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DOCTORAL THESIS

STOCKHOLM, SWEDEN 2018

SynchrophasorsbasedSteadyStateModelSynthesisofActiveDistributionNetworks

FARHAN MAHMOOD

Synchrophasor based Steady

State Model Synthesis of

Active Distribution Networks

FARHAN MAHMOOD

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Thesis Supervisor:

Dr. Luigi Vanfretti, Associate Professor, Rensselaer Polytechnic Institute, Troy, NY, USA.

Members of the Examination Committee:

Dr. Qiuwei Wu, Associate Professor, Technical University of Denmark (DTU), Denmark.

Dr. Ali Mehrizi-Sani, Associate Professor, Washington State University, USA.

Dr. Cecilia Boström, Senior Lecturer (Docent), Uppsala University, Sweden.

Opponent:

Dr. Francisco Gonzalez-Longatt, Lecturer, Loughborough University, UK,

KTH Royal Institute of Technology

Department of Electric Power and Energy Systems

School of Electrical Engineering and Computer Science

SE-10044 Stockholm

Sweden

TRITA-EECS-AVL-2018:30

ISBN 978-91-7729-741-3

Submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy.

Copyright © Farhan Mahmood, August 2018.

Printed by: Universitetsservice US-AB

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Abstract

With the increased penetration of distributed energy resources (DERs) at lower voltage levels, distribution networks (DNs) are being transformed into active grids. This has led to a paradigm shift in the operation, planning and control of DNs. Traditional monitoring infrastructure is unlikely to satisfy the requirements that active distribution networks (ADNs) pose in terms of higher speed networking, time synchronization and signal resolution, precision and accuracy, scope, etc. As a result, high performance monitoring infrastructures are needed to fully utilize the potential of sensing devices at DNs, capable of monitoring ADNs in real-time. In this context, phasor measurement units (PMUs) have emerged as one of the most promising alternatives for ADNs monitoring in real-time.

The focus of this thesis is to exploit PMU measurements to perform real-time steady state model synthesis (SSMS) of ADNs. To this end, methods for pre-processing PMU data are developed in this thesis. As the focus of this thesis is the development of a steady state PMU application, the methods presented herein extract the quasi-steady state component in PMU measurements and feeds them to the SSMS application. In addition, the methods are capable of filtering noise, compensating for missing data, and removing the outliers in PMU signals in real-time.

The synthesis method can be applied to multiple sections of unbalanced ADNs requiring measurements from multiple PMUs. The proposed approach is generic and can be applied to any portion of a DN with any feeder configuration. The performance and the effectiveness of the proposed methodology have been illustrated in details by using real-time hardware-in-the-loop (HIL) experiments.

A detailed sensitivity analysis of the SSMS application is performed in order to show how sensitive the output of the SSMS method is to changes in its inputs. An extended version of the total vector error (TVE) was developed as an evaluation metric. The location of PMUs, system operating point and the occurrence of different disturbances are considered when evaluating the SSMS method. The sensitivity analysis is performed through several case studies as discussed above.

Finally, the thesis provides extensive experimental validation experiments on the SSMS application. Syncrophasor measurements acquired from real PMUs installed at an actual active distribution feeder in a university campus were used for this purpose. A detailed performance assessment of the SSMS method is conducted for different conditions. Additionally, a comprehensive analysis is performed to help power system operators to determine how to configure the SSMS application.

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Sammanfattning

Med den ökade användningen av distribuerade energiresurser (DER) vid lägre spänningsnivåer förvandlas distributionsnät (DN) till aktiva nät. Detta har lett till ett paradigmskifte i driften, planeringen och styrningen av DNs. Traditionell övervakningsinfrastruktur kommer sannolikt inte att uppfylla kraven som aktiva distributionsnät (ADN) ställer på nätverken när det gäller högre hastighet tidssynkronisering och signalupplösning, precision och noggrannhet, omfattning osv. Därför behövs övervakningsinfrastrukturen vara högpresterande för att fullt ut kunna utnyttja potentialen i sensorsanordningar vid DN, som kan övervaka ADN i realtid. I detta sammanhang har fasvektormätare, engelska: Phasor Measurement Units (PMUs), utvecklat sig som ett av de mest lovande alternativen för övervakning av ADN i realtid.

Denna avhandling fokuserar på att utnyttja PMU-mätningar för att utföra modellsyntes i stationärt tillstånd, engelska: ”steady state model synthesis”, (SSMS), av ADN. För detta ändamål utvecklas metoder för förbehandling av PMU-data i denna avhandling. Då fokus för denna avhandling ligger på utveckling av en PMU-applikation för stationära tillstånd, extraherar de häri presenterademetoderna den kvasi-stationära komponenten från PMU-mätningar och matar dem till SSMS-applikationen. Dessutom kan metoderna filtrera bort brus, kompensera för bortfallen data och ta bort ytterlighetsvärden från PMU-signaler i realtid.

Syntesmetoden kan appliceras på flera sektioner av obalanserade ADN som kräver mätningar från flera PMU:er. Det föreslagna tillvägagångssättet är generiskt och kan appliceras på valfri del av en DN med vilken konfiguration av matare som helst. Den föreslagna metodens prestanda och effektivitet har illustrerats i detalj genom experiment med hårdvara i en återkopplingsslinga, engelska: hardware-in-the-loop (HIL).

En detaljerad känslighetsanalys av SSMS-applikationen harutförts för att visa hur känslig utsignaler från SSMS-metoden för ändringar i dess insignaler. En utvidgad version av de totala vektorfelet, engelska: Total Vector Error (TVE), utvecklades som en utvärderingsmetod. Placeringen av PMU, systemets driftspunkt och förekomst av olika störningar beaktades vid utvärderingen av SSMS-metoden. Känslighetsanalysen utfördes genom flera fallstudier som diskuterats ovan.

Slutligen innefattar avhandlingen omfattande valideringsexperiment för SSMS-applikationen. Synkroniserade fasvektormätningar från verkliga PMU:er installerade vid en aktiv matardistribution på ett universitetsområde användes för detta ändamål. En detaljerad prestandabedömning av SSMS-metoden utfördes under olika förhållanden. Dessutom utfördess en omfattande analys som hjälper systemoperatörer att bestämma hur man ska konfigurera SSMS-applikationen.

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Acknowledgments

First and foremost, I would like to express my deepest gratitude to my main supervisor Dr. Luigi Vanfretti, first, for offering me this PhD position and later for supporting me throughout the studies. He always guided me towards the right direction in my PhD research work. His unmatched commitment to his work, courageous approach and leadership skills were really inspiring. I would like to acknowledge his amazing ability of providing valuable feedback, which really improved the quality of my publications. All in all, it was great having you as my supervisor.

I would like to thank Dr. Hossein Hooshyar for being a great mentor and a good friend. The majority of the scientific work and the publications in this dissertation would not have been possible without your substantial technical help, guidance and support. It was an amazing experience working with someone who is knowledgeable, organized and really helpful. My sincere gratitude goes to Prof. Mario Paolone for giving me an opportunity to be a guest researcher in his laboratory at EPFL, Lausanne, Switzerland. A big thanks goes to Marco Pignati for all the help and discussions.

I would like to thank my office mates and colleagues, particularly, Maxime, Jan, Tetiana, Francisco, Wei, Reza, Omar, Harold, Tin, Fabian, Dimitris, Dina, Ilias, Taha and Asif for all the interesting discussions, gossips and the nice time we spent together. Especially, I am really grateful to Shoaib Almas for all the help and support provided during the years at KTH. A special thanks goes to Jan for partially reviewing my thesis and for Swedish translation of the abstract of the thesis.

In addition, my sincere thanks go to all my Pakistani friends in Sweden for providing me a feeling like home. Especially, I would like to express my gratitude to Hamad, Usman Malik, Zeeshan Ali Khuram, Zeeshan Talib, Zeeshan Ahmed, Noman Ahmed, Naveed Khan, Umair, Ali Shaheen, Amir, Moeen, Abdul Saboor, Awais Ayjwat and Fareed.

I owe everything to my parents. Their love and support has given me strength and motivation all these years. I dedicate my thesis to my wonderful parents, particularly to my father, who always been my biggest inspiration. I am really proud to have you both in my life.

Most Importantly, I am very grateful to my lovely wife for her motivation, care and never ending love. I can never forget the way you stood beside me during thick and thin of my PhD studies. My PhD would not have been possible without your kind help and support. How can I forget my cute son Momin? ; A big thanks along with a bundle of love to him for all the remarkable and lovely

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moments. It was your presence in my life that helped me in reducing all the stress and tensions during the bad patches of my PhD. I am so happy to have you both in my life. Looking forward to all the amazing years coming ahead in our life!

