2R}b8I1Crg zd%)pv^rHOQ+S+&)Dav*eR5~+!R~TCJP{c%3sEi&kmyS_=aL2mBn5_3W97Xw!qH6Y#QUg*-&5_{Bv`4e&0 z7;9`0$F#+5>!y)fagxBZLl&vd(Nbj84{$U2SMkyb`1y_Rrlc2Y0mn%ZQBe!03NRSV zd2hKdLp!5$XTEJ>9rs!4x|M2)Y_-F%Pt z^~v^2+{P>B%l%B~XPZOGuDXY(oilD$`VwsO&l9+mf0F~z4(x|NHFkD)hk`$nYb1Kn zpQ~Ymg%&;bSB+=Nt<@lpYaNDx+xWsg7sgTT!(HA4pqL_n+x2K`+QZV!!XQMFE~CqX zm;%I?x#u)cWv|Y)gj<$deKRt!NTBC|R)mF-W}sQ7 z925EuOe5=B7;kS#oN#VNWF!!DC*jYgR;p2ZEQ_dxt!5gV3hh>nMtx)|diP+(CB!L94g-Mc0=Mnqer|Md%yw~7T baToOdF*&&T#-lT0PY%%4G(eQWpM?DnVlL7c literal 0 HcmV?d00001 diff --git a/docs/source/obectivemts.png b/docs/source/obectivemts.png new file mode 100644 index 0000000000000000000000000000000000000000..484654d5ebc78c941424bac2ae2355865705d507 GIT binary patch literal 27408 zcmcG$Ralj4)HX_obSNz;AgGigT_UA`bazU(bV~@*C5@nTiKMiopn%dKjdV)qKjvEN z`>uaq`(&T&0|S`6^L?M^8F9y$;V%@V@orGwKte*ola-NFMnXbWfd4OHVZh(z11<^h z53;kev;MnbxE2k{44R+(uR3CZe%tfaWA zyZ%-NW&&yFSZ4&2OhPtVES*-k9I3F3edlK)=Jgo4NN&o4<} z$)Zsz{C9;otcU6U{TdUIB_GkhuaIFFba-PFMJrlX``-_-#lPO|(yTInYc*9<%BEXa z!KT;nx$MrrS7AcK%O^M5nyg-r65M|A$a+-uSH7YK1&_HZNAt;h5xIY_AseQegwrHX z-IK_!F&S9nvf9x5rz5LFxoW>Y${$kvd&QWJ?D-{!hF3dfGd{<96WimJ zxt=Q-uT;+t*37d0TL@a05ob6Kon-f)s|MP&^gAPutcvQTq5o8?d6IB)(UdP*N{LX)drT=^200|9Y%>Cc5 zX2XZj&JH)EbN^k^7*mO_y#f8{{3=%;6*9D|t;ZBW0Q+0ZgieAKwb$Fts50=^e@ zMK5v!CmTJgME+;h*>oM9$Y=eoo5v*%zml(LU=i2q(r4KK(2GVikd?Pk-{|CSd2VLEk4xIN0skBnbB|1IH? 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b4b7995..ace2a61 100644 --- a/docs/source/usage.rst +++ b/docs/source/usage.rst @@ -15,7 +15,7 @@ Contribute Pull requests and any feedback regarding the code are very welcome. 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z15C8nex~Ldh7u=Z1H(9*WfW)yN>pdEj0|4~jdr273L(9O_ECgTNFN{lKE@b9nrR`q1S3h>Ox(G3vDRh;1n*9FT^NjJzLq@Qo0TRoD&PaJ{)Y9Z{-?WRT~gag&(zopr|cZoBX^XH5T8iSEs~ z+#Qv4mY`=+AmO^jW)~|Brbyn3q{`U_3{bh?8K7Em*{x7Qi9#QOlcp z;F4$!E zT@JmSzH@nin^d4Cl+D1)Eq3>R$w;SLZgj=*Dm~9IVq0w=+51M#OO4-Tk_AyGn$S?c ziC@>3$DO~i%+?!ygYFVGVtQba4z5+4gFEcq)m*O>#c;Ht7p}j|5*cewO-;R&5=6($ zC4!?KS5@`!PaqQa?iR!7m}VAXVXY~$?G0I7iIpASy3IsG`(e~=hmp1;t|PGN`mk6A z7<;2#`t|`(M{AYFxx~uZDH8_gDIn!NYA=UG?{1Tj$;+1C%plN_KZ5ll(yT>@`wwT%ooDm(=2iJEV zhJb}5uZO%lgIz!2k&kZXX9(CW(Sz0pv{j9{N-v10ax*J$3CK}41hHkAV^Ays(*WJy zJvDKeMlgWK%#&Ox2zqKEdJ&sZF1w(M}H;< zJnLr+=w3F!v)lLZ_maco1^ond8SNBd0vcIjG8?)7p4e_(lLtk@9J2IDhaB-9f=suO-12_e5stN|Nj7Nfnw?a literal 0 HcmV?d00001 From 8600043b941757c1a372db706e7e3205499ed3ee Mon Sep 17 00:00:00 2001 From: Amedeo Ceruti Date: Wed, 27 Nov 2024 14:47:40 +0100 Subject: [PATCH 6/8] Add cd in readme --- README.md | 5 +++- docs/source/modules.rst | 9 +++++++ docs/source/setup.rst | 7 ++++++ docs/source/tests.rst | 53 +++++++++++++++++++++++++++++++++++++++++ 4 files changed, 73 insertions(+), 1 deletion(-) create mode 100644 docs/source/modules.rst create mode 100644 docs/source/setup.rst create mode 100644 docs/source/tests.rst diff --git a/README.md b/README.md index 4fc86bd..d7475c6 100644 --- a/README.md +++ b/README.md @@ -157,7 +157,10 @@ In the topotherm root directory run: Then make the hmtl documentation files: :: -```make html``` +``` +cd docs +make html +``` The documentation is located under docs/build/html. diff --git a/docs/source/modules.rst b/docs/source/modules.rst new file mode 100644 index 0000000..d9dfad3 --- /dev/null +++ b/docs/source/modules.rst @@ -0,0 +1,9 @@ +tt-docs-ossama +============== + +.. toctree:: + :maxdepth: 4 + + setup + tests + topotherm diff --git a/docs/source/setup.rst b/docs/source/setup.rst new file mode 100644 index 0000000..552eb49 --- /dev/null +++ b/docs/source/setup.rst @@ -0,0 +1,7 @@ +setup module +============ + +.. automodule:: setup + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/tests.rst b/docs/source/tests.rst