# Networks¶

The network class handles preprocessing, solving and post-processing. We will walk you through all the important steps.

## Setup¶

### Network container¶

The TESPy network contains all data of your plant, which in terms of the calculation is represented by a nonlinear system of equations. The system variables of your TESPy network are a subset of the following:

mass flow,

pressure,

enthalpy and

the mass fractions of the fluids

of every connection.

The solver will simplify the variable space in a presolving step and then solve
for the remaining variables. If your **system includes fluid mixtures**, you
might want to **make use of the value ranges** for the system variables. This
improves the stability of the algorithm. Try to fit the boundaries as tight as
possible, for instance, if you know that the maximum pressure in the system will
be at 10 bar, use it as upper boundary.

Note

Value ranges for pure fluids are not required as these are dealt with automatically.

```
>>> from tespy.networks import Network
>>> my_plant = Network()
>>> my_plant.p_unit
'Pa'
>>> my_plant.set_attr(p_unit='bar', h_unit='kJ / kg')
>>> my_plant.set_attr(p_range=[0.05, 10], h_range=[15, 2000])
>>> my_plant.p_unit
'bar'
>>> my_plant.p_range_SI.tolist()
[5000.0, 1000000.0]
```

#### Printouts and logging¶

TESPy comes with an inbuilt logger. If you want to keep track of debugging-messages, general information, warnings or errors you should enable the logger. At the beginning of your python script e.g. add the following lines:

```
>>> from tespy.tools import logger
>>> import logging
>>> ();logger.define_logging(
... logpath="myloggings", log_the_path=True, log_the_version=True,
... screen_level=logging.INFO, file_level=logging.DEBUG
... );() # +doctest: ELIPSIS
(...)
```

The log-file will be saved to `~/.tespy/log_files/`

by default. All
available options are documented in the
`API`

.

Prior to solving the network there are options regarding the **console**
**printouts for the calculation progress**. Specify, if you want to enable or
disable convergence progress printouts:

```
>>> my_plant.iterinfo
True
# disable iteration information printout
>>> my_plant.set_attr(iterinfo=False)
>>> my_plant.iterinfo
False
# enable iteration information printout
>>> my_plant.set_attr(iterinfo=True)
```

#### Adding connections¶

As seen in the introduction, you will have to create your networks from the components and the connections between them. You can add connections directly or via subsystems using the corresponding methods:

```
>>> my_plant.add_conns()
>>> my_plant.add_subsys()
```

Note

You do not need to add the components to the network, as they are inherited via the added connections. After having set up your network and added all required elements, you can start the calculation.

#### Busses: Energy Connectors¶

Another type of connection is the bus: Busses are connections for massless transfer of energy e.g. in turbomachinery or heat exchangers. They can be used to model motors or generators, too. Add them to your network with the following method:

```
>>> my_plant.add_busses()
```

You will learn more about busses and how they work in this part.

### Start calculation¶

You can start the solution process with the following line:

```
my_plant.solve(mode='design')
```

This starts the initialisation of your network and proceeds to its calculation.
The specification of the **calculation mode is mandatory**, This is the list of
available keywords:

`mode`

is the calculation mode (`'design'`

-calculation or`'offdesign'`

-calculation).`init_path`

is the path to the network folder you want to use for initialisation.`design_path`

is the path to the network folder which holds the information of your plant’s design point.`max_iter`

is the maximum amount of iterations performed by the solver.`min_iter`

is the minimum amount of iterations before a solution can be accepted (given the convergence criterion is satisfied).`init_only`

stop after initialisation (True/False).`init_previous`

use starting values from previous simulation (True/False).`use_cuda`

use cuda instead of numpy for matrix inversion, speeds up simulation in some cases by outsourcing calculation to graphics card. For more information please visit the cupy documentation.

There are two calculation modes available (`'design'`

and
`'offdesign'`

), which are explained in the subsections below. If you
choose `offdesign`

as calculation mode the specification of a
`design_path`

is mandatory.

