IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2020

Open Source Model of the Nordic Power System for EU Project Spine

ARAVIND SATHEESKUMAR

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

Authors

Aravind S Kumar <aravinds@kth.se>Electric Power EngineeringKTH Royal Institute of Technology

Place for Project

Division of Electric Power and Energy SystemsKTH Royal Institute of TechnologyStockholm, Sweden

Examiner

Lennart SöderDivision of Electric Power and Energy SystemsKTH Royal Institute of Technology

Supervisor

Iason Kouveliotis Lysikatos

Division of Electric Power and Energy Systems

KTH Royal Institute of Technology

Open Source Model of the Nordic Power System for

EU Project Spine

Aravind S Kumar

September 7, 2020

Abstract

Decision problems in operation and planning of power systems often rely on large-scale models

and data sets. Lack of historical power flow data due to regulatory restrictions often limits

researchers to study the system with aggregated network models. Aggregated data from the

electricity market operators (Nordpool in the Nordics) and the Transmission System Operator

(TSO) (from ENTSO-E) are openly available, and can be used to study the power flow and

exchanges between different regions but do not directly provide information about intra-region

flows. This project builds upon the Nordic 490 system, a previously built model of the Nordic

power system. The main objective of this work is to improve the existing open source power

flow model of the Nordic power system, in order to become in turn available for the multi-

energy modelling and simulation software Spine.

The N490 model generates a model of the Nordic power system consisting of various

nodes/buses which represent substations at different voltage levels. Then, it distributes the

aggregated production, consumption and power exchange data from Nordpool to the various

buses. In this project, different possible improvements are evaluated for the model, aiming at

estimating a set of network parameters that minimize the errors between the calculated inter-

region flows and the ones from the open data repositories.

The different improvements which are evaluated are the following. Firstly, the load distribution

is modified and reassigned to match the regional electricity consumption. The generators and

wind farms are then reallocated to different bus based on their bidding region and proximity to

the bus. The databases are improved and the power balance relation modified. Transmission

line parameters are then investigated, first to standard recommended values and then by solving

an optimisation problem formulated to extract the parameters from the market data. Finally,

the model is also tested with wind and solar generation modelled as a generator rather than as

a negative load.

i

Keywords

Nordic Power System, power system modelling, power flow analysis, optimisation,

transmission line parameter estimation

ii

Svensk Sammanfattning

Beslutsproblem gällande drift och planering av kraftsystemet baseras ofta på storskaliga

modeller och datamängder. Bristen på historiska data gällande effektflöden beror

på säkerhetsrestriktioner vilket begränsar forskare till att enbart studera aggregerade

nätverksmodeller. Det finns tillgängliga aggregerade data från den nordiska elmarknadsplatsen

Nordpool och organisationen ENTSO-E som kan användas för att studera effektflöden mellan

olika regioner, dock finns det inte direkta data för flöden inom regionerna. Det här projektet

bygger på det nordiska 490-systemet, en tidigare byggd modell av det nordiska kraftsystemet.

Huvudsyftet med detta arbete är att förbättra den existerande effektflödesmodellen av det

nordiska kraftsystemet, för att i sin tur bli tillgänglig för multienergimodelleringar och

simuleringsprogramvaran Spine.

N490-modellen genererar en modell för det nordiska kraftsystemet som innehåller olika noder

som presenterar ställverk med olika spänningsnivåer och modellen ger också aggregerade

data för produktion, konsumtion och effektutbyte mellan de olika noderna från Nordpool. I

detta projekt utvärderades olika möjliga förbättringar för modellen som syftar till att uppskatta

nätverkets parametrar som kan minimera felen mellan beräkningar av flöde inom regionen och

data från öppna datalagringskällor.

Följande förbättringar gjordes: Först har lastens fördelning modifierats och ändrats för att

matcha den regionala elkonsumtionen. Generatorer och vindkraftsparker allokerades till

olika noder baserad på elhandelsområden och närhet till noderna. Databasen förbättrades

för att erhålla en bättre effektbalans per område. Kraftledningarnas parametrar ändrades

först till rekommenderade standardvärden, vilka sedan förbättrades genom att formulera ett

optimeringsproblem för att extrahera parametrarna från markandsdata. Slutligen testades

modellen genom att presentera vind- och sol-produktion som generatorer istället för som

negativ förbrukning.

iii

Nyckelord

Nordic Power System, modellering av kraftsystem, effektflödesanalys, optimering,

uppskattning av transmissionslinje-parametrar

iv

Acknowledgements

It is with great pleasure and satisfaction, that I present the project at this juncture. I feel obliged

to acknowledge the support and guidance that I received from various quarters during the course

of the project.

With immense pleasure, I offer my heartiest gratitude to Iason Kouveliotis Lysikatos,

for his constant support and guidance without which the project would not have been

successful.

I would like to thank Lennart Söder, the examiner, for his inputs and suggestions for

the project.

Special thanks to Elis Nycander, who was helpful in gathering data and also for his

inputs for the project.

I also extend my gratitude to my parents and friends for giving moral support and

encouragement in all possible ways.

v

Contents

List of Figures x

List of Tables xi

List of Abbreviations xii

Nomenclature xiii

1 Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Purpose/Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.4 Contribution of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.5 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6 Benefits, Ethics and Sustainability . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6.1 Benefits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.6.2 Ethics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.6.3 Sustainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.7 Stakeholders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.8 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Background 72.1 Power System Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Python for Power System Analysis . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3 PyPSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.3.1 PyPSA-Eur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Nordic Power System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.5 The Spine Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Literature Review 12

vi

Contents

3.1 The ENTSO-E Transparency Platform . . . . . . . . . . . . . . . . . . . . . . 12

3.2 Disaggregation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3 Network Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Load Flow Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.5 Nordic Market Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4 Methodology 184.1 The Nordic 490 Model - Base Model . . . . . . . . . . . . . . . . . . . . . . . 18

4.2 Load Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 Electricity Consumption Statistics . . . . . . . . . . . . . . . . . . . . 22

4.2.2 Coping with the Missing Data . . . . . . . . . . . . . . . . . . . . . . 23

4.2.3 Obtaining Geographical Coordinates . . . . . . . . . . . . . . . . . . . 24

4.2.4 Mapping of Municipalities to Buses . . . . . . . . . . . . . . . . . . . 24

4.2.5 Load Shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.3 Generators and Wind Farms . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.3.1 Mapping of generators and wind farms to buses . . . . . . . . . . . . . 26

4.3.2 Auxiliary Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.4 HVDC Links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.4.1 Norway - Russia grid connection . . . . . . . . . . . . . . . . . . . . . 28

4.5 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.6 Transmission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.6.1 Line Compensation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.6.2 Estimation of Line Parameters . . . . . . . . . . . . . . . . . . . . . . 31

4.7 Validating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.7.1 Preparing the network . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.7.2 Power flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.7.3 Comparison and Error Calculation . . . . . . . . . . . . . . . . . . . . 35

5 Results 365.1 Summary of Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.2 Model Conformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.3 Correction factor for ENTSO-E generation data . . . . . . . . . . . . . . . . . 38

5.4 Reassigning Load Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.5 Reassigning Generator Bus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.6 Effect of adjusting of the line parameters . . . . . . . . . . . . . . . . . . . . . 42

vii

5.7 Norway-Russia Interconnection . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.8 Effect of Modifying Power Balancing Expression . . . . . . . . . . . . . . . . 45

5.9 Inter Area Power Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.10 Power flow for 2017 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.11 AC Power Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.12 Wind as Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.13 Estimation of Line Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.14 Summary of the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

6 Conclusions 596.1 Summary of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.2 Results and Interpretation of Findings . . . . . . . . . . . . . . . . . . . . . . 59

6.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.4 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

6.5 Final Words . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

Appendices 63A Key for Data Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

B Geodetic coordinates to plane coordinates . . . . . . . . . . . . . . . . . . . . 68

References 72

viii

List of Figures

1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 European Transmission Network Model [4] . . . . . . . . . . . . . . . . . . . 9

2.2 Synchronous grids of Europe and North Africa [6] . . . . . . . . . . . . . . . . 10

2.3 Elspot market bidding areas [7] . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Time scales for electricity markets. Source: Training module electricity market

regulation session by leornado energy 2009 . . . . . . . . . . . . . . . . . . . 16

4.1 The N490 model structure diagram . . . . . . . . . . . . . . . . . . . . . . . . 19

4.2 N490 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.3 Electricity consumption statistics for Sweden . . . . . . . . . . . . . . . . . . 23

4.4 Example of curve fitting for estimating missing consumption data . . . . . . . 24

4.5 Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.6 Wind farms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.7 Comparison of generator mapping . . . . . . . . . . . . . . . . . . . . . . . . 27

4.8 Grid connection between Norway and Russia . . . . . . . . . . . . . . . . . . 29

4.9 Flow chart for optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.1 Municipalities in the Nordics . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5.2 Deviations from the actual location . . . . . . . . . . . . . . . . . . . . . . . . 39

5.3 Effect of modified load distribution - overall improvement of 1.24% in MAE

an 1.05% in RMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5.4 Effect of reassigning generator - overall improvement of 18.41% in MAE and

12.69% in RMSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.5 Effect of modified line parameters - overall improvement of 21.62% and

13.59% in MAE and RMSE respectively . . . . . . . . . . . . . . . . . . . . . 43

5.6 Effect of NO4-RU interconnection - 22.10% in MAE and 15.33% in RMSE

improvement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

ix

List of Figures

5.7 With balance relation modified, overall improvement is 35.86% in MAE and

26.33% in RMSE compared with base model . . . . . . . . . . . . . . . . . . 46

5.8 Power exchanges during winter . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.9 Power exchanges during summer . . . . . . . . . . . . . . . . . . . . . . . . . 50

5.10 % improvement with wind modelled as generator compared with base model.

There is an overall improvement of 37.67% in MAE and 27.44% in RMSE . . 53

5.11 Optimised line parameters results in improvement of 3.28% inMAE and 1.25%

in RMSE compared with modified model . . . . . . . . . . . . . . . . . . . . 55

5.12 % improvement after each modification . . . . . . . . . . . . . . . . . . . . . 56

5.13 Cumulative improvement compared to base model . . . . . . . . . . . . . . . 56

5.14 Errors during network congestion and outages . . . . . . . . . . . . . . . . . . 57

x

List of Tables

4.1 Bus info of N490 model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.2 Municipalities in the Nordics . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.3 HVDC links in the Nordics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.4 Transformers in the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.5 Standard overhead line parameters [32] . . . . . . . . . . . . . . . . . . . . . 30

4.6 Series compensation for lines . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5.1 Comparison of installed capacity, values in MW . . . . . . . . . . . . . . . . . 37

5.2 Comparison of transmission line lengths . . . . . . . . . . . . . . . . . . . . . 37

5.3 Scaling factors for ENTSO-E generation data for Nordics . . . . . . . . . . . . 38

5.4 Errors after modifying load distribution . . . . . . . . . . . . . . . . . . . . . 40

5.5 Errors with generators and wind farms reassigned . . . . . . . . . . . . . . . . 41

5.6 Effect of modifying line parameters . . . . . . . . . . . . . . . . . . . . . . . 43

5.7 Errors after Norway-Russia interconnection added . . . . . . . . . . . . . . . . 44

5.8 Errors after miscellaneous changes . . . . . . . . . . . . . . . . . . . . . . . . 45

5.9 Errors for 2017 Jan - Sept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.10 ac power flow results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.11 Errors with wind farms as generators . . . . . . . . . . . . . . . . . . . . . . . 53

5.12 Errors after optimisation compared with modified model . . . . . . . . . . . . 55

5.13 Average error in power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

A.1 Key for generator dataframe . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

A.2 Key for bus dataframe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.3 Key for transformer dataframe . . . . . . . . . . . . . . . . . . . . . . . . . . 65

A.4 Key for HVDC links . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

A.5 Key for transmission lines dataframe . . . . . . . . . . . . . . . . . . . . . . . 66

A.6 Key for wind farms dataframe . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A.7 Key for municipality details . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

xi

List of Abbreviations

DCPF DC power flow

ENTSO-E European Network of Transmission System Operators for Electricity

HVDC High Voltage Direct Current

L-BFGS-B Limited memory Broyden - Fletcher - Goldfarb - Shanno - Bounded

MAE Mean Absolute Error

MAPE Mean Absolute Percentage Error

N490 Nordic 490

NTC Net Transfer Capacities

opf optimal power flow

OPSD Open Power Systems Data

PPM Power Plant Matching

PTDF Power Transfer Distribution Factor

PyPSA Python for Power System Analysis

RMSE Root Mean Square Error

SLSQP Sequential Least Squares Programming

TP Transparency Platform

TSO Transmission System Operator

xii

Nomenclature

Indices

bi, bj: Bidding regions, bi, bj ∈ (SE1, SE2, ...F I,DK2)

i, j -> iteration from-to/at, i,j ∈ (1,...n)

t: time, t ∈ (1, ...T)

Notations

kV: kilo Volts

comp: compensation factor

X: line reactance

X: line reactance upper bound

X: line reactance lower bound

Xtrfr: Transformer reactance

Xtrfr: transformer reactance upper bound

Xtrfr: transformer reactance lower bound

n: total number of steps

Pmeasured: Measured active power flow

Pmodelled: Modelled active power flow

xiii

Chapter 1

Introduction

This chapter describes in brief what the thesis is about. The background and the problem

statement are explained and the goal and purpose of the thesis are then revealed. Finally, the

outline of the report is briefed.

