development of emt components and reference grid in

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 TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Development of EMT components andreference 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

ii

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

iii

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

iv

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 fromModeling 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.

v

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

vi

Contents

1 Introduction 11.1 General context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Context of the project . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 About Modelica 42.1 Modelica language . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Reference libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Modelica Standard Library . . . . . . . . . . . . . . . . . . . . . 62.2.2 OpenIPSL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2.3 ModPowerSystems . . . . . . . . . . . . . . . . . . . . . . . . . 7

3 Developed EMT library in OpenModelica 93.1 Basic components models . . . . . . . . . . . . . . . . . . . . . . . . . 93.2 Transmission line models . . . . . . . . . . . . . . . . . . . . . . . . . . 123.3 Transformers models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.4 Load models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.5 Generator models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.5.1 ModPowerSystems generator model . . . . . . . . . . . . . . . 163.5.2 OpenIPSL generator model . . . . . . . . . . . . . . . . . . . . . 18

3.6 Control models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.6.1 Simple control models . . . . . . . . . . . . . . . . . . . . . . . . 203.6.2 Implementation of control models for comparison . . . . . . . . 23

4 Reference grid: 3buses 26

5 Validation of results 285.1 Deviation from reference values in steadystate . . . . . . . . . . . . . 28

vii

CONTENTS

5.1.1 Comparison with EMT reference . . . . . . . . . . . . . . . . . . 285.1.2 Comparison with phasor reference . . . . . . . . . . . . . . . . . 29

5.2 Response to load loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2.1 Comparison with EMT reference . . . . . . . . . . . . . . . . . . 315.2.2 Comparison with phasor reference . . . . . . . . . . . . . . . . . 32

5.3 Response to disconnection from the system . . . . . . . . . . . . . . . 335.3.1 Comparison with EMT reference . . . . . . . . . . . . . . . . . . 335.3.2 Comparison with phasor reference . . . . . . . . . . . . . . . . . 34

6 Conclusions 376.1 Discussion on the results . . . . . . . . . . . . . . . . . . . . . . . . . . 376.2 Identified difficulties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386.3 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

References 40

viii

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 andmethods 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

1

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 themost 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 beendevelopedwithin the scope of Architecture andSystemsprogram,

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. Inmany

2

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 ofModelica language anddevelopment ofmodeling skills inOpenModelica

• 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.

3

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 languageModelica. 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 tomodel components

that can be reused in more complex models, providing hierarchical structuring.

• Multidomainmodeling capability enabling tomodel 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

4

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 ofmodeling hybrid systems, that contain both continuous anddiscrete

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 themodeling 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].

5


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 withModelica language by theModelica 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

6


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,

7


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

8

Chapter 3

Developed EMT library inOpenModelica

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,

9

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 amodel that allows

setting the base values of the system regarding the base power and the frequency. This

model is called System and is definedwith the prefix inner. ThisModelica 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 basicmodels 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

10


the following equation:

vreal

vimaginary

= 2/3 ·

1 cos(2π3) cos(4π

3)

0 sin(2π3) sin(4π

3)

·

vA

vB

vC

(3.1)

where vreal and vimaginary are the real and imaginary components of a certain variable

in phasor form, and vA, vB and vC 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 referencewill beminimized

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: vreal′

vimaginary′

=

cos(−θ) −sin(−θ)

sin(−θ) cos(−θ)

·

vreal

vimaginary

(3.2)

being θ the product of the system angular speed by the simulation time, vreal and

vimaginary the real and imaginary components of the voltage in stationary reference

and vreal′ and vimaginary′ 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,

11


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. P12 andQ12 are the active and reactive power

injected at the end 1 of the line and P21 and Q21 those 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, namedwith the subindices

12 and 21. However, itmight differ from the nomenclature used in [13] and inModelica

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

directlywritten in this interface. The behaviour of the linemodel 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

12


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

13


comparisonwith 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. P12 andQ12, 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 + vimaginary · iimaginary (3.3)

2/3 ·Q = −vreal · iimaginary + vimaginary · ireal (3.4)

This way, using the variables for the voltage and current at the sending end, −→vs and−→is

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, −→vr and−→ir , the power

injected at n, P21 and Q21, are calculated. The same procedure to calculate the active

and reactive powerwill 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.