Farhan Mahmood

Stockholm, August 2018

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Contents

1 Introduction ............................................................................... 1

1.1 Background ............................................................................................. 1

1.1.1 Traditional Distribution Networks (Passive) ............................ 3 1.1.2 Active Distribution Networks .................................................. 3

1.2 Motivation and Research Scope ............................................................ 4

1.2.1 Existing Monitoring Technologies ........................................... 5 1.2.2 Phasor Measurement Units (PMUs) ......................................... 6 1.2.3 Adoption of PMUs for Distribution Networks ......................... 6 1.2.4 Model Synthesis for ADNs ...................................................... 8

1.3 Challenges in Steady State Model Synthesis of ADN .......................... 9

1.3.1 PMU Data Processing .............................................................. 9 1.3.2 Lack of Network Observability ................................................ 9 1.3.3 Distribution Network Modelling & Synthesis Issues ............. 10 1.3.4 Interface between TSOs and DSOs ........................................ 10 1.3.5 Performance Analysis & Validation ...................................... 11

1.4 Contributions of This Thesis ............................................................... 11

1.4.1 Pre-processing methodologies for PMU data ......................... 12 1.4.2 Steady state model synthesis for active distribution networks 12 1.4.3 Sensitivity Analysis of the steady state model synthesis

application ......................................................................... 13 1.4.4 Experimental validation of the steady state model synthesis

application .............................................................................. 13

2 Processing of PMU data .......................................................... 15

2.1 Introduction .......................................................................................... 15

2.2 PMU Data Processing .......................................................................... 17

2.2.1 Extraction of Specific Signal Features ................................... 17 2.2.2 Bad Data in PMU Measurements ........................................... 18

2.3 Traditional Kalman Filter ................................................................... 19

2.4 The Proposed Kalman Filter Methods ............................................... 20

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2.4.1 KF Method Based on Windowing .......................................... 20 2.4.2 The Modified KF Method ...................................................... 22

2.5 Experimental Setup for KF LabVIEW Real-Time Application ....... 25

2.6 Performance Comparison of Proposed KF Methods ........................ 26

2.6.1 Difference Between Simulated Data and PMU Data ............. 26 2.6.2 Performance Comparison of Proposed Methods (For Voltage

Magnitude Signal) .................................................................. 27 2.6.3 Performance Comparison of Proposed Methods (For Voltage

Angle Signal) .......................................................................... 29

2.7 KF Performance Analysis .................................................................... 30

2.7.1 Impact of Varying Rolling Window Length on Smoothing ... 30 2.7.2 Performance Analysis Using an Evaluation Metric ................ 32

2.8 Summary ............................................................................................... 33

3 Steady State Model Synthesis ................................................. 35

3.1 Introduction .......................................................................................... 35

3.2 Methodology .......................................................................................... 37

3.2.1 Model Synthesis Based on Two PMU Measurement Points at the Distribution Network ........................................................ 37

3.2.2 Model Synthesis Based on ‘N’ Number of PMU Measurement Points at the Distribution Network ......................................... 41

3.2.3 Model Synthesis Based on One PMU Measurement Point at the Distribution Network ........................................................ 42

3.3 HIL Experimental Test Setup for SSMS LabVIEW Real-Time Application ........................................................................................... 43

3.4 Case Studies .......................................................................................... 45

3.4.1 Reproduction of the Equivalent Model Parameters in Real-Time ....................................................................................... 45

3.4.2 Incorporating the Effect of Mutual Inductances ..................... 46 3.4.3 Model Synthesis of a Sample Active Distribution Network ... 47

3.5 Summary ............................................................................................... 51

4 Sensitivity Analysis of the SSMS Method ............................. 53

4.1 Introduction .......................................................................................... 53

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4.2 Methodology for Sensitivity Analysis of the SSMS Method ............. 54

4.2.1 End-to-End Total Vector Error (TVE) ................................... 54 4.2.2 Methodology of calculating End-to-End TVE ....................... 56 4.2.3 End-to-End TVE as Evaluation Metric .................................. 57

4.3 HIL Real-Time Testing Setup ............................................................. 57

4.4 Sensitivity Analysis of the SSMS Method........................................... 58

4.4.1 Case Study 1: Change in system operating point ................... 59 4.4.2 Case Study 2: Occurrence of Disturbances ............................ 61 4.4.3 Case Study 3: Change in PMU Location................................ 62

4.5 Summary ............................................................................................... 63

5 Experimental Validation of the SSMS Method .................... 65

5.1 Introduction .......................................................................................... 65

5.2 The EPFL Campus Active Distribution Network.............................. 66

5.3 Methodology ......................................................................................... 67

5.3.1 Data Acquisition .................................................................... 67 5.3.2 Detailed Validation Model ..................................................... 68 5.3.3 Equivalent Model ................................................................... 69 5.3.4 Pre-Processing of P for use in the RTS .................................. 70

5.4 Performance Evaluation Metrics ........................................................ 71

5.4.1 End-to-End Total Vector Error (TVE) ................................... 71 5.4.2 Power Flow Comparison ........................................................ 71

5.5 Case Studies and Experimental Validation Results .......................... 72

5.5.1 Case Study 1: A Typical Load Profile ................................... 72 5.5.2 Case Study 2: Active Network Conditions (A Summer

Weekend) ............................................................................... 77 5.5.3 Case Study 3: Passive Network Conditions (A Winter Night)80 5.5.4 Case Study 4: Solar Eclipse 2015 .......................................... 82

5.6 Discussion .............................................................................................. 85

5.7 Summary ............................................................................................... 88

6 Conclusions .............................................................................. 91

Appendices ............................................................................... 95

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Appendix A: EPFL network, line parameters corresponding to Fig 5.1. .......................................................................................... 95

Appendix B: End-to-End TVEs along with the mean values corresponding to Table 5.1. .................................................... 95

Bibliography ............................................................................ 97

List of Publications ................................................................ 105

Equation Chapter (Next) Section 1

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List of Acronyms

ADN Active Distribution Network

AMI Advanced Metering Infrastructure

CIM Common Information Model

CRIO Compact Reconfigurable Input Output

DER Distributed Energy Resources

DESL Distributed Energy System Laboratory

DG Distributed Generation

DMS Distribution Management System

DN Distribution Network

EKF Extended Kalman Filter

EV Electric Vehicles

FIR Finite Impulse Response

FiTs Feed-in Tariffs

FLIR Fault Location Isolation and Restoration

GPS Global Positioning System

HIL Hardware-in-the-Loop

ICT Information and Communication Technology (ICT)

IDE4L Ideal Grid for All

IED Intelligent Electronic Device

KF Kalman Filter

KVL Kirchhoff’s Voltage Law

LTC Load Tap Changer

LVDN Low Voltage Distribution Networks

OECD Organization for Economic Co-operation and Development

PDC Phasor Data Concentrator

PMU Phasor Measurement Unit

PV Photovoltaics

REI Radial Equivalent and Independent

RLV Random Load Variation

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ROCOF Rate of Change of Frequency

RTS Real Time Simulator

RW Rolling Window

S3DK SmartGrid’s Syncrophasor Development Kit

SCADA Supervisory Control and Data Acquisition

SD Standard Deviation

SmarTSLab Smart Transmission System Laboratory

SSMS Steady State Model Synthesis

TCP Transmission Control Protocol

TSO Transmission System Operator

TVE Total Vector Error

UTC Coordinated Universal Time

WAMS Wide Area Monitoring System

Chapter 1

1 Test jkkj

Introduction

1.1 Background

Global electrical energy demand is growing rapidly which requires new investments to electricity production and delivery. However, environmental concern has caused major shift in energy policies towards a more environmentally friendly and sustainable energy system. According to International Energy Agency, electrical energy demand and its associated CO2 emissions are expected to increase by more than 30 % by 2040 [1]. Renewable sources of energy showed 40 % increase in the primary demand and their explosive growth in the power sector marks the end of the boom years for coal. As projected in [1], renewables capture two third of global investment in power plants to 2040 as they become, for many countries the least-cost source of new generation.

Fig. 1.1 shows the global average annual net capacity additions by type. Rapid deployment of solar photovoltaics (PV), helps solar becomes the largest source of low-carbon capacity by 2040. In European Union, renewables account for 80 % of new capacity and wind power becomes the leading source of electricity soon after 2030; due to rapid growth of both onshore and offshore wind generation [1].