1.1 Background

The electricity sector all over the world is undergoing some fundamental changes. With the

increasing share of highly intermittent renewable energy sources, the traditional base and peak

power plants are slowly being phased out. To promote further investments in renewable power,

energy markets all over the world are slowly being deregulated.

Power system modelling is a critical aspect for the optimal operation and management of

electricity networks. However, the interaction between the conventional grid infrastructure

and the renewable power generation units is highly complex. Analysing their interplay requires

computer models and detailed information of high spatial and temporal resolution.

Electricity system modeling is a widely accepted method to answer research questions, help

make investment decisions and even advice policy makers. With the intermittent nature of

wind and solar power, modelling the system and testing the effects of introducing renewable

energy sources is critical for evaluating the system’s stability and economic operation.

Various power system analysis tools exist such as: DIgSILENT, DINIS, ERACS, ETAP etc.,

which can model the interactions between the electrical grid and the consumers and generators

[1]. However, these are not freely distributed and the users are forced to accept the assumptions

made by the software. Also, most of the decisions and operation planning in power system rely

1

Introduction

on large data sets and scaled models which are hardly accessible.

One of the objectives of this project is to improve the existing 490-bus model in order to become

available for Spine energy modelling software. Spine provides the means to define, manage,

and execute complex data processing and computation tasks, such as energy system models. It

can be used for flexible and realistic planning of future European energy grids.

1.2 Problem

For conducting accurate power system studies modelling both active and reactive power flows,

the power consumption at each grid node is required to be known. Within a market regulated

energy landscape, the majority of the data regarding the operation of the system remains hidden.

Due to regulatory limitations and/or privacy protection laws, it is often difficult to acquire

historical power flow data. With the deregulated market landscape, there are many new and

minor participants and hence the available power system data are often scattered.

Figure 1.1 shows the problem definition. The power system data published by Nordpool,

Europe’s leading power market and the market operator in the Nordic, consists of the net inter-

area power exchanges, aggregated generation and consumption per area data. The intra-area

power flow data is not available. In simpler terms, the aggregated generation and consumption

data for different regions and the net exchange between these regions are available, while the

data of the power flows within each region and on each line are not.

Ground truth data from aggregated data sets are difficult to extract and hence accuracy of

the disaggregated model might introduce errors. Moreover, it is also difficult to obtain open

source data for transmission line parameters and transformer specifications for different voltage

levels. This means that most of the model does some estimation, which might not give the most

accurate results.

1.3 Purpose/Goal

The purpose/goal of this project is to develop an accurate power flow model of the Nordic

power system from openly available data from the Nordpool market platform and the ENTSO-

E transparency platform. This is achieved by improving upon the previous work, the existing

model - from here on referred to as the base model.

The thesis evaluates the base model and identify the short comings to better improve upon the

2

Introduction

N1

~

~

N2

~

N3~

~

~~

~

P13

∑PG1, ∑PD1 ∑PG3, ∑PD3

∑PG2, ∑PD2

Figure 1.1: Problem Statement

model. The database and model is verified to make sure all the interconnections and power

exchanges are accounted for.

Additional data gathered from different sources are compiled and brought to a standard format.

The existing code will be cleaned and commented so that it is easier to follow.

Convergence issues with the ac power flow in the base model is also rectified.

The thesis also dives into extracting the line parameters by reverse engineering from the

network.

Finally, the model description and explanation are properly documented with assumptions and

motivations clearly reasoned.

The thesis results in a more accurate system with minimal error in inter area power exchanges

between the modelled system and the measurements from the power market.

1.4 Contribution of the Thesis

The main contribution of the thesis is improving the base model. This is done by

• Improving the different databases which constitutes the model by adding missing

information and correcting certain entries

3

Introduction

• Proposing and evaluating an alternative distribution of the load at each bus, in order to

reflect annual energy consumption statistics of each country

• Reallocating the generators and the wind farms to appropriate buses using inpolygon

function and shortest distance

• Improving the model to better reflect market data from Nordpool so that the inter area

power exchange errors are minimal

• Formulating an optimisation problem to estimate line parameters

• Fixing and improving the source code

• Commenting and cleaning out the script and databases

• Documenting the model

1.5 Methodology

The work evaluates the possibilities of alternate ways to better distribute the loads and

generators to the buses in the network.

Moreover, the thesis also builds up an optimisation problem to estimate the transmission line

parameters and the transformer impedance to further improve the model.

The results are compared with the measured market values from Nordpool to evaluate the

conformity of the designed model.

1.6 Benefits, Ethics and Sustainability

The ethical and sustainability aspects taken into consideration for the project are discussed here.

The potential benefits from the project is also mentioned.

1.6.1 Benefits

Energy, and especially, electricity system modeling can be used as an important tool to answer

research questions or advice policy makers and investment decisions.

The impact of decommissioning of nuclear power plants or commissioning of large wind farms

can be studied using the model. The need for reinforcement of transmission lines between

different price areas can be predicted.

4

Introduction

If the model is accurate, it can potentially have many applications for both research and

industry.

1.6.2 Ethics

There can be a lot of ethical issues when modelling transmission grids. Since data from many

sources are used, one must validate the genuineness and credibility of the sources. One must

also be careful when estimating for the transmission line parameters, since no data is openly or

easily available for these and that they have a significant impact on the results, if performing

transient studies.

Open source models should be transparent and if the work is to be used and further developed

in future, it should be easily understandable for developers. The methodology and the program

sources are to be properly documented and the data sets used should be openly available so that

if needed it can be modified/updated regularly.

1.6.3 Sustainability

Due to environmental problems, limitations and restrictions on extensive usage of fossil fuels,

the process of transformation to a low carbon energy system based on renewable sources is

gaining pace. By creating an open source power system model, this can be used by different

actors in the electricity field, whether it be policy makers or researchers or investors, for

studying or comparing varying scenarios or for making investment decisions.

1.7 Stakeholders

If a good result is obtained, the model can have many applications both in industry and

academia.

The fact that this is an open source project means that any researcher can further build upon

this model, modify or even further improve this.

1.8 Outline

Chapter 1 introduces the thesis, the problem and solution. In chapter 2, the theoretical

background for the project is explored. The literature review on ongoing research which serves

as a reference for this work is briefed in Chapter 3. The methodology adopted is highlighted in

5

Introduction

Chapter 4. Chapter 5 discusses the results and observations from the thesis. Chapter 6 presents

the conclusions, summary of findings, limitations and future scope of the work.

6

Chapter 2

Background

The chapter discusses the background knowledge required for better understanding the thesis.

The chapter begins by introducing software tools for power system modelling and analysis,

using the python programming language. Then, the python-based PyPSA model and the

Nordic power system are discussed. A short description of the Spine Project concludes the

chapter.

2.1 Power System Modelling

Electrical power systems constitute large and highly complex and interconnected cyber-

physical systems, composed of many subsystems that transform energy sources into electricity,

transmit them over long distances and distribute them, so that the energy can be used by the

users. A typical system contains generators, transformers, transmission lines and loads.

Power system simulations are necessary for long term planning and evaluation of different

scenarios in order to improve the system operation and optimize the planning of its future

expansions. It is therefore, critical for its successful operation and management.

The limitations in studying power systems is that due to its complexity, there are many

assumptions and simplifications which are made while modelling its components. There are

many power system simulation tools such as the MATLAB-based free software PSAT or the

commercial package DIgSILENT PowerFactory, for performing power system studies.

Proprietary software packages however, limit the freedom to modify the source code for

changing certain assumptions which might be essential to understand the behaviour of the

system. To overcome this, open software packages can be used. These are usually based on

7

Background

GAMS, python, C or JAVA and can be used for energy system modelling.

For this project, the focus is on python as the programming language and a software

package called PyPSA. Another python power system tool PYPOWER, which is based on the

MATLAB-based MATPOWER, is used for solving the power flow problem.

2.2 Python for Power System Analysis

Power system studies requires the software or program to easily and efficiently perform basic

mathematical functions and nonlinear calculations, deal with multi-dimensional arrays and

complex numbers and generate quality plots. These along with personal preference that the

software should be open source, limits the choice to a handful of programming languages.

More detailed analysis of as to why python environment is appropriate for scripting power

system analyses and examples of power system modelling written in python can be found in

[2].

2.3 PyPSA

Python for Power System Analysis (PyPSA) is a free software toolbox for simulating and

optimising modern power systems that include features such as conventional generators with

unit commitment, variable wind and solar generation, storage units, coupling to other energy

sectors, and mixed alternating and direct current networks. PyPSA is designed to scale well

with large networks and long time series [3].

PyPSA can be used to perform static power flow, linear optimal power flow and security

constrained optimal linear power flow. Moreover, it has inbuilt models for all types of

generators and standard types for lines and transformers.

2.3.1 PyPSA-Eur

PyPSA-Eur is an open model dataset of the European power system at the transmission network

level that covers the full European Network of Transmission System Operators for Electricity

(ENTSO-E) area. It contains alternating current lines at and above 220 kV voltage level and all

high voltage direct current lines, substations, an open database of conventional power plants,

time series for electrical demand and variable renewable generator availability [4].

8

Background

Figure 2.1: European Transmission Network Model [4]

The Grid data for the model is taken from the ENTSO-E grid map. The model consists of only

220 kV, 300 kV and 380 kV voltage levels.

2.4 Nordic Power System

The Nordic power system is a synchronous grid with uniform frequency and electrically

interconnected during normal operation. It is a single electricity market consisting of the

transmission grids of Sweden, Norway, Finland and eastern Denmark. It is further connected

to the Baltic and United Kingdom (UK) through High Voltage Direct Current (HVDC) links.

The connection to the UK, the North Sea Link, is still under construction and is expected to be

commissioned in 2021 [5].

The Norwegian grid is under stress due to large distances between generation and consumption.

9

Background

Figure 2.2: Synchronous grids of Europe and North Africa [6]

Figure 2.3: Elspot market bidding areas [7]

The large capacity hydro power generation is located in the western part of the country whereas

the bulk of consumers are located in the east. Sweden also faces a similar issue with most of

its hydro generation up in the north while the consumption is in south. Moreover, Sweden is

at the center of the Nordic market and connects the market to the European continent. The

10

Background

increased integration results in an increased stress and a varying flow patterns in the Swedish

grid [8].

The Nordic power system is divided into different sub areas as shown in Figure 2.3, which help

indicate constraints in the transmission systems. These regions usually have different prices for

electricity, referred to as area prices. The price is based on the balance price between the supply

and demand for all the participants in the market. Power flows from area with lower prices to

the higher priced areas. The transmission capacity limits the flow between two regions.

The decision of strategy for treating bottleneck circumstances is different in Norway and

Sweden. Sweden follows a counter purchase principle whereas in Norway the system price

mechanism is used. According to the counter purchase principle Svenska Kraftnät, TSO in

Sweden, pays for the upward and downward regulation costs which are recovered through

tariffs. Under the system price mechanism, in Norway, participants are charged capacity costs.

The price is decreased in the surplus area and increased in the deficit area until the transmission

need is reduced to the capacity limit. However, in the spot-market the price system is utilized

to deal with bottlenecks between announcing regions with Sweden and Norway.

2.5 The Spine Project

The main objective of the Spine project is to develop and validate an end-to-end energy

modelling toolbox that will enable open, practical, flexible and realistic planning of future

European energy grids [9]. The idea is that the toolbox should be modular and adaptable

so that it can be used for detailed and complex energy system modelling and for large scale

problems.

The Spine Model is flexible in terms of temporal, geographical, technological and sectoral

dimensions, which will allow integrated analyses in several levels of the energy grids. These

features make the Spine Toolbox state-of-the-art in energy system modelling, and allow grid

operators, energy producers and researchers to carry out analyses that are not possible with

current modelling systems. The toolbox aims to help less experienced users to model energy

systems easily.

11

Chapter 3

Literature Review

The chapter presents the literature review on the existing methods and research on the topics,

serving as a guide for the project.

3.1 The ENTSO-E Transparency Platform

Model-based studies for electricity systems require time series data, including hour-by-

hour information on electricity consumption, wind and solar generation, import and export

constraints and prices. This information is not readily available to the public in most parts of

the world.

ENTSO-E, which represents 42 electricity TSOs from 35 countries across Europe, has made

this data available for the public through their Transparency Platform (TP) [10]. However,

ENTSO-E does not generate these data, but acquires them from various TSOs and producers,

sometimes from entities called data providers.

In [11], the authors assess the quality of the TP. One of the main drawbacks is that the data is

available only from 2015. Moreover, there are short gaps in the database and for a few countries

larger gaps. Due to different definitions of load, the statistics for load data in the TPmight differ

from other sources such as those from local TSOs, in many cases. There are also inconsistencies

and gaps in generation data.