14


3.4 Load models

In theLoads package of the developed library, three basicmodels 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.

15


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

stability.

This package also presents amodel 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

16


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

to the threephase stationary reference:

vdvq

= 2/3 ·

cos(θ) cos(θ − 2π3) cos(θ + 2π

3)

− sin(θ) − sin(θ − 2π3) − sin(θ + 2π

3)

·

vA

vB

vC

(3.5)

where vd and vq are components of the voltage in DQ reference in p.u., vA, vB and vC

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 vA, vB and vC 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 generatormodel, 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

555MVA.

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.

17


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 generatormodels 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 packageMachines 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

18


in the code.

vreal

vimaginary

=

cos(θ − π2) −sin(θ − π

2)

sin(θ − π2) cos(θ − π

2)

·

vdvq

(3.6)

where vd and vq are the components of the stator voltage in DQ reference, vreal and

vimaginary 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 themain 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 generatormodel, 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 andmagnitude 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

19


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:

Pm = Pref +Kgain(fref − f) (3.7)

where Pm is the mechanical power provided to the generator, Pref is the reference

mechanical power input,Kgain is a constant modeling the gain of the controller, fref is

the reference frequency, generally the system frequency, and f is the actual frequency

value at the generator windings. Kgainwill set the dynamics of the frequency controller,

and as the first approach, it has been set as Pnom/30.2

, being Pnom the nominal power of the

machine inW and 0.2 a threshold for the frequency deviation. Since Pnom is 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.

20


(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, TA will be set in 0.04s

and the overall gain KA, 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:

VR = Efd/KA (3.8)

whereVR is the voltage reference in p.u.,KA the overall gain andEfd 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,

21


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 themagnitudeRMS 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: Generatormodel with simple frequency control and AC4A exciter control

22


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 controlmodels that present the samebehaviour

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/30.2

as in the simpler frequency control model. However, when

working in p.u., Pnom is 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

23


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 comparisonwith the phasormodel, 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,

24


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

25

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 100MVA and the system frequency to

50Hz. 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

26

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 P12 and Q12 stand for the power injected at one end of the line whereas P21 and

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

27

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 themwill be calculated according to equation 5.1, whereXHypersim are the

values obtained in Hypersim, used as a reference, and XEMT1 are the values obtained

28

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.

errorX [%] =XHypersim −XEMT1

XHypersim

· 100 (5.1)

Table 5.1.1: Deviation from Hypersim in steadystate for 3buses case study in EMT

BUS errorV [%] errorangle[%] errorP [%] errorQ[%]

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 flowinginto 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.

29


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 ismotivated 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:

errorX [%] =Xphasor −XEMT2

Xphasor

· 100 (5.2)

where Xphasor are the values from the phasor simulation and XETM2 the values from

the EMT simulation, which slightly differ fromXETM1 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 EMTsimulation in OpenModelica


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 casestudy in EMT in OpenModelica

Line errorP12[%] errorP21[%] errorQ12[%] errorQ21[%]

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,

30


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 ismore 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 7.62MVAr 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.


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

31


Figure 5.2.1: Comparison of current flowing into the lines in Hypersim andOpenModelica 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.


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.

32


Figure 5.2.2: Comparison of the current into the the remaining load in phasor and inEMT 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.


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,

33


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 andOpenModelica when the fault occurs


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

generatormodel will be the one presented in Fig. 3.6.7a with default parameters except

forK1, 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 generatormodel 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

34


Figure 5.3.2: Comparison of voltage at the bus connected to the infinite bus in phasorand 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 3buses reference grid when the infinite bus is disconnected

Itmight 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

35


system frequency changes, a difference might appear between the rotating speed of

the variables in the system and the rotating reference in which they are expressed.