2 CHAPTER 1. INTRODUCTION

Fig. 1.1 Global Trends for Renewable Increase, adapted from [1]

The trends show that the renewable power is expected to be the largest contributor of net additions to power capacity over the medium term. According to [2], renewables are expected to cover more than 60 % of the increase in world electricity generation over the medium term. China is the undisputed renewable growth leader and is alone responsible for over 40 % of global renewable capacity growth. According to International Energy Agency, China, United States and India will account for two thirds of global renewable expansion to 2022.

While this trend can help mitigate environmental impact of electricity generation, it comes up with unprecedented challenges for the power system. The high penetration of utility scale variable renewable sources introduces large fluctuations on the supply side, and therefore existing prime movers have to ramp up and down their production capacity [3]. This can lead to increased operational cost and in general adds more complexity in the operation and control of the power system [4], [5].

The reduced cost of PV combined with local incentives for end users like feed-in tariffs (FiTs) has facilitated the penetration of solar PV in residential and commercial areas, connected to low voltage distribution networks (LVDN) [3]. In developing markets, such as Western China, India, the Middle East, Africa and countries in the Americas that are not the member of the Organization for Economic Co-operation and Development (OECD), there is an increasing trend

1.1 BACKGROUND 3

in the share of utility scale PVs. Whereas, in Europe the focus is clearly on the development of residential and commercial PV installations.

The medium and LVDNs were originally designed as passive networks that only allows power transfer from the transmission network to the end customer (See details in section 1.1.1). Whereas, with the increase of renewable distributed generator (DGs) at lower voltage levels, distribution networks (DNs) are being transformed into active grids. This has created a paradigm shift in the operation, planning and control of DNs. Increased penetration of DGs such as PV and wind introduces several impacts on DNs such as voltage rise, reverse power flow and voltage unbalance etc., [6]–[9] (See details in section 1.1.2).

1.1.1 Traditional Distribution Networks (Passive)

Fig. 1.2 shows a traditional passive DN; where, the production of electricity is carried out, mostly, using synchronous based power generators and transmitted via long transmission lines from the power plants to load centers. The flow of electrical power is mostly uni-directional from generation points towards the consumers. The uncertainties in the operation, planning and control are relatively low. DNs are traditionally designed to be over dimensioned, in order to maintain quality of supply constraints [10].

Fig. 1.2 Passive Distribution Network.

1.1.2 Active Distribution Networks

Due to the dramatic increase in distributed energy resources (DERs) connected to low voltage grids, DNs are being transformed from passive to active grids in the last decade [11]–[13]. Fig. 1.3, shows an active distribution network (ADN), having distributed and variable generation sources (e.g. domestic rooftop photovoltaic, wind turbines, micro biomass plants etc.). Due to intermittent nature of DERs, uncertainties in the operation and control of ADNs becomes relatively high as compared to passive networks [14]. Moreover,


distribution grids are essentially being required to operate under different stress conditions (for those they were not initially designed for). Therefore, ADNs are need to become flexible, agile and better adaptable to changes brought by uncertainty [15].

Fig. 1.3 Active Distribution Network.

1.2 Motivation and Research Scope

Increased penetration of DERs introduces fundamental challenges in the operation, planning, control and management of ADNs. The presence of DGs at LVDNs may cause bi-directional flow of active power, voltage rise (specially at the feeders where PVs are connected), voltage phase unbalances, thermal overloading of components, relay coordination problems, unpredicted harmonic content and increased energy losses at LV grids [6], [8]–[10]. With the increased penetration of single phase rooftop PVs, the impact of voltage unbalances and network asymmetries become severe [6]. The unbalanced operation of three phase DN can influence the performance of induction motors and power electronics converters [11], [12].

The integration of Information and Communication Technology (ICT) technologies in electricity grids with the large share of DERs provides several new capabilities for the operation of ADNs. As indicated in [10], the new operating modes must be realized for an improved reliability by introducing the new concepts, such as; demand management, DER integration into operation, charging mechanism of plug-in electric vehicles (EVs), etc. Moreover, some advanced tools need to be explored for a better management of DERs and for an enhanced flexibility of the future ADNs. However, lack of a common

1.2 MOTIVATION AND RESEARCH SCOPE 5

architecture for information and communication systems, deficiency of standardization and inadequate framework for the interaction between Transmission System Operators (TSOs) and Distribution System Operators (DSOs) pose severe technical challenges.

Due to the passive nature of DNs, the lower value associated with its assets (compared to transmission) and the use of large design margins greatly reduced the need of monitoring within DNs during the past [16]. However, with the transformation of DNs into ADNs, adequate monitoring of DNs becomes essential due to the following reasons:

In ADNs, there are frequent violations of operational constraints (e.g. voltage limits and line ampacities) [17].

According to [16], 90 % of the customer interruptions originate from distribution systems. This motivates the need for a real-time monitoring of the network to reduce service interruptions, thus allowing for improved reliability.

The active nature of ADNs makes its operation, planning and control more complex, e.g. complexities such as bi-directional flows, phase unbalances and voltage rise, emphasize for better monitoring and management of DERs [16], [18].

As mentioned in [10], [19]–[21], the evolving role of DSOs highlights the necessity of improved monitoring and control framework for DNs.

Finally, as recommended in [22], [23], better monitoring of DNs may provide an improved situational awareness to TSOs of their connected DNs.

1.2.1 Existing Monitoring Technologies

Historically, electric grid planners and operators had limited measurements from primary and secondary distribution systems for the understanding its status and behavior. They considered designing the system only for worst cases, i.e. peak loads and faults, and tried to make sure that the grid operated with in expected limits [18]. Using this approach, they were able to obtain sufficient knowledge about the operating state of those passive DNs. Although, recently, smart metering helped in providing new information on the customer load demand and energy usage, meter data are limited in terms of the following:

Granularity, i.e. time resolution (measures every 15 minutes), and spatial resolution, i.e. number of locations.

Lack of variable measured (it may not measure voltages). Latency (most systems do not collect smart data in real-time). Scope (can only be used for measuring energy usage). Digital information integration, data from different locations and

devices is not fully interoperable.


Traditionally, relatively few number of system planners have relied on the measurements from supervisory control and data acquisition (SCADA) systems, typically available at several-seconds intervals from substations and without time synchronization, in general. Traditional SCADA scans field devices asynchronously every few seconds and is incapable of tracking grid dynamics [24], [25]. In addition, some of the physical variables of the AC network were not directly measureable, but could be estimated using the model data, based on equipment ratings and specifications. For instance, complex voltage or time shifted voltage waveforms were not observable at every node [18]. The solution for estimating the states based on these models worked in the past because of the passive nature of DNs (only having unidirectional power flows with negligible DGs at low voltage level).

Consequently, traditional monitoring infrastructure is not fit for ADNs, due to their limitations in terms of time resolutions, precision, accuracy, scope, etc. These limitations call for new monitoring tools for ADNs. A high performance monitoring infrastructure is needed to fully utilize the potential of sensing devices at DNs, capable of monitoring ADNs in real-time. In this context, phasor measurement units (PMUs) have emerged as one of the most promising alternatives for the monitoring of DNs in real-time [26], [27].

1.2.2 Phasor Measurement Units (PMUs)

According to IEEE Std.C37.118.1-2011 [28], PMU is a device that provides an estimate of the syncrophasors, frequency and rate of change of frequency (ROCOF) of the input voltage and /or current waveform, based on a common UTC time reference1. Typically a PMU is installed into an electrical substation and interfaced to the electric grid via standard current and voltage transformers. PMUs provide irreplaceable advantages for situational awareness as compared to traditional measurement devices. For instance, the reporting rate of a PMU can be as high as up to 120 samples/ seconds. Moreover, PMUs have the ability to measure phase angle changes at multiple locations which allow grid operators to detect and characterize the grid behaviors such as fast dynamic oscillations, which could not be observed using traditional devices. In addition to that, time synchronized measurement from PMUs enable aggregation, and comparison of measurements from multiple locations, which helps in improving the coordination of the operation of electric grid.