A similar study has been conducted in [12] with the objective of comparing the ENTSO-E data

with other sources for Germany and the findings reveal that a scaling factor should be used to

match the actual representation and the representative factors provided by ENTSO-E are a poor

proxy for proper scaling factors.

12

Literature Review

3.2 Disaggregation Techniques

Accurate information about electricity production and consumption are required for power

system modelling and analysis. Several institutions keep track and record of these data and

these are often available as time series. Time-series is a finite-length sequence of ordered real

values at specific time instants.

Extracting information from a time series consists of translating the informative content of time-

series data into scalar quantities. Such procedure may be a time-consuming step should avoid

loss of information [13].

There are various disaggregation techniques. The simplest and most common one is the Naive

algorithm, which calculates an average value of the aggregated series for each interval [14].

For a price insensitive demand nature, this method will give a reasonable estimate.

Authors Chow and Lin, in [15], proposed a Generalized Least Squares (GLS) disaggregation

technique that can be extended to disaggregate yearly data to quarterly estimates. But this

method requires a consistent interval and cannot effectively deal with varying length of each

month.

As mentioned before, the data available from TSO and utility companies are usually data sets

aggregated over a geographical region and time. In [16], the authors try to define and formalize

the network disaggregation problem proposing two algorithms for it. The paper tries to map

the aggregated time series to loads and generations at each bus that are most consistent with the

given data.

In this approach a power network is modelled. With the knowledge of admittance matrix, and

the load data, the ground truth data for generations is then found by using an optimal power

flow (opf) problem. With the susceptance matrix, an dc optimal power flow problem and the

aggregated data, the DC disaggregation is formulated.

To solve this disaggregation problem, a game theory based algorithm and a bi-level

programming algorithm are used. The game theory based approach is based on Nash

equilibrium and the bi-level approach is based on Stackelberg game. The method produces

satisfactory disaggregation of the ground truth solution from the aggregated data set.

13

Literature Review

3.3 Network Models

To analyse the power flows between different regions, based on geography and/or price zones,

at different instances of time, does not require a detailed power system model. To save time

and effort simplified/reduced network models are preferred in such instances.

A simple machine learning method based on Gauss-Seidel power flow solver is presented in

[17]. This paper proposes an average network model for power system from publicly available

data. The created network models can be used to obtain power flows from net-exchanges in

different bidding zones.

In this study, the line reactances are initialized to a certain value and the admittance matrix

is then calculated. With the active and reactive power net-exchange for each node and the

admittance matrix as inputs to the solver, the power flow equations are solved. The root mean

square error of the measured and the obtained power flow as a percent of branch capacity is

calculated. The reactances for the next iteration are then changed by a small value and these

steps are repeated until the difference between each step is below a set tolerance value.

These results are validated using two methods - using a validation set (30% samples of the

training set) and a Power Transfer Distribution Factor (PTDF)-based solution. In the second

method power flows obtained by PTDFs and the created model are compared and also results

from a change in active power net-exchange from one node to another are compared. The

results indicate that simplified network models can be trusted.

3.4 Load Flow Analysis

The power flow model of a power system is built using network, generation and load data.

Power flow analysis is performed by solving the nodal power balance equations. A load flow

study determines the operating state of the system by solving nonlinear power flow equations.

The numerical methods mostly used for solving power flow equations are:

• Gauss-Seidel

• Newton-Raphson

However, in transmission grids, the active power flow is not very sensitive to voltagemagnitude

and the reactive power is not too sensitive to voltage angle difference. Hence these terms can be

decoupled and the Jacobian matrix simplified. This property is used in Fast Decoupled power

flow analysis. The main advantage for this method is that it decreases the memory requirement

14

Literature Review

for storing Jacobian but at the same time it increases the number of iterations needed to converge

[18].

The non-linear nature of ac power flow often causes computational challenges for large systems.

If a good initial guess is not available, convergence is hard to attain. Hence for many

applications, a linearized approximation is widely adopted.

The DC power flow (DCPF) is a linear approximation of the nonlinear ac system where a flat

voltage profile is assumed for all the buses. It considers only the active power flow, neglecting

reactive power flows and active power losses. The voltage angle differences are also considered

to be very small. It is an extension of the fast decoupled load flow. Analyses regarding the

accuracy of DCPF can be found in [19] and [20].

In modern electricity markets, active and reactive power can be treated separately as different

commodities with active power being a tradable commodity and reactive power an ancillary

service that has to be provided by the system operator [20]. Due to its simplicity, and linear

nature, DCPF is very often used for techno-economic studies of power systems for assessing the

influence of commercial energy exchanges on active power flows in the transmission network

[20][21].

3.5 Nordic Market Mechanisms

The Nordic electricity market consists of different time scales for electricity trading, namely

the day-ahead market, the intra-day market and the balancing market. The day-ahead and

the intra-day markets are regulated by Nordpool, while the balancing market falls under the

responsibilities of TSOs.

The day-ahead market is a forward market where the participants submit an offer 24 hours prior

to the actual market time. These accepted offers or bids can be chosen not to be delivered in

the actual market (due to reasons such as poor wind forecast) for as long as the difference in

the margin is compensated financially [22]. This results in power imbalances which are either

traded for in the intra-day markets and/or adjusted for by the market reserves.

The intra-day markets are correction markets in the sense that participants can trade the balance

and adjust previous bids submitted on the day-ahead market. The market closes one hour before

the delivery hour.

The balancing market or regulation power ensures system security. These usually trade on the

15

Literature Review

reserves which operate either automatically or manually depending on the TSO.

The majority of the electricity trading happens in the day-ahead market and the system price is

set by this. For both day-ahead and real-time markets, the auction result is a market clearing

with uniform energy prices at each bidding area, called area price. Buyers pay this price at their

location and sellers are paid the area price at their locations.

Electricity flows from areas with lower electricity prices (surplus generation) to the areas

with higher electricity prices (higher demand). When transmission capacity limits the price

convergence between areas, network congestion will create different prices for these areas.

These congestions also cause a net reduction in the transfer capacity between different price

areas. The Nordic TSOs use the Net Transfer Capacities (NTC) model to factor this information

when calculating area prices [23].

Figure 3.1: Time scales for electricity markets. Source: Training module electricity marketregulation session by leornado energy 2009

The Nordpool and the ENTSO-E databases are based on the real time, post energy balancing.

Hence the thesis will also be working on the real time market data. The power imbalances

between generation and consumption in real time, are compensated in the balancing (regulating

power) market by the TSOs. Hence an estimation is done for this power data. Later on, better

estimates are obtained but different data sources usually publish the market data within 2-3

hours after the market for that hour is closed. Since post adjustments are done to the energy

volumes, not all data sources are updated at the same time. This might cause some discrepancies

between the different data sources.

Also, market settlements, which reflect the actual values, are done later on. However, due to

16

Literature Review

the delay in the availability of these data (which could take up to months), real time market data

from the Nordpool website are used for this thesis, instead of the post market settlement data

from Svenska Kraftnät or other TSOs.

17

Chapter 4

Methodology

This chapter explains the methodology and approach used for this thesis. The chapter begins

with an introduction to the Nordic 490 (N490) model. The formulation of the power system

model is described in detail in the following sections.

4.1 The Nordic 490 Model - Base Model

The existing N490 network equivalent is a model under development covering the Nordic

synchronous area. The topology is mainly taken from PyPSA-Eur model which is based on the

ENTSO-E open grid map and improved for the Nordic region. The model consists of roughly

490 buses which represents different substations at different voltage levels and the transmission

lines between them. The various generators and combined loads at the buses are also included.

Since the project is an open source project, the data used for modelling is also open source data.

Figure 4.1 shows the structural diagram of the N490 model.

The base model takes in the raw data from the PyPSA-Eur and assigns them to different bid

zones, corresponding to the price areas of the Nordic system. Isolated parts of the grid are

removed and the topology is adjusted. The generator data is taken from ENTSO-E database

and from Open Power Systems Data (OPSD) [24]. The hydro power for Sweden is based on

the KTH’s data set and the wind farms is from the compiled database within the division of

Electric Power and Energy Systems at KTH.

The model takes in data from PyPSA-Eur database and makes some topological modifications

and restructuring in the database. This returns 6 dataframes, which are 2-dimensional python

data structure with columns of different types, and are saved as the input for the N490 class.

18

Methodology

DenmarkRegionalelectricityconsumptionstatistics

GISinformation

NordicPowerSystem

PYPOWER

NetworkPlots

Sweden

Finland

Norway

Generators

optimalpowerflowDCpowerflow

Transmissionlines

Substations

TransformersHVDCLinks

ACpowerflow

PowerFlowAnalysis

DataProcessing

DatabaseStores as pandas dataframes with GIS information

Buses/Substations

HVDCLinks

Geopy

NordpoolMarket

data

Aggregated Hourly Time Series

production

consumption

exchange

HourlyTime Series ENTSO-E

DatabaseGenerationpertype

Transformers

Lines

Generators

WindFarms

Wind FarmDatabase

KTH HydroPower PlantDatabase

PyPSA EurDatabse

RegionalElectricity

Consumption

Modified Model

N490 Class

Figure 4.1: The N490 model structure diagram

These corresponds to

• bus: buses

• gen: generators

• trafo: transformers

• link: HVDC links

• line: transmission lines

• farms: wind farms

The keys and data structure of these dataframes, which are used as inputs to the model are

explained in Appendix A.

Wind farms are separated from the other generators because there are many upcoming wind

farm projects and some of the old one get decommissioned faster than the other generators. In

order to modify and keep the list up-to-date, it is easier to modify it, if it exists as a separate

data set.

19

Methodology

The topology contains 494 buses, which corresponds to different substations at different voltage

levels, and the 11 bidding regions in the Nordic power system namely NO1-NO5, SE1-SE4, FI

and DK2. The bus distribution in the model is shown in Table 4.1. The system transmission

voltage levels are 132, 220, 300 and 380 kV.

Table 4.1: Bus info of N490 model

Country Price area No of buses Total buses

Sweden

SE1 13

194SE2 101SE3 67SE4 13

Norway

NO1 23

169NO2 56NO3 21NO4 30NO5 39

Finland FI 69 69

Denmark DK2 62 62

Total 494 494

The N490 class is capable of building the Nordic power system and assigning the network

parameters from the stored database. The model can also distribute the net generation,

consumption and HVDC power exchanges data for specific time intervals to the various nodes.

This class runs power flow studies by using/calling PyPower [25], a standard predefined python

library for performing power flow analysis. However, the inter area power exchanges obtained

after executing the power flow does not match perfectly with the market data from Nordpool.

The base model fails to converge for ac power flow studies. The model can also generate

interactive network plots.

The Improved N490 Model

In the following sections, the different improvements that were evaluated on the base model

are presented.

20

Methodology

380 kV300 kV220 kV or less

Figure 4.2: N490 model

21

Methodology

4.2 Load Modelling

The base model follows a load distribution based on the population density. To further improve

the model, different assumptions and methods are to be identified and tested to improve the

load distribution.

In this thesis, to model the load at the various buses, the annual power consumption statistics

of the countries are obtained per municipality. The current load distribution for the N490

system is revamped and the loads of each municipalities are assigned to the nearest bus in the

corresponding price area. The number of municipalities (kommunes) in the Nordic countries

are highlighted in Table 4.2. The data for Norway is based on 2018 records.

Table 4.2: Municipalities in the Nordics

Country Price area No of kommunes Total kommunes

Sweden

SE1 17

290SE2 35SE3 174SE4 64

Norway

NO1 103

423NO2 97NO3 89NO4 91NO5 43

Finland FI 311 311

Denmark DK2 46 46

The Norwegian government as of 2020, has implemented an administrative reform and the

number of counties was reduced to 11 from 19 and the number of municipalities from 422 to

356. This has not been factored due to lack of availability of data for the new regions.

4.2.1 Electricity Consumption Statistics

The historical annual electricity consumption statistics of Sweden, Norway, Finland and

Denmark are obtained from various sources. For Sweden these are available from Statistics

Sweden (SCB), and for Norway, it is obtained from Statistics Norway (SSB). The data for

Denmark is obtained from Energi Data Portal which is the energy data service portal of the

Danish TSO. The statistics for Finland are also acquired from within the division of Electric

Power and Energy Systems at KTH.

22

Methodology

Figure 4.3 shows a snapshot of the electricity consumption statistics for Sweden. This

data is reformatted into the same form as the dataframes defined in section 4.1 for all the

countries.

Figure 4.3: Electricity consumption statistics for Sweden

4.2.2 Coping with the Missing Data

It can be observed from Figure 4.3, that there are missing values in the obtained data. For

the cases where there are missing data, the accuracy of the model is evaluated after estimating

these values by inferring from some underlying relation. Curve fitting using linear regression

approach is tested in this thesis.

Linear regression attempts to model the relationship between two variables by fitting a linear

equation to the observed data. One variable is considered to be an explanatory variable, and

the other is considered to be a dependent variable [26]. In this case, the consumption is the

dependent variable, and the year is considered the explanatory variable.

