Merge pull request #252 from CRESYM/dev

Merge all PRs to main

Author: GJCRESYM

pages/models/generations/GENQEC/GENQEC_blocks.png

@@ -80,8 +80,8 @@ The GENQEC model is suitable for EMT as it models with detail the non-linearitie
 
 <div style="font-weight: bold;">Electric Dynamics Equations:</div>
 
-$$ V_d = \frac{\omega_m}{\omega_s} E_d'' + I_q X_{qsat}'' - I_dR_a$$
-$$ V_q = \frac{\omega_m}{\omega_s} E_q'' - I_d X_{dsat}'' - I_qR_a$$
+$$ V_d = \frac{\omega}{\omega_s} E_d'' + I_q X_{qsat}'' - I_dR_a$$
+$$ V_q = \frac{\omega}{\omega_s} E_q'' - I_d X_{dsat}'' - I_qR_a$$
 $$ \frac{1}{\omega_s} \frac{d\Psi_0}{dt} = R_s I_0 + V_0$$
 $$ E''_q = E_{q1} + E_{q2} - I_d (X_{dsat} - X''_{dsat}) $$
 $$ E''_d = E_{d1} + E_{d2} + I_q (X_{qsat} - X''_{qsat}) $$
@@ -169,7 +169,7 @@ $$ X_{mdsat} I_{fd} = \left( X_{dsat} - X_l \right) I_{fd} = \frac{X_d - X_l}{Sa
 The following figure shows the block diagram for this GENQEC model [[2]](#2):
 
 <p align="center">
-<img src="{{'/pages/models/generations/GENQEC/GENQEC_blocks.png' | relative_url }}"
+<img src="{{'/pages/models/generations/GENQEC/GENQEC_blocks.svg' | relative_url }}"
      alt="Block diagram of the GENQEC model"
      style="float: center; width: 600px;" />
 </p>

pages/models/generations/GENQEC/GENQEC_blocks.svg

@@ -16,7 +16,7 @@ Voltage Source Converters (VSC) are widely used in power systems for a variety o
 
 ## Model use, assumptions, validity domain and limitations
 
-The model described allows performing phasor studies of the dynamics of a grid-following voltage source converter. It is specially useful in applications where there are slow-transients that want to be studied, such as transient stability studies or interarea oscillations [[1]](#1), allowing for fast simulations with bigger time steps than the EMT without loosing precision on these types of phenomena. 
+The model described allows performing phasor studies of the dynamics of a grid-following voltage source converter. It is specially useful in applications where there are slow-transients that want to be studied, such as transient stability studies or interarea oscillations [[1]](#1), allowing for fast simulations with bigger time steps than the EMT without losing precision on these types of phenomena. 
 
 The assumptions made are:
 
@@ -257,6 +257,8 @@ The technical constraints of the VSC can be included in the controls using satur
 * **Normal operation**: The converter will follow the $$i^q$$ component setpoint, prioritizing the active power, and then $$i^d$$ will be limited by the operational limits of the converter $$i^d_{max} = \sqrt{I_{max}^2 - \max{i^q, i^{q*}}} $$.
 * **Transient or fault operation**: The converter will now prioritize the $$i^d$$ component, which will follow its reference, and $$i^q_{max} = \sqrt{I_{max}^2 - \max{i^d, i^{d*}}^2} $$.
 
+More details on how the anti-windup controls are implemented can be found in the [EMT Grid Following page](../EMTGridFollowingVSC/).
+
 ## Derived Models
 
 The model presented can have some of its dynamics simplified in order to perform low-frequency domain studies with higher time step (which means, faster execution times). Listed below, ordered from high to low accuracy, some of this models with its assumptions are presented:

pages/models/generations/GENQEC/index.md

@@ -23,8 +23,6 @@ The exponential load model can be used for steady-state studies. The assumptions
 * This time dependency can be omitted, just assuming a constant value for the exponent. A common combination of exponents is $$a=1$$ for active power and $$b=2$$ for reactive power.
 * The frequency is constant, and the load is balanced.
 
