Development of EMT components and reference grid in OpenModelica

IN

DEGREE PROJECT ELECTRICAL ENGINEERING, SECOND CYCLE, 30 CREDITS

STOCKHOLM SWEDEN 2021,

Development of EMT components and reference grid in OpenModelica

ALBA FERNÁNDEZ HORCAJUELO

KTH ROYAL INSTITUTE OF TECHNOLOGY

SCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Development of EMT components and reference grid in OpenModelica

AUTHOR: Alba Fernández Horcajuelo DATE: March 2021

HOST COMPANY: SuperGrid Institute

INDUSTRIAL SUPERVISOR: Laurent Chédot ACADEMIC SUPERVISOR: Ilka Jahn

EXAMINER: Staffan Norrga

School of Electrical Engineering and Computer Science KTH Royal Institute of Technology

Abstract

Power systems simulation tools enable to study and evaluate the performance of electrical power systems in different scenarios. This allows the development and implementation of new solutions to the challenges electrical grids face nowadays. In this sense, electromagnetic transient (EMT) simulation provides detailed information on the behaviour of the different components involved in the system. Moreover, among the wide range of existing tools, those based in Modelica language present certain advantages for power system simulation, such as equation­based modeling and the possibility of working in open­source environments.

This project presents the development of components and reference grid in EMT formalism in the open­source environment OpenModelica, based on Modelica language. With the purpose of power system simulation, electrical components have been modeled in OpenModelica and gathered in a library for EMT simulation

The performance of the different components has been validated by comparing the results of the EMT simulation of a 3­buses reference grid in different case studies in OpenModelica and other EMT­based software. Furthermore, the comparison has been also established with phasor simulation in OpenModelica, enabling the evaluation of the differences between phasor and EMT simulation.

The results show the main advantages and drawbacks of working with OpenModelica regarding other simulation tools and the lack of information provided by the phasor simulation, particularly in the case of a fault event. Additionally, certain difficulties encountered when working with OpenModelica have also been identified.

Keywords

Power system simulation, EMT simulation, Modelica, OpenModelica

Sammanfattning

Simulering av kraftsystem gör det möjligt att studera och utvärdera prestandan i olika scenarion. Genom detta kan utveckling och implementering av nya lösningar på de utmaningar som elnäten står inför framöver ske. Elektromagnetisk transient (EMT)­simulering ger detaljerad information om beteendet hos de olika komponenterna i systemet. Bland de många befintliga verktygen innehåller de som är baserade på Modelica­språket dessutom vissa fördelar för kraftsystemsimulering, såsom ekvationsbaserad modellering och möjligheten att arbeta i miljöer med öppen källkod.

Den här uppsatsen presenterar en utveckling av komponenter och test­elnät i EMT­

formalism i öppen källkodsmiljö OpenModelica, baserat på programmeringsspråket Modelica. Elektriska komponenter har modellerats i OpenModelica och samlats i ett bibliotek för EMT­simulering. Målet är en detaljerad simulering av elkraftsystem.

Komponenternas prestanda har validerats genom att jämföra resultatet av EMT­

simuleringen av ett 3­bussreferensnät i olika fallstudier i OpenModelica och annan EMT­baserad programvara. Sedan har jämförelsen även utförts med simuleringar i fasorformalism i OpenModelica. Den här jämförelsen har också möjliggjort utvärderingen av skillnaderna mellan fasor och EMT­simulering.

Resultaten visar de största fördelarna och nackdelarna med att arbeta med OpenModelica njämfört med andra simuleringsverktyg. De visar också bristen på information om fasorsimuleringen, särskilt i fallet med ett elektriskt fel. Dessutom har vissa svårigheter identifierats med att arbeta med OpenModelica.

Nyckelord

Kraftsystemsimulering, EMT­simulering, Modelica, OpenModelica

Acknowledgements

I would like to express my gratitude to SuperGrid Institute for giving me the opportunity to carry out this project with them. A special thank you to my supervisor, Laurent Chédot, and to all the team from Modeling and Simulation group. It has been a pleasure to work by their side.

I would also like to thank my academic supervisor, Ilka Jahn, for all her support and recommendations.

And finally, thanks to my family and friends, that have always been there for me either in person or from the distance.

Acronyms

DAE Differerential­Algebraic Equations EMT Electro­magnetic transient

HVDC High­Voltage Direct Current IEESGO IEEE governor model

MVDC Medium­Voltage Direct Current PI Proportional Integral

SI International System TGOV1 Turbine­governor model

Contents

1 Introduction

1.1 General context . . . 1

1.2 Context of the project . . . 2

1.3 Objectives . . . 3

2 About Modelica

2.2 Reference libraries . . . 6

2.2.1 Modelica Standard Library . . . 6

2.2.2 OpenIPSL . . . 7

2.2.3 ModPowerSystems . . . 7

3 Developed EMT library in OpenModelica

3.2 Transmission line models . . . 12

3.3 Transformers models . . . 14

3.4 Load models . . . 15

3.5 Generator models . . . 16

3.5.1 ModPowerSystems generator model . . . 16

3.5.2 OpenIPSL generator model . . . 18

3.6 Control models . . . 20

3.6.1 Simple control models . . . 20

3.6.2 Implementation of control models for comparison . . . 23

4 Reference grid: 3­buses

5 Validation of results

CONTENTS

5.1.1 Comparison with EMT reference . . . 28

5.1.2 Comparison with phasor reference . . . 29

5.2 Response to load loss . . . 31

5.2.1 Comparison with EMT reference . . . 31

5.2.2 Comparison with phasor reference . . . 32

5.3 Response to disconnection from the system . . . 33

5.3.1 Comparison with EMT reference . . . 33

5.3.2 Comparison with phasor reference . . . 34

6 Conclusions

6.2 Identified difficulties . . . 38

6.3 Future work . . . 39

References

Chapter 1 Introduction

1.1 General context

These days, we are living in a society in constant evolution and subject to significant changes, where the growing of energy demand, together with the traditional energy sources, are leading to an unsustainable situation. As a consequence, the way energy is produced and, in particular, electricity, is changing to adapt to the increasing need, but also to ensure sustainable development for the future.