new file mode 100644 index 0000000..2e80877 --- /dev/null +++ b/docs/source/tests.rst @@ -0,0 +1,53 @@ +tests package +============= + +Submodules +---------- + +tests.conftest module +--------------------- + +.. automodule:: tests.conftest + :members: + :undoc-members: + :show-inheritance: + +tests.hydraulics module +----------------------- + +.. automodule:: tests.hydraulics + :members: + :undoc-members: + :show-inheritance: + +tests.mts module +---------------- + +.. automodule:: tests.mts + :members: + :undoc-members: + :show-inheritance: + +tests.sts module +---------------- + +.. automodule:: tests.sts + :members: + :undoc-members: + :show-inheritance: + +tests.test\_setup module +------------------------ + +.. automodule:: tests.test_setup + :members: + :undoc-members: + :show-inheritance: + +Module contents +--------------- + +.. automodule:: tests + :members: + :undoc-members: + :show-inheritance: From 23448298a15d60e2005ef222279ddb91e0133ea5 Mon Sep 17 00:00:00 2001 From: Ossama Elshimy Date: Mon, 2 Dec 2024 13:19:52 +0100 Subject: [PATCH 7/8] updated methedology equations --- docs/source/conf.py | 4 +- docs/source/documentation.rst | 3 +- docs/source/methodology.rst | 189 +++++++++++++++++++++++----------- docs/source/modules.rst | 9 ++ docs/source/setup.rst | 7 ++ docs/source/tests.rst | 53 ++++++++++ 6 files changed, 200 insertions(+), 65 deletions(-) create mode 100644 docs/source/modules.rst create mode 100644 docs/source/setup.rst create mode 100644 docs/source/tests.rst diff --git a/docs/source/conf.py b/docs/source/conf.py index ae420bf..778326a 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -10,8 +10,8 @@ import sys project = 'Topotherm' -copyright = '2024, Amedeo' -author = 'Amedeo' +copyright = '2024, Lambert, Jerry and Ceruti, Amedeo' +author = 'Jerry Lambert & Amedeo Ceruti' release = '0.2.0' # -- General configuration --------------------------------------------------- diff --git a/docs/source/documentation.rst b/docs/source/documentation.rst index 27ad51e..544fe9f 100644 --- a/docs/source/documentation.rst +++ b/docs/source/documentation.rst @@ -5,7 +5,7 @@ Activate the topotherm environment: :: conda activate topotherm -Then, install the optional requirments if needed :: +Then, install the optional requirements if needed :: pip install sphinx sphinx-rtd-theme or pip install .[docs] @@ -15,6 +15,7 @@ In the topotherm root directory run: :: Then make the hmtl documentation files: :: + cd docs make html The documentation is located under docs/build/html diff --git a/docs/source/methodology.rst b/docs/source/methodology.rst index 386441e..154703b 100644 --- a/docs/source/methodology.rst +++ b/docs/source/methodology.rst @@ -18,33 +18,51 @@ Initial Assumptions Calculations ^^^^^^^^^^^^^ +The following equations are used to form a full nonlinear thermohydraulic model of a district heating pipe. -.. figure:: darcy.png +Calculating the pressure loss between the nodes i and j: + +.. math:: + + \Delta p_{ij} = f_{ij} \cdot \frac{\text{l}_{ij}}{d_{ij}} \cdot \frac{v_{ij}^2}{2} \cdot \rho - Calculating the pressure loss between the nodes i and j +Calculating the Reynolds Number: + +.. math:: + + Re_{ij} = \frac{\rho \cdot v_{ij} \cdot d_{ij}}{\mu} + +Calculate the friction factor for a turbulent flow (Re > 2300) with pipe roughness 𝜀 + +.. math:: -.. figure:: reynolds.png + f_{ij} = \left[ -1.8 \cdot \log \left( \left(\frac{\varepsilon}{3.7 \cdot d_{ij}}\right)^{1.11} + \frac{6.9}{Re_{ij}} \right) \right]^{-2} - Calculating the Reynolds Number +An iterative calculation (using SciPy) is performed to determine the maximum velocity in a pipe with a given inner diameter. The specific pressure drop per meter pipe length