-The model does not take into account the time-response performance of the load, therefore it is not useful for dynamic studies.
-
 ## Model description
 
 ### Parameters

pages/models/generations/Sources/VSC/PhasorGridFollowingVSC/index.md

@@ -21,8 +21,6 @@ The frequency dependent load model can be used for static analysis considering v
 * The variation of the load when the frequency changes are modeled using a factor dependent on the frequency deviation
 * The load is balanced 
 
-The model does not take into account the time-response performance of the load, therefore it is not useful for dynamic studies.
-
 ## Model description
 
 ### Parameters
@@ -50,8 +48,8 @@ The model does not take into account the time-response performance of the load,
 
 <div style="background-color:rgba(0, 0, 0, 0.0470588); text-align:center; vertical-align: middle; padding:4px 0;">
 
-$$P(V, f) = P(V) (1 + k_p\Delta f) $$
-$$Q(V, f) = Q(V) (1 + k_q \Delta f) $$
+$$P(V, f) = P(V) (1 + k_p\frac{\Delta f}{f_0}) $$
+$$Q(V, f) = Q(V) (1 + k_q \frac{\Delta f}{f_0}) $$
 </div>
 
 ## Operational principles
@@ -60,11 +58,11 @@ The model considers the load as a general function of voltage for both active an
 
 <div style="background-color:rgba(0, 0, 0, 0.0470588); text-align:center; vertical-align: middle; padding:4px 0;">
 
-$$P(V, f) = P(V) (1 + k_p\Delta f) $$
-$$Q(V, f) = Q(V) (1 + k_q \Delta f) $$
+$$P(V, f) = P(V) (1 + k_p\frac{\Delta f}{f_0}) $$
+$$Q(V, f) = Q(V) (1 + k_q \frac{\Delta f}{f_0}) $$
 </div>
 
-where $$k_p$$ and $$k_q$$ are the frequency variation coefficients for active and reactive power, respectively, and $$\Delta f = f - f_0$$ is the frequency deviation, with $$f_0$$ being the nominal frequency of the grid.
+where $$k_p$$ and $$k_q$$ are the frequency variation coefficients for active and reactive power, respectively, and $$\Delta f = f - f_0$$ is the frequency deviation, with $$f_0$$ being the nominal frequency of the grid. The deviation is scaled in per-untis with respect to the nominal frequency.
 
 ## Open source implementations
 

pages/models/loads/ExpLoad/index.md

@@ -21,8 +21,6 @@ The ZIP load model can be used for steady-state studies. The assumptions made fo
 * The total load can be represented as a function of the bus voltage by adding the three types of loads in a weighted polynomial.
 * The frequency is constant, and the load is balanced.
 
-The model does not take into account the time-response performance of the load, therefore it is not useful for dynamic studies.
-
 ## Model description
 
 ### Parameters

pages/models/loads/FDLoad/index.md

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pages/models/loads/ZIPLoad/index.md