The method of least-squares is used for fitting a regression line. This method calculates the

best-fitting line for the observed data by minimizing the sum of the squares of the vertical

deviations from each data point to the line. The solution tries to fit a line to the data points such

that it minimizes the squared error:

E =k∑

j=0

|p(xj)− yj|2 (4.1)

where p(xj) represents corresponding point on the regression line. The missing data are then

estimated using linear regression. An example case for linear regression is shown in Figure

4.4

23

Methodology

Figure 4.4: Example of curve fitting for estimating missing consumption data

4.2.3 Obtaining Geographical Coordinates

The data obtained for various municipalities in the Nordic countries contain only the code and

the name of the kommune (municipality) and its annual electricity consumption. In order to

aggregate the loads to the buses, the kommunes are to be mapped into appropriate buses in

their bidding areas.

To obtain the geographical coordinates for the municipalities, geopy is used for geocoding.

Geopy is a python client for several popular geocoding web services, which makes it easier for

developers to locate the coordinates of addresses, cities, countries, and landmarks across the

globe using third-party geocoders and other data sources [27].

The geographical coordinates (latitude and longitude) for the municipalities in Sweden,

Norway, Denmark and Finland are obtained using geopy.

In order to map these geodetic coordinates on to a map, these are transformed into

Cartesian/plane coordinates. A standard projection method is applied and the reference used for

this project is the SWEREF99TM. SWEREF99 stands for Swedish Reference Frame 1999 and

is a realization of the European system ETRS89. The conversion from latitude and longitude

to SWEREF99 coordinates is explained in detail in Appendix B.

The database for the municipality for each country is then updated with electricity consumption

and locations in both coordinates for easier conversion to other reference frames.

4.2.4 Mapping of Municipalities to Buses

Once all the required data - electricity consumption and positional coordinates for the

municipalities are obtained, these are assigned to the appropriate buses using the methodology

24

Methodology

discussed next.

The model maps the municipalities to the nearest bus within the appropriate price area. A script

calculates the Euclidean distance of each municipality to all the buses and sorts them by their

distance. The bus, which is closest, and in the appropriate bidding zone is assigned for the

municipality. The distance is calculated using the relation:

d = |»

(x1 − x2)2 + (y1 − y2)2| (4.2)

To make sure that the mapping is done within the correct country and price area, the region

is also checked for before assigning to bus. In the case, that the shortest distance is in a

different country or pricing area, the next shortest distance that satisfies the regional condition

is assigned.

4.2.5 Load Shares

To reflect the modified load distribution the existing loads at the buses are cleared. New loads

are distributed to the buses as a fraction of the total load per bidding area. All the loads assigned

to the corresponding buses are added up and the total load at the buses per bidding area is

calculated. The loads are then assigned as a fraction of this total load.

load share =load at bus∑

load of all the buses in that bidding zone(4.3)

4.3 Generators and Wind Farms

The lack of both regulation and standardised format for reporting country wise power plant

capacities means that a single source cannot be used for getting accurate data. Moreover,

with renewable generators being added to the grid on frequent intervals not all databases are

necessarily up to date.

The generator data for the N490 is downloaded from the PyPSA-Eur model. The PyPSAmodel

uses the Power Plant Matching (PPM) tool [28] to search for different databases and combine

the data into a standard tabular form and remove redundancies.

The PPM collects data published under free licenses and combines them into a structured table.

The various data-sources include OPSD, ENTSO-E [29] and GPD [30], to name a few.

25

Methodology

The main types of generators in the model are hydro, nuclear, thermal and wind. Hydro power

plants include pumped storage, run-of-river and reservoir. Wind power includes both onshore

and offshore wind farms. Solar power generation is added with the wind power since solar

power is not modelled separately. The remaining power plants such as coal, bio, oil and waste

are classified as thermal in the model.

In this work, the wind farms are modelled as a negative load considering only active power. The

net power generation from an area is divided among the generators as a share of their installed

capacity. However, this might not be the actual case, where certain generators are always set to

run at maximum capacity.

4.3.1 Mapping of generators and wind farms to buses

The previous model uses Voronoi cells for mapping generators to buses. Voronoi cells or

polygons for a set points are plane boundaries such that every point within the cell is closer

its corresponding generating point.

In [4], the authors accept that using Voronoi cells to aggregate load and generator data to

transmission network substations ignores the topology of the underlying distribution network,

meaning that assets may be connected to the wrong substation.

A modified method is to map the generators to their closest bus in the appropriate price area,

similar to the way that the loads have been mapped. This makes sure that the generation is

aggregated to the proper bidding zone. Hence all the generators and wind farms are reassigned

to their nearest bus in their respective bidding zone. Figures 4.5 and 4.6 show the locations of

generators and wind farms and the buses and Figure 4.7 shows the difference in the generator

allocation. The red highlight shows that there are differences between the bidding zone and/or

the allocated bus in the modified model.

4.3.2 Auxiliary Generators

The N490model generator database does not include any thermal power plants in SE1 and SE2.

But from the ENTSO-E generation per type data set, it is evident that there is power production

from thermal power plants in these regions. These are currently curtailed. In order to account

for this, two auxiliary generators with an installed capacity of 1000 MW are installed in SE1

and SE2.

26

Methodology

Figure 4.5: Generators Figure 4.6: Wind farms

Figure 4.7: Comparison of generator mapping

4.4 HVDC Links

There are 20 HVDC links in the Nordic region, 3 of which are under construction. These

are shown in Table 4.3. The HVDC links are modelled as a negative (or positive depending

on flows direction) load. These loads are time varying and the values are obtained from

Nordpool. Import and exports are correspondingly added to the respective buses for each time

step to account for the power exchanges. The power exchange through between Finland and

Russia through the ac grid interconnection is accounted for in the FiRus connection which is

27

Methodology

an additional link in the N490 model.

Table 4.3: HVDC links in the Nordics

name from area to area from bus to bus

Nord Balt LT SE4 - 6125SwePol PL SE4 - 6136Kontek DK2 DE 5525 -Storebaelt DK2 DK1 5530 -Baltic Cable 400 kV SE4 DE 5572 -NorNed - 450 kV NL NO2 - 6207Gotland SE3 SE3 6101 6139Konti-Skan SE3 DK1 6116 -Konti-Skan SE3 DK1 6116 -Store-Belt2 DK1 NO2 - 6209Store-Belt1 DK1 NO2 - 6209Skagerak NO2 DK1 6209 -Estlink 2 EE FI 6305 6315150 k (Estlink) FI EE 6313 6299Fenno-Skan 1 400 kV FI SE3 6331 6342Fenno-Skan 2 (500kV) FI SE3 6331 6360ÅL-Link (80 kV) FI FI 6332 6368NordLink NO2 DE 6203 -Sydvästlänken SE3 SE4 6132 5574North Sea Link(500 kV) GB NO2 - 6435FiRus RU FI - 6318

4.4.1 Norway - Russia grid connection

The base model did not take into account the grid interconnection between Norway and Russia

and hence the power exchanges through this line were not taken into account.

The grids of Norway and Russia are interconnected by a 132 kV transmission line and

power exchanges occur between these regions. In order to integrate this into the model, this

interconnection is modelled as a time varying load (similar to a HVDC link in the model), and

is assigned a time series with data from Nordpool.

4.5 Transformers

Transformers at three voltage levels are modelled in the system. Due to lack of information

on the transformer nameplate details, the reactances have been assumed as shown in Table

4.4.

28

Methodology

Figure 4.8: Grid connection between Norway and Russia

Table 4.4: Transformers in the model

high voltage winding (kV) Reactance (pu) Resistance (pu)

380 0.028 0.00056300 0.040 0.00080220 0.070 0.0014

The transformer database in the basemodel does not include any information of the bus voltages

directly. It searches for the bus voltages to assign impedance for each transformer. This is

improved by adding a ratio information into the database, so that the searching is avoided and

speeds up the model. The ratio information represents the transformer’s voltage ratio, i.e. the

ratio of the voltages at the from and to bus between which the transformer is located.

4.6 Transmission Lines

The line data is also obtained from the PyPSA-Eur. The model is derived from the ENTSO-E

map [31] which is an approximate representation and doesn’t follow the exact contours. This

results in the deviations in total line lengths compared with the actual statistics. The exact

impedance of the lines is also not known and hence approximations based on line lengths and

standard parameters have been made.

The current parameters are changed to reflect a more realistic representation for the model.

Table 4.5 shows the line impedance used for running this model. These are obtained from the

29

Methodology

standard AC line types that are used in the PyPSA-Eur model.

Table 4.5: Standard overhead line parameters [32]

Voltagelevel (kV) Wires Series Resistance

(Ω/km)Series InductiveReactance (Ω/km)

Shunt Capacitance(Ω/km)

Current ThermalLimit (A)

Apparent PowerThermal Limit (MVA)

220 2 0.06 0.301 12.5 1290 492300 3 0.04 0.265 13.2 1935 1005380 4 0.03 0.246 13.8 2580 1698

The distance of the manually added 380 kV line connecting the buses 6415 and 6421 in the

base model database, was assigned a value 5m in the base model. This has been corrected to

8489.613m, which represents the actual distance.

4.6.1 Line Compensation

The performance of high voltage long distance transmission lines is improved by introducing

a series compensation device, usually a capacitor. Addition of such devices often result in

improvement of power transfer capacity, system stability and voltage regulation. A detailed

analysis on the effects and reasons for including a compensation device is studied in [33].

The addition of these compensation devices, results in lower transmission line impedance and

the ratio of XC/XL is called as the compensation factor. Typical values for this is in the range

of 40% to 70%.

The base model has introduced some scaling factor for long transmission lines, 380 kv and

>200 km, of 40%. This is implemented as:

Xi,j = Xi,j ∗ 0.4 (4.4)

Not all long lines are installed with series compensation devices. The Swedish power grid has a

higher capacitance in their lines, especially the high voltage lines between the SE2-SE3. Hence

only these lines are given a series compensation. In the model, a compensation factor of 0.5 is

introduced for these lines using the following relation. Table 4.6 shows the lines where series

compensation is introduced in the model.

Xi,j = Xi,j ∗ (1− comp) (4.5)

30

Methodology

comp =XC

XL

(4.6)

Table 4.6: Series compensation for lines

from area to area from bus to bus distance (km) voltage (kV)

SE3 SE2 6381 6567 473.31 380SE3 SE2 6377 6582 460.27 380SE3 SE2 6385 6582 378.20 380SE3 SE2 6383 6544 374.37 380SE3 SE2 6377 6586 371.51 380SE3 SE2 6337 6535 367.11 380SE3 SE2 6365 6549 288.68 380SE3 SE2 6365 6550 210.58 380

4.6.2 Estimation of Line Parameters

For the assumed model, the network data which are the investigated comprise, the resistance

(R), reactance (X) and shunt susceptance (B) values, for the assumed transmission lines.

Standard transmission line parameters are used to constrain and initialize the parameter

estimation procedure. To increase the validity of the model, accurate parameters are

required.

In order to obtain the network parameters, an optimisation problem is formulated, similar to the

one described in Section 3.3. The goal with the optimisation is to obtain relative branch data

for the network which minimises the error in power exchanges between price areas.

The problem formulation and algorithm for the optimisation is shown in Figure 4.9. The flow

chart steps can be explained as follows.

1. The process starts by initialising first/ initial guess values for the optimisation parameters.

Since DCPF is the main focus of the thesis, only line reactance and transformer

impedance are optimised.

2. Power flow equations are then solved with after rebuilding the N490 model with new

parameters.

3. The objective function is calculated using the difference between measured and modelled

active power flows over all branches and all samples

4. The optimisation checks for the termination condition, i.e. if the solution results in the

31

Methodology

Define the objectivefunction

Input Parameter bounds and initial guess

Solve the objectivefunction

Update parametersTermination?(Mimimum value)

No

Optimal Solution

Yes

Start

Figure 4.9: Flow chart for optimisation

minimal value.

5. If the optimal solution is not obtained, variables are changed and steps 2-4 are repeated.

6. The optimisation ends when values result in the minimal error. The results are printed

and saved.

The math for the optimisation problem is shown below. The objective function is formulated

as:

minX,Xtrfr

1

n∗∑i,j

T∑t=1

| Pmeasuredbi−bj ,t− Pmodelledbi−bj ,t

|

s.t. Pmodelledbi−bj ,t= f(X,Xtrfr) ∀ t

X ≤ X ≤ X

Xtrfr ≤ Xtrfr ≤ Xtrfr

(4.7)

32

Methodology

The power flow equation here is shown as a variable function of line parameters, but it is solved

using the standard form with active power exchanges at each nodes as input, which remain

constant throughout the optimization process.

The solver uses Sequential Least Squares Programming (SLSQP) algorithm to converge to the

solution. An external python script is coded for performing this optimisation. The script calls

in the N490 class and then passes the line parameters as variables to it. In order to account for

any abnormalities, the power flow during optimisation is run for a week.

4.7 Validating the Model

To validate the system, the steady state response of the electrical model is built using power

generation and consumption data from the available databases and the inter area price exchanges

are compared.

4.7.1 Preparing the network

Hourly data for power generation is obtained from the ENTSO-E transparency platform [10]

and the Nordpool website and they are matched as described next. The data from the TP is

generation per type data and the sum of all different types for each time step is scaled to match

the corresponding production data from Nordpool. Time series for active power consumption

and power exchanges between the price areas are downloaded fromNordpool. The downloaded

data are aggregated per bidding area. Hence power generation at each generator for each time

step is determined based on bid zone totals.