The voltage and currents in the system in phasor formalism, are no longer a constant,

but they vary according to the difference between the original frequency and the value

reached after the event. One of the consequences of this circumstance is that the

values calculated for the voltage phase at the buses are no longer reliable. In contrast,

the results obtained from the EMT simulation are not affected by this change in the

rotating reference of the system since they are expressed in a stationary reference and

the angular speed leading their variation is computed considering this reference. The

frequency drop only emphasizes the need for the development ofmeasuring techniques

andmodels for the phase voltage at the buses. In the presented case studies, the system

frequency value was assumed constant for the approximated measure. In this case,

since the frequency value presents a certain variation, this assumption of constant

frequency used to compute the angle when measuring might induce certain error in

the results.

Fig. 5.3.4 presents the values for the real and imaginary components of the voltage at

the buses in the phasor simulation of the 3buses reference grid when the infinite bus

is disconnected after 10 sec of simulation. The mentioned variation can be observed

after the event.

Figure 5.3.4: Real and imaginary components of the voltage at the buses in phasorsimulation of 3buses reference grid

36

Chapter 6

Conclusions

6.1 Discussion on the results

After evaluating the results obtained from the simulation of the reference grids

built with the components developed in EMT formalism in OpenModelica, some

conclusions can be drawn:

• The results obtained from the comparison of the same reference grids simulated

in other EMT software, Hypersim in this case, allow the validation of the

behaviour of the developed components in OpenModelica.

• Unlike other software, the development of components in OpenModelica enable

to have access to the equations that model the behaviour of the system,

facilitating its understanding. The main difficulties when building components

and grids for comparison is to reproduce the models used by other software,

whose code is not as accessible as in OpenModelica. This can be an obstacle to

direct comparison of results.

• The values obtained from the power flow analysis, performed in an environment

different fromOpenModelica, have a significant impact on the results, since they

are used for the initialization of the simulation.

• The simulation in EMT formalism enable to obtain more information on the

transient performance regarding the simulation in phasor formalism, being

particularly interesting in the case of an event. To this extent, the components

created in the scope of the EMT library developed in OpenModelica can be

37

CHAPTER 6. CONCLUSIONS

implemented to study the behaviour of the system in faulty situations with a

satisfactory outcome.

• Also, for steadystate simulation, the simulation in EMT provides more

information on the behaviour of the model. The lack of information procured

in phasor formalism might present some difficulties when creating models for

comparison. This is due to the large number of simplifications encountered

in the phasor models, which might become inconvenient specially when trying

to reproduce the same model in other EMT environments different from

OpenModelica.

• The direct comparison with the simulation of the reference grids developed in

phasor presents certain difficultieswhen it comes to the validation of results since

the outcome is presented in a different formalism.

6.2 Identified difficulties

As previously discussed, one of the main drawbacks of working with OpenModelica

is that the results from the simulations are highly dependable on the values used

for initialization. This circumstance, together with the lack of tools to perform a

power flow analysis directly in OpenModelica, bring up the need of using the support

of other environments. This stands as a major difficulty found when working with

OpenModelica.

The development of models in OpenModelica has also been influenced by the lack

of references available when it comes to specific errors than can appear during the

compilation and simulation process. In this sense, the identification of the source of

these errors can become problematic and in some cases, such identification stands also

as an outcome of this project, regarding future OpenModelica users.

Additionally, working with OpenModelica, either to create new components or to build

new models with the existing libraries present certain challenges associated with the

opensource paradigm. The opensource platform enables the exchange of models and

facilitates access to numerous resources. But at the same time, it can hinder the dayto

day development due to compatibility issues when combining resources at a different

stage of development. This has been other of the main difficulties found.

38

CHAPTER 6. CONCLUSIONS

In conclusion, OpenModelica stands as an interesting tool for power system simulation

and there is certainly room for the development of models in EMT. However, it needs

the support of solid references in other environments and, in thewriter’s opinion, there

is a long way to go andmuch development to do before its use can be generalized.

6.3 Future work

In the short term, it would be interesting to work in the development of components

that facilitate the comparison with phasor models, such as voltage angle measurement

devices in EMT. Also, the creation of different transmission linemodels based on other

theoretical developments could probably improve the validation of the results.