The usage of an initialisation path is always optional but highly recommended,
as the convergence of the solution process will be improved, if you provide
good starting values. If you do not specify an `init_path`

, the
initialisation from saved results will be skipped.
`init_only=True`

usually is used for debugging. Or, you could use this
feature to export a not solved network, if you want to do the parametrisation
in .csv-files rather than your python script.

The `init_previous`

parameter can be used in design and offdesign
calculations and works very similar to specifying an `init_path`

.
In contrast, starting values are taken from the previous calculation. Specifying
the `ìnit_path`

overwrites `init_previous`

.

#### Design mode¶

The design mode is used to design your system and is always the first
calculation of your plant. **The offdesign calculation is always based on a**
**design calculation!** Obviously as you are designing the plant the way you
want, you are flexible to choose the parameters to specify. However, you can
not specify parameters that are based on a design case, as for example the
isentropic efficiency characteristic function of a turbine or a pump.
Specifying a value for the efficiency is of course possible.

#### Offdesign mode¶

The offdesign mode is used to **calculate the performance of your plant, if**
**parameters deviate from the plant’s design point**. This can be partload
operation, operation at different temperature or pressure levels etc.. Thus,
before starting an offdesign calculation you have to design your plant first.
By stating `'offdesign'`

as calculation mode, **components and**
**connections will switch to the offdesign mode.** This means that all
parameters provided as design parameters will be unset and all parameters
provided as offdesign parameters will be set instead. You can specify a
connection’s or component’s (off-)design parameters using the
`set_attr`

method.

For example, for a condenser you would usually design it to a maximum terminal temperature difference, in offdesign the heat transfer coefficient is selected. The heat transfer coefficient is calculated in the preprocessing of the offdesign case based on the results from the design-case. Of course, this applies to all other parameters in the same way. Also, the pressure drop is a result of the geometry for the offdesign case, thus we swap the pressure ratios with zeta values.

```
mycomponent.set_attr(
design=['ttd_u', 'pr1', 'pr2'], offdesign=['kA', 'zeta1', 'zeta2']
)
```

Note

Some parameters come with characteristic functions based on the design case properties. This means, that e.g. the isentropic efficiency of a turbine is calculated as function of the actual mass flow to design mass flow ratio. You can provide your own (measured) data or use the already existing data from TESPy. All standard characteristic functions are available at tespy.data module.

For connections it works in the same way, e.g. write

```
myconnection.set_attr(design=['h'], offdesign=['T'])
```

if you want to replace the enthalpy with the temperature for your offdesign. The temperature is a result of the design calculation and that value is then used for the offdesign calculation in this example.

To solve your offdesign calculation, use:

```
my_plant.solve(mode='offdesign', design_path='path/to/network_designpoint')
```

## Solving¶

A TESPy network can be represented as a linear system of nonlinear equations,
consequently the solution is obtained with numerical methods. TESPy uses the
n-dimensional Newton-Raphson method to find the system’s solution, which may
only be found, if the network is parameterized correctly. **The number of**
**variables n changes depending on your system’s topology and your**
**specifications**. Generally, masA presolving step reduces the amount of variables, see below
for more information.

**General preprocessing**

check network consistency and initialise components (if network topology is changed to a prior calculation only).

create a topology representation of the components and the connections.

simplify the variable space based on the plant’s topology.

perform design/offdesign switch (for offdesign calculations only).

preprocessing of offdesign case using the information from the

`design_path`

argument.

The network check is used to find errors in the network topology, the
calculation can not start without a successful check. The design/offdesign
switch is described in the network setup section. For offdesign calculation the
`design_path`

argument is required. The design point information is
extracted from that path in preprocessing. For this, you will need to save
your network’s design point information using:

```
my_plant.save('path/for/savestate')
```

**Simplifying the variable space**

To reduce the size of the system of equations a reduction of the variable space is performed in the initialisation of a calculation. For every of the primary variables (mass flow, pressure, enthalpy and fluid mass fractions), if a value is directly specified by the user, the respective variable is removed from the variable space, because it does not need to be solved.