In this context, the integration of renewable energies has gained in relevance and, at the same time, has presented some challenges that the traditional power grid needs to face. Some of these challenges are related to volatile electric power generation from renewable sources that can lead to unstable situations for the system. Moreover, the development of new technologies that enable this integration and improve the system, such as power electronics or High­Voltage Direct Current (HVDC) links, also lead to new scenarios.

Therefore, the study of the impact of these technologies on the power grid becomes really important to ensure the reliable and efficient operation of the system. When it comes to this study, especially to the reliability of the power grid, it is necessary to develop certain tools and methods that allow us to evaluate the behaviour of the system in these new scenarios without any risk for its integrity.

In this light, simulations of the electrical network and especially, those that allow to study its behaviour in detail, become indispensable to understand the dynamics of the

CHAPTER 1. INTRODUCTION

system and enable the development of the research in this domain. To this extent, Electro­magnetic transient (EMT) studies involve the simulation of the power systems at a high precision level [1] [2].

Moreover, in order to boost this development and the transition into the power grid of the future, the collaboration between different countries and stakeholders is a key element. For this reason, there is an increasing interest in the development of open­source tools, that would facilitate and promote this collaboration. Among these tools, those based on the Modelica language are gaining visibility in the power grid sector. This language, Modelica, has gained international recognition in the field of engineering in the past few years, being one of the most used and advanced declarative modeling languages [3].

1.2 Context of the project

This Master’s degree project has been carried out at SuperGrid Institute, as the final stage to complete a MSc in Electric Power Engineering at KTH Royal Institute of Technology.

SuperGrid Institute is an independent research and innovation centre dedicated to the development of technologies for the future power transmission system, the “supergrid”, including HVDC and Medium­Voltage Direct Current (MVDC) technologies. It presents a multi­disciplinary approach providing a wide range of services and solutions for the development of power systems, equipment and components, thanks to its comprehensive expertise but also to advanced simulation capabilities and test platforms.

In this framework, SuperGrid Institute presents different research programmes such as SuperGrid Architecture and Systems, which specializes in system architecture to allow the integration of intermittent renewable energy sources, while ensuring network security and stability. Other programmes focus on high voltage substation equipment, power electronics and converters, HVDC cable systems and junctions and power storage and balancing.

This project has been developed within the scope of Architecture and Systems program, where most of the activities are based on advanced power system simulation models and tools, required for the research in the field of power transmission systems. In many

CHAPTER 1. INTRODUCTION

cases, such models and tools must be developed, implemented and validated to adjust to the research process. This project in particular is framed in the research activities of the Modeling and Simulation group, whose objective is to develop accurate simulation models and platforms to study HVDC grids. To this extent, the simulation of HVDC grids and hybrid AC­DC grids is complicated since they are based on power electronics converters and their control systems, which accurate modeling is complex.

1.3 Objectives

The objective of the internship proposed by SuperGrid Institute is to develop reference models, components and grid, in the electromagnetic­transient formalism, EMT, in Modelica language, in particular, in the open­source environment OpenModelica. To this end, reference grid models in phasor formalism and in other EMT environments are used for comparison and validation.

To accomplish the main objective, different targets are pursued:

• Study of Modelica language and development of modeling skills in OpenModelica

• Study of the reference model and libraries in phasor formalism

• Study of EMT models for the different components of the reference network

• Development of the EMT model in OpenModelica according to the reference

• Validation of the new model through its comparison with the reference phasor model and an equivalent model in developed in a different EMT­based software

• Extension of the model.

Chapter 2

About Modelica

The objective of this project is to develop an EMT model, components and grid, in the open­source environment OpenModelica, based on the language Modelica. Therefore, as a first step, it becomes necessary to provide an approximation to this language.

2.1 Modelica language

Modelica is a declarative object­oriented language for modeling physical systems with the purpose of efficient simulation. Their main characteristics are [4][5]:

• Equation­based language, enabling acausal modeling. Components are directly modeled by the equations that govern their physical behaviour. The model dynamic behaviour is not described with a predetermined input­to­output data flow, but with a set of time­varying Differerential­Algebraic Equations (DAE) and discrete equations. Since the equations do not specify a certain data flow direction, acausal modeling gives better reuse of model components, that can be adapted to different data flow contexts.

• Object­oriented language based on the notion of class. Objects in Modelica have a class that defines their data and behaviour. Classes allow to model components that can be reused in more complex models, providing hierarchical structuring.

• Multi­domain modeling capability enabling to model components corresponding to objects from different domains such as electrical, mechanical, hydraulic or thermodynamic for example, and its interactions. This is possible thanks to the

CHAPTER 2. ABOUT MODELICA

notion of connector, a specific kind of class that provides an interface between models, even if they come from different domains.

• Continuous and discrete event modeling, allowing to introduce discrete changes or events during the simulation of a continuous physical system. This brings the possibility of modeling hybrid systems, that contain both continuous and discrete parts.

These characteristics present some advantages for power systems modeling. The declarative formulation allows to set the focus on the content of the model rather than on the way it should be computed and problem­solving strategies [3]. On one hand, the equation­based modeling of the power systems components present the full implementation of the model in an understandable and usable way for power system stakeholders, not necessarily familiarized with the solving algorithms.

On the other hand, the separation between the modeling and the solving parts facilitate the exchange of models and ensure its flexibility. The increased complexity of power system dynamics and the growing number of interconnections between different power systems make necessary the collaboration between different actors in these systems. In this context, this decoupling is interesting because it brings the possibility to exchange predefined models, parameters and equations in a standard modeling language [6].

Moreover, the Modelica language needs an environment to be transformed into executable code and be able to run simulations. These environments could be commercial, or open­source, as it is the case of OpenModelica. Open­source tools and software present advantages compared to commercial tools when it comes to these possibilities of sharing models and collaborating in their development.

Also, Modelica enables the graphical definition of complex networks. The use of the graphical editor to develop simulations and connect the models for the different components definitely stands as an advantage when it comes to the modeling of large networks. However, the large number of equations appearing when simulating large systems is one of the main drawbacks for this paradigm, and the performance of full Modelica environments for solving complex power systems might be question [6].

CHAPTER 2. ABOUT MODELICA

2.2 Reference libraries

When it comes to power system simulation with OpenModelica, there are several libraries, developed by different research groups all over the world, that include models for electrical components, from simple passive devices to complex control schemes.

The objective of this section is to offer a review of certain parts of some of these libraries that will be used as a reference for the development of new components in EMT formalism.