Finally, the development of interfaces that allow to include components and controls

for the integration of HVDC grids in the existing EMT reference grid could be definitely

the next step in the research presented in this project.

39

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https://www.opal-rt.com/systems-hypersim/

https://www.opal-rt.com/systems-hypersim/

Appendix Contents

A PSSE load model 43

B Generator control parameters 47B.1 Turbinegovernor control default parameters . . . . . . . . . . . . . . . 47B.2 Exciter system control default parameters . . . . . . . . . . . . . . . . . 47

C Reference grid: Kundur twoareas 49C.1 Description of the grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49C.2 Study of the deviation from reference values in steadystate . . . . . . 50

C.2.1 Comparison with EMT reference . . . . . . . . . . . . . . . . . . 50C.2.2 Comparison with phasor reference . . . . . . . . . . . . . . . . . 51

42

Appendix A

PSSE load model

In order to be able to compare with the phasor models developed with OpenIPSL,

one of the load models have been studied and adapted to EMT in particular the static

load model PSSE Load found within the models of OpenIPSL library, as part of the

OpenIPSL.Electrical.Loads.PSSE library. As suggested by its name, the loads classes

here gathered, aremodelled according to the static loadmodel developed by PSSE [19].

PSSE main load model is based on the polynomial or ZIP model, that describes the

voltage dependency of the model by a second order polynomial equation [13]:

SZIP = S0 · (sZ · V2

V02 + sI ·

V

V0

+ sP ) (A.1)

In this model, the power is obtained from the composition of constant impedance,

constant current and constant power components, being sZ , sI , and sP the coefficients

that define the proportion of each component, V the bus voltage and V0 and S0 the

voltage and the apparent power at initial conditions respectively. Thisway ofmodelling

the load according to these three components, responds to the need to represent the

load as an aggregate of constant power, constant current and constant impedance

characteristics for higher accuracy of the modelling.

Similarly, in PSSE, each load can be a composition of loads with three different

characteristics, being these constant power load characteristic, constant current load

characteristic and constant admittance load characteristic. The constant power load

characteristic assumes a constant value for the load power for voltage values over a

43

APPENDIX A. PSSE LOADMODEL

certain parameter, PQBRAK, whose default value is generally set at 0.7 p.u. [19]. For

voltages below this value, the constant power load component switches to elliptical

currentvoltage characteristic.

Figure A.0.1: Constant Power Load Characteristic [19]

Likewise, the constant current load characteristic considers a constant value for

the current for voltage values above 0.5 p.u, assuming an elliptical currentvoltage

characteristic for voltage values under this threshold. As for the constant admittance

load characteristic, the value of the admittance is considered as constant regardless the

value of the voltage.

Based on these considerations, it is possible to model the load as:

S = SY · V 2 +KI · SI · V +KP · SP (A.2)

WhereSY ,SI andSP are the load components associated to the impedance, current and

power respectively, V is the bus voltage andKI andKP are two coefficients depending

on the voltage value. According to the load characteristics previously presented, KI

will be equal to 1 when the voltage is higher than 0.5 p.u., whereas KP will be 1 when

the voltage is over PQBRAK. Below these values, these coefficients are adjusted to the

correspondent elliptical currentvoltage characteristic.

44


Figure A.0.2: Constant Current Load Characteristic [19]

According to the PSSE model presented, each load component is built from the initial

constant power, current or admittance load in addition to a certain load transfer

occurred when the power flow is established, due to the voltage dependency of the

load [15]. This transfer is presented as a conversion process in PSSE where constant

power load is reassigned as constant current or constant admittance load.