Furthermore, there are three steps to simplify the variable space, i.e. regarding mass flow, regarding the fluid composition and regarding pressure and enthalpy.

First, based on the topology of the network, different branches are created. These are:

branches, in which the mass flow is equal in every of its connections and

branches, in which the fluid composition is equal in every of its connections.

For every mass flow branch, the variable space is reduced to a single mass flow. For example, in a simple Clausius Rankine cycle there will only be a single mass flow in the variable space. Analogously in every fluid composition branch, the variable space is reduced to a single vector containing the variable fluids of that branch. For example, if a mass flow is split in two streams using a splitter, the fluid composition remains constant downstream of the splitter. Therefore, all connections downstream of the splitter share the same fluid composition as upstream of the splitter.

The next step is a reduction of the fluid vector specifications: Consider a case with a couple of potential fluids on a fluid branch, e.g. oxygen, nitrogen, argon, carbon dioxide and water at the outlet of a combustion chamber. All fluid mass fractions specified by the user will be fixed and removed from the variable space. If then, only a single fluid remains with “unknown” mass fraction, we can assign a mass fraction to that fluid, which is equal to 1 minus the sum of all other fluids’ mass fractions.

Finally, presolving is applied to pressure and enthalpy, whenever the fluid composition is fixed. If either pressure or enthalpy is specified by the user and on top of that temperature, vapor quality or temperature difference to saturation temperature, the respective variable (enthalpy or pressure) can directly be calculated. Similarly, if temperature and temperature difference to saturation temperature or vapor quality are specified, both pressure and enthalpy can be deducted.

**Finding starting values**

The algorithm requires starting values for all variables of the system, thus an
initialisation of the system is run prior to calculating the solution. **High**
**quality initial values are crucial for convergence speed and stability**, bad
starting values might lead to instability and diverging calculation can be the
result. The following steps are performed in finding starting values:

fluid composition guessing.

fluid property initialisation.

initialisation from previous simulation run (

`ìnit_previous`

).initialisation from .csv (setting starting values from

`init_path`

argument).

Starting value generation for your calculations starts with the fluid composition guessing in case the fluid composition is not fixed. The available fluids will be assigned the same mass fraction \(x\), if no starting value is supplied. The mass fractions are distributed to 1 minus the sum of all user specified mass fractions: \(x=\frac{1-\sum\text{x_spec}}{n}\). If you are using combustion chambers these will be replaced by a generic flue gas composition will be calculated prior to the propagation.

Next the fluid property initialisation uses user specified starting values or
the results from the previous simulation to set starting values for mass flow,
pressure and enthalpy. Otherwise, generic starting values are generated on basis
of which components a connection is linked to. If you **do not want** to use the
results of a previous calculation, you need to specify
`init_previous=False`

on the `Network.solve`

method call.

Last step in starting value generation is the initialisation from a saved
network state. In order to initialise your calculation with this method, you
need to provide the path to the saved network in the `init_path`

argument
of the solve method. TESPy searches through the connections.csv file. If a
connection with the respective label is found, the starting values for the
system variables are taken over from that file.

Note

The files do not need to contain all connections of your network. You can
build your network step by step and initialise the existing parts of your
network from the `init_path`

. Be aware that a change within the fluid
vector does not allow this practice! If you plan to use additional fluids
in parts of the network you have not touched until now, you will need to
state all fluids from the beginning.

### Algorithm¶

In this section we will give you an introduction to the solving algorithm implemented.