2.2.1 Modelica Standard Library

This library is developed together with Modelica language by the Modelica Association, and it provides constants, types, connectors and components models from different fields, such as electrical, mechanics, magnetic or thermal. It also includes interdisciplinary blocks for graphical modeling and complex math functions.

Even though it is a large library, in this project the focus will be set on the electrical sublibrary, presented in Fig. 2.2.1, which includes components for the simulation of electrical networks in different contexts. For EMT simulation, the components enabling multi­phase modeling stand out as an interesting reference [7].

Figure 2.2.1: Detail of Modelica Standard Library: Electrical sublibrary, multiphase

CHAPTER 2. ABOUT MODELICA

2.2.2 OpenIPSL

OpenIPSL stands for ”Open­Instance Power System Library” and was developed out of the iPSL, ”iTesla Power System Library”, an open­source modeling library created in the framework of the ”iTesla” project. This project, funded by the European Commission, took place between 2012 and 2016 and aimed at reducing the dependency of the power system model from the power system simulation tool. The library was conceived to include power system components models for phasor time­domain simulations based on reference models used in other power system tools, enabling the comparison with them [8], [9].

When the ”iTesla” project ended, some of the developers of this library, in particular, those attached to the SmartTS Lab from KTH, decided to continue contributing to this development and created OpenIPSL, which not only aims at providing reference models but also test networks compatible with OpenModelica, to use in research and teaching [9], [10].

One of these test networks, KundurTwoAreas and its further developments, has been used as a reference for the study of the OpenModelica environment and different electrical components in phasor formalism. Therefore, some of the models developed in the framework of the OpenIPSL library will be used as a reference for their translation into EMT component models. Fig. 2.2.2 shows different parts of the Electrical package of OpenIPSL library.

Figure 2.2.2: Detail of OpenIPSL: Electrical package

2.2.3 ModPowerSystems

ModPowerSystems is a library developed by the Institute of Automation of Complex Power System, in the E.ON Energy Research Center from RWTH University Aachen,

CHAPTER 2. ABOUT MODELICA

in Germany. It includes power system models in static phasor formalism, dynamic phasors and EMT [11],[12], providing reference models that can be used as a base for more complex components.

As presented in Fig. 2.2.3, this library is divided into different packages for single­

phase modeling or three­phase modeling for each formalism, where the components are included in different sections such as slack, loads or generation, together with some examples modeling simple networks.

Another interesting part of this library is the Interfaces package, which includes different connectors classes that enable to connect components models depending on whether they are modeled in phasors or EMT, in single or three­phase. Those connectors used to interface components modeled in phasor formalism define the electrical variables for voltage and current as complex variables, whereas those used in EMT modeling handle voltage and current as real variables. This difference in the way the electrical variables are defined is a good example of the reason that prevents using components modeled with different connectors in the same network, avoiding the re­utilization of components from different libraries in the EMT development of reference grids.

Moreover, some of the components included in this library, such as the synchronous generator, are modeled according to the equations of [13], and stand out as useful references for the EMT components development, since [13] is also used as a reference for the models in other EMT software platforms [14].

Figure 2.2.3: Detail of ModPowerSystems library: Base package

Chapter 3

Developed EMT library in OpenModelica

A new library for EMT modeling of power systems has been developed in OpenModelica, based on the models and reference libraries previously presented.

It has been considered more interesting to directly use the components from the reference libraries when possible and adapt them to the requirements of the new modeling schemes, rather than to duplicate elements that were already developed.

The EMT library is structured according to the different sets of components needed for power systems simulation and will be described in general terms.

3.1 Basic components models

The first step in the development of this new library is the choice of the connector that will be used to interface the components since it includes the definition of the electrical variables. In Modelica Standard Library, the connector used to interface multi­phase components is called Plug and enables to work with three­phase voltage and currents in International System (SI) units. This will be the connector class used in EMT modeling.

The compatibility with the connector class allows using other components from the Multi­phase package from Modelica library, such as the models for passive elements.

These components models, in particular those for the resistor, inductor and capacitor,

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

will be directly extended from Modelica library in the developed library.

The second step in the development of this library is the creation of a model that allows setting the base values of the system regarding the base power and the frequency. This model is called System and is defined with the prefix inner. This Modelica functionality enables to refer to the parameters included in System, such as the frequency of the grid, in a separate model by addressing the System component with the prefix outer. This is interesting when developing models for large networks, to ensure the same system base in all components.

Figure 3.1.1: Detail of developed EMT library: Basic package

Some other basic models of the developed library are the buses, included in the package with the same name. The bus bar is used for measurement in high voltage grids and, in the case of the simulation in OpenModelica, can be used to set the initial values of the voltage magnitude and angle, if known from a previous load flow study. In large networks studies, the initialization of certain voltage levels at the bus bars can become necessary to perform the simulation.

The basic bus model includes certain functions from Modelica Standard Library that enable to measure the voltage values to validate the results. First, the quasiRMS function allows to obtain the RMS value of the three­phase voltage of the bus. Second, the function ToSpacePhasor, from the Machines models in Modelica Electrical package, allows to transform the three­phase voltage into phasor form according to

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

the following equation:



 v_real v_imaginary



 = 2/3 ·



 1 cos(^2π₃ ) cos(^4π₃ ) 0 sin(^2π₃ ) sin(^4π₃ )



 ·





 v_A v_B vC





 (3.1)

where v_realand v_imaginary are the real and imaginary components of a certain variable in phasor form, and v_A, v_B and v_C are its value at each phase.

Finally, in order to measure the voltage angle, calculated as the arctan of the ratio between the imaginary and the real components of the voltage, it is necessary to perform a rotation to obtain these components in a rotatory reference, i.e. rotating at the same angular speed of the system. As a first approach, it will be considered that the voltage rotates at the angular speed of the system. The validity of this assumption will depend on the system frequency, whose deviation from the reference will be minimized by the control models. Therefore, the real and imaginary components of the voltage will be rotated with the function Rotator from Modelica Standard Library as:



 v_real′

vimaginary^′



 =



 cos(−θ) −sin(−θ) sin(−θ) cos(−θ)



 ·



 v_real vimaginary



 (3.2)

being θ the product of the system angular speed by the simulation time, v_real and v_imaginary the real and imaginary components of the voltage in stationary reference and v_real′ and v_imaginary′ the real and imaginary components of the voltage in rotatory reference.