should range from 70Pa/m to 350Pa/m and the initial velocity is 0.5 m/s. -.. figure:: haaland.png +.. math:: + + v_{max} = \sqrt{\frac{2 \cdot \Delta p_{max} \cdot d}{f \cdot \rho}} +After calculating the maximum speed the maximum flow rate can be calculated using (𝑚̇ = 𝜌 ⋅ 𝑣 ⋅ 𝑑² ⋅ 𝜋∕4) - Calculate the friction factor for a turbulent flow (Re > 2300) with pipe roughness 𝜀 +To model the thermal behavior of an insulated pipe buried underground the temperature difference 𝛩 between the water temperature in the pipe and the outside temperature is introduced: + +.. math:: + + \Theta_{ij} = \Theta_{i} \cdot \exp\left(\frac{{-\text{l}_{ij}}{-l_{ij}}}{c_p \cdot \dot{m}_{ij} \cdot R_{ij}}\right) -.. figure:: vmax.png - An iterative calculation (using SciPy) is performed to determine the maximum velocity in a pipe with a given inner diameter. The specific pressure drop per meter pipe length should range from 70Pa/m to 350Pa/m and the initial velocity is 0.5 m/s. After calculating the maximum speed the maximum flow rate can be calculated using (𝑚̇ = 𝜌 ⋅ 𝑣 ⋅ 𝑑² ⋅ 𝜋∕4) -.. figure:: deltat.png +The combined thermal resistance 𝑅𝑖𝑗 of the pipe and soil per unit length is calculated with the ratio 𝑟 between outer and inner diameter. the buried depth of a pipe ℎ, as well as the thermal conductivities of the ground (𝑘ᵍ) and of the pipe’s insulation (𝑘ⁱⁿˢᶸˡ) are used to calculate the combined thermal resistance. - To model the thermal behavior of an insulated pipe buried underground the temperature difference 𝛩 between the water temperature in the pipe and the outside temperature is introduced -.. figure:: rij.png +.. math:: + + R_{ij} = \frac{\ln{\frac{4h}{r \cdot d_{ij}}}}{2\pi \cdot k_{g}} + \frac{\ln{r}}{2\pi \cdot k_{insul}} - The combined thermal resistance 𝑅𝑖𝑗 of the pipe and soil per unit length is calculated with the ratio 𝑟 between outer and inner diameter. the buried depth of a pipe ℎ, as well as the thermal conductivities of the ground (𝑘ᵍ) and of the pipe’s insulation (𝑘ⁱⁿˢᶸˡ) are used to calculate the combined thermal resistance. Linear regression ^^^^^^^^^^^^^^^^^^ -The previous equations form a full nonlinear thermohydraulic model of a district heating pipe. To represent the considered diameter range in a MILP, the nonlinear dependencies have to be represented as continuous and linear within the optimization problem. The linearization in this study is performed with a simple linear regression 𝑦 = a ⋅ 𝑥 + b, where 𝑦 is the dependent variable, 𝑥 is the independent variable, and the factors a and b are the regression coefficients. This approach is adopted to formulate an optimization problem that can be solved within a feasible computing time, consistent with the methodologies of previous works. +To represent the considered diameter range in a MILP, the nonlinear dependencies have to be represented as continuous and linear within the optimization problem. The linearization in this study is performed with a simple linear regression 𝑦 = a ⋅ 𝑥 + b, where 𝑦 is the dependent variable, 𝑥 is the independent variable, and the factors a and b are the regression coefficients. This approach is adopted to formulate an optimization problem that can be solved within a feasible computing time, consistent with the methodologies of previous works. For pipes ranging from DN 20 to DN 400, the thermal losses are calculated through the temperature difference between the water and the pipe calculated earlier using the maximal mass flow rate, while the total investment costs for piping are adapted from `Nussbaumer & Thalmann (2016) `_ @@ -61,14 +79,18 @@ Graphical representation A graph representation of a district heating network has to be introduced to mathematically