Dummy Model description - ID1643
This model page can be used as template for your own model. If you want to download this page in qmd format, click here:
Do not provide the title here (to avoid duplicate display) as it should be included in the Metadata block. Each model post must be a consistent whole that cannot be subdivided into sub-models without loss of understanding (for example, due to a consistent notation system, intertwined equations, etc.)
Context (mandatory)
A short paragraph reminding the history of the model, in which context it was developed for, what are the physics and the modelling approximations behind it.
Example:
The synchronous machine is one of the most studied component of a power system, being its main source of electrical energy. It is the most common type of generators, and it is present in most power plants (thermal, hydro, and some wind) as an interface between the mechanical energy and electrical energy. The mathematical model presented in this article develops the dynamic equations of synchronous machines [1] It only covers the physical part of the machine (see Section 3) not the regulations nor protections schemes.
Model use, assumptions, validity domain and limitations (mandatory)
Each model is an approximation of the reality, and considers some assumptions.
In this section, details should be given on:
- the validity domain of the model (frequency range, type of dynamics, type of stability phenomena) that the model covers,
- the model assumptions (e.g., neglecting the DC side of the converter, simplistic PLL representation)
- the limitations of the model (what people shouldn’t use the model for)
Example:
The model presents the general expressions in abc reference frame of the differential equations that model a general synchronous machine with the following assumptions: - There are three stator windings ( \(a, b, c\)) distributed 120º apart one from each other, each of them with equal parameters (i.e. same resistance, inductance…). - The three phases are balanced, meaning the power is shared equally. - The rotor has one winding with a field (\(e_f\)) applied and three damper windings, with no power source, one of them with the axis parallel to the field winding (\(1d\)) and the other two with a perpendicular axis (\(1q,2q\)). - The magnetic field produced by the rotor winding oscillates sinusoidally. - The machine may have 2 or more poles, noted as \(p_f\) The model is suitable for transient stability analysis but not for electromagnetic transient analysis.
Model description (mandatory)
This section gives the full description of the different model’s components. For each component, is given: a brief explanation about the functioning of the component (how it works, what it is made of, which implementation choices are made) and the component equations or control diagram. The author can also point to another component page if the component is already explained in another page. In such case, he clearly needs to make coherence is achieved with the rest of the model in terms of notation, convention, and connection aspects.
For the equation system / algorithm : the author can use Latex language, which is fully compatible with markdown. He can also use numbered equations. The variables and parameters should be clearly specified, as well as their type (complex, real, etc.), unit (MW, MVA, etc), and meaning (phase to neutral voltage for the output terminal A). The notation should follow scientific standards.
Images or Electric/Electronic/Control/Phasor diagramscan be added for clarity. The image must be of good quality and more preferably in .svg format. Diagrams can be used instead of equations to describe the component. The selected control blocks should be unambiguous, that is to say that their equations should be clearly understood from the diagram. A list of basic blocks can be found in colib here: pages/models/controlBlocks/. Several packages can be used to display diagrams, e.g.: draw.io plugin for github allows you to make your own diagram easily. The diagram is fully editable with github commit using a graphical interface, and allowing multiple format outputs (for more details, see: draw.io github).
Initial equations/boundary conditions: when initial equations or boundary conditions are necessary to fully described the system, a subsection dedicated to those aspects can be added in this section.
Example:
Physical description
The following schematic shows the components that participate in the synchronous machine operation:
[…]
Synchronous machine equations
Variables
| Variable | details | Unit |
|---|---|---|
| \(\theta_{shaft}\) | Rotor angle | \(rad\) |
| \(\omega\) | Electrical rotational speed | \(rad/s\) |
| \(T_m\) | Mechanical torque | \(Nm\) |
| \(T_e\) | Electrical torque | \(Nm\) |
[…]
Parameters
| Parameter | Description | Unit |
|---|---|---|
| \(J\) | Moment of inertia | \(kgm^2\) |
| \(p_f\) | Number of pole pairs | - |
| \(R_a\), \(R_b\), \(R_c\) | Stator phase resistances | \(\Omega\) |
[…]
System of equations
The following system of equations describe a general synchronous machine with the considered assumptions. Some of its parameters are generally non-constant, meaning it is not directly solved without making some additional assumptions. The particular models are derivations of this system of equations.
The equations Equation 1, Equation 2 represent the mechanical dynamic equations: \[ J\frac{2}{p_f} \frac{d\omega_m}{dt} = T_m - T_e - T_{fw} \tag{1}\] \[\frac{d\theta_{shaft}}{dt} = \frac{2}{p_f} \omega \tag{2}\]
[…]
Source code (optional)
This section is a code section that provides the source code for model described above.
The code should correspond strictly the equations/diagram/algorithm described before and should have been validated in a tool. The date of the code should be specified at the beginning of the section, the code should be clean, readable and organized.
Example: The code can be presented in a modeling language code block like this:
model VoltageSource "Constant AC voltage"
extends Interfaces.Source;
parameter SI.Frequency f(start=1) "Frequency of the source";
parameter SI.Voltage V(start=1) "RMS voltage of the source";
parameter SI.Angle phi(start=0) "Phase shift of the source";
equation
omega = 2*Modelica.Constants.pi*f;
v = Complex(V*cos(phi), V*sin(phi));
end VoltageSource;Open source implementations (if any)
This section give a list of the different open source implementations of this model. It provides the reader with links and languages/software used for each implementations. A markdown table can be used to display such list.
Example:
This model has been successfully implemented in :
| Software | URL | Language | Open-Source License | Last consulted date | Comments |
|---|---|---|---|---|---|
| Software name | Link | modelica | MPL v2.0 | XX/0X/20XX | Comments can contain implementations details such as validation means, implementations key choices, etc. |
Table of references & license
This section lists all the references. It must comply with current citation standards. Quarto uses BibTeX for managing reference.