Therefore, being Sp the consumption of original constant power load, Si the

consumption of original constant current load, Sy the consumption of original constant

shunt admittance load, a the load transfer fraction for constant current load, b the

load transfer fraction for constant shunt admittance load, it is possible to express the

different load components as:

SP = Sp · (1− a− b) (A.3)

SI = Si + a · Sp

V0

(A.4)

SY = Sy + b · Sp

V02 (A.5)

Equations (A.3)(A.5) can be combined with equation A.2 to obtain the value of the

load, S, as a function of the bus voltage, V, the initial value of the bus voltage, V0,

45


Figure A.0.3: Reallocation of constant power load [15]

and the data for Sp, Si, Sy. In the case of the reference model, KundurTwoAreas, the

consumption of original constant current load, Si, and the consumption of original

constant shunt admittance load, Sy, can be set to 0, whereas the values for Sp and V0

can be obtained from the power flow previously performed. The rest of the parameters

present in the equations are established in the model.

46

Appendix B

Generator control parameters

B.1 Turbinegovernor control default parameters

Tables B.1.1 and B.1.2 present the parameters for TGOV1 and IEESGO control blocks

used for the comparison with Hypersim and phasor simulation respectively.

Parameter Description Value

R Governor gain, 1/R [pu] 0.6

Dt Speed drop [pu] 1

T1 Control time constant [s] 0.12

T2 Control time constant [s] 0


VMAX Max. valve position [pu] 1

VMIN Min. valve position [pu] 0

Table B.1.1: TGOV1

B.2 Exciter system control default parameters

Tables B.2.1 and B.2.2 show the parameters for the exciter control adapted from

Hypersim and the simplified excitation system model used for the comparison with

Hypersim and phasor simulation respectively.

47

APPENDIX B. GENERATOR CONTROL PARAMETERS


K1 Governor gain, 1/pu regulation 1.667

K2 Fraction [pu] 0

K3 Fraction [pu] 0

T1 Controller lag [s] 0

T2 Controller lead compensation [s] 0

T3 Governor lag [s] 0

T4 Control time constant [s] 0.12

T5 Reheater delay [s] 0

T6 Turbine delay [s] 0

PMAX Upper power limit [pu] 10

PMIN Lower power limit [pu] 10

Table B.1.2: IEESGO


Kr Voltage measurement gain [pu] 1

Tr Voltage measurement time constant [s] 0

Ka Voltage regulator gain [pu] 200

Ta Voltage regulator time constant [s] 8

Kf Damping filter feedback gain [pu] 0

Tf Damping filter feedback time constant [s] 1

VMAX Max. limit for excitation voltage [pu] 5.64

VMIN Min. limit for excitation voltage [pu] 4.53

Table B.2.1: Exciter control adapted from Hypersim


K Governor gain [pu] 200

T Lag time constant [s] 0.04



VMAX Max. limit for excitation voltage [pu] 5.64

VMIN Min. limit for excitation voltage [pu] 4.53

Table B.2.2: Simplified excitation system

48

Appendix C

Reference grid: Kundur twoareas

C.1 Description of the grid

In this chapter a second reference grid, more complex the the 3buses reference, is

presented. This second case study is the simple twoareas system presented in the Fig.

E12.8 from [13]. This model has been previously developed in phasor formalism in

the scope of OpenIPSL, thus using the components included in this library. Regarding

the system from [13], the phasor model presents some simplifications, mostly derived

from the development of all the components in per unit formalism. Table C.1.1 shows

the power flow data used in the phasor model for initialization. For the value of power

exchanged at each bus, positive values stand for power injected into the grid at the

bus.

To be able to compare the Kundur twoareas system in phasor and in EMT in

OpenModelica, an equivalent model is implemented in this environment using the

components from the developed EMT library. This model, shown in figure Fig. C.1.1

presents the same simplifications than the phasor version and the parameters have

been kept unchanged, but calculated in SI units.

Figure C.1.1: EMT Kundur twoareas reference grid in OpenModelica

49

APPENDIX C. REFERENCE GRID: KUNDUR TWOAREAS

Table C.1.1: Power flow data for Kundur Two Areas reference grid

BUS V[pu] angle[°] P[MW] Q[MVar]

1 1.03 20.27 700 185.03

2 1.01 10.51 700 234.61

3 1.03 6.8 719.09 176.03

4 1.01 16.99 700 202.08

5 1.01 13.78

6 0.98 3.71

7 0.96 4.69 967 84.7

8 0.95 18.51

9 0.97 32.15 1767 230.2

10 0.98 23.71

11 1.01 13.41

The main difference between Kundur twoareas model in phasor and in EMT are load

components, since in the EMT version these aremodeled as RLC load but in the phasor

version, a more complex model is used, presented in appendix A.