represent pipes, junctions, producers, and consumers. The district heating systems’ pipes correspond to the graph’s edges and the network’s junctions to the nodes. The district heating network consists of a feed and return network with edges of opposite directions. This superstructure contains all possible connections and pathways from the heat source to the consumers. -.. figure:: nodes.png +The set of all nodes N is subdivided into three different subsets: int denotes all nodes without a consumer or a producer, the subscript p describes all nodes connected to at least one producer, and the subscript c all nodes connected to at least one consumer. - Thi set of all nodes is subdivided into three different subsets: int denotes all nodes without a consumer or a producer, the subscript p describes all nodes connected to at least one producer, and the subscript c all nodes connected to at least one consumer. +.. math:: + + \mathcal{N}_{int} \cup \mathcal{N}_{p} \cup \mathcal{N}_{c} = \mathcal{N} + -.. figure:: edges.png +This set 𝐴 representing all edges of the network is subdivided into three different subsets: int represents the geometrical pipe connection between two different internal nodes. p and c denote the state transition between the district heating system and a producer or a consumer, respectively. - This set 𝐴 representing all edges of the network is subdivided into three different subsets: int represents the geometrical pipe connection between two different internal nodes. p and c denote the state transition between the district heating system and a producer or a consumer, respectively. - +.. math:: + + \mathcal{A}_{int} \cup \mathcal{A}_{p} \cup \mathcal{A}_{c} = \mathcal{A} A certain network node will be referred to as 𝑛, whereas a directed edge going from node 𝑖 to node 𝑗 as 𝑖𝑗 ∈ A. @@ -81,44 +103,61 @@ The bidirectionality of the network (two edges per pipe) is explicitly considere The constraints of the sts solution are as follows: -.. figure:: heatbalancests.png +* The heat balance of the pipe, which contains the heat outflow of each pipe Qout, the heat inflow Qin and the thermal losses over the length l𝑖𝑗.The thermal losses are determined by the linear regression coefficients aₜₕₑᵣₘ and bₜₕₑᵣₘ while the binary variable 𝜆𝑖𝑗 represents the flow direction of the considered pipe. - The heat balance of the pipe, which contains the heat outflow of each pipe Qout, the heat inflow Qin and the thermal losses over the length l𝑖𝑗.The thermal losses are determined by the linear regression coefficients aₜₕₑᵣₘ and bₜₕₑᵣₘ while the binary variable 𝜆𝑖𝑗 represents the flow direction of the considered pipe. +.. math:: + + \dot{Q}_{ij,0} - \dot{Q}_{ij,1} -\left(a_{therm} \cdot \dot{Q}_{ij,0} + b_{therm} \cdot \lambda_{ij} \right) \cdot \text{l}_{ij} = 0 \qquad \forall ij \in \mathcal{A}_{int} -.. figure:: bigmsts.png +* A big-M constraint is formulated to enforce zero thermal power flow if the direction 𝑖𝑗 is not used. ̇ 𝑄max is modeled as a sufficiently large constant power flow. - A big-M constraint is formulated to enforce zero thermal power flow if the direction 𝑖𝑗 is not used. ̇ 𝑄max is modeled as a sufficiently large constant power flow. +.. math:: -.. figure:: energyconsts.png + \dot{Q}_{ij,0} \leq \dot{Q}_{max,cons} \cdot \lambda_{ij} \qquad \forall ij \in {\mathcal{A}_{int}} - Each consumer connection to the district heating grid is modeled as unidirectional, and thus no heat feed-in from a consumer is possible. Moreover,energy conservation is assumed in every node under consideration of the consumer’s heat demand and the heat source’s feed-in -.. figure:: unidirecionalsts.png +* Each consumer connection to the district heating grid is