The Buses package includes also a model for an infinite bus, slack bus or swing bus.

This component performs as a perfect voltage source, also allowing to set the voltage magnitude and angle. It is used to balance the active and reactive power in the system during the simulation, absorbing or emitting power according to the requirements of the load flow. In the model developed, the estimated values of the power exchanged by the infinite bus can be used to initialize the power and the currents flowing through the plug connecting the bus to the system.

Finally, a model for a breaker, partially based on the breaker model from ModPowerSystems reference library, has been also included. The breaker model presented enables to disconnect a certain part of the system at the established time,

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

t1, and to reconnect at time t2. To avoid numerical problems during the simulation, it presents a certain resistance value, both when it is open or closed, having a non­ideal behaviour.

3.2 Transmission line models

In order to model the transmission lines, the equivalent π circuit has been developed according to [13]. Fig. 3.2.1 shows the reference for the definition of the electrical variables, being −→v1 and −→v2 the voltage and −→

i1 and−→

i2 the current in the sending and receiving ends, called 1 and 2 respectively. P₁₂and Q₁₂are the active and reactive power injected at the end 1 of the line and P₂₁and Q₂₁those injected at the end 2.

This nomenclature has been chosen to facilitate the comparison with the reference library OpenIPSL regarding the power flowing in the lines, named with the sub­indices 12 and 21. However, it might differ from the nomenclature used in [13] and in Modelica Standard library.

Figure 3.2.1: Equivalent π circuit of a transmission line

The Lines package of the library includes three developments for the line model according to this circuit. In the first approach, shown in Fig. 3.2.2, the model has been built using the graphical interface of OpenModelica, by dragging the passive components to build the circuit and connecting their ends. The parameters for the line resistance, inductance and capacitance can be modified and expressed regarding the line length.

In the second approach, Fig. 3.2.3, the same model has been built but this time, using the text interface, where the equations describing the behaviour of the components are directly written in this interface. The behaviour of the line model is the same, but in this version, the variables and equations are explicitly defined in the line model, whereas in the previous development, each passive component was independently defined. By

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

Figure 3.2.2: Diagram view for π line graphically modeled in OpenModelica

defining the behaviour of the line through equations more flexibility is obtained since it is possible to access to each variable, but on the other hand, the independence and modularity of the circuit components are lost. This stands out as a good example of the different ways of working with Modelica. Fig. 3.2.3 shows the graphical interface of OpenModelica in this case. In contrast with Fig. 3.2.2, the diagram for the model based on equations offers no information of the line layout. To have access to this information, it would be necessary to go through the model equations, which might be less straight forward than directly observing the diagram.

Figure 3.2.3: Diagram view for π line modeled by equations in OpenModelica

In both these models, it has only been considered the self­reactance and admittance of the line. The third version of the line model merely presents a modification to include also the mutual components of the reactance by redefining the dimension of the parameters into a matrix form.

Also, the Lines package includes a simple component called LineParameters that enables to transform the data for the parameters into the expected units, facilitating the

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

comparison with phasor grids, where all the parameters are expressed in per unit.

Moreover, in order to calculate the value for the active and reactive power injected into the line, e.g. P₁₂and Q₁₂, the three­phase voltage and current variables are transformed into phasor form, so it is possible to use their real and imaginary components. The only objective of this transform, performed using the function ToSpacePhasor and shown previously in equation 3.1, is to calculate the real and imaginary components of the apparent power injected in the line, thus the active and reactive power. However, this calculation would not provide the actual values in an unbalanced system. For a balanced power system, the values for the active and reactive power, P and Q, are calculated as:

2/3· P = vreal· ireal+ v_imaginary · iimaginary (3.3) 2/3· Q = −vreal· iimaginary+ v_imaginary· ireal (3.4)

This way, using the variables for the voltage and current at the sending end, −→v_s and−→ i_s respectively, it is possible to calculate the active and reactive power injected at p, P₁₂ and Q₁₂, and using the voltage and current at the receiving end, −→v_r and−→

i_r, the power injected at n, P₂₁ and Q₂₁, are calculated. The same procedure to calculate the active and reactive power will be further used for the calculation of power injected or absorbed from the grid in the generator or loads models respectively, thanks to the three­phase voltage and currents exchanged in the connector in these models.

3.3 Transformers models

The Transformers package include simple models from transformers, from an ideal transformer to more complex models including a resistor and an inductor to represent the impedance at the primary or secondary windings. In the ideal transformer, the voltage and current arriving at the primary end of the component are respectively multiplied or divided by the ratio between the voltage at the primary and the secondary windings.

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

3.4 Load models

In the Loads package of the developed library, three basic models for load are included:

RL series, RC series and RLC parallel. These three models present the same scheme where the active and reactive power absorbed by the load is used together with the voltage at the connection point, to calculate the value of the passive component parameters, i.e. the value for R, L and C. This is the same scheme used in the model for ZLoad in [11].

(a) RLC load (b) RC Load (c) RL Load Figure 3.4.1: Load models in OpenModelica

To calculate these values, the sign criteria is established so positive values for the power means absorbed power. Therefore, the value of the active power will be always positive but for the reactive power, it will have a positive value for the RL load and a negative value for the RC load. In the case of the RLC load, an if­statement is included in the code so when the reactive power has a positive value it will behave as a parallel RL load and otherwise, as a parallel RC.

Another important aspect presented in the load models is the initialization of the variables for voltage and currents. The data obtained from a previous power flow analysis, carried out with a software different than OpenModelica, enable to obtain the expected values for the voltage magnitude and angle at the bus, i.e. at the point where the load is connected to the system. Thanks to these data, the initial value for the voltage at each phase can be calculated. Then, with the values from the absorbed power at the load from the power flow analysis, the initial values of the current are also calculated with the equations 3.3 and 3.4. The initialization of the voltage and current variables with the data from the power flow at the connector facilitates finding the expected solution in steady­state when running the simulation. Depending on the model, it can be necessary to provide the correct initial values to find any solution.

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

Without adequate initial values, the simulation can face problems related to numerical stability.