C.2 Study of the deviation from reference values in

steadystate

C.2.1 Comparison with EMT reference

As presented for the 3buses reference grid, a comparison will be established between

Kundur twoareas reference grid simulated in Hypersim and in OpenModelica. In

order to validate the results, the grid will be implemented in Hypersim with the same

simplifications, data and parameters than the model in OpenModelica. The generator

scheme from Fig.3.6.7b will be used for the four generators in the model, keeping the

default values for all the parameters except for the governor gain, R, that will be set

in 0.005. The choice of a stronger response for the frequency controller is motivated

by the lack of infinite bus in this case study. The deviation of the values of the EMT

simulation in OpenModelica in steadystate regarding the power flow values from

Hypersim are computed using equation 5.1 and shown in table C.2.1.

50


Table C.2.1: Error in steadystate values for Kundur twoareas reference grid EMTsimulation in OpenModelica


1 0.12 0.21 1.19 1.26

2 0.24 1.24 1.45 4.15

3 0.16 6.54 1.13 1.13

4 0.30 3.24 1.50 4.76

5 0.19 0.78

6 0.10 5.16

7 0.08 7.19 0.78 0.78

8 0.05 2.81

9 0.11 2.21 0.83 0.83

10 0.13 2.60

11 0.15 4.03

Figure C.2.1: Comparison between Hypersim and OpenModelica of currents flowinginto the lines in steadystate for Kundur twoareas reference grid

C.2.2 Comparison with phasor reference

The deviation between the values obtained in steadystate in phasor and EMT

simulation has been also computed for Kundur twoareas reference grid. In this case,

the generator control presented in 3.6.7a has been implemented for all the generators

in the system, both for the phasor simulation and for the EMT. The default parameters

have been kept unchanged except for the controller gain,K_1, that has been set to 200

51


for the reason stated in section 5.1.1. Once the simulation reaches the steadystate, the

error in computed according to equation 5.2.

Table C.2.2: Deviation from phasor simulation in in steadystate for Kundur twoareasEMT simulation in OpenModelica


1 0.01 2.35 1.12 2.14

2 0.70 5.74 0.69 4.69

3 0.72 6.94 1.02 2.56

4 0.75 3.52 0.43 6.06

5 0.13 3.94

6 0.31 17.03

7 0.14 14.43 0.78 0.78

8 0.33 3.69

9 0.28 1.97 0.83 0.83

10 0.49 2.61

11 0.63 3.94

It can be observed that the error values obtained from the comparison between phasor

and EMT simulation in steadystate, are higher for Kundur twoareas reference grid

than for the 3buses reference grid. These differences can be due to several reasons.

First, Kundur twoareas reference grid is larger than the 3buses grid and more

components have been implemented. If the behaviour of any of this components

slightly differs from the expected, the error can be propagated and become noticeable

in different parts of the system.

Second, Kundur twoareas grid does not include a component for infinite bus, thus

the system frequency is not externally set. Even if the turbinegovernor gain has been

strengthen, there is a slight deviation from the system reference frequency, whereas

in the 3buses case there was not such deviation. Therefore, the measurement of the

voltage angle in the buses might present some error, as shown in table C.2.2. The

values for the error in the angle in buses 6 and 7 are the highest, being for 3 and 4

also significant. These values are higher for these buses because the error computed

in table C.2.2 is the relative error, but when calculating the absolute deviation it can

be observed that the deviation in the voltage angle at the buses is always around 0.6°.

This deviation is more noticeable in the case of low values for the angles, as in buses 6

and 7, where the expected value for the angles is 3.71° and 4.69° respectively.

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development of emt components and reference grid in

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