modeled as unidirectional, and thus no heat feed-in from a consumer is possible. Moreover,energy conservation is assumed in every node under consideration of the consumer’s heat demand and the heat source’s feed-in - To ensure a unidirectional use of a pipe and to reduce the solution space during the Branch-and-Bound, this constraint prevents the simultaneous use of the direction 𝑖𝑗 and 𝑗𝑖. +.. math:: -.. figure:: connectedconsumersts.png + \dot{Q}_{ni,0} - \dot{Q}_{jn,1} - \dot{Q}_{c,n} + \dot{Q}_{p,n} = 0 \qquad \forall n \in \mathcal{N}, \; (ni, jn) \in {\mathcal{A}_{int}} - In this study, all consumers must be connected to the district heating system grid therefore, the direction 𝜆𝑖𝑗 of pipe 𝑖𝑗 to a consumer node 𝑗 is set to 1, forcing the edge to be used and heating to be supplied. +* To ensure a unidirectional use of a pipe and to reduce the solution space during the Branch-and-Bound, this constraint prevents the simultaneous use of the direction 𝑖𝑗 and 𝑗𝑖. -.. figure:: thermalcapacitysts.png +.. math:: - The thermal power output ̇ 𝑄𝑝 is constrained by the installed thermal capacity of the source ̇ 𝑄inst𝑝 + \lambda_{ij} + \lambda_{ji} \leq 1 \qquad \forall ij \in {\mathcal{A}_{int}} \; -.. figure:: annuitysts.png +* In this study, all consumers must be connected to the district heating system grid therefore, the direction 𝜆𝑖𝑗 of pipe 𝑖𝑗 to a consumer node 𝑗 is set to 1, forcing the edge to be used and heating to be supplied. - The annuity method distributes investment costs of pipes or heat sources over the defined life span 𝑛years with an interest rate w. +.. math:: -.. figure:: supconstraint.png + \lambda_{ij} = 1 \qquad \forall ij \in {\mathcal{A}_{c}} - Additional constraints with redundant information can help to tighten further the Branch-and-Bound during the optimization. To that end, a supplementary constraint is formulated to ensure the total system energy conservation. +* The thermal power output ̇ 𝑄𝑝 is constrained by the installed thermal capacity of the source ̇ 𝑄inst𝑝 -Finally, the objective function minimizes the district heating network’s total investment and operational costs. +.. math:: + \dot{Q}_{p} \leq \dot{Q}_{\text{inst},p} \qquad \forall p \in \mathcal{N}_{p} -.. figure:: objectivefunctionsts.png +The annuity method distributes investment costs of pipes or heat sources over the defined life span 𝑛years with an interest rate w. + +.. math:: + + an = \frac{(1+w)^{n_{years}} \cdot w}{(1+w)^{n_{years}} -1} - The investment costs are determined by the linear regression factors aᶜᴼˢᵗ and bᶜᴼˢᵗ. By introducing full load hours flh, the investment and operational costs are weighted. +Additional constraints with redundant information can help to tighten further the Branch-and-Bound during the optimization. To that end, a supplementary constraint is formulated to ensure the total system energy conservation. +.. math:: + + \sum_{p \in {\mathcal{A}_p}} \dot{Q}_p - \sum_{ij \in {\mathcal{A}_{int}}} \left(\dot{Q}_{ij,0} - \dot{Q}_{ij,1}\right) - \sum_{ji \in {\mathcal{A}_{int}}} \left(\dot{Q}_{ji,0} - \dot{Q}_{ji,1}\right) - \sum_{c \in {\mathcal{A}_c}} \dot{Q}_c = 0 \; + +Finally, the objective function minimizes the district heating network’s total investment and operational costs. + +The investment costs are determined by the linear regression factors aᶜᴼˢᵗ and bᶜᴼˢᵗ. By introducing full load hours flh, the investment and operational costs are weighted. + +.. math:: + + \text{min} \; \bigg\{& \sum_{p \in {\mathcal{N}_p}} {\dot{Q}_{\text{inst},p}} \cdot {c_{\text{inv},p}} \cdot an_p + \sum_{p \in {\mathcal{N}_p}} \dot{Q}_{p} \cdot {c_{\text{fuel},p}} \cdot {\text{flh}} \\ & + \sum_{ij \in \mathcal{A}_{int}} \left(a_{cost} \cdot (\dot{Q}_{ij,0}+\dot{Q}_{ji,0}) + b_{cost} \cdot (\lambda_{ij}+\lambda_{ji}) \right) \cdot {\text{l}_{ij}} \cdot an_{pipe} \bigg\} Multiple Time Step Formulation ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -127,50 +166,70 @@ In order to optimize district heating systems with multiple time steps and chang The constraints of the mts solution are as follows: -.. figure:: heatbalancemts.png +* The heating power balance of each pipe is enforced. 