Pgb,i,t = Pgmaxb,i∗

Pgb,type,t∑ni=1 Pgmaxb,i

(4.8)

where Pb,i,t represents power generation in ith power plant during time i and Pgmaxb,ishows

the peak installed capacity of the same power plant. Pgb,type,t shows the net aggregated power

generation per generation type in bidding zone b at time t. Wind and solar power generation

are also computed using the same relation, but separately since they are modelled as negative

loads.

Aggregated consumption data per bidding zone is available from the Nordpool database. These

are distributed among the buses with respect to their load shares. Finally, the net power at each

33

Methodology

bus is calculated as:

Pbusi,t = Pload_sharei,t ∗ Pnetb,t − Pg−windb,t − PHVDCi,t(4.9)

Pnetb,t indicates the net active power at bidding region b. Pbusi,t represents the net power at bus

i, Pload_sharei,t shows the share of load at the corresponding bus and PHVDCi,tshows the time

series for HVDC exchanges.

There are some discrepancies in the Nordpool database. The net sum of production,

consumption, imports and exports for all regions do not tally for all time steps. For a lossless

closed system, net sum of injections at all the nodes at any instant of time should be zero, or

in other words the net generation should be equal to the net consumption. In order to make

sure that this condition is met, a scaling expression is used. The base model ensures this power

balance as shown in Eq 4.10. Rather than adjusting the excess generation, the modified model

varies the load to ensure the power balance.

To improve the base model, a modified scaling expression is evaluated by using the following

two approaches: Eq 4.11 - that equally divides the load among all buses, and Eq 4.12 - 4.14

- that divides the load among the bidding regions as a share of their total contribution. The

difference in total generation to the total load at any instant of time is denoted as imbal, and

shown in Eq 4.12.

Pg = Pg ∗∑

Pload∑Pg

(4.10)

Pbusi = Pbusi ∗∑

Pgen∑Pbusi

(4.11)

imbal =∑

Pgi −∑

Pbusi (4.12)

ratio =

∑Ploadb,i∑Ploadi

(4.13)

P ′busi

= Pbusi + Pload_sharei ∗ ratio ∗ imbal (4.14)

34

Methodology

4.7.2 Power flow

The PYPOWER python package [25] is used for running the power flow. PYPOWER is a

port of MATPOWER [34] to the python programming language. In order to run a power flow

analysis, the network should be passed on as a data structure. The fields of the data structure are

version, baseMVA, bus, branch, and gen, where baseMVA is a scalar and the rest are matrices.

The version field is to make the version 2 explicit. More details regarding the data structure

format can be found at [35], under caseformat.

The N490 model is executed as a PYPOWER case and solves a dc power flow and the results

are saved. The model then calculates the power exchanges between the bidding zones and

stores it. The model is also capable of performing dc optimal power flow and ac power flow

by modifying the PYPOWER power flow command.

4.7.3 Comparison and Error Calculation

The accuracy of the model is validated by comparing the modelled and measured active power

exchanges between the different price areas. Mean absolute error, mean absolute percentage

error and root mean square error are calculated for the different solutions.

MAEbi−bj =1

n∗

T∑t=1

| Pmeasuredbi−bj ,t− Pmodelledbi−bj ,t

| (4.15)

MAPEbi−bj =1

n∗

T∑t=1

| Pmeasuredbi−bj ,t− Pmodelledbi−bj ,t

|Pmeasuredbi−bj ,t

∗ 100 (4.16)

RMSEbi−bj =

Ã1

n∗

T∑t=1

( Pmeasuredbi−bj ,t− Pmodelledbi−bj ,t

)2 (4.17)

35

Chapter 5

Results

In this chapter the results of the study are presented and compared with the base model. The

chapter first verifies the conformity of the model to the actual system and then compares

the ENTSO-E generation database with the Nordpool production data. Then the effect of

redistribution of load and reassigning the generator buses is discussed. Other changes made in

the model are also outlined. The results from the estimation of the line parameters are described

last.

5.1 Summary of Assumptions

The various assumptions and approximations used for modelling are:

1. The loads and generators are mapped to the nearest bus

2. Lossless model - dc power flow

3. Standard transmission line model and parameter for all lines

4. Wind power plants are modelled as negative load, i.e. considers only active power

generation

5. Wind farms and generators are commissioned from the beginning of each year

6. Wind farms and generators are decommissioned at the beginning of the year

36

Results

5.2 Model Conformity

To check for the accuracy of the built model, the total installed capacity in the model by type of

generation is compared with the actual installed capacity in each country. This is represented

in Table 5.1. The auxiliary thermal generators added for SE1 and SE2 are not shown in this

table.

Table 5.1: Comparison of installed capacity, values in MW

Type Sweden Norway Finlandactual modelled actual modelled actual modelled

Hydro 16315 15639.85 32684 32824.50 3243.37 3037.24Thermal 7009 4011.00 700 1514.40 9175.42 9936.93Wind 7406 7032.85 2582 2021.50 2251.91 2292.20Nuclear 8614 8626.00 0 0 2794 2784Solar 435 0 0(120) 0 1 0

Total 39779 35309.70 35966 36360.40 17465.70 18050.37

The actual installed capacity is obtained from various governmental organisations of the

respective country. The statistics for Sweden are obtained from Energiföretagen Sverige and it

shows the capacity as of December 2018. The figures for Norway is from March 2020 and is

taken from Norges vassdrags - og energidirektorat (NVE). Data for Finland is as of Feb 2019

and is obtained from the Finnish Energy Authority’s power plant register. The N490 base model

is based on the PyPSA-Eur database (from September 2019).

Table 5.2: Comparison of transmission line lengths

Length of transmissionsystem (km) Source of actual

Country Actual Model information

Sweden 15000 14030 Svenska kraftnätNorway 11000 8760 energifaktanorgeFinland 14600 6660 Fingrid

Similarly, the overall transmission system lengths are also compared and the results are shown

in Table 5.2. The errors here are due to the limitations with the open source information and also

the model database being an approximate representation of these lines. The bigger difference in

case of Finland is because of not including the 110 kV lines in the model. The modified N490

model still uses the values from the PyPSA-Eur database, because detailed information about

the lines are not openly available.

37

Results

5.3 Correction factor for ENTSO-E generation data

As mentioned in Section 3.1, the ENTSO-E data needs scaling/correction factors to match

with the actual case. In this project, it was compared with the Nordpool market data for the

corresponding bidding areas. Table 5.3, displays the aggregated average scaling factors for the

ENTSO-E data for different bidding areas. The ratio shows the net aggregated power generation

from Nordpool to that of the ENTSO-E database.

Table 5.3: Scaling factors for ENTSO-E generation data for Nordics

Bidding Area SE1 SE2 SE3 SE4 NO1 NO2 NO3 NO4 NO5 FI DK2

Jan 1.02728 1.03947 1.03048 1.18326 1.00024 0.99994 1.00003 0.99990 0.99999 1.03018 0.98506Feb 1.02022 1.02994 1.03005 1.21342 0.99995 0.99994 1.00006 0.99988 0.99999 1.01841 0.98590Mar 1.01214 1.02875 1.03108 1.23998 1.00000 1.00000 1.00012 0.99997 0.99994 1.00702 0.98727Apr 1.00942 1.02746 1.02636 1.18428 0.99978 0.99857 1.00177 0.99807 0.99718 1.03418 0.97807May 1.00828 1.01666 1.02965 1.29900 1.00020 0.99991 1.00005 1.00001 1.00000 1.01739 0.97401Jun 1.01520 1.02734 1.03111 1.36694 0.99997 0.99991 0.99994 1.00003 0.99993 1.03917 0.97019Jul 1.01834 1.05263 1.03622 1.54013 1.00006 0.99989 1.00018 1.00001 0.99986 1.03582 0.98193Aug 1.01159 1.03753 1.03713 1.36898 0.99999 0.99999 1.00000 1.00002 0.99989 1.07487 0.97263Sep 1.00854 1.03278 1.03505 1.28423 0.99950 0.99993 0.99972 0.99810 0.99585 1.07203 0.97350Oct 1.00606 1.02899 1.02276 1.23060 0.99993 0.99990 1.00008 1.00000 0.99998 1.08230 0.97995Nov 1.00222 1.00777 1.01715 1.27781 0.99997 1.00167 1.00003 1.00048 1.00003 1.06904 0.98110Dec nan nan nan nan 0.99989 0.99992 1.00009 0.99997 1.00001 1.07522 0.98248

Mean 1.01266 1.02994 1.02973 1.28988 0.99996 0.99997 1.00017 0.99970 0.99939 1.04630 0.97934

It can be inferred from the table that the generation time series from ENTSO-E for the Nordic

countries are almost accurate and matches with the Nordpool data. The differences are mostly

due to the sources and estimation of a few data.

5.4 Reassigning Load Distribution

The load data obtained per municipality is mapped to the closest bus as described in Section

4.2. Figure 5.1 shows the municipalities and buses in the model. Due to the scaled nature of

the map, it is hard to identify small islands, which is why at certain places the placeholders are

denser.

It can be seen that a fewmunicipalities in Norway lie away from the land. A closer investigation

reveals that for other points which lie on this is due to the inherent results from geopy. While

geocoding the locations, the coordinates returned by geopy for a few locations deviate from the

mainland but are still close to the actual location. Figure 5.2 shows two cases to verify this.

Hence themapping of loads is still to the correct bus even from this location. Fewmunicipalities

such as Askvoll and Sandøy in Norway, are reassigned manually, so that they are mapped onto

the correct bus.

38

Results

Figure 5.1: Municipalities in the Nordics

Figure 5.2: Deviations from the actual location

39

Results

With the loads redistributed and the model run for 2018 from 01-01-2018 to 13-12-2018

(downloaded data for Sweden is not available beyond this date), the Mean Absolute Error

(MAE) and Root Mean Square Error (RMSE) obtained are shown in the Table 5.4. Figure

5.3 shows the change in errors when compared with the base model. Due to zero exchanges

between the regions at certain intervals, Mean Absolute Percentage Error (MAPE) results in

division by zero and hence is not shown.

Table 5.4: Errors after modifying load distribution

MAE RMSEBase Modified Base Modified

Regions MWh % MWh % MWh % MWh %

SE3-NO1 138.11 15% 142.13 16% 168.90 19% 172.63 19%SE4-DK2 64.05 13% 64.05 13% 72.48 14% 72.48 14%SE1-FI 65.41 7% 81.09 9% 84.64 10% 100.42 11%SE1-NO4 141.73 51% 142.92 51% 175.08 62% 176.06 63%SE2-NO3 152.65 48% 153.09 48% 184.92 58% 185.53 58%SE2-NO4 77.88 84% 88.83 96% 101.46 110% 109.88 119%SE1-SE2 148.69 19% 155.60 20% 199.63 25% 207.35 26%SE2-SE3 121.06 4% 119.46 4% 211.12 6% 209.90 6%SE3-SE4 139.24 5% 139.24 5% 155.56 5% 155.56 5%NO4-FI 79.66 271% 100.57 342% 84.37 287% 104.35 355%NO1-NO2 212.37 17% 207.82 16% 243.97 19% 239.72 19%NO1-NO5 336.35 21% 294.53 19% 361.65 23% 320.61 20%NO2-NO5 228.38 125% 223.31 122% 248.70 136% 243.82 133%NO1-NO3 70.35 72% 66.25 68% 88.40 90% 84.66 87%NO3-NO4 110.94 20% 109.19 19% 139.42 25% 138.11 25%NO3-NO5 103.40 45% 75.04 32% 119.58 52% 91.20 39%

Total 2190.27 16% 2163.12 16% 2639.89 19% 2612.27 19%

The error % in the table is calculated based on the average power transfer in the corresponding

exchange corridor.

5.5 Reassigning Generator Bus

Table 5.5 shows the aggregate errors in power flow modelled for the system from 01/01/2018

to 13/12/2018 after the generators and wind farms are reassigned. The results are improved

because the generators are now assigned to their correct bidding zones. However, certain

offshore wind farms are manually adjusted so to be mapped on to the appropriate bidding

zone.