@@ -0,0 +1,91 @@
+---
+layout: page
+title: Single-cage induction motor model
+tags: ["#200", "Induction motor", "RMS", "Dynawo", "Opensource"]
+date: 09/08/2024
+last-updated: 09/08/2024
+authors: Frédéric Sabot (ULB)
+reviewers: Lampros Papangelis (CRESYM)
+---
+
+
+## Context
+
+Motors are a particular kind of load that can account for a large share of the total load especially in industrialised countries. Adequate representation of motors is important, especially in short-term voltage stability studies as motors can cause fault-induced delayed voltage recovery. This page presents a single-cage induction motor model based on the textbook three-phase induction motor equivalent circuit [[1]](#1).
+
+## Model use, assumptions, validity domain and limitations
+
+The motor model can be used for short-term voltage stability studies. The assumptions made for this model are:
+
+* The rotor resistance is constant (no skin-effect or double-cage motors).
+* The motor is balanced.
+* The magnetic circuit is considered to be linear, neglecting saturation effects.
+* The mechanical torque varies as a constant power of the rotor speed (e.g. constant torque or quadratic torque).
+
+The model does not take into account transient and subtransient phenomena and is therefore not suitable for systems with a very large motor share (>50% of the total load) or to compute the short-circuit contribution from motors.
+
+## Model description
+
+The model is based on the equivalent circuit represented below.
+
+<img src="{{'/pages/models/motors/SimpleMotor/MotorEquivalentCircuit.drawio.svg' | relative_url}}" alt="Equivalent circuit of the induction motor"/>
+
+### Parameters
+
+| Parameter| Description | Unit | Typical value
+| ---| ---  | --- | --- |
+| $$\omega_s$$ | Synchronous speed | $$rad/s$$ | $$314rad/s$$ |
+| $$R_s$$ | Stator resistance | $$\Omega$$ | $$0.02pu$$ |
+| $$X_s$$ | Stator leakage reactance  | $$\Omega$$ | $$0.1pu$$ |
+| $$R_r$$ | Rotor resistance | $$\Omega$$ | $$0.02pu$$ |
+| $$X_r$$ | Rotor leakage reactance  | $$\Omega$$ | $$0.1pu$$ |
+| $$X_m$$ | Magnetising reactance  | $$\Omega$$ | $$3pu$$ |
+| $$J$$ | Moment of inertia | $$kgm^2$$ | 0.1 to 5s |
+| $$\eta$$ | Exponent of the torque speed dependency | Unitless | 0 to 3 |
+| $$C_{l, 0}$$ | Initial load torque | $$Nm$$ | N/A |
+| $$\omega_0$$ | Initial rotor speed | $$rad/s$$ | N/A |
+
+### Variables
+
+| Variable | Description | Unit |
+| --- | --- | --- |
+| $$V$$ | Stator voltage | $$V$$ |
+| $$I_s$$ | Stator current | $$A$$ |
+| $$I_r$$ | Rotor current | $$A$$ |
+| $$I_m$$ | Magnetising current | $$A$$ |
+| $$C_e$$ | Electrical torque | $$Nm$$ |
+| $$C_l$$ | Load torque | $$Nm$$ |
+| $$s$$ | Rotor slip | Unitless |
+| $$\omega$$ | Rotor speed | $$rad/s$$ |
+
+### Equations
+
+<div style="background-color:rgba(0, 0, 0, 0.0470588); text-align:center; vertical-align: middle; padding:4px 0;">
+
+<div style="font-weight: bold;">Electrical equations:</div>
+
+$$V = j X_m * I_m + (R_s + j X_s) I_s$$
+$$I_s = \frac{V}{(R_s + j X_s) + \frac{1}{\frac{1}{X_m} + \frac{s}{R-r + j X_r * s}}}$$
+$$I_s = I_m + I_r$$
+
+<div style="font-weight: bold;">Mechanical equations:</div>
+
+$$2 J  \frac{d\omega}{dt} = C_e - C_l$$
+$$s = \frac{\omega_s - \omega}{\omega_s}$$
+$$C_e = R_r * \frac{\left|I_r\right|^2}{\omega_s s}$$
+$$C_l = C_{l, 0} \left(\frac{\omega}{\omega_0}\right)^\eta$$
+
+</div>
+
+## Open source implementations
+
+This model has been successfully implemented in :
+
+| Software      | URL | Language | Open-Source License | Last consulted date | Comments |
+| --------------| --- | --------- | ------------------- |------------------- | -------- |
+|Dynawo|[Link](https://github.com/dynawo/dynawo/blob/master/dynawo/sources/Models/Modelica/Dynawo/Electrical/Machines/Motors/SimplifiedMotor.mo)| modelica | [MPL v2.0](https://www.mozilla.org/en-US/MPL/2.0/)  | 09/08/2024 | no comment |
+
+
+## Table of references
+
+<a id="1">[1]</a> Guru, B. S.; Warrier, R. K. "Electric Machinery and Transformers", 3th ed., New York, United States, 2001, Oxford University Press