This package also presents a model for RL or Z load with voltage curtailment according to the component developed in the OpenIPSL reference library, based on the static load model from [15]. In this case, the voltage magnitude at the connection point is introduced in a voltage characteristic function that enables to curtail the power demanded by the load for low voltage values. Also, it enables to set certain parameters to define whether constant power load characteristic, constant current or constant admittance load characteristic is used to model the behaviour of the load. This way it is possible to compare with one of the phasor load models included in OpenIPSL, presented in appendix A, whose behaviour will differ otherwise, particularly in case of an event.

3.5 Generator models

There are two generators models included in the developed EMT library, based on the existing models from ModPowerSystems reference library and OpenIPSL.

3.5.1 ModPowerSystems generator model

In the reference library ModPowerSystems [11], in the package Generation from the section for EMTThreePhase, it is possible to find a model called SynchronousGenerator_FullModel whose equations describe the behaviour of a synchronous generator according to [13]. This is a complete model that calculates the output for the generator from the mechanical power and the value of the excitation voltage for certain operating conditions. It models the generator behaviour under steady­state conditions, neglecting the response to transitory events and saturation.

The variables for voltage and current in the stator of the generator are expressed in p.u. in the rotatory reference of the rotor, therefore in the DQ reference. The different equations to calculate the electrical variables in the generator are also in the same reference, enabling to distinguish between those variables in the d­axis and those in the q­axis. In order to calculate the voltage and the current variables in the stator in the three­phase stationary reference of the system, the following transformation from

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

[13] is performed to change the reference from the two­components rotatory reference to the three­phase stationary reference:



vd

v_q



 = 2/3 ·



 cos(θ) cos(θ−^2π₃ ) cos(θ + ^2π₃ )

− sin(θ) − sin(θ − ^2π₃ ) − sin(θ +^2π₃ )



 ·





 v_A v_B v_C





 (3.5)

where v_dand v_q are components of the voltage in DQ reference in p.u., v_A, v_B and v_C the voltage components in three­phase reference and θ is the rotor angle in electrical radians, i.e. the position of the rotor at each instant regarding the stationary reference.

The values of v_A, v_B and v_C are later changed to SI units in order to be coherent with the rest of the components of the system. The same transformation is performed for the currents.

Regarding the parameters for this generator model, such as the value of the resistances and inductances for stator and rotor, the default parameters from ModPowerSystems are kept in the first instance, even though they can be easily modified during the model implementation. These default parameters refers to the example 3.2 from [13], where the p.u.values for resistances and inductances are given for a 24 kV generator of 555 MV A.

As explained for the load model, it is necessary to initialize certain variables to find a solution when many components are involved in the simulation. For this reason, all the variables in the model are initialized with the values for voltage and generated power obtained thanks to a previous power flow analysis. With these values and the set of equations for the steady­state behaviour of the generator, i.e. for constant angular speed, the initial values are calculated and used as parameters that can be forced to be the value of the correspondent variables at the beginning of the simulation.

Nevertheless, in most cases, these initial values are used as a mere indication to help finding the desired solution.

Aiming at using the generator from ModPowerSystems with the minimum amount of changes possible, the SynchronousGenerator_FullModel is extended into a new model in the developed EMT library, called BaseSyncGen, where all the variables and parameters are kept, but it is possible to include certain outputs blocks to monitor certain variables. Thanks to these outputs, it will be possible to use the variables from the generator model in the control schemes.

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

Even though this generator model enables to simulate simple reference grids, its simplicity prevents a reasonable comparison with the components modeled with the phasor paradigm from the OpenIPSL library or with those developed in other EMT environments such as [14]. On this account, a more complex model for the generator will be presented in the following section.

3.5.2 OpenIPSL generator model

OpenIPSL library includes several models for synchronous generators, modeled accordingly to different references, such as [16]. The main advantage of this way of modeling is the possibility of comparing them with the original models in these other environments. In this sense, the implementation of OpenIPSL generator models in the developed EMT library not only offers the chance of comparing them with OpenIPSL phasor components but also with the original references. However, as previously mentioned, the connector used in OpenIPSL components only enables simulations in the phasor paradigm. For this reason, it is necessary to adapt the generator model to EMT.

Among the wide range of options for the generator that could be used as a reference for this adaptation, the focus has been set in a model for round­rotor generator called GENROU, from [16], presented in the package Machines from the Electrical section of OpenIPSL library. The reason for this choice is that this is the generator used in some of the phasor reference grids later used for the comparison with EMT.

In this case, it is not possible to extend the generator model from the original library as with ModPowerSystems generator because further changes need to be done regarding the reference for voltage and current in the terminals of the generator. In OpenIPSL models, the generator is connected to the system by a specific type of connector whose information regarding voltage and currents exchanged refers to the phasor paradigm. In the developed model in EMT, the generator will be connected to the system by a connector type Plug. Therefore, the stator voltage and current in DQ reference, i.e. in the rotatory reference of the rotor, not only will need to be rotated to the system reference, as they already are in the phasor generator model but also transformed from a two­components to a three­phase stationary reference. This way, to the rotation transform already performed in the original model, shown in equation 3.6, an additional transformation as the one shown in equation 3.1 will be implemented

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

in the code.



 vreal

v_imaginary



 =



 cos(θ− ^π₂) −sin(θ − ^π₂) sin(θ−^π₂) cos(θ−^π₂)



 ·



vd

v_q



 (3.6)

where v_d and v_q are the components of the stator voltage in DQ reference, v_real and v_imaginary are the real and imaginary components of the voltage expressed in phasor form and θ in the position of the rotor in electrical radians regarding the stationary reference of the system. The same transform will be also performed for the stator currents.

At this point, it is necessary to mention that in the original phasor model from OpenIPSL, the system reference is still a rotatory reference. However, for EMT simulation, the system reference will be stationary, so it is possible to see the variation of the electrical variables at the system frequency. This is the main difference regarding the generator model in phasor and EMT. The rest of the equations from GENROU model, from OpenIPSL library, have been kept unchanged in the EMT model, making possible the comparison between the two paradigms.

These equations are those from [16], indicating the d­axis and q­axis. This is interesting because it allows observing that these diagrams are very similar to those presented in other EMT software, as [14], facilitating the comparison of the performance of these components with those developed in OpenModelica.

Also in the case of this generator model, all the variables presented in the equations are initialized with the values calculated for the steady state solution at certain operating conditions. Therefore, it is necessary to perform a previous power flow analysis to know the value of the voltage angle and magnitude and the expected active and reactive power generated.