40

Results

-3%

0%

-24%

-1% 0%

-14%

-5%

1% 0%

-26%

2%

12%

2%

6%

2%

27%

-2%

0%

-19%

-1% 0%

-8%

-4%

1% 0%

-24%

2%

11%

2%4%

1%

24%

-30%

-20%

-10%

0%

10%

20%

30%

40%

% c

han

geMAE RMSE

Figure 5.3: Effect of modified load distribution - overall improvement of 1.24% in MAE an1.05% in RMSE

Table 5.5: Errors with generators and wind farms reassigned

MAE RMSEBase Modified Base Modified

Regions MWh % MWh % MWh % MWh %

SE3-NO1 138.11 15% 88.98 10% 168.90 19% 117.51 13%SE4-DK2 64.05 13% 55.55 11% 72.48 14% 62.05 12%SE1-FI 65.41 7% 54.45 6% 84.64 10% 68.70 8%SE1-NO4 141.73 51% 165.49 59% 175.08 62% 197.33 70%SE2-NO3 152.65 48% 124.10 39% 184.92 58% 150.07 47%SE2-NO4 77.88 84% 54.18 59% 101.46 110% 75.76 82%SE1-SE2 148.69 19% 189.17 24% 199.63 25% 231.22 30%SE2-SE3 121.06 4% 202.19 6% 211.12 6% 277.01 8%SE3-SE4 139.24 5% 151.37 5% 155.56 5% 166.96 6%NO4-FI 79.66 271% 24.89 85% 84.37 287% 32.55 111%NO1-NO2 212.37 17% 114.28 9% 243.97 19% 186.19 15%NO1-NO5 336.35 21% 154.34 10% 361.65 23% 213.44 13%NO2-NO5 228.38 125% 106.90 58% 248.70 136% 155.43 85%NO1-NO3 70.35 72% 57.73 59% 88.40 90% 75.35 77%NO3-NO4 110.94 20% 147.55 26% 139.42 25% 174.21 31%NO3-NO5 103.40 45% 95.81 41% 119.58 52% 121.06 52%

Total 2190.27 16% 1786.97 13% 2639.89 19% 2304.85 17%

41

Results

36%

13%17%

-17%

19%

30%

-27%

-67%

-9%

69%

46%

54% 53%

18%

-33%

7%

30%

14%19%

-13%

19%25%

-16%

-31%

-7%

61%

24%

41%38%

15%

-25%

-1%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

% c

han

geMAE RMSE

Figure 5.4: Effect of reassigning generator - overall improvement of 18.41% in MAE and12.69% in RMSE

5.6 Effect of adjusting of the line parameters

Modifying the transmission line parameters results in small improvement of the results. The

modified parameters, the line reactances, resistances and susceptances, achieve convergence for

the ac power flow, which is discussed in section 5.11. The results obtained for this adjustment

are shown below.

5.7 Norway-Russia Interconnection

The effect of adding the missing Norway-Russia (NO4-RU) inter-connection is only visible

during certain time intervals. This is because the power exchanges on this line are zero for most

of the time. However, even though marginal, this results in an overall improvement compared

with the base case.

The MAE and RMSE obtained for 2018 is shown in Table 5.7 and the change compared with

base model in Figure 5.6.

42

Results

Table 5.6: Effect of modifying line parameters

MAE RMSEBase Modified Base Modified

Regions MWh % MWh % MWh % MWh %

SE3-NO1 138.11 15% 90.65 10% 168.90 19% 119.42 13%SE4-DK2 64.05 13% 81.94 16% 72.48 14% 98.92 19%SE1-FI 65.41 7% 120.63 14% 84.64 10% 149.81 17%SE1-NO4 141.73 51% 173.98 62% 175.08 62% 205.16 73%SE2-NO3 152.65 48% 126.90 40% 184.92 58% 152.62 48%SE2-NO4 77.88 84% 54.03 58% 101.46 110% 75.86 82%SE1-SE2 148.69 19% 126.98 16% 199.63 25% 176.55 23%SE2-SE3 121.06 4% 138.15 4% 211.12 6% 224.36 7%SE3-SE4 139.24 5% 91.71 3% 155.56 5% 109.68 4%NO4-FI 79.66 271% 24.96 85% 84.37 287% 32.57 111%NO1-NO2 212.37 17% 114.56 9% 243.97 19% 186.51 15%NO1-NO5 336.35 21% 153.91 10% 361.65 23% 212.75 13%NO2-NO5 228.38 125% 107.04 59% 248.70 136% 155.62 85%NO1-NO3 70.35 72% 58.22 60% 88.40 90% 75.66 77%NO3-NO4 110.94 20% 158.06 28% 139.42 25% 185.43 33%NO3-NO5 103.40 45% 95.10 41% 119.58 52% 120.12 52%

Total 2190.27 16% 1716.83 12% 2639.89 19% 2281.04 16%

34%

-28%

-84%

-23%

17%

31%

15%

-14%

34%

69%

46%54% 53%

17%

-42%

8%

29%

-36%

-77%

-17%

17%25%

12%

-6%

29%

61%

24%

41%37%

14%

-33%

0%

-100%

-80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

% c

han

ge

MAE RMSE

Figure 5.5: Effect of modified line parameters - overall improvement of 21.62% and 13.59%in MAE and RMSE respectively

43

Results

Table 5.7: Errors after Norway-Russia interconnection added

MAE RMSEBase Modified Base Modified

Regions MWh % MWh % MWh % MWh %

SE3-NO1 138.11 15% 91.43 10% 168.90 19% 121.54 13%SE4-DK2 64.05 13% 55.58 11% 72.48 14% 62.07 12%SE1-FI 65.41 7% 55.90 6% 84.64 10% 70.38 8%SE1-NO4 141.73 51% 150.93 54% 175.08 62% 183.35 65%SE2-NO3 152.65 48% 136.44 43% 184.92 58% 163.43 51%SE2-NO4 77.88 84% 54.07 59% 101.46 110% 76.12 82%SE1-SE2 148.69 19% 176.11 22% 199.63 25% 218.37 28%SE2-SE3 121.06 4% 166.67 5% 211.12 6% 249.83 8%SE3-SE4 139.24 5% 151.41 5% 155.56 5% 166.99 6%NO4-FI 79.66 271% 24.87 85% 84.37 287% 32.60 111%NO1-NO2 212.37 17% 118.58 9% 243.97 19% 191.04 15%NO1-NO5 336.35 21% 145.97 9% 361.65 23% 203.07 13%NO2-NO5 228.38 125% 109.52 60% 248.70 136% 159.89 87%NO1-NO3 70.35 72% 64.33 66% 88.40 90% 83.48 85%NO3-NO4 110.94 20% 134.00 24% 139.42 25% 159.53 28%NO3-NO5 103.40 45% 70.36 30% 119.58 52% 93.47 40%

Total 2190.27 16% 1706.16 12% 2639.89 19% 2235.17 16%

34%

13% 15%

-6%

11%

31%

-18%

-38%

-9%

69%

44%

57%52%

9%

-21%

32%28%

14% 17%

-5%

12%

25%

-9%

-18%

-7%

61%

22%

44%

36%

6%

-14%

22%

-60%

-40%

-20%

0%

20%

40%

60%

80%

% c

han

ge

MAE RMSE

Figure 5.6: Effect of NO4-RU interconnection - 22.10% in MAE and 15.33% in RMSEimprovement

44

Results

5.8 Effect of Modifying Power Balancing Expression

Power balance refers to ensuring that the net generation equals net consumption. The matching

of net power generation to the net consumption is modified such that instead of curtailing the

excess generation, the load is increased by a corresponding margin in all bidding zones.

On comparing the final results using both equations, Eq 4.11 and Eq 4.12 - 4.14, it is found that

the second relation gives a better result and hence is used in the model. The MAE and RMSE

obtained for 2018 is shown in Table 5.8.

Table 5.8: Errors after miscellaneous changes

MAE RMSEBase Modified Base Modified

Regions MWh % MWh % MWh % MWh %

SE3-NO1 138.11 15% 111.83 12% 168.90 19% 136.56 15%SE4-DK2 64.05 13% 11.39 2% 72.48 14% 13.646 3%SE1-FI 65.41 7% 54.70 6% 84.64 10% 69.48 8%SE1-NO4 141.73 51% 126.88 45% 175.08 62% 164.24 59%SE2-NO3 152.65 48% 138.34 43% 184.92 58% 165.64 52%SE2-NO4 77.88 84% 52.51 57% 101.46 110% 75.941 82%SE1-SE2 148.69 19% 129.44 17% 199.63 25% 177.01 23%SE2-SE3 121.06 4% 99.93 3% 211.12 6% 196.35 6%SE3-SE4 139.24 5% 24.98 1% 155.56 5% 41.761 1%NO4-FI 79.66 271% 25.75 87% 84.37 287% 33.48 114%NO1-NO2 212.37 17% 116.20 9% 243.97 19% 180.18 14%NO1-NO5 336.35 21% 148.79 9% 361.65 23% 211.15 13%NO2-NO5 228.38 125% 114.15 62% 248.70 136% 165.82 91%NO1-NO3 70.35 72% 64.58 66% 88.40 90% 83.059 85%NO3-NO4 110.94 20% 126.96 23% 139.42 25% 152.69 27%NO3-NO5 103.40 45% 58.33 25% 119.58 52% 77.788 34%

Total 2190.27 16% 1404.76 10% 2639.89 19% 1944.8 14%

5.9 Inter Area Power Flow

In order to validate the accuracy of the model, simulations are executed for a year from January

1st to 13th December 2018 and the power exchanges are compared for each hour.

Figures 5.8 and 5.9 shows the inter area power exchanges. The blue curves represent the

measured values from Nordpool database and the green one represents the modelled power

exchanges. The orange curve shows the exchanges for the base model.

45

Results

19%

82%

16%

10% 9%

33%

13%17%

82%

68%

45%

56%

50%

8%

-14%

44%

19%

81%

18%

6%10%

25%

11%7%

73%

60%

26%

42%

33%

6%

-10%

35%

-20%

0%

20%

40%

60%

80%

100%

% c

han

geMAE RMSE

Figure 5.7: With balance relation modified, overall improvement is 35.86% in MAE and26.33% in RMSE compared with base model

The week chosen for winter is 01/01/2018 to 07/01/2018 and for summer 01/07/2018 to

07/07/2018. The scales are different in different exchanges and the normalized MAE for

each case is shown along with the corresponding curves, to facilitate the evaluation of the

results.

46

Results

13-07-2020

1

-2500-2000-1500-1000

-5000

5001000150020002500

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE3 - NO1Measured Base Model Modified Model

nMAE = 0.178958 nMAE = 0.080057

-1500

-1000

-500

0

500

1000

1500

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE4 - DK2Measured Base Model Modified Model

nMAE = 0.121862 nMAE = 0.018051

-2000

-1500

-1000

-500

0

500

1000

1500

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE1 - FIMeasured Base Model Modified Model

nMAE = 0.173665 nMAE = 0.10419

-800

-600

-400

-200

0

200

400

600

800

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE1 - NO4Measured Base Model Modified Model

nMAE = 0.429347 nMAE = 0.346218

13-07-2020

1

-1000

-800

-600

-400

-200

0

200

400

600

800

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE2 - NO3Measured Base Model Modified Model

nMAE = 0.667227 nMAE = 0.593664

-250-200-150-100

-500

50100150200250

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE2 - NO4Measured Base Model Modified Model

nMAE = 0.39777 nMAE = 0.221619

-2500

-2000

-1500

-1000

-500

0

500

1000

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE1 - SE2Measured Base Model Modified Model

nMAE = 0.089746 nMAE = 0.073447

-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE2 - SE3Measured Base Model Modified Model

nMAE = 0.023226 nMAE = 0.018938

47

Results13-07-2020

1

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

SE3 - SE4Measured Base Model Modified Model

nMAE = 0.031084 nMAE = 0.009902

-100

-50

0

50

100

150

200

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

NO4 - FIMeasured Base Model Modified Model

nMAE = 4.222606 nMAE = 1.277887

0

500

1000

1500

2000

2500

3000

3500

4000

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

NO1 - NO2Measured Base Model Modified Model

nMAE = 0.113208 nMAE = 0.019523

0

500

1000

1500

2000

2500

3000

3500

4000

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

NO1 - NO5Measured Base Model Modified Model

nMAE = 0.203659 nMAE = 0.038674

13-07-2020

1

-1000

-800

-600

-400

-200

0

200

400

600

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

NO2 - NO5Measured Base Model Modified Model

nMAE = 0.839191 nMAE = 0.240237

-500-400-300-200-100

0100200300400500

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

NO1 - NO3Measured Base Model Modified Model

nMAE = 0.271848 nMAE = 0.365116

0

200

400

600

800

1000

1200

1400

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

NO3 - NO4Measured Base Model Modified Model

nMAE = 0.116827 nMAE = 0.150291

-300

-200

-100

0

100

200

300

400

500

600

01-01-18 02-01-18 03-01-18 04-01-18 05-01-18 06-01-18 07-01-18 08-01-18

Ener

gy [M

Wh]

Time

NO3 - NO5Measured Base Model Modified Model

nMAE = 0.631578 nMAE = 0.179759

Figure 5.8: Power exchanges during winter

48

Results12-07-2020

1

-1500

-1000

-500

0

500

1000

1500

2000

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18Ener

gy [M

Wh]