#### Newton-Raphson method¶

The Newton-Raphson method requires the calculation of residual values for the equations and of the partial derivatives to all system variables (Jacobian matrix). In the next step the matrix is inverted and multiplied with the residual vector to calculate the increment for the system variables. This process is repeated until every equation’s result in the system is “correct”, thus the residual values are smaller than a specified error tolerance. All equations are of the same structure:

calculate the residuals

Jacobian matrix J

derive the increment

while

Note

You have to provide the exact amount of required parameters (neither less nor more) and the parametrisation must not lead to linear dependencies. Each parameter you set for a connection and each energy flow you specify for a bus will add one equation to your system. On top, each component provides a different amount of basic equations plus the equations provided by your component specification.

For example, consider a pump: Total mass flow as well as the fluid mass fractions of the mixture entering the pump will be identical at the outlet. The pump delivers two mandatory equations. If you additionally specify, e.g. the power \(P\) to be 1000 W, the set of equations will look like this:

#### Convergence stability¶

One of the main downsides of the Newton-Raphson method is that the initial step width is very large and that it does not know physical boundaries, for example mass fractions smaller than 0 and larger than 1 or negative pressure. Also, the large step width can adjust enthalpy or pressure to quantities that are not covered by the fluid property databases. This would cause an inability e.g. to calculate a temperature from pressure and enthalpy in the next iteration of the algorithm. In order to improve convergence stability, we have added a convergence check.

**The convergence check manipulates the system variables after the increment**
**has been added**. This manipulation has four steps, the first two are always
applied:

Cut off fluid mass fractions smaller than 0 and larger than 1. This way a mass fraction of a single fluid component never exceeds these boundaries.

Check, whether the fluid properties of pure fluids are within the available ranges of CoolProp and readjust the values if not.

The next two steps are applied, if the user did not specify an
`init_path`

and the iteration count is lower than 3, thus in the first
three iteration steps of the algorithm only. In other cases this convergence
check is skipped.

Fox mixtures: check, if the fluid properties (pressure, enthalpy and mass flow) are within the user specified boundaries (

`p_range, h_range, m_range`

) and if not, cut off higher/lower values.Check the fluid properties of the connections based on the components they are connecting. For example, check if the pressure at the outlet of a turbine is lower than the pressure at the inlet or if the flue gas composition at a combustion chamber’s outlet is within the range of a “typical” flue gas composition. If there are any violations, the corresponding variables are manipulated. If you want to look up, what exactly the convergence check for a specific component does, look out for the

`convergence_check`

methods in the`tespy.components module`

.

In a lot of different tests the algorithm has found a near enough solution after the third iteration, further checks are usually not required.

Tip

To check if the solver successfully found a solution for your model you can check the .converged attribute of the Network class after calling the solve method. It will be True in case no linear dependency was and the residual value of all equations is below the minimum threshold.

#### Calculation speed improvement¶

For improvement of calculation speed, the calculation of specific derivatives
is skipped, if the change of the corresponding variable was below a
threshold of `1e-12`

in the iteration before.

As a user you can take two more measures to improve calculation speed: Specify primary variables whenever possible/reasonable. This will not only reduce the variable space but also remove the necessity to calculate partial derivatives towards them.

#### Troubleshooting¶

In this section we show you how you can troubleshoot your calculation and list
up common mistakes. If you want to debug your code, make sure to enable the
logger and have a look at the log-file at `~/.tespy/`

(or at your
specified location).

First, make sure your network topology is set up correctly, TESPy will prompt an Error, if not. TESPy will prompt an error, too, if you did not provide enough or if you provide too many parameters for your calculation, but you will not be given an information which specific parameters are under- or over-determined.

Note

Always keep in mind, that the system has to find a value for mass flow, pressure, enthalpy and the fluid mass fractions. Try to build up your network step by step and have in mind, what parameters will be determined by adding a component without any parametrisation. This way, you can easily determine, which parameters are still to be specified.

If you are modeling a cycle, e.g. the Clausius Rankine cylce, you need to make a cut in the cycle using the cycle_closer or a sink and a source not to over-determine the system. Have a look in the tutorial section to understand why this is important and how it can be implemented.