1.2.3 Adoption of PMUs for Distribution Networks

The installation of PMUs on transmission systems was one of the main recommendations of the 2003 Northeastern U.S blackout study Task Force [16]. The idea was to give system operators a broader overview of their network that could help them in detecting cascading failures and to take rapid preventive/

1 The readers are referred to [28] for the definitions of syncrophasors, frequency and ROCOF.

1.2 MOTIVATION AND RESEARCH SCOPE 7

corrective actions. Since 2003 many new tools have been developed which use PMU data have been installed at the transmission system, contributing in improving system operations and reliability. Initially, less importance have been given for installing PMUs in DNs. However, in the last decade, a sharp increase in the penetration of DERs at low and medium voltage networks resulted in many real installations of PMUs at DNs. Primarily, most of the installations were either at the universities campuses (e.g. UC Berkeley campus [29], École Polytecnique Fédérale de Lausanne [30] and Illinois Institute of Technologies [31]) or at a research Laboratory (e.g. Lawrence Berkeley National laboratory [32], [33]) or within research projects (e.g., FP7-ICT Projects [34]).The readers are referred to Appendix B of [18] for a detailed list of deployments of PMUs at DNs.

The presence/installation of PMUs at DNs offers many advantages. Some of the most relevant benefits in situational awareness of DNs are listed below:

(a) In addition to measuring voltage and current (which can also be measured by simpler devices), a PMU also measures voltage phase angle, frequency and ROCOF. These additional measurements may help to improve distribution model validation process, DER monitoring, etc.

(b) Phase angle measurements helps to detect the bi-directional flows in ADNs. Moreover, phase angle measurements across the distribution systems can be used for impedance calculations, improving the distribution modelling accuracy.

(c) Frequency measurements allow local generation to continue to operate as an electrical island even if its connection to the main grid is lost. Accurate information about the frequency is essential for keeping a balance between generation and load during islanded operation, and for reconnecting to the main grid [16].

(d) Higher refresh rates offered by PMUs allow monitoring DERs with increased level of uncertainties and variabilities due to the penetration of DERs. Such a higher level of time granularity i.e. on the order of sample per seconds, allows enhancing DN modelling, which in turn could improve the stability and planning studies based on more accurate models.

(e) Time synchronization feature of PMU enables the assessment of measurements from multiple locations, which helps in detecting topological changes, and thus may provide better system overview for simultaneously analyzing disturbance events and may provide a vital input for several control and protection functionalities for Distribution Management System (DMS), e.g. Fault location, isolation and restoration (FLIR) etc.


The aspects that might support the adoption of PMUs at distribution systems are summarized as follows:

1. Cost vs Benefits: First, since, the installation cost of a PMU (including the cost of communication infrastructure, security features and labor cost) is much higher than its equipment (PMU device) cost, therefore, optimizing the installation cost would definitely reduce the overall cost of PMUs [35]. Secondly, PMU prices and installation cost have been considerably decreased since 2010 [36]. On the other side, the cost of installation of PMUs at DNs provides attractive benefits for ADNs. For instance, PMU measurements could enable DSOs to have synchronized monitoring of their networks; for DER management, and thus offer a potential monitoring framework for the future automation of ADNs [16].

2. Integration with existing devices: PMU functionalities have already been

integrated in some commercial devices, e.g. (relays) intelligent electronic devices (IEDs), digital fault recorders etc [37]. Although such devices are mostly been used in the transmission context, some of them been installed at distribution substations. In the distribution context, the most important research question would be that, if PMU functionality can be embedded in common devices such as transformers, inverters or protective relays, etc, this would definitely result in sharp increase in PMUs installations at distribution system in near future [18].

3. Practicability of sensing & deployment: The cost associated with installing

multiple PMUs at once can be justified by the fact that several applications may take same sensing device which makes incremental cost of adding applications less than the advantages received based on those applications [16]. Secondly, once a PMU network is deployed at the DN, the same network can be used for monitoring traditional quantities, probably at higher resolution, at relatively low additional cost [18]. Moreover, the use of electronic sensors (e.g. clamp on flexible Rogowski coils) enables the deployment of sensing devices quickly and without affecting current substation infrastructure [38].

4. Limited covering area: As the area covered by DNs are much smaller as compared to transmission networks, a smaller number of PMU devices are needed to fully monitor it. Communication costs latency associated with PMU technology would be lower as a lower bandwidth would be required for incorporating a smaller geographical area.

1.2.4 Model Synthesis for ADNs

To analyze and study any phenomenon in power distribution system, it is necessary to obtain models that accurately describe the behavior of the

1.3 CHALLENGES IN STEADY STATE MODEL SYNTHESIS OF ADN 9

phenomenon. The modeling of these systems is based on laws of physics and model parameters are determined based on different experiments performed on individual components. However, this way of modeling has a weakness that the components change their property due to ageing or changing operating conditions. Therefore, models need to be updated regularly to represent the reality. Real time measurements can provide accurate information about the present system behavior. Moreover, models based on these measurements can be updated more frequently and can accurately represent the current state of the system.

In addition, large amount of real-time measurements will lead to larger computational resources. This call for the need for methods to synthesize reduced equivalent models of a DN. Currently, most of the TSOs, uses aggregated models of their connected DNs for their network studies. The methods used to determine reduced model requires a detailed model to be reduced and often make assumptions such as “pure load” that are no longer valid for ADNs. Moreover, the models are updated yearly and cannot be automatically updated. Therefore, a method for real-time model synthesis of DNs is attractive.

In this context, PMU measurements from multiple locations in DNs can be exploited to be used for steady state model synthesis.

1.3 Challenges in Steady State Model Synthesis of ADN

1.3.1 PMU Data Processing

PMU measurements are usually polluted with noise, outliers and missing samples. Moreover, measurements obtained from PMUs during different events in power systems may contain different signal features at different time scales, i.e. they contain features of different types of power system dynamics. Not all PMU applications need the same type of signals. For example, for a steady state application, the presence of dynamical oscillations may negatively impact the performance of the application. Thus, they cannot be directly fed to any application without adequate processing. Therefore, PMU data should be appropriately processed before feeding it to any target application.

1.3.2 Lack of Network Observability

As mentioned earlier, there was a little need to monitor DNs in the past. However, with the increase of DERs, especially at the low voltage network, DNs have transformed into active grids, requiring much better monitoring than before. Improved network observability will help system operators in maintaining security of supply [22]. Unavailability of measurements at DNs is one of the major challenges in model synthesis of ADNs.


1.3.3 Distribution Network Modelling & Synthesis Issues

There are some serious challenges associated with DN modelling. First, DN models are not updated regularly; therefore they may not fully represent the actual behavior of the network. Planning studies based on outdated models may lead to inaccurate results. Secondly, DN models may not be as accurate as expected [16], [39]. This is because, the accuracy and performance of those models cannot be guaranteed, due to the lack of sufficient measurements at the DNs for modeling purposes.

Current methods used by TSOs to determine the reduced models of their DNs requires a detailed model of the network to be reduced [40], and often make assumptions e.g., aggregating whole DN into a pure load. However, this assumption is no longer valid, considering the active nature of DNs. In some studies, a portion of the detailed models are used for voltage stability studies, however, the models are updated yearly and cannot be updated automatically. As DNs are mostly unbalanced, reduced models of these networks should preserve their unbalanced behavior. In addition to that, keeping in mind the increased level of variabilities and uncertainties in ADNs, their network models should be updated much faster to get a real-time situational awareness of the network.

Therefore, an appropriate methodology should be developed to synthesize reduced equivalent models for unbalanced, three phase ADNs, in real-time.

1.3.4 Interface between TSOs and DSOs

According to ENTOS-E [22] operational & planning interactions between TSOs and DSOs are insufficient for existing and future needs, and therefore, should be improved. In this context, a systematic revision is taking place determine the roles and the responsibilities for both TSOs and DSOs. It was recommended in [22] that TSOs will need to continue to have the leading responsibility for balancing, frequency control and system restoration, whereas DSOs will maintain their responsibility for managing their networks, particularly, emphasizing on congestion and voltage management.

As discussed in [22], [41], that the information exchange between TSOs and DSOs for the purpose of network planning should be based on a structured approach. However, lack of standardized data formats, is one of the biggest challenges in the information exchange between TSOs and DSOs. The use of common information model (CIM) [42], can be one of the solutions to be adopted for exchanging useful information between TSOs and DSOs [43].

In this context, developing a methodology for synthesizing steady state models of ADNs, provides a first step towards improving the interactions between TSOs and DSOs. Reduced equivalent model of ADNs may potentially be used in energy management functions of TSOs, which, facilitates the need of exchanging those models with TSOs. To this end, an appropriate framework should be

1.4 CONTRIBUTIONS OF THIS THESIS 11

developed for exchanging those models of ADNs with TSOs. However, note that this thesis does not cover the development of such a framework and is out of the scope of this research.