Time

SE3 - NO1Measured Base Model Modified Model

nMAE = 0.204995 nMAE = 0.041601

-1500

-1000

-500

0

500

1000

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

SE4 - DK2Measured Base Model Modified Model

nMAE = 0.115787 nMAE = 0.023317

-2000

-1500

-1000

-500

0

500

1000

1500

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

SE1 - FIMeasured Base Model Modified Model

nMAE = 0.048272 nMAE = 0.041856

-300-200-100

0100200300400500600700

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

SE1 - NO4Measured Base Model Modified Model

nMAE = 0.223755 nMAE = 0.241217

12-07-2020

1

-1000

-800

-600

-400

-200

0

200

400

600

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

SE2 - NO3Measured Base Model Modified Model

nMAE = 0.224769 nMAE = 0.173835

-250-200-150-100

-500

50100150200250

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

SE2 - NO4Measured Base Model Modified Model

nMAE = 2.463875 nMAE = 1.553679

-2500

-2000

-1500

-1000

-500

0

500

1000

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

SE1 - SE2Measured Base Model Modified Model

nMAE = 0.20244 nMAE = 0.07267

-6000

-5000

-4000

-3000

-2000

-1000

0

1000

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

SE2 - SE3Measured Base Model Modified Model

nMAE = 0.02538 nMAE = 0.015277

49

Results12-07-2020

1

-5000-4500-4000-3500-3000-2500-2000-1500-1000

-500001-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

SE3 - SE4Measured Base Model Modified Model

nMAE = 0.065656 nMAE = 0.005458

-100

-50

0

50

100

150

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18Ener

gy [M

Wh]

Time

NO4 - FIMeasured Base Model Modified Model

nMAE = 1.946185 nMAE = 0.532229

-1000

-500

0

500

1000

1500

2000

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

NO1 - NO2Measured Base Model Modified Model

nMAE = 0.237059 nMAE = 0.117194

-500

0

500

1000

1500

2000

2500

3000

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

NO1 - NO5Measured Base Model Modified Model

nMAE = 0.362039 nMAE = 0.08969

12-07-2020

1

-400

-300

-200

-100

0

100

200

300

400

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

NO2 - NO5Measured Base Model Modified Model

nMAE = 2.139581 nMAE = 0.853078

-400

-300

-200

-100

0

100

200

300

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

NO1 - NO3Measured Base Model Modified Model

nMAE = 0.643373 nMAE = 0.340993

0

100

200

300

400

500

600

700

800

900

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

NO3 - NO4Measured Base Model Modified Model

nMAE = 0.099624 nMAE = 0.095877

-200

-100

0

100

200

300

400

500

01-07-18 02-07-18 03-07-18 04-07-18 05-07-18 06-07-18 07-07-18 08-07-18

Ener

gy [M

Wh]

Time

NO3 - NO5Measured Base Model Modified Model

nMAE = 0.614944 nMAE = 0.218006

Figure 5.9: Power exchanges during summer

50

Results

5.10 Power flow for 2017

Power flow analysis is performed for a different time frame, 01/01/2017 to 16/09/2017 in the

modified model. The errors obtained for this scenario are shown in table 5.9.

Table 5.9: Errors for 2017 Jan - Sept

MAE RMSERegions MWh % MWh %

SE3-NO1 109.95 14% 143.48 18%SE4-DK2 11.17 2% 13.51 2%SE1-FI 41.11 4% 71.23 7%SE1-NO4 114.60 32% 149.15 41%SE2-NO3 119.58 43% 156.69 56%SE2-NO4 64.53 74% 77.21 88%SE1-SE2 134.97 16% 164.42 19%SE2-SE3 102.89 3% 134.36 3%SE3-SE4 15.15 0% 19.65 1%NO4-FI 28.14 72% 34.05 88%NO1-NO2 73.33 8% 97.71 11%NO1-NO5 100.69 7% 134.19 9%NO2-NO5 73.96 30% 97.10 39%NO1-NO3 90.42 74% 108.26 88%NO3-NO4 92.53 23% 127.78 32%NO3-NO5 69.90 54% 101.65 79%

Total 1242.92 9% 1630.44 11%

From the table, it is visible that the errors agrees with the previous results and hence validates

the accuracy of the modified N490 model for different time frames. The base model, however

was not run for 2017.

5.11 AC Power Flow

There were convergence issues with the ac power flow for the base model. With the modified

model and trimmed transmission line parameters, convergence is now obtained for ac power

flow.

Since the reactive power compensation devices in the system are not modelled and due to the

lack of data reactive power generation and consumption information, the errors are high. The

results when ac power flow is run for 1st week of January 2018 is shown in table below.

51

Results

Table 5.10: ac power flow results

MAE RMSE

SE3-NO1 202.35 213.33SE4-DK2 602.24 708.46SE1-FI 66.10 73.05SE1-NO4 77.21 89.13SE2-NO3 216.21 238.67SE2-NO4 20.64 27.10SE1-SE2 48.42 61.71SE2-SE3 400.93 494.99SE3-SE4 619.38 716.21NO4-FI 33.23 38.05NO1-NO2 73.98 88.08NO1-NO5 67.69 88.14NO2-NO5 55.84 69.85NO1-NO3 42.91 53.29NO3-NO4 120.46 132.68NO3-NO5 27.04 32.88

Total 2674.63 3125.62

5.12 Wind as Generator

The base model and the modified model models wind farms as negative loads rather than as

generators. This is mostly due to wind farms assumed to not generate reactive power. But

with modern converters and compensation equipment, wind farms can support the voltage by

injecting reactive power and there by act similarly to a conventional generator.

Since for the dc power flow a flat voltage profile is assumed and reactive power flows are

neglected, modelling wind farms as generators ideally should not affect the overall results.

But, when wind farms are modelled as generators, a difference is obtained in the results. The

improvement in this case, despite still being a dc power flow, is because of how the database

imbalances (mentioned in Section 4.7.1) gets distributed. With wind generation no longer being

subtracted from the loads at the buses, the resultant loads at the buses changes. Hence, the

resulting ratio of the load contribution from each area changes, even though the imbalances

still remain the same.

TheMAE and RMSE obtained when wind farms are modelled as generators for the year 2018 is

shown in Table 5.11. There is an improvement of about 2% when compared with the previous

result.

52

Results

Table 5.11: Errors with wind farms as generators

MAE RMSEBase Modified Base Modified

Regions MWh % MWh % MWh % MWh %

SE3-NO1 138.11 15% 116.75 13% 168.90 19% 141.63 16%SE4-DK2 64.05 13% 12.00 2% 72.48 14% 14.50 3%SE1-FI 65.41 7% 55.93 6% 84.64 10% 70.98 8%SE1-NO4 141.73 51% 109.07 39% 175.08 62% 153.61 55%SE2-NO3 152.65 48% 129.13 41% 184.92 58% 155.26 49%SE2-NO4 77.88 84% 52.21 57% 101.46 110% 76.59 83%SE1-SE2 148.69 19% 120.88 15% 199.63 25% 170.06 22%SE2-SE3 121.06 4% 101.94 3% 211.12 6% 198.05 6%SE3-SE4 139.24 5% 22.95 1% 155.56 5% 38.89 1%NO4-FI 79.66 271% 32.50 110% 84.37 287% 40.00 136%NO1-NO2 212.37 17% 118.12 9% 243.97 19% 181.33 14%NO1-NO5 336.35 21% 142.44 9% 361.65 23% 207.65 13%NO2-NO5 228.38 125% 113.52 62% 248.70 136% 165.29 90%NO1-NO3 70.35 72% 59.68 61% 88.40 90% 77.62 79%NO3-NO4 110.94 20% 121.72 22% 139.42 25% 147.15 26%NO3-NO5 103.40 45% 56.41 24% 119.58 52% 77.00 33%

Total 2190.27 16% 1365.22 10% 2639.89 19% 1915.61 14%

15%

81%

15%

23%

15%

33%

19%16%

84%

59%

44%

58%

50%

15%

-10%

45%

16%

80%

16%12%

16%

25%

15%

6%

75%

53%

26%

43%

34%

12%

-6%

36%

-20%

0%

20%

40%

60%

80%

100%

% c

han

ge

MAE RMSE

Figure 5.10: % improvement with wind modelled as generator compared with base model.There is an overall improvement of 37.67% in MAE and 27.44% in RMSE

53

Results

5.13 Estimation of Line Parameters

Since the model is validated using dc power flow, only the line reactance and transformer

reactance affect the result. Hence optimisation is run only for these parameters for the time

being.

The optimisation is run considering the model for a week from 01/01/2018 to 07/01/2018. The

initial bounds given for the parameters given are (0.2, 0.6) for the transmission line reactance,

(0.028, 0.1) for 380 kV (hvwinding) transformer, (0.04, 0.15) for 300 kV transformer and (0.07,

0.15) for 220 kV transformer. The bounds are selected considering the extreme values for the

parameters under study.

Output from optimisation gives values of 0.542, 0.538, 0.562 Ω per km for 380, 300 and both

220 and 132 kV lines respectively and transformer impedance of 0.028, 0.040 and 0.15 per unit

for 380, 300 and 220 kV (high voltage side) transformers respectively.

The optimisation is also run with a different algorithm to check the accuracy and this case is

based on the Limited memory Broyden - Fletcher - Goldfarb - Shanno - Bounded (L-BFGS-B)

algorithm [36]. This method failed to converge but kept iterating around the same set of values

towards the end and the minimal of these was 0.572, 0.588, 0.6 Ω for per km for 380, 300

and both 220 and 132 kV lines respectively and transformer reactance of 0.028, 0.04 and 0.15

Ω for 380, 300 and 220 kV (high voltage winding) transformers.

These values are on the higher side and should be interpreted as, for the time being, the values

which best fit the given data rather than as the actual line parameters. This is due to multitude of

factors such as errors in line lengths, compensation equipment, unavailability of lines at certain

intervals etc. Also, the model currently does not differentiate between single and double circuit

lines and sees them as one.

The errors are calculated only from the interconnectors (lines which connect different pricing

regions). Since such lines have higher effect on the results, the results point to higher than

typical impedance on such lines, which is why the overall values are higher. This is due to

static power flow controllers installed on these lines.

However, with the optimised values, the resulting improvement for the model is about 3.28%

in MAE from the modified model. Table 5.12 shows the errors when the model is run with the

above obtained parameters for 2018, compared with the modified model.

Due to computational limitations, the optimisation is run only for one week time frame and

54

Results

Table 5.12: Errors after optimisation compared with modified model

MAE RMSEBase Modified Base Modified

Regions MWh % MWh % MWh % MWh %

SE3-NO1 111.83 12% 112.50 12% 136.56 15% 138.35 15%SE4-DK2 11.39 2% 11.39 2% 13.65 3% 13.65 3%SE1-FI 54.70 6% 55.57 6% 69.48 8% 70.10 8%SE1-NO4 126.88 45% 104.10 37% 164.24 59% 152.00 54%SE2-NO3 138.34 43% 129.04 40% 165.64 52% 155.26 49%SE2-NO4 52.51 57% 54.41 59% 75.94 82% 79.90 86%SE1-SE2 129.44 17% 112.73 14% 177.01 23% 163.78 21%SE2-SE3 99.93 3% 101.83 3% 196.35 6% 197.35 6%SE3-SE4 24.98 1% 24.98 1% 41.76 1% 41.76 1%NO4-FI 25.75 87% 28.04 95% 33.48 114% 35.57 121%NO1-NO2 116.20 9% 123.41 10% 180.18 14% 187.02 15%NO1-NO5 148.79 9% 148.72 9% 211.15 13% 214.49 14%NO2-NO5 114.15 62% 119.75 65% 165.82 91% 172.02 94%NO1-NO3 64.58 66% 63.74 65% 83.06 85% 82.67 85%NO3-NO4 126.96 23% 111.72 20% 152.69 27% 139.03 25%NO3-NO5 58.33 25% 56.69 25% 77.79 34% 77.51 34%

Total 1404.76 10.12% 1358.62 9.79% 1944.80 14.01% 1920.46 13.84%

-1%

0%

-2%

18%

7%

-4%

13%

-2%0%

-9%

-6%

0%

-5%

1%

12%

3%

-1%

0%

-1%

7%6%

-5%

7%

-1% 0%

-6%-4%

-2%-4%

0%

9%

0%

-15%

-10%

-5%

0%

5%

10%

15%

20%

% c

han

ge

% IMPROVEMENT CHART

MAE RMSE

Figure 5.11: Optimised line parameters results in improvement of 3.28% in MAE and 1.25%in RMSE compared with modified model

with a higher step size (10−3) used for numerical approximation of the Jacobian (of the

optimisation problem). The modified parameters improve the results but requires more work.

55

Results

The optimisation should be done on individual lines to extract accurate parameters.

5.14 Summary of the Results

The improvement after each change and the overall cumulative improvement compared with

the base case is shown in Figure 5.12 and 5.13. The model was improved by about 36% overall

compared to the base model.

1.24%

17.39%

3.92%

0.62%

17.67%

2.81%1.05%

11.77%

1.03%2.01%

12.99%

1.50%

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

Load Gen Line No-Ru Balance Wind

% im

prov

emen

t

IMPROVEMENT

MAE RMSE

Figure 5.12: % improvement after each modification

1.24%

18.41%21.62% 22.10%

35.86%37.67%

1.05%

12.69% 13.59%15.33%

26.33% 27.44%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

Load Gen Line No-Ru Balance Wind

% im

prov

emen

t

CUMULATIVE IMPROVEMENTMAE RMSE

Figure 5.13: Cumulative improvement compared to base model

The average mean absolute errors for the different interconnectors are shown in Table 5.13.

These are the values after modifying the power balancing expression and not with wind

modelled as generator. The % error is based on the average for the entire year.