Regarding the parameters for this model, in the first instance, those from the example 4.1 from [13] for a 555MVA generator are introduced, except for the values to parameterize the saturation curve, which is included in this model. Here the default parameters from OpenIPSL are kept. Nevertheless, all these parameters can be easily modified for each case study.

As done for the previous case, certain output blocks are included in the generator model so the information regarding certain outcomes such as the frequency, the speed

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

deviation or the voltage magnitude at the generator terminal can be used for the control.

3.6 Control models

This package refers to the control blocks used in the control of the synchronous generator, both for frequency and excitation voltage control. As a first approach to the control scheme of the generator simple models were developed. Then the parameters from more complex schemes included in the library OpenIPSL were adapted for the parameters of the generator model.

3.6.1 Simple control models

First, for the frequency control, the model Freq_Control presents a simple control scheme with the following behaviour:

P_m = P_ref + K_gain(f_ref − f) (3.7)

where P_m is the mechanical power provided to the generator, P_ref is the reference mechanical power input, K_gainis a constant modeling the gain of the controller, f_ref is the reference frequency, generally the system frequency, and f is the actual frequency value at the generator windings. K_gainwill set the dynamics of the frequency controller, and as the first approach, it has been set as^Pnom_0.2^/3, being P_nomthe nominal power of the machine in W and 0.2 a threshold for the frequency deviation. Since P_nomis expressed in W, also the mechanical power reference should be introduced in W.

According to the equation 3.7, if the frequency of the currents in the stator of the generator is higher than the system frequency, there will be a reduction of the mechanical power introduced as an input to the generator regarding the reference power, aiming at reducing the electrical speed of the current. Therefore, this simple scheme allows stopping the frequency drop when there is a variation of the charge or the generation in the system.

Regarding the excitation voltage control, in a first step of the development of the library, Proportional Integral (PI) control blocks for Modelica Standard Library were implemented by adjusting the parameters according to those of the generator.

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

(a) Icon view (b) Diagram view

Figure 3.6.1: Frequency control block in OpenModelica

However, the behaviour achieved by implementing this type of controller is very limited and the response obtained differs from the expected values. For this reason, a more specific control scheme was developed. This is the IEEE AC4A exciter control model, from [13]. This model has been implemented in OpenModelica using certain blocks from OpenIPSL library to model the behaviour, such as a simple lagging with limiter.

The type AC4A exciter model represents an alternator­supplied controlled­rectifier excitation system whose parameters have been determined according to the sample data for the exciter and regulator from [13]. Therefore, to evaluate the response of the generator model developed, the time constant of the controller, T_Awill be set in 0.04s and the overall gain K_A, in 200. Since the load compensator will not be used in this case, the voltage at the terminal of the generator will be the input of the exciter control model, whereas the voltage reference will be calculated as:

V_R= E_{f d}/K_A (3.8)

where V_Ris the voltage reference in p.u., K_Athe overall gain and E_{f d}the reference value of the field voltage in steady­state in non­reciprocal p.u. system, for a certain operation point [13]. The output of this scheme will be the value of the excitation voltage in non­

reciprocal p.u. that will be introduced as an input for the generator, with the pertinent adjustment of p.u. system if necessary.

The development of these simple control models enables to include both control loops,

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

Figure 3.6.2: AC4A control model

for the frequency and for the exciter, in the generator models previously presented.

This stands as a first step in the development of a generator model in EMT that allows the comparison between phasor and EMT simulation in OpenModelica and also with other EMT environment. Fig. 3.6.3 shows the complete model of a generator type GENROU, with Freq_Control and AC4A exciter control loops. For the first loop, the mechanical power in steady­state and the frequency of the stator currents are the output of the generator model and the input for the control, whereas, for the second control loop, the value of the magnitude RMS line­to­line voltage at the terminals of the generator together with the field voltage in steady­state are the inputs for the control model.

Figure 3.6.3: Generator model with simple frequency control and AC4A exciter control

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

3.6.2 Implementation of control models for comparison

The second step toward the comparison both with phasor and with other EMT environments is the implementation of control models that present the same behaviour of those in phasor or in EMT. At this point, it becomes interesting to use those control blocks already developed in OpenIPSL library and adapt their parameters, since they are not exclusively modeled for phasor simulation.

First, for the frequency control, the simplest steam turbine models found in OpenIPSL library have been studied and their parameters have been adapted for the generator model. These are the Turbine­governor model (TGOV1) and the IEEE governor model (IEESGO), developed according to [17]. The overall gain in both cases has been adjusted to be ^Pnom_0.2^/3 as in the simpler frequency control model. However, when working in p.u., P_nomis considered as 1 p.u.

(a) TGOV1

(b) IEESGO

Figure 3.6.4: Steam turbine models from OpenIPSL library

Then, for the excitation voltage control, the parameters for the model Simplified excitation system model, developed in OpenIPSL according to [16], have been modified to represent the same behaviour as the simple model previously described.

The Simplified excitation system model is particularly useful when the excitation system must be represented but its detailed design is not known, and it has been

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

already implemented in some phasor grid designs in OpenIPSL reference.

Figure 3.6.5: Simplified excitation system model

Finally, an additional exciter control model has been developed to be able to compare with other EMT environments. In this case, the software used for this comparison will be Hypersim, which allows to simulate complex grid models in EMT formalism [14], [18]. The proposed control scheme is similar to the one shown in Fig. 3.6.2 and the parameters have been modified to represent the same behaviour, but its design allows a direct comparison with the generator in Hypersim [14], which include an internal excitation voltage control with the same scheme.

Figure 3.6.6: Exciter control adapted from Hypersim

The implementation of these control models together with the developed generator model allows having different options and combination for the simulation of EMT grids. Regarding the comparison with the phasor model, the generation scheme shown in Fig. 3.6.7a stands out as the most interesting, whereas for the comparison with other EMT software, the one in Fig. 3.6.7b will be generally preferred. However,

CHAPTER 3. DEVELOPED EMT LIBRARY IN OPENMODELICA

the parameters in both cases have been modified to represent the same behaviour, therefore the solution of the simulation in steady­state will be the same.