1.3.5 Performance Analysis & Validation

After the development of PMU data-based method, one of the biggest challenges is to test the robustness of the method’s output in the presence of various uncertainties, for which a detailed sensitivity analysis is required. Moreover, development of an extensive performance analysis procedure is a prerequisite, to test and validate the method’s performance both in a laboratory environment and on a real system.

This thesis develops and uses testing, validation and performance analysis for a model synthesis application. The methods have been developed exclusively for the application in mind. However, they serve as an example of the different approaches and considerations that should be taken into account when developing a new PMU application.

1.4 Contributions of This Thesis

The focus of this research is to exploit syncrophasor measurements for performing real-time steady state model synthesis (SSMS) of ADNs. The thesis begins by presenting the development of the methodologies for pre-processing of PMU data to be used in the steady state models synthesis method. It is then followed by a comprehensive method development for SSMS for multiple portions of unbalanced ADNs. The proposed approach is generic and can be applied to any feeder configuration. The performance of the developed techniques has been assessed by using a real-time hardware-in-the-loop (HIL) laboratory simulation setup, in the first step.

Furthermore, the robustness of the SSMS method is demonstrated in the presence of various uncertainties by conducting a detailed sensitivity analysis of SSMS method. Finally, an extensive field validation of the SSMS method is carried out by applying the method in a real active DN feeder, where measurements from the real PMUs installed at the EPFL campus are used.

The contributions of the thesis can be summarized as follows:

1) Development of the methods that perform pre-processing of PMU data to be used in SSMS method, and real-time implementation & testing of the applications based on those methods.

2) Design and implementation of the detailed methodology that performs three phase, steady state model synthesis (SSMS), for multiple portions of unbalanced ADNs, and real-time implementation, testing and


validation of the SSMS application in SmarTSLab laboratory environment.

3) A comprehensive sensitivity analysis of the SSMS method. 4) Extensive experimental (field) validation of the SSMS methodology.

Each of these contributions will be covered in a separate chapter and the following sub-sections will briefly describe each contribution.

1.4.1 Pre-processing methodologies for PMU data

Previous works do not consider that different applications will only utilize information about a specific time-scale contained in PMU data. The contribution of this thesis is to apply the Kalman filter (KF) technique to separate the different time-scales. The application of KF is presented based on two different methods for PMU data processing in real-time. The first KF method applies windowing of the PMU data; therefore it has limitations when utilized in the real-time applications. Therefore, a second KF method (i.e., “the modified KF”) is proposed, which is suitable for real-time applications as it does not perform windowing of PMU data.

The added value of proposed methodologies is to provide the “right” kind of information contained in the PMU data for specific time-scales at which different applications operate. As the focus of this thesis was the development of steady state model synthesis (SSMS) application, the KF presented herein extracts the quasi-steady state component in PMU measurements and feeds them to SSMS application.

In addition to that, the proposed methods are capable of reducing noise, compensating for missing data and filtering outliers from input PMU signals in real-time. A comparison of proposed methods has been carried out using the PMU data generated from a hardware-in-the-loop (HIL) experimental setup. In addition, a performance analysis of the proposed methods is performed using a specific evaluation metric.

The proposed methods and their details are discussed in Chapter 2, and the results have been published in a paper in MDPI Journal of Energies [44] and in a paper presented at IEEE 15th International Conference on Environment and Electrical Engineering (EEEIC), 2015 [45].

1.4.2 Steady state model synthesis for active distribution networks

This thesis proposes a methodology that performs steady state model synthesis (SSMS), for multiple sections of unbalanced ADNs using dynamic measurements (time series) from multiple PMUs. The proposed approach is generic and can be applied to any portion of a DN with any feeder configuration. Although having more PMUs provides better observability and allows the SSMS

1.4 CONTRIBUTIONS OF THIS THESIS 13

application to determine more detailed models, the developed SSMS application does not put any requirement in terms of the number of installed PMUs. The performance and the effectiveness of the proposed methodology have been illustrated in details by using RT-HIL simulation setup at SmarTS-Lab.

The thesis presents a direct application for synthesizing the reduced models for DNs in real-time. Although, it provides a first step for answering the need of reduced models, especially in ADN, the question regarding how to use and integrate this application into current power system operation and planning tools, is out of the scope of this thesis.

The proposed methodology i.e. SSMS is discussed in Chapter 3, and the method with application examples has been published in a journal paper in the IEEE Transactions on Power Delivery [46].

1.4.3 Sensitivity Analysis of the steady state model synthesis application

The first challenge related to the performance analysis of the SSMS application was to test how sensitive the output of the SSMS method is to the changes in the inputs to the application. The requirement was to vary each input at a time, so that its impact on the output of the application could be investigated.

In this context, this thesis presents a detailed sensitivity analysis of SSMS application. An extended version of the Total Vector Error (TVE) is used as a metric to evaluate the sensitivity of the output of the application to the changes in the inputs. Location of PMUs in the system, system operating point, and occurrence of different disturbances are considered as the input to the SSMS method. The sensitivity analysis is performed through several case studies each containing changes in one of the inputs.

A detailed summary of the sensitivity analysis is presented in Chapter 4. The main results of the case studies based on the analysis are published in a paper presented at the IEEE Power & Energy Society General Meeting, 2017 at Chicago, IL, USA [7].

1.4.4 Experimental validation of the steady state model synthesis application

By successfully testing a methodology on real systems, not only demonstrates its applicability, but also shows the practical feasibility of the method. This adds a significant value to the method itself, moreover, also facilitates its implementation on real systems.

The contributions to this thesis in methods for experimental testing and validation are:


An HIL experimental validation method of the PMU-based SSMS application.

A performance assessment of the SSMS application using “real” PMU data from a distribution feeder.

A detailed analysis of the parametrization of the SSMS application w.r.t. model parameter estimation update rate.

The contributions summarized are further explained in the subsequent section. In this thesis, an extensive experimental validation of the SSMS application is performed. The syncrophasor measurements were acquired from the real PMUs installed at an actual active distribution feeder at EPFL’s campus, Lausanne, Switzerland. The extended version of the Total Vector Error (TVE) concept (first introduced in [7]) and power flow comparisons at the PMU buses were used as performance evaluation metrics.

In this thesis, a detailed performance assessment of the SSMS method is conducted by testing the method extensively under different conditions. The method was tested by utilizing the PMU data for the days of the year when the targeted distribution feeder at EPFL campus was mostly active (i.e. with a surplus of PV generation) and for the time when it was mostly passive (i.e. with minimal PV generation). Moreover, the partial solar eclipse event of 2015 that occurred in Switzerland [47] was analyzed in order to investigate its impact on the performance of the SSMS method.

Additionally, a comprehensive analysis is presented, which might help power system operators to configure a target application based on the SSMS method. It is shown how the performance of the SSMS method, and hence the estimation error, varies by varying the update rate of the target application. The tradeoff between estimation accuracy (tracking) and update rate (speed) is determined.

A detailed description of the experimental validation procedure is given in Chapter 5. The most important results of the field validation are published in a journal paper in the IEEE Access [48].


Chapter 2

2 Test jkkj

Processing of PMU data

2.1 Introduction

Funded by the European Commission’s 7th Framework Programme for Research and Technological Development program (FP7), the Ideal Grid for All (IDE4L) project, has defined, developed and demonstrated a distribution network (DN) automation system, IT systems and applications for active network management [10]. As part of work package 6 of the project, intelligent applications for monitoring, control and protection of ADNs are developed by exploiting PMU data. This motivates the need for exploring some appropriate methodologies for PMU data processing.

As required by IEEE standard [28], the total vector error (TVE) between a measured phasor and its reference value should be less than 1 % under steady state operation. However, in field installations, this criterion might not be met due to the presence of different measurement uncertainties in PMU data [49]. Bad PMU data can distort Wide Area Monitoring System (WAMS) displays, jam calculation engines, or cause false alarms [50]. Therefore, there is a clear need to process PMU data before using it in different applications.

PMU measurements are usually polluted with noise, outliers, and missing samples. Thus, they cannot be directly fed to an application without adequate

16 CHAPTER 2 PROCESSING OF PMU DATA

processing. Moreover, measurements obtained from PMUs during different events in power systems contain different signal features at different time scales. Hence they contain features of different types of power system dynamics. In addition, not all PMU applications need the same type of signals. In order to feed PMU data to different applications effectively, it should be appropriately processed in different ways before feeding it to applications. For steady state applications, like conventional state estimation, the presence of oscillations and noise around the steady state will negatively impact the performance of the application [51]. Therefore there is a need to remove these dynamic components from signals to effectively use them in steady state applications.