If you have provided the correct number of parameters in your system and the calculations stops after or even before the first iteration, there might be a couple reasons for that:

Sometimes, the fluid property database does not find a specific fluid property in the initialisation process, have you specified the values in the correct unit?

A linear dependency in the Jacobian matrix due to bad parameter settings stops the calculation (over-determining one variable, while missing out on another).

A linear dependency in the Jacobian matrix due to bad starting values stops the calculation.

The first reason can be eliminated by carefully choosing the parametrisation.
**A linear dependency due to bad starting values is often more difficult to**
**resolve, and it may require some experience.** In many cases, the linear
dependency is caused by equations, that require the **calculation of a**
**temperature**, e.g. specifying a temperature at some point of the network,
terminal temperature differences at heat exchangers, etc.. In this case,
**the starting enthalpy and pressure should be adjusted in a way, that the**
**fluid state is not within the two-phase region:** The specification of
temperature and pressure in a two-phase region does not yield a distinct value
for the enthalpy. Even if this specific case appears after some iterations,
better starting values often do the trick.

Another frequent error is that fluid properties move out of the bounds given by
the fluid property database. The calculation will stop immediately.
**Adjusting pressure and enthalpy ranges for the convergence check** might help
in this case.

Note

If you experience slow convergence or instability within the convergence process, it is sometimes helpful to have a look at the iteration information. This is printed by default and provides information on the residuals of your systems’ equations and on the increments of the systems’ variables. Maybe it is only one variable causing the instability, its increment is much larger than the increment of the other variables?

Did you experience other errors frequently and have a workaround/tips for resolving them? You are very welcome to contact us and share your experience for other users!

## Post-processing¶

A post-processing is performed automatically after the calculation finished. You have further options:

Automatically create a documentation of your model.

Print the results to prompt (

`print_results()`

).Save the results in structure of .csv-files (

`save()`

).Generate fluid property diagrams with an external tool.

### Automatic model documentation¶

Using the automatic TESPy model documentation you can create an overview of all input parameters, specifications and equations as well as characteristics applied in LaTeX format. This enables high

**transparency**,**readability**and**reproducibility**.

In order to use the model documentation, you need to import the corresponding method and pass your network information. At the moment, you can the following optional arguments to the method:

`path`

: Basepath, where the LaTeX data and figures are exported to.`filename`

: Filename of the report.`fmt`

: A formatting dictionary, for a sample see below.

```
from tespy.tools import document_model
fmt = {
'latex_body': True, # adds LaTeX body to compile report out of the box
'include_results': True, # include parameter specification and results
'HeatExchanger': { # for components of class HeatExchanger
'params': ['Q', 'ttd_l', 'ttd_u', 'pr1', 'pr2']}, # change columns displayed
'Condenser': { # for components of class HeatExchanger
'params': ['Q', 'ttd_l', 'ttd_u', 'pr1', 'pr2']
'float_fmt': '{:,.2f}'}, # change float format of data
'Connection': { # for Connection instances
'p': {'float_fmt': '{:,.4f}'}, # change float format of pressure
's': {'float_fmt': '{:,.4f}'},
'h': {'float_fmt': '{:,.2f}'},
'params': ['m', 'p', 'h', 's'] # list results of mass flow, ...
'fluid': {'include_results': False} # exclude results of fluid composition
},
'include_results': True, # include results
'draft': False # disable draft mode
}
document_model(mynetwork, fmt=fmt)
```

Note

Specified values are displayed in any case. The selection of which parameters to show and which to exclude only applies to results.

After having exported the LaTeX code, you can simply use `input{}`

in your main LaTeX document to include the documentation of your model. In
order to compile correctly you need to load the following LaTeX packages:

graphicx

float

hyperref

booktabs

amsmath

units

cleveref

longtable

For generating different file formats, like markdown, html or restructuredtext, you could try the pandoc library. For examples, of how the reports look you can have a look at the examples repository, or just try it yourself :).