(a) IEESGO and simplified excitation system control

(b) TGOV1 and exciter adapted from Hypersim control

Figure 3.6.7: Generator model with different control combinations

Chapter 4

Reference grid: 3­buses

The case study used to evaluate the performance of the developed components is a simple grid with 3 buses and 3 transmission lines connecting one generator and one RLC Load to an infinite bus as seen in Fig. 4.0.1. The utilization of this case study is motivated by its simplicity, since it allows observing the behaviour of most of the component developed, interacting in a simple grid.

In this case, system base power has been set in 100 MV A and the system frequency to 50 Hz. The base voltage at the transmission level is 138 kV, whereas for the generator, connected to bus 2 through an ideal transformer, it is 24 kV. Table 4.0.1 shows voltage magnitude and angle at each bus together with the power exchanged with the grid in this bus, obtained from a power flow analysis performed in Hypersim. These values are used to initialize the different components. Notice that positive values for active and reactive power stand for the power injected in the bus.

Table 4.0.1: Power flow data for 3­buses case study

BUS V[pu] angle[°] P[MW] Q[MVar]

1 1 0 308 ­81

2 1.05 ­2.07 200 267

3 0.98 ­8.79 ­500 ­100

Table 4.0.2 present data for reactances of the lines, modeled according to the π equivalent with zero value for the shunt admittance. The values for R and X are the same for lines 12 and 13 and differs in the case of line 13. Since the data for the reactances are presented in per unit, a small block called LineParameters has been

CHAPTER 4. REFERENCE GRID: 3­BUSES

included in the model to calculate the values in SI units by using the base values for voltage and power. Table 4.0.2 also shows the power injected at each end of the line, where P₁₂and Q₁₂stand for the power injected at one end of the line whereas P₂₁and Q₂₁ for the power injected at the opposite end. For example, for line 23, P₁₂ is the power injected into the end connected to bus 2 flowing towards bus 3 and P₂₁ is the power injected into the end connected to 3, flowing towards 2. Notice that the naming convention 12 has also been used for the name of line 12.

Table 4.0.2: Lines reactances and power exchanged

LINE 12 13 23

R [pu] 0.0047 0.0062 0.0047

X [pu] 0.0474 0.0632 0.0474

P12 [MW] 69 239 268

P21 [MW] ­68 ­236 ­264

Q12 [MVAr] ­111 29 148

Q21 [MVAr] 119 7 ­107

Figure 4.0.1: 3­buses grid in OpenModelica

Chapter 5

Validation of results

To validate the performance of the models for the different components developed in OpenModelica, a comparison with the phasor reference grid in this environment and with other EMT­based environments will be performed. First, the comparison will be established for steady­state values, where the deviation between certain variables and the original power flow values used for their initialization will be measured. Second, the response to fault events will be also studied.

5.1 Deviation from reference values in steady­state

First step in the validation of the components developed in OpenModelica will be the comparison of the solution reached in steady­state with other EMT simulation environments and with phasor simulation. The achievement of the same values in steady­state in the EMT simulation in OpenModelica will allow to verify the proper behaviour of the different components.

5.1.1 Comparison with EMT reference

The 3­buses case study shown in Fig. 4.0.1 will be simulated in Hypersim and OpenModelica. The control schemes used for the generator will be those of Fig. 3.6.7b and the parameters, shown in B.1, will be the same in both cases to validate the results.

Once the simulation reaches the steady­state values, these will be gathered and the error between them will be calculated according to equation 5.1, where X_Hypersimare the values obtained in Hypersim, used as a reference, and X_{EM T 1}are the values obtained

CHAPTER 5. VALIDATION OF RESULTS

from simulation with OpenModelica. These reference values are used to initialize the different components in the OpenModelica simulation, therefore, the error obtained allows to measure the final deviation from the desired solution.

error_X[%] = XHypersim− XEM T 1

X_Hypersim · 100 (5.1)

Table 5.1.1: Deviation from Hypersim in steady­state for 3­buses case study in EMT BUS error_V[%] error_angle[%] error_P[%] error_Q[%]

1 0 0 0.66 1.33

2 0.02 1.21 0 0.07

3 0.04 0.47 0.33 0.33

In order to validate the behaviour of the model, Fig. 5.1.1 presents the values for phase A of the three­phase current flowing into each of the lines of the grid. The similarities for the values in a certain instant of the EMT simulation allow validating the behaviour of the developed components in a steady­state.

Figure 5.1.1: Comparison between Hypersim and OpenModelica of currents flowing into the lines in steady­state for 3­buses reference grid

5.1.2 Comparison with phasor reference

In this section, a similar comparison has been established to compare the performance in EMT of the 3­buses reference grid with the phasor simulation in OpenModelica.

CHAPTER 5. VALIDATION OF RESULTS

To be able to compare with the phasor model of the reference grid, the model from Fig. 4.0.1 has been simplified by removing the transformer between the generator and bus 2. This change is motivated by the absence of the transformer in the phasor version of the grid, where all the variables are expressed in per unit formalism. Also, for this comparison, the generator model has been changed and the control blocks shown in Fig. 3.6.7a have been used, also with the default parameters.

Once the simulation of the 3­buses reference grid in phasor formalism and in EMT in OpenModelica has reached the steady­state, the values obtained are evaluated. With this purpose, the error between these values has been calculated as:

error_X[%] = Xphasor− XEM T 2

X_phasor · 100 (5.2)

where X_phasor are the values from the phasor simulation and X_{ET M 2} the values from the EMT simulation, which slightly differ from X_{ET M 1}because of the different control blocks employed. The results are shown in table 5.1.2.

Table 5.1.2: Deviation from phasor simulation in in steady­state for 3­buses EMT simulation in OpenModelica

BUS error_V[%] error_angle[%] error_P[%] error_Q[%]

1 0 0 0.30 0.41

2 0.01 0.52 0 0.25

3 0 0.22 0.18 0.01

In this case, due to the difficulty of comparing voltage and current expressed in phasor and EMT formalism, table 4.0.1 shows the deviation in the power injected into the lines in the EMT simulation regarding the flow in the phasor simulation.