In [37]–[39] some methods of correcting different types of errors in PMU measurement are presented. The application of Kalman filters (KFs) in state estimation using PMU data has been extensively discussed in [51]–[55]. In [51], a method for extracting the steady state of input PMU data using finite impulse response (FIR) and median filters was presented. However, important aspects of dealing with noise, outliers and replacing missing data from PMU measurements are not considered. Furthermore, the method has been discussed only for offline applications.

In [52], a PMU data conditioning algorithm for the PMU data was implemented using Kalman filters. In [53], an optimal assessment of the process noise covariance matrix Q on the accuracy of state estimation is made. A two-stage KF approach is presented in [54] to simultaneously estimate the static and dynamic states. In [56], a procedure is presented that uses iterated KF to perform state estimation of an ADN by utilizing PMU measurements. In [57], an application of a state estimation algorithm is proposed for re-synchronization of distributed generation in a distribution system. In [58]–[60], dynamic state estimation for synchronous machines are presented using Extended KF (EKF) that utilize PMU measurements. None of these approaches presented in these works, focus on the steady state estimation and are not suitable to extract steady state components from input PMU data. Therefore, a method is required to perform both data processing and extraction of steady state components from input PMU data in real-time.

Additionally, previous works do not consider that different applications will only utilize information which lies in the time scale of interest. The novel contribution of this chapter of the thesis is to apply the KF technique to separate the different time-scales. The thesis presents the application of a KF technique for PMU data processing in real-time. As the ultimate goal of this thesis is the development of steady state model synthesis (SSMS) application, therefore, KF presented herein extracts the quasi-steady state components of PMU measurements and feeds them to SSMS application.

Two methods have been presented using KF technique to extract quasi-steady state components. The first KF method applies windowing of the PMU data;

2.2 PMU DATA PROCESSING 17

therefore it has limitations when utilized in the real-time applications. Therefore, a second KF method (i.e., “the modified KF”) is proposed, which is suitable for real-time applications as it does not perform windowing of PMU data. The methods are capable of filtering noise, compensate for missing data and removes outliers in PMU measurements in real-time.

2.2 PMU Data Processing

2.2.1 Extraction of Specific Signal Features

Figure. 2.1 shows a signal containing the power system response to typical events, which leads to the dynamics at different time scales. Typical power system dynamic phenomena that can be identified from different components of the PMU signal are:

Discrete Events (e.g., transmission line switching, transient stability) ~ milliseconds

Small-signal stability ~ seconds

Tap changer operation (voltage stability) ~ minutes

Identifying these events can help system operators to take appropriate actions in time. Depending upon the nature of these events, actions can be preventive, corrective or restorative [61]. Therefore, it is very important that the PMU applications that are used to identify these type of dynamic process are provided with ”clean” data so that no unnecessary actions can be taken based on an application’s results. The power system’s response to these events as captured by the PMU data has to be processed in different ways before being fed to different applications. Moreover, processing of PMU data should be application specific, i.e., the correct feature of the signal shown in Fig. 2.1 should be extracted and fed to each application. The focus of this thesis is the development of steady state applications, which means that the raw PMU data should be processed appropriately in order to extract the steady state components from the signals.


Fig. 2.1 Signal features belonging to different time scales in a PMU signal.

2.2.2 Bad Data in PMU Measurements

Figure 2.2 shows a voltage magnitude as generated by a PMU using a hardware-in-the-loop (HIL) lab setup. Discrete events, such as tap changer operation result in outliers in PMU data, as can be seen on the left hand side of Fig. 2.2. These outliers can affect the performance of target applications. The other problem shown in Fig. 2.2 is missing data. Missing data is not accounted for many applications and may negatively affect the calculated output. Also shown in the zoomed in part of Fig. 2.2 is the problem of measurement noise. Feeding noisy data to steady state applications can lead to wrong results. Therefore, all of these practical problems need to be addressed by using appropriate data processing methods. The data processing methods using KF, adopted in this thesis to overcome these issues, will be discussed in Section 2.4.

Fig. 2.2 Problems in PMU voltage measurement.

2.3 TRADITIONAL KALMAN FILTER 19

2.3 Traditional Kalman Filter

A linear discrete-time controlled process is assumed to have linear stochastic process equations and measurement equations:

1 1x Ax Bu wk k k kz Hx vk k k

= + +- -= +

(2.1)

where x is the state vector, z is the measurement vector, A is the n × n matrix that relates the state at previous time step k−1 to the state at current step k, which is assumed to be constant in each iteration, B is the control input matrix which relates the input u to the state x and H is the m × n matrix which relates state xk to the measurements zk. The process noise ωk and measurement noise vk are assumed to be two mutually independent random variables with normal probability distributions:

( ) (0, )

( ) (0, )

p w N Q

p v N R

(2.2)

where Q is the process noise covariance matrix and R is the measurement noise covariance matrix. These two matrices are usually assumed to be constant but can be updated at each time step. The KF algorithm can be divided into two parts, as discussed below.

(a) Time Update Equations (Prediction)

The time update equations are responsible of projecting forward (in time) the previous state estimate

1ˆ kx and the estimated error covariance

1kP to give a

priori state estimates ˆkx and a priori error covariance estimate kP- for the next

step k:

ˆ ˆ 1 1

1

x Ax Buk k kTP AP A Qk k

- = +- --= +-

(2.3)

(b) Measurements Update Equations (Correction)

Measurement update equations are responsible for providing feedback by incorporating a new measurement zk into a priori estimate to obtain an improved a posteriori estimate:


1( )

ˆ ˆ ˆ( )

( )

T TK P H HP H Rk k kx x K z Hxk k k k kP I K H Pk k k

- - -= +- -= + -

-= - (2.4)

where K is an n × m matrix known as Kalman gain matrix, zk is the actual measurement at step k,

kHx- is the predicted measurement,

kx is the a posteriori

estimate, which is a linear combination of an a priori estimate kx - and the

weighted difference between an actual measurement and predicted measurement. From the above expressions it can be concluded that reducing the magnitude of the elements of R, an actual measurement zk is trusted more and predicted measurement

kHx- is trusted less. On the other hand, as the a priori estimated

error covariance kP- approaches zero, the predicted measurement is trusted more

than the actual measurement.

To summarize, the KF is a predictor-corrector algorithm. After each time and measurement update pair, the process is repeated with the previous a posteriori estimates used to project a new a priori estimate. In addition, the KF does not require all the previous data at each estimate, instead, it just recursively conditions the current estimate on all the past measurements. This makes the KF a suitable method for real time applications. Moreover, the accuracy of a KF output is influenced by the measurement and process noise covariance matrices, i.e., R and Q [62]. Therefore these two parameters can be exploited in a proper way to perform bad data processing and also extracting the proper signal feature of the PMU data.

2.4 The Proposed Kalman Filter Methods

2.4.1 KF Method Based on Windowing

Originally introduced in [45], this proposed KF technique is implemented to extract the steady state components from PMU signals while attempting to mitigate all kinds of bad data from it. This is carried out by assuming that the dynamic components in the PMU data are measurement noise. The KF is applied to reduce the noise and to increase the accuracy of PMU data, and is adaptively updating the value of R in each KF iteration. The KF algorithm was implemented in MATLAB. PMUs usually have a minimum of four state variables to be estimated, i.e., V, ϴ, I and δ which correspond to the variables that a PMU measures [63]. In the assumed process model given in (2.1), i.e., we set A to be the identity matrix, because the time step between KF iterations are small enough to assume that the current state is equal to the previous state, B chosen to be zero

2.4 THE PROPOSED KALMAN FILTER METHODS 21

as there is no input u to the process. Finally, in the measurement update equations, H is also the identity matrix because the states are directly measured.

An overview of the KF implementation is shown in Fig. 2.3. The initial estimates of

1ˆ kx and

1kP are used as the input to the time update (prediction

step). The predictor step is the same as given in (2.3), projecting forward (in time) the previous state and error covariance estimate to produce the predicted state and error covariance for the next step. The corrector step is, however, not the same as used in conventional KF. Instead, in addition to (2.4), the residue is calculated in (2.5), for each sample, as the difference between state estimation

kx

and actual measurement zk:

ˆResidue k kx z= - (2.5)

Fig. 2.3 Kalman filter windowing method overview.