𝑄out𝑖𝑗,𝑡 is the mean power outflow of each pipe, ̇ 𝑄in𝑖𝑗,𝑡 the inflow and ̇ 𝑄loss𝑖𝑗,𝑡 the thermal losses during time step 𝑡.These equations can be adapted for different time steps durations by changing from a power flow to an energy flow with 𝑄𝑡= ̇ 𝑄𝑡 ⋅𝛥𝑇𝑡. + +.. math:: - The heating power balance of each pipe is enforced. 𝑄out𝑖𝑗,𝑡 is the mean power outflow of each pipe, ̇ 𝑄in𝑖𝑗,𝑡 the inflow and ̇ 𝑄loss𝑖𝑗,𝑡 the thermal losses during time step 𝑡.These equations can be adapted for different time steps durations by changing from a power flow to an energy flow with 𝑄𝑡= ̇ 𝑄𝑡 ⋅𝛥𝑇𝑡. + \dot{Q}_{ij,0}[t] - \dot{Q}_{ij,1}[t] - {\dot{Q}_{\text{loss},ij}[t]} = 0 \qquad \forall ij \in {\mathcal{A}_{int}}, \forall t \in \mathcal{T} -The thermal losses for pipe 𝑖𝑗 need to be modeled as an independent variable and cannot be incorporated into the equation directly. This is due to the thermal losses along a pipe being nearly independent of the inflowing mass flow rate and depending mostly on the installed diameter +* The thermal losses for pipe 𝑖𝑗 need to be modeled as an independent variable and cannot be incorporated into the equation directly. This is due to the thermal losses along a pipe being nearly independent of the inflowing mass flow rate and depending mostly on the installed diameter -.. figure:: thermallossesmts.png +.. math:: - l𝑖𝑗 is the pipe length, atherm and btherm are linear regression coefficients calculated previously, and 𝜆𝑖𝑗,𝑡 is the binary decision to operate direction 𝑖𝑗 in time step t. + &{\dot{Q}_{\text{loss},ij}[t]} - \dot{Q}_{max,cons} \cdot \lambda_{ij}[t] \leq 0 & \forall ij \in {\mathcal{A}_{int}}, \forall t \in \mathcal{T} \label{eq:loss_1}\\ &\left(a_{therm} \cdot {\dot{Q}_{\text{cap},ij}} + b_{therm} \cdot \lambda_{ij}[t]\right) \cdot {\text{l}_{ij}} - {\dot{Q}_{\text{loss},ij}[t]} - \dot{Q}_{max,cons} \cdot \left(1-\lambda_{ij}[t]\right) \leq 0 & \forall ij \in {\mathcal{A}_{int}}, \forall t \in \mathcal{T} + +l𝑖𝑗 is the pipe length, atherm and btherm are linear regression coefficients calculated previously, and 𝜆𝑖𝑗,𝑡 is the binary decision to operate direction 𝑖𝑗 in time step t. If the direction 𝑖𝑗 is not used,the first equation ensures that the heat losses equal 0. The second equation enforces the heat loss calculation with the maximal built thermal capacity ̇ 𝑄max according to the flow direction in the pipe. -.. figure:: thermalflowmts.png +* This constraint enforces zero thermal flow if the direction 𝑖𝑗 of a pipe is not used. + +.. math:: + + \dot{Q}_{ij,0}[t] \leq \dot{Q}_{max,cons} \cdot \lambda_{ij}[t] \qquad \forall ij \in {\mathcal{A}_{int}}, \forall t \in \mathcal{T} - This constraint enforces zero thermal flow if the direction 𝑖𝑗 of a pipe is not used. +* Additionally, the maximal thermal power inflow ̇ 𝑄in𝑖𝑗,𝑡 at each time step 𝑡∈T is limited to the maximal thermal capacity of a pipe and maximal thermal capacity to the binary decision 𝜆built𝑖𝑗 if a pipe is built or not. -.. figure:: qcapmts.png +.. math:: - Additionally, the maximal thermal power inflow ̇ 𝑄in𝑖𝑗,𝑡 at each time step 𝑡∈T is limited to the maximal thermal capacity of a pipe and maximal thermal capacity to the binary decision 𝜆built𝑖𝑗 if a pipe is built or not. + &\dot{Q}_{ij,0}[t] \leq {\dot{Q}_{\text{cap},ij}} \qquad & \forall ij \in {\mathcal{A}_{int}}, \forall t \in \mathcal{T} \\ & {\dot{Q}_{\text{cap},ij}} \leq \dot{Q}_{max,cons} \cdot {\lambda_{\text{built},ij}} \qquad & \forall ij \in {\mathcal{A}_{int}} -.. figure:: decisionmts.png - The decision to build a pipe has to be linked with the possibility to use a certain direction of the pipe. +* The decision to build a pipe has to be linked with the possibility to use a certain direction of the pipe. -.. figure:: unidirectionalmts.png +.. math:: + + \lambda_{ij}[t] - {\lambda_{\text{built},ij}} \leq 0 \qquad \forall ij \in {\mathcal{A}_{int}}, \forall t \in \mathcal{T} + +* The simultaneous use of the direction 𝑖𝑗 and 𝑗𝑖 is prevented using this constraint. + +.. math:: + + \lambda_{ij}[t] + \lambda_{ji}[t] \leq 1 \qquad \forall ij \in {\mathcal{A}_{int}}, \forall t \in \mathcal{T} - The simultaneous use of the direction 𝑖𝑗 and 𝑗𝑖 is prevented using this constraint. +* In this study, all consumers must be connected to the district heating system grid.Therefore at a node 𝑗 with a consumer,the binary direction 𝑖𝑗 pipe and the binary building decision of that pipe is set to 1 -.. figure:: consumersmts.png +.. math:: + &\lambda_{ij} = 1 & \forall ij \in {A_{c}}\\ & {\lambda_{\text{built},ij}} = 1 & \forall ij \in {\mathcal{A}_{c} \; .} - In this study, all consumers must be connected to the district heating system grid.Therefore at a node 𝑗 with a consumer,the binary direction 𝑖𝑗 pipe and the binary building decision of that pipe is set to 1 +* Additional constraint for energy conservation -.. figure:: energyconmts.png +.. math:: + + \sum_{p \in \mathcal{A}_{p}} \dot{Q}_p[t] - \sum_{ij \in \mathcal{A}_{int}} \left( \dot{Q}_{\text{loss},ji}[t] + \dot{Q}_{\text{loss},ji}[t] \right) - \sum_{c \in \mathcal{A}_{c}} \dot{Q}_c[t] = 0 \qquad \forall t \in \mathcal{T} - Additional constraint for energy conservation +* The thermal power of the source ̇ 𝑄𝑝,𝑡 is limited by the optimal installed thermal power ̇ 𝑄inst𝑝. -.. figure:: qoptimalmts.png +.. math:: + + \dot{Q}_{p}[t] \leq \dot{Q}_{\text{inst},p} \qquad \forall p \in \mathcal{N}_{p} , \forall t \in \mathcal{T} - The thermal power of the source ̇ 𝑄𝑝,𝑡 is limited by the optimal installed thermal power ̇ 𝑄inst𝑝. +The objective function of the sts case is adapted to depict multiple time steps and flow directions. The full load hours are scaled according to the simulated time period and adjust the considered heat demand to the yearly heat demand. +.. math:: -.. figure::objectivemts.png + \text{min} \; \bigg\{& \sum_{p \in \mathcal{N}_{p}} \dot{Q}_{\text{inst},p} \cdot c_{\text{inv},p} \cdot an_p + \sum_{t \in \mathcal{T}} \sum_{p \in \mathcal{N}_{p}} \dot{Q}_{p}[t] \cdot c_{\text{fuel},p} \cdot \text{flh} \\ & + \sum_{ij \in \mathcal{A}_{int}} \left(a_{cost} \cdot \dot{Q}_{\text{cap},ij} + b_{cost} \cdot \lambda_{\text{built},p} \right) \cdot \text{l}_{ij} \cdot an_{pipe} \bigg\} - The objective function of the sts case is adapted to depict multiple time steps and flow directions. The full load hours are scaled according to the simulated time period and adjust the considered heat demand to the yearly heat demand. The forced expansion assumed can be easily modified for a planned expansion by eliminating the constraints connecting all consumers and modifying the objective function to economic indicators, such as revenue maximization. @@ -179,10 +238,16 @@ Simplified Multiple Time Step Formulation As previously mentioned, the thermal losses in a pipe do not depend on the thermal power flow into the pipe but rather on the installed capacity of the pipe.As the consideration of the installed capacity of the pipe earlier is computationally expensive, an