This feature is introduced in version 0.4.0 and still subject to changes. If you have any suggestions, ideas or feedback, you are very welcome to submit an issue on our GitHub or even open a pull request.

### Results printing¶

To print the results in your console use the `print_results()`

method.
It will print tables containing the component, connection and bus properties.
Some results will be colored, the colored results indicate

if a parameter was specified as value before calculation.

if a parameter is out of its predefined value bounds (e.g. efficiency > 1).

if a component parameter was set to

`'var'`

in your calculation.

The color for each of those categories is different and might depend on the console settings of your machine. If you do not want the results to be colored you can instead call the method the following way:

```
my_plant.print_results(colored=False)
```

If you want to limit your printouts to a specific subset of components,
connections and busses, you can specify the `printout`

parameter to block
individual result printout.

```
mycomp.set_attr(printout=False)
myconn.set_attr(printout=False)
mybus.set_attr(printout=False)
```

If you want to prevent all printouts of a subsystem, add something like this:

```
# connections
for c in mysubsystem.conns.values():
c.set_attr(printout=False)
# components
for c in mysubsystem.comps.values():
c.set_attr(printout=False)
```

### Save your results¶

If you choose to save your results the specified folder will be created containing information about the network, all connections, busses, components and characteristics.

In order to perform calculations based on your results, you can access all components’ and connections’ parameters:

The easiest way to access the results of one specific component looks like this

```
eff = mycomp.eta_s.val # isentropic efficiency of mycomp
P = mycomp.P.val
```

and similar for connection parameters:

```
mass_flow = myconn.m.val # value in specified network unit
mass_flow_SI = myconn.m.val_SI # value in SI unit
mass_fraction_oxy = myconn.fluid.val['O2'] # mass fraction of oxygen
specific_volume = myconn.vol.val # value in specified network unit
specific_entropy = myconn.s.val # value in specified network unit
volumetric_flow = myconn.v.val # value in specified network unit
specific_exergy = myconn.ex_physical # SI value only
```

On top of that, you can access pandas DataFrames containing grouped results for the components, connections and busses. The instance of class Network provides a results dictionary.

```
# key for connections is 'Connection'
results_for_conns = my_plant.results['Connection']
# keys for components are the respective class name, e.g.
results_for_turbines = my_plant.results['Turbine']
results_for_heat_exchangers = my_plant.results['HeatExchanger']
# keys for busses are the labels, e.g. a Bus labeled 'power input'
results_for_mybus = my_plant.results['power input']
```

The index of the DataFrames is the connection’s or component’s label.

```
results_for_specific_conn = my_plant.results['Connection'].loc['myconn']
results_for_specific_turbine = my_plant.results['Turbine'].loc['turbine 1']
results_for_component_on_bus = my_plant.results['power input'].loc['turbine 1']
```

The full list of connection and component parameters can be obtained from the respective API documentation.

# Network reader¶

The network reader is a useful tool to import networks from a data structure using .csv-files. In order to re-import an exported TESPy network, you must save the network first.

```
my_plant.export('mynetwork')
```

This generates a folder structure containing all relevant files defining your network (general network information, components, connections, busses, characteristics) holding the parametrization of that network. You can re-import the network using following code with the path to the saved documents. The generated network object contains the same information as a TESPy network created by a python script. Thus, it is possible to set your parameters in the .csv-files, too. The imported network is handled identically as a manually created network.

```
from tespy.networks import load_network
imported_plant = load_network('path/to/mynetwork')
imported_plant.solve('design')
```

Note

Imported busses, components and connections are accessible by their label,
e.g. `imported_plant.busses['total heat output']`

,
`imported_plant.get_comp('condenser')`

and
`imported_plant.get_conn('myconnectionlabel')`

respectively. If
you did not provide labels for your connections, by default, the
connection’s label will be according to this principle:
`'source-label:source-id_target-label:target-id'`

, where source and
target are the labels of the connected components.