The variance of the calculated residue in (2.5) is computed in each step in (2.6) using rolling windows. This gives the measurement covariance matrix R:

2

(Residue)

[(Residue [Residue]) ]new

new

R Var

R E E

=

= - (2.6)


where, E is the mathematical expectation of the value. The estimated measurement covariance matrix R is therefore updated in each time step, and is used for the next correction step:

newR R= (2.7)

As explained, instead of using a whole parcel of data at a time, the proposed method processes rolling windows of PMU data to attempt to filter small signal oscillations and noise. As can be inferred from the equations (2.1) – (2.7), existence of any oscillation, noise or outlier leads to a large difference between the actual measurement zk and the state estimation

kx , causing the residue to

become larger. As R is calculated on the basis of the residue, R becomes larger as well. In this case the actual noisy measurement zk is trusted less, while a priori

state estimate kx- is trusted more when calculating the new estimate

kx . Therefore

most of the oscillations can be easily filtered out and a smoother response is obtained for steady state applications. It is worth noting that although the proposed KF method can be implemented in real-time, it’s not an optimal solution as it requires keeping a rolling window of data for calculation of the residue. Therefore, an improved KF method was developed which will be discussed next.

2.4.2 The Modified KF Method

The main idea behind this development is that R and Q can be updated in real-time to perform both bad data handling and extracting the steady state components of the PMU data. As we are only interested in the quasi-steady state component of the true state, any oscillations appearing in the measured signal should be identified and removed. The estimated measurement covariance matrix R will be updated depending upon the quality of the measurements to filter out the bad data and extract the steady state component. The estimated process covariance matrix Q will be updated to treat the un-modeled process noise which is, in our case, any change in the steady state value of the measured signal. This is because the process model, A, is set to the identity matrix, I, in order to force the output of the KF to settle at its steady state value.

The starting point of the proposed method relies on the concepts of innovation (Inov) and residue (Ires), mentioned in [54], in order to detect and differentiate between the bad data and the process noise:

ˆ( )

ˆ( )nov

res

Hk kH

k k

I z x

I z x

--

-

==

(2.8)

2.4 THE PROPOSED KALMAN FILTER METHODS 23

where, for linear systems, Inov has a normal probability density function and covariance Sk referred as innovation covariance which is calculated as:

( )k

TH H Rk

S P- += (2.9)

Note that the mean value of Inov is normally zero, however, during abnormal conditions (i.e., there exists noise or bad data in the measurements) the mean value can shift such that the normalized innovation, described in (2.10), will exceed a predetermined threshold value, τQ:

nov

k

nov norm

II

S-= (2.10)

Similarly, Ires under steady state conditions, has a normal probability density function and covariance Tk referred to as residual covariance that can be calculated as:

1kR Rk

T S-= (2.11)

Again, the mean value of Ires is normally zero, however in the presence of bad data, the mean value can shift such that the normalized residue, described in (2.12), will exceed a pre-determined threshold value, τR. Note that the process noise does not affect Ires-norm. It is also worth noting that, in contrast to [10], we are using two separate threshold values for Inov-norm and Ires-norm in order to have a degree of freedom in differentiating between the process noise and the bad data:

res

k

res norm

II

T-= (2.12)

For simplicity the current time step k will be omitted from now on. Note that as a general rule, in KF methods, inflating Q leads to less dependence on the process model, i.e., matrix A, and inflating R leads to less dependence on the measurements.

The Algorithm:

Fig. 2.4 shows the flowchart of the proposed algorithm. The different steps of the algorithm are elaborated below:

1. Start the prediction step. Afterwards, calculate Inov-norm.

2. If Inov-norm ≥ τQ, it indicates that there exists either process noise or bad data in the measurements that has caused Inov-norm to exceed τQ. Assume that the


R

1kP

-

1kx-

-

k

k

x

P

k

k

x

P

k

k

x

P

ˆk

k

x

P

-

-

No Yes

NoYes

k

k

x

P

RD

1R

2R

R

R

Q

Q

Fig. 2.4 The Modified KF Method overview.

problem is originating from the process noise, so reduce Inov-norm back to τQ through inflating Q by ΔQ, as shown in (2.13) – (2.15).

2

nov nov

Q

Qnov norm

I II S S

S St

t-

é ùê ú

= = D = -ê úê ú+D ê úë û

(2.13)

( ) ( )( ) 11T TP PS H H H HS

--- -D = D D = D (2.14)

infQ P Q Q Q-

D =D += D (2.15)

3. In this step, calculate Ires-norm considering the inflated Q. If Ires-norm < τR, it means that the assumption in step 2 is correct, otherwise it indicates that the problem is caused by the bad data in the measurements. So this requires to deflate Q back to its original value and instead, inflate R such that Inov-norm

and Ires-norm are reduced back to τQ (through (2.16) and (2.17)) and τR

2.5 EXPERIMENTAL SETUP FOR KF LABVIEW REAL-TIME APPLICATION 25

(through (2.18) and (2.19)), respectively. Note that as (2.19) is a nonlinear equation, it must be solved numerically, e.g., R2 can be increased iteratively starting from R until R2 (cte+R2)

–1 ≥ T2. Finally, note that, as shown in (2.20), the inflated R is equal to the maximum of R1 and R2.

2

nov nov

Q

Qnov norm

I II S S

S St

t-

é ùê ú

= = D = -ê úê ú+D ê úë û

(2.16)

1R S R R RD = D = + D (2.17)

2

2

2

res res

R

Rres norm

I II T

Tt

t-

é ùê ú

= = = ê úê úê úë û

(2.18)

( ) 1

2 2 2 2T R cte R R-

= + (2.19)

inf 1 2max ( , )R R R= (2.20)

4. The correction step is performed using (2.4) to incorporate the inflated Q or R. If neither Q nor R is inflated, the method uses the original Q and R.

5. The inflated Q or R is deflated using an exponential decaying factor in the beginning of the next execution to treat temporary problems, e.g., outliers, etc. The parameters of the decaying factor can be customized by users, according to their expectation and the specific circumstances.

2.5 Experimental Setup for KF LabVIEW Real-Time Application

This section describes the HIL real-time simulation setup in which the KF methods developed in thesis (as presented in section 2.4) are validated. As shown in Fig. 2.5, two measurement locations have been specified on a grid model [64] that is simulated using the OPAL-RT technologies real-time simulator [65]. The measured voltages and currents are fed to PMUs through the analogue output ports of the OPAL-RT simulator.

As indicated in the figure, the PMUs used in this setup are Compact Reconfigurable IO systems (cRIO) from National Instruments Corporation [66], programmed with LabVIEW graphical programming tools to perform phasor calculations [67]. As the figure shows, the current signals are passed through the current amplifiers by Megger [68] before being fed to the PMUs. Syncrophasors


are then sent to a Phasor Data Concentrator (PDC) [69], which streams the data over TCP/IP to a workstation computer holding SmartGrid’s Synchrophasor Development Kit (S3DK) [70], the real-time data mediator that parses the PDC data stream and makes it available to KF application in the LabVIEW environment. The output of the KF application is stored in a reconfigurable data buffer, from which the steady state applications read the data.

PDC Stream

SEL-PDC 5073

Gri

d m

od

el is

si

mu

late

d in

rea

l-ti

me

S3DK real-time data mediator

Node 1 Node 2

Raw PMU Data

Filtered PMU data

Kalman Filter LabVIEW Application

KF Algorithms

data buffer

NI-cRIO PMU1Current Amplifier

V1 I1


V2I2

Phase Unwrapping

Opal-RT Simulator

Steady state ApplicationsControl signals

Fig. 2.5 Hardware-in-the-Loop (HIL) Lab Setup.

2.6 Performance Comparison of Proposed KF Methods

2.6.1 Difference Between Simulated Data and PMU Data

PMU application development should, in general, not rely on offline simulation data only. There are many practical issues that can only be observed from real PMUs because they are not present in offline simulations. As an example, Fig. 2.6 shows a clear illustration to support this argument. A power system is disturbed with random load variations (RLV) activated at t = 45 s and deactivated at t = 115 s. The voltage response from the simulation and the HIL PMU setup is shown in Fig. 2.6. It can be clearly seen that the voltage from the HIL PMU setup has missing data, which is due to the fact that the PMU data is delayed for a longer time than the PDC maximum waiting time. Also, for samples just after the discrete event of connection and disconnection of the RLV,

2.6 PERFORMANCE COMPARISON OF PROPOSED KF METHODS 27

the PMU generates outliers. Hence, in the development of methods in Section 2.4 and the illustrations below, only data from the RT HIL setup is used.

Fig. 2.6 The difference between voltage responses from simulation and an actual PMU for the same disturbance.

2.6.2 Performance Comparison of Proposed Methods (For Voltage Magnitude Signal)

The developed KF methods were applied on HIL PMU data in this case study. A power system is disturbed with RLV activated at t = 5 s and deactivated at t = 75 s. The performances of both methods proposed in Section 2.4 are compared. Fig. 2.7 shows the KF algorithm performance for both methods for the PMU voltage magnitude signal. When the disturbance was applied at t = 5 s and removed at t = 75 s, outliers were generated in the PMU voltage signal. The RLV excites small signal oscillations, which should be filtered out from the PMU signal before feeding in to a steady state application.

As Fig 2.7 shows, by applying the proposed methods, the dynamics and outliers are filtered, giving smoother responses to be used in steady state applications. The response of “the modified KF” is better than the windowing method with a rolling window (RW) with a length of 0.5 s. In addition, the resulting time varying estimates of R are shown in Fig. 2.8. It can be noticed from the figure that R increases for both methods when outliers are present in the data. However, for “the modified KF”, R returns back to its normal state much faster because it does not require data windowing. The response of the both KF


methods during normal operation of power system has also been shown on top of the Fig. 2.7. It is worth noticing that both KF methods also reduce the noise even during the steady-state operation of the power system (no events).

0 20 40 60 80 100 120 140 160

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Time (s)

Vm

ag (p.u

.)

Raw data

Windowing KFThe modified KF

Fig. 2.7 Performance comparison of two proposed KF methods (for PMU’s voltage magnitude signal)

Fig. 2.8 Comparison for updating R for proposed KF methods (for voltage magnitude signal).

0 20 40 60 80 100 120 140 1600

1

2

3

4x 10

-7

Time (s)

R

Windowing KF

0 20 40 60 80 100 120 140 1600

10

20

30

40

Time (s)

R

The modified KF

2.6 PERFORMANCE COMPARISON OF PROPOSED KF METHODS 29

2.6.3 Performance Comparison of Proposed Methods (For Voltage Angle Signal)

Fig. 2.9 shows the application of the proposed methods for the PMU voltage angle signal. Similar to the voltage magnitude, RLV excites the small signal oscillations in PMU voltage angle signal. These dynamic components are removed from the voltage angle signal for both methods, by updating either R and/or Q in the correction step of the algorithm. Hence smoother estimation for the voltage angle is obtained as shown in Fig. 2.9.

The resulting responses of R are shown in Fig. 2.10. It is worth noticing that the responses of updating R are different in both methods based upon the fact that both methods used a different logic to update R. Although there were no outliers in voltage angle signal, R increases for both methods during the period having the oscillations. For “the modified KF”, R comes back to its normal state much faster than with the windowing method.

Fig. 2.9 Performance comparison of two proposed KF methods (for PMU’s voltage angle signal).

0 20 40 60 80 100 120 140 160-4

-3

-2

-1

0

1

2

3

4

5

Time (s)

Van

g (

rad

)

Raw data

Windowing KFThe modified KF


Fig. 2.10 Comparison for updating R for proposed KF methods (for voltage angle signal).

2.7 KF Performance Analysis

The performance of both methods is analyzed in this section. The first method (as presented in the Section 2.4.1) uses data windowing; therefore the impact of changing the window length is first investigated. Secondly, an evaluation metric is introduced to quantify and compare the performance of both methods.

2.7.1 Impact of Varying Rolling Window Length on Smoothing

The size of the rolling window (RW) affects the smoothing of the states in the presence of outliers and oscillations. By varying the RW length, the updating of R varies, resulting in different responses for signal smoothing. Fig. 2.11 shows different responses for the PMU voltage magnitude with different lengths of RW. For a length of RW = 0.5 s, a fast KF response is obtained together with a smoothed output which captures the exponential decay of the small signal oscillations. However, as soon as the RW length increases, the response of the KF becomes slower. For example the response for RW = 5 s is slow and it could not produce accurate smoothing. It can be thought of an over-filtered response. It can be concluded from the discussion above that a smaller RW length produces better smoothing and a faster response, this can be observed clearly from Fig. 2.12 (i.e. the zoomed-in view of the encircled part of Fig. 2.11).

20 40 60 80 100 120 1400

1

x 10-4

Time (s)

R

Windowing KF

0 20 40 60 80 100 120 140 1600

2000

4000

6000

Time (s)

R

The modified KF

2.7 KF PERFORMANCE ANALYSIS 31

Fig. 2.11 Performance analysis for voltage magnitude signal.

0 20 40 60 0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

Time (s)

Vm

ag (

p.u

.)

Raw data

Wind KF (RW=0.5sec)

Wind KF(RW=2sec)Wind KF (RW=5sec)

The modified KF

Fig. 2.12 Performance analysis for voltage magnitude signal (zoomed in view of the encircled part of Fig. 2.11 )

Vm

ag

(p

.u.)


2.7.2 Performance Analysis Using an Evaluation Metric

Table 2.1 shows a performance analysis of the KF windowing algorithm for different RW lengths and for “the modified KF”. The steady state value of the raw PMU data (as shown in Fig. 2. 12) is calculated by assuming it as the average value of the signal between the time period t1 and t2, which comes out to be 0.904 p.u. (green line in Fig. 2. 12).

Table 2.1 Performance analysis using an evaluation metric (A/K).

Method Area (Ai) A/K

Windowing KF (RW = 0.5 s) 134.93 0.45

Windowing KF (RW = 2 s) 214 0.71

Windowing KF (RW = 5 s) 256.14 0.85

The Modified KF 99.95 0.33

The area (Ai) between the steady state value and each filtered signals (shown in Fig. 2. 12) corresponding to Table 2.1 are calculated in the following steps:

1. The area of the rectangle2 with a width of (t2-t1) and a height of (y2-y1) (as shown in Fig. 2.12) is calculated as follows:

e 2 1 2 1(t t )*( )

r ctA y y= - - (2.21)

2. The total area under each filtered signals is calculated by integrating3 each function as follows:

2

1

( )t

T

i i

t

A f t dt= ò (2.22)

where, i = 1, 2 and 3 correspond to the filtered signals with RW lengths of 0.5, 2 and 5 s, respectively and i = 4 for “the modified KF” (see Fig. 2.12).

3. Finally, the area between the steady state value and each filtered signals is calculated by subtracting the area of the rectangle (calculated in step 1), from the total area for each filtered signals (calculated in step 2).

e

T

i i r ctA A A= - (2.23)

2 The rectangle is not clearly visible in Fig 2.12, but can be visualized as the rectangular area

below the steady state line. Where t1=0, t2=75, y1=0 and y2=0.904. 3 Note that the integrals are computed in MATLAB using the trapezoidal numerical integration

“trapz” command.

2.8 SUMMARY 33

Where iA is the area between the steady state value and each filtered signal i,

T

iA is the total area under the curve for each filtered signal i, and er ct

A is the area

of the rectangle under the steady state line.

The term A/K, as shown in Table 2.1, represent the area’s value in per unit and is defined as the evaluation metric to compare the performance of the proposed KF methods, where K is the base value for calculating per unit area. The metric is used to assess the performance of the first method (data windowing) with the different lengths of RWs. As a general rule, the response having a small per united area (the value of A/K) will be considered the most accurate result (i.e. most accurately follows the quasi-steady state value).

The evaluation metric A/K has the highest value for windowing method for the case RW = 5 s and lowest for the case RW = 0.5 s. This means that RW = 5 is the worst in following the quasi-steady state value and RW = 0.5 has the best performance as can be seen from Fig.2.12. By comparing the performance of both methods (i.e., windowing method and “the modified KF”), the response for “the modified KF” has the minimum value of the evaluation metric, which shows that it outperforms the windowing method.

2.8 Summary

This chapter presented methodologies for pre-processing of PMU data based on Kalman filter technique. The results presented show that the proposed methods are suitable for processing PMU data to be fed to any steady state applications. It has been shown that by updating the value of the measurement noise covariance matrix R in the windowing method, dynamics and bad data can be filtered out from raw PMU data.

In the case of “the modified KF”, R will be updated depending upon the quality of the measurements to filter out the bad data and to extract quasi-steady state components. In addition, Q will be updated to treat the un-modeled process noise which is, in our case, any change in the quasi-steady state value of the measured signal.

Although both of the proposed KF methods have been developed for real time implementation, “the modified KF” is more suitable for real time applications as it does not perform any data windowing. The performance comparison analysis shows that “the modified KF” has the best performance in tracking the quasi quasi-steady-state, when a disturbance is applied.


Chapter 3

3 Test jkkj Steady State Model Synthesis

3.1 Introduction

With the increase of renewable generation sources in the distribution