alternative formulation named topothermmts_easy is formulated, where the thermal losses do not depend on the maximal thermal pipe capacity but rather on the thermal power inflow at each time step. -.. figure:: heatbalanceeasy.png +Modified heat balance constraint: + +.. math:: + + \dot{Q}_{ij,0}[t] - \dot{Q}_{ij,1}[t] -\left(a_{therm} \cdot \dot{Q}_{ij,0} + b_{therm} \cdot \lambda_{ij}[t] \right) \cdot {\text{l}_{ij}} = 0 \qquad \forall ij \in {\mathcal{A}_{int}}, \forall t \in \mathcal{T} \; + +Modified objective function - Modified heat balance constraint +.. math:: -.. figure:: objectiveeasy.png + \sum_{p \in \mathcal{A}_{p}} \dot{Q}_p[t] - \sum_{ij \in \mathcal{A}_{int}} \left(\dot{Q}_{ij,0}[t] - \dot{Q}_{ij,1}[t\right) - \sum_{ji \in \mathcal{A}_{int}} \left(\dot{Q}_{ji,0}[t] - \dot{Q}_{ji,1}[t]\right) - \sum_{c \in \mathcal{A}_{c}} \dot{Q}_c[t] = 0 \quad \forall t \in \mathcal{T} - Modified objective function \ No newline at end of file + \ No newline at end of file diff --git a/docs/source/modules.rst b/docs/source/modules.rst new file mode 100644 index 0000000..d9dfad3 --- /dev/null +++ b/docs/source/modules.rst @@ -0,0 +1,9 @@ +tt-docs-ossama +============== + +.. toctree:: + :maxdepth: 4 + + setup + tests + topotherm diff --git a/docs/source/setup.rst b/docs/source/setup.rst new file mode 100644 index 0000000..552eb49 --- /dev/null +++ b/docs/source/setup.rst @@ -0,0 +1,7 @@ +setup module +============ + +.. automodule:: setup + :members: + :undoc-members: + :show-inheritance: diff --git a/docs/source/tests.rst b/docs/source/tests.rst new file mode 100644 index 0000000..2e80877 --- /dev/null +++ b/docs/source/tests.rst @@ -0,0 +1,53 @@ +tests package +============= + +Submodules +---------- + +tests.conftest module +--------------------- + +.. automodule:: tests.conftest + :members: + :undoc-members: + :show-inheritance: + +tests.hydraulics module +----------------------- + +.. automodule:: tests.hydraulics + :members: + :undoc-members: + :show-inheritance: + +tests.mts module +---------------- + +.. automodule:: tests.mts + :members: + :undoc-members: + :show-inheritance: + +tests.sts module +---------------- + +.. automodule:: tests.sts + :members: + :undoc-members: + :show-inheritance: + +tests.test\_setup module +------------------------ + +.. automodule:: tests.test_setup + :members: + :undoc-members: + :show-inheritance: + +Module contents +--------------- + +.. automodule:: tests + :members: + :undoc-members: + :show-inheritance: From ff42b05bdc9c7b55f996b2284e38db0b8e1bf0d4 Mon Sep 17 00:00:00 2001 From: Ossama Elshimy Date: Mon, 2 Dec 2024 13:24:41 +0100 Subject: [PATCH 8/8] remove superflous images --- docs/source/annuitysts.png | Bin 8142 -> 0 bytes docs/source/bigmsts.png | Bin 6606 -> 0 bytes docs/source/connectedconsumersts.png | Bin 3790 -> 0 bytes docs/source/consumersmts.png | Bin 10620 -> 0 bytes docs/source/darcy.png | Bin 6271 -> 0 bytes docs/source/decisionmts.png | Bin 7120 -> 0 bytes docs/source/deltat.png | Bin 8408 -> 0 bytes docs/source/edges.png | Bin 2633 -> 0 bytes docs/source/energyconmts.png | Bin 13938 -> 0 bytes docs/source/energyconsts.png | Bin 10015 -> 0 bytes docs/source/haaland.png | Bin 14315 -> 0 bytes docs/source/heatbalanceeasy.png | Bin 9948 -> 0 bytes docs/source/heatbalancemts.png | Bin 7967 -> 0 bytes docs/source/heatbalancests.png | Bin 11957 -> 0 bytes docs/source/nodes.png | Bin 3038 -> 0 bytes docs/source/obectivemts.png 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Lambert, Jerry and Ceruti, Amedeo and Spliethoff, Hartmut, Benchmark of Mixed-Integer Linear Programming Formulations for District Heating Network Design. 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