Table 5.1.3: Deviation in power injected into the lines in steady­state for 3­buses case study in EMT in OpenModelica

Line error_{P 12}[%] error_{P 21}[%] error_Q12[%] error_Q21[%]

12 0.57 0.57 0.29 0.32

13 0.21 0.21 0.03 2.18

23 0.14 0.14 0.19 0.16

The low values obtained for the errors, both in tables 5.1.2 and 5.1.3 allow to validate the performance of the EMT simulation. In the case of the power injected into the lines,

CHAPTER 5. VALIDATION OF RESULTS

since the error values presented in table 5.1.3 are kept constant at both ends of the line for the active power, these results could lead to think that the main differences found between the phasor and the EMT solution come from the behaviour of the inductive part of the transmission line, since there is a slight difference in the consumption of reactive power in the lines. This difference is more noticeable in the case of the reactive power injected in line13 flowing from bus 3 to 1, Q₃₁, since the calculated values stand for the relative error. The magnitude of the deviation in absolute terms for Q₃₁ does not represent a significant deviation regarding other lines, but due to the low value expected for Q₃₁, of 7.62 MVAr in the phasor simulation, the value obtained for the error is significantly higher in this case.

5.2 Response to load loss

Aiming at evaluating the behaviour of the developed components in case of load loss, the reference grid from Fig. 4.0.1 is modified to introduce a fault event. The RLC load connected to bus 3 is split into two parallel RLC loads and half of the original active and reactive power is demanded to each. After 10 sec of simulation, the second load is disconnected, thus the values of the total load connected to bus 3 are halved.

5.2.1 Comparison with EMT reference

For the comparison with the EMT reference, the simulation is performed in Hypersim and OpenModelica, where the generator from Fig. 3.6.7b is used keeping the same parameters as in section 5.1.1. Fig. 5.2.1 shows the comparison of the results obtained for phase A of the three­phase current flowing into the lines when the event occurs.

The choice of showing the currents flowing into the lines is motivated by the need of studying the response to the event at different parts of the system, not to be influenced by the behaviour of any component in particular. At this point, it has been assumed that if the power flowing into the lines is the same both in Hypersim and in OpenModelica simulations, it is because the components connected at the ends of these lines present a similar behaviour when the fault occurs.

Nevertheless, these results allow observing that even though the control schemes and the parameters used in both simulations are the same, there are still some differences in the response to the event. It seems that the response obtained from Hypersim

CHAPTER 5. VALIDATION OF RESULTS

Figure 5.2.1: Comparison of current flowing into the lines in Hypersim and OpenModelica when the fault occurs

simulation is slower than the response from OpenModelica. However, there are major difficulties when it comes to find the source of these differences due to the lack of information from the models and the variables obtained from Hypersim since the modeling paradigm is not as accessible as in OpenModelica.

5.2.2 Comparison with phasor reference

The same simulation is now performed with the phasor model, where the same modifications have been implemented in the load. In this case, to compare between the simulation in phasor and EMT in OpenModelica, the generator model from Fig. 3.6.7a is utilized. The parameters for the control blocks are those presented in B.1.

The objective of this comparison is to observe the differences in the information obtained from the phasor and the EMT simulation of OpenModelica, not only to validate the developed components. For this reason, Fig. 5.2.2 presents the values, both in phasor and in EMT formalism of the current flowing into the remaining load when the fault occurs.

Results show the transient behaviour for the EMT simulation. The values reached during the event are not noticeable in the phasor simulation, which might hinder the detection of the fault by protection systems when simulating in phasor formalism.

CHAPTER 5. VALIDATION OF RESULTS

Figure 5.2.2: Comparison of the current into the the remaining load in phasor and in EMT simulation in OpenModelica when the fault occurs

5.3 Response to disconnection from the system

A third case study has been implemented to validate the results. In this case, the response in EMT of the 3­buses reference grid when the infinite bus is disconnected will be evaluated to study the response to fault events.

5.3.1 Comparison with EMT reference

First, the comparison will be established between Hypersim and OpenModelica. The grid from Fig. 4.0.1 will be modified to include a breaker between the infinite bus and bus 1, that will open after 10 sec of simulation. The disconnection of the infinite bus represents a more severe fault since not only larger values of exchanged power will be affected, but also the reference for the system frequency will be lost. For this reason, the value for the controller gain, R, will be set in 0.005, to ensure the restoration of the steady­state after the event. Except for this, the default parameters will be used with the generator from Fig. 3.6.7b.

Fig. 5.3.1 shows the comparison between the results obtained with Hypersim and OpenModelica simulation, in EMT formalism. As in section 5.2.1, the values of the power flowing into the lines allow validating the response to the event in different parts of the system. In this case, the response to the event in Hypersim is also noticeable,

CHAPTER 5. VALIDATION OF RESULTS

especially in line 12, presenting the higher power flow of the lines connected to the affected bus.

Figure 5.3.1: Comparison of current flowing into the lines in Hypersim and OpenModelica when the fault occurs

5.3.2 Comparison with phasor reference

The response to the same situation in phasor and EMT has been also compared in OpenModelica. The breaker has been implemented in the phasor reference grid, between the infinite bus and bus 1 and it will open after 10 sec of simulation. The generator model will be the one presented in Fig. 3.6.7a with default parameters except for K₁, set in 200 because of the reasons previously stated.

The differences in the transient behaviour between phasor and in EMT are presented in Fig. 5.3.2, which shows the value of the voltage at bus 1 at the moment of the event.

Regarding the previous fault simulated, where the total load connected to the system was halved, it can be observed that the peak reached in this case is more pronounced due to the increased severity of the faulty event. However, the normal behaviour of the voltage is rapidly restored and a new steady­state is achieved after a few seconds.

Moreover, since the generator model and the parameters for the controller are the same both in phasor and in EMT, the frequency drop when the system frequency reference from the infinite bus is lost will be the same, and the system frequency will be restored to the same value. Fig. 5.3.3 presents the value of the frequency in the grid before and

CHAPTER 5. VALIDATION OF RESULTS

Figure 5.3.2: Comparison of voltage at the bus connected to the infinite bus in phasor and in EMT simulation in OpenModelica when the fault occurs

after the event, computed in the terminals of the generator.

Figure 5.3.3: Comparison of frequency drop in phasor and in EMT simulation in 3­

buses reference grid when the infinite bus is disconnected

It might be interesting to observe how the change in the system frequency can affect the results provided by the phasor simulation. As mentioned in section 3.5.2, the values for steady­state voltage and currents in OpenIPSL phasor models are expressed in a rotatory reference, rotating at the theoretical angular speed of the system. When the