56

Results

Table 5.13: Average error in power

Interconnector Measured(MWh)

Modelled(MWh) Error Error in

base model

SE3-NO1 901.28 851.43 6% 4%SE4-DK2 509.84 506.51 1% 2%SE1-FI 875.43 869.31 1% 4%SE1-NO4 280.25 312.82 12% 15%SE2-NO3 318.69 307.58 3% 6%SE2-NO4 92.39 86.43 6% 25%SE1-SE2 783.66 820.73 5% 10%SE2-SE3 3288.09 3319.93 1% 2%SE3-SE4 2874.47 2863.32 0% 5%NO4-FI 29.44 35.56 21% 124%NO1-NO2 1265.26 1238.05 2% 12%NO1-NO5 1584.90 1534.95 3% 20%NO2-NO5 182.96 239.00 31% 24%NO1-NO3 97.68 146.05 50% 50%NO3-NO4 563.54 482.94 14% 9%NO3-NO5 231.03 236.22 2% 33%

Total 13878.90 13850.84 0.20% 2.90%

A closer investigation reveals that the errors are very high for certain time steps whichmagnifies

the total errors. These are due to power flows during network outages and congestion in lines.

This is shown in Figure 5.14. The magnitude of errors are high in when power flow exceeds the

maximum NTC or when the measured exchange between areas is zero. These extreme values

increase the mean error. The errors are higher in the Norwegian grids and this is concurrent

with the results from [23] that the Norwegian interconnectors have prolonged reductions in their

NTC. The model behaves within the tolerable limits for instants when market interventions are

minimal.

Figure 5.14: Errors during network congestion and outages

57

Results

Given that the current work focuses on dc power flow, network outages of the lines for specific

hours and the corresponding NTC reductions cannot be modelled. However these can be

accounted for in an opf study. Due to the lack of generator cost functions and ampacity limits

of the lines, this cannot be performed with the current database.

58

Chapter 6

Conclusions

This chapter concludes the report. The summary of the work is presented, and the results

and findings are discussed and interpreted. The limitations of the work are listed and

recommendations for future work are mentioned. Final words conclude this chapter.

6.1 Summary of Research

Power systemmodels are an important tool for the decisionmaking and successful planning and

operation of power systems. The aim of the project was to improve upon the previous work on

the power flow model for the Nordic power system. An open source model of the same is built

on python using openly available data and properly documented. The designed/built model is

then tested for accuracy with the available market data.

6.2 Results and Interpretation of Findings

The modified model is tested in terms of accuracy by performing a power flow study for the

year 2018. The active power exchanges between different bidding zones are then compared

with the market data from Nordpool and the results are matching.

Lack of a national generator database means that not all generators are included and there might

be discrepancies in the net installed capacity. Certain generators are backup generators and

hence are not dispatched always. There are also generators, like thermal and nuclear, which

have a minimum generation limit when in operation. Since there is no open availability of such

data, themodel cannot account for these and all generators are assumed to be in operation.

59

Conclusions

Various changes made to the N490 model have resulted in different levels of improvement.

Changing the load distribution resulted in about 1.2% improvement, modifying the generator

and wind farm buses resulted in 18.4% improvement. Other changes resulted in minor

improvements and when the power balance is modified, the change is significant, jumping from

22.10% to 35.86%. Further when the model is run with wind farms modelled as generators,

rather than as negative load, there is a improvement of additional 2.8%. This is due to the

difference in how the database imbalances are settled. When compared with the base model,

the final improvement is about 37.67%, that is a substantial improvement compared to the base

model.

Network outages are not accounted for in the improved model. Due to planned maintenance or

sudden interruption, lines between regions (interconnectors) are put out of service at different

instances of time and these are not accounted for. Market interventions by the TSOs during

these instants reroutes power flow and hence causes higher errors in the model during these

time intervals.

From the results it can be observed that the flow errors are higher in the Norwegian grid. These

are mainly due to the loop flows in the grid due to the lower combined conductivity of the

adjacent Swedish grid. Since this is not reflected in the model, these loop flows cannot be

accurately rerouted. Also, line outages and NTC reductions are more for these interconnectors

and hence power flow in these lines are often at a reduced capacity.

The optimisation results improve the performance of the model for the time frame for which

it is run, but the values are not realistic and should be interpreted as the values which best fit

the data rather than as actual line parameters. In order to get more accurate parameters, the

optimisation should be done running the model over a year so that all seasons are accounted

for and that abnormalities get cancelled out and also for individual lines. This however, would

require to run it on high performance computers with code prepared to be executed in a parallel

computing environment.

With the openly available data and the limitations of these, the adjusted N490 model represents

an improved power flow model of the Nordic power system.

6.3 Limitations

Since there is no clear boundary definition for the pricing areas easily accessible, these are

estimated, possibly resulting in certain loads and generators to be mapped to the wrong bidding

60

Conclusions

zone. Also, some municipalities lie in two bidding zones and currently, they are aggregated to

only one bidding zone. This will cause marginal errors.

There might be discrepancies in the generator database, since it is set up from different data

sources which are combined. Solar power generation is not modelled separately due to lack of

availability of sources and the small installed capacity.

Transmission line parameters are estimated and hence do not reflect the true value. The model

is derived from the ENTSO-E map and is an artistic representation and does not follow the

exact contours. Hence line lengths are not 100% accurate.

Transmission outages and capacity reductions on interconnectors are not accounted for in the

improved model. Moreover, market mechanisms and interventions are not considered and

hence actual power flow during congestion deviates from the actual case.

6.4 Future Work

General quality of the database can be improved in terms of line parameters and by adding

missing names to the substations and generators. The database should be implemented to be

used in Spine toolbox.

Convergence is obtained for ac power flow. But owing to the lack of reactive power data, the

errors are high. Ac power flow studies taking reactive power compensation equipment and

consumption could be performed.

The optimisation should be run with smaller time steps for Jacobian approximation and can

be optimised for all lines or at least on the lines connecting the different regions. Certain

lines/regions have differences in reactances compared to their adjacent ones. Machine learning

techniques can also be implemented for this.

Similarly by adding general dynamic models for generators to the model, power system

stability analysis can be studied. Adding generator cost functions to the model, optimal power

flow can be performed with line limits, capacity reductions and network outages taken into

consideration.

61

Conclusions

6.5 Final Words

With the lack of openly available power flow data due to market regulations and security

issues, an improved open source power flow model of the Nordic power system was built and

evaluated.

62

Appendices

63

Appendix A

Key for Data Sets

The data sets used in the model is collected from various sources and combined together. This

section describes the indexes/keys used in the dataframes/data sets for easier understanding for

the reader.

Table A.1: Key for generator dataframe

Parameter Explanation

Index Generator index as in PyPSAname Gen nametype Generator type - hydro, nuclear and thermaltype2 More detailed typePmax Maximum active power (MW)bidz Assigned bidding zonebus Connected to bus numberuc Under construction: 0 for n/a, 2020 for year 2020, -2018 for dismantled year 2018lat latitudelon longitudex x coordinate (SWEREF99TM)y y coordinate (SWEREF99TM)country Country of locationsource source of the informationinfo dict with possible additional info

64

Key for Data Sets

Table A.2: Key for bus dataframe

Parameter Explanation

Index Bus index as in PyPSAname Bus namebidz Assigned Nordic Bidding zoneVbase Base voltage (kV)uc Under construction: 0 for n/a, 2020 for year 2020, -2018 for dismantled year 2018lat latitudelon longitudex x coordinate (SWEREF99TM)y y coordinate (SWEREF99TM)country Country of locationsource source of informationinfo dict with possible additional infoload_share share of load in bidding zone

Table A.3: Key for transformer dataframe

Parameter Explanation

Index Transformer index as in PyPSAbus0 From busbus1 To busarea0 From Bidding zonearea1 To Bidding zoneuc Under construction: 0 for n/a, 2020 for year 2020, -2018 for dismantled year 2018source source of informationinfo dict with possible additional inforatio turns ratioX Reactance (p.u.)R Resistance (p.u.)B Susceptance (p.u.)

65

Key for Data Sets

Table A.4: Key for HVDC links

Parameter Explanation

Index Link index as in PyPSAname HVDC link namearea0 From bidding zonearea1 To bidding zoneuc Under construction: 0 for n/a, 2020 for year 2020, -2018 for dismantled year 2018bus0 From busbus1 To buslat latitudelon longitudex x coordinate (SWEREF99TM)y y coordinate (SWEREF99TM)source source of informationinfo dict with possible additional info

Table A.5: Key for transmission lines dataframe

Parameter Explanation

Index Line index as in PyPSAarea0 From bidding zonearea1 To bidding zonebus0 From busbus1 To buslength length in kmcircuits Number of circuitsVbase Base voltageug Under grounduc Under construction: 0 for n/a, 2020 for year 2020, -2018 for dismantled year 2018lat latitudelon longitudex x coordinate (SWEREF99TM)y y coordinate (SWEREF99TM)source source of information (can be several)info dict with possible additional infoX Reactance (p.u.)R Resistance (p.u.)B Line charging susceptance (p.u.)

66

Key for Data Sets

Table A.6: Key for wind farms dataframe

Parameter Explanation

Index Indexstatus 1 for operationaloffshore True if it is an offshore plantlat latitudelon longitudePmax Maximum capacity (MW)AEP Estimated annual energy productioncountry Countrybidz bidding zonestart_date Date of production startstop_date Date of production stop (if dismantled)name NameRD Rotor diameterHH Hub heightPA Specific power (W/m2)x x coordinate (SWEREF99TM)y y coordinate (SWEREF99TM)bus bus numberuc Under construction: 0 for n/a, 2020 for year 2020, -2018 for dismantled year 2018

Table A.7: Key for municipality details

Parameter Explanation

Index Municipality codename Municipality namelat latitudelon longitudex x coordinate (SWEREF99TM)y y coordinate (SWEREF99TM)bidz Bidding areacountry Countrysource Source of Dataload Annual electricity consumptionbus Connected bus

67

Appendix B

Geodetic coordinates to plane

coordinates

The latitude and longitude are not particularly useful for practical applications and technical

use.

Lantmäteriet has published on their website the transformation method that they follow - Gauss

Conformal Projection, for transforming geodetic data into SWEREF99 reference. The same

conversion is used in this thesis and is attached.

68

L A N T M Ä T E R I E T

1 (5)

Geodesi 2008-08-01

Gauss Conformal Projection (Transverse Mercator)

Krüger’s Formulas

Symbols and Definitions a semi-major axis of the ellipsoid

f flattening of the ellipsoid 2e first eccentricity squared

geodetic latitude, positive north ϕ

geodetic longitude, positive east λ

x grid coordinate, positive north

y grid coordinate, positive east

longitude of the central meridian 0λ

scale factor along the central meridian 0k

difference δλ 0λ−λ

FN false northing

FE false easting

All angles are expressed in radians. Please note that the x-axis is directed to the north and the y-axis to the east.

The following variables are defined out of the ellipsoidal parameters a and f:

)2(2 ffe −=

)2( ffn−

=

⎟⎠⎞

⎜⎝⎛ +++

+= ...

641

411

)1(42 nn

naâ

Lantmäteriet Informationsförsörjning Geodetiska utvecklingsenheten 801 82 Gävle

BESÖKSADRESS Lantmäterigatan 2C TELEFON VÄXEL 0771-63 63 63 E-POST geodesi@lm.se INTERNET www.lantmateriet.se/geodesi

L a n t m ä t e r i e t 2008-08-01 2

Conversion from geodetic coordinates λ),(ϕ to grid coordinates (x,y). Compute the conformal latitude *ϕ1

( ). . . sinsinsincossin* 642 ++++−= ϕϕϕϕϕϕϕ DCBA

The coefficients A, B, C, and D are computed using the following formulas:

2eA =

( )64 ee561B −=

( ). . . e45e104120

1C 86 +−=

( ). . . e12371260

1D 8 +=

Let and 0λ−λ=δλ

)cos/*arctan(tan δλϕ=ξ′

)sin*(cosharctan δλϕ=η′

then

FNakx +⎟⎟⎠

⎞⎜⎜⎝

⎛+′′+

+′′+′′+′′+′=

Kηξβηξβηξβηξβξ

8cosh8sin6cosh6sin4cosh4sin2cosh2sin

ˆ4

3210

FEaky +⎟⎟⎠

⎞⎜⎜⎝

⎛+′′+

+′′+′′+′′+′=

Kηξβηξβηξβηξβη

8sinh8cos6sinh6cos4sinh4cos2sinh2cos

ˆ4

3210

1 Older Swedish literature refers to this quantity as the isometric latitude. Today the term isometric latitude is applied to the quantity

. The isometric latitude is related

to the conformal latitude by

)]sine1/()sine1)[(2/4/tan( ln 2/eϕ+ϕ−ϕ+π=ψ)2/*4/tan(ln ϕ+π=ψ . Cf. John P. Snyder: Map Projections -

A Working Manual, U.S. Geological Survey Professional Paper 1395.

L a n t m ä t e r i e t 2008-08-01 3

where the coefficients are computed by 4321 and , , ββββ

. . . n18041n

165n

32n

21 432

1 +++−=β

. . . n1440557n

53n

4813 432

2 ++−=β

. . . n140103n

24061 43

3 +−=β

. . . n16128049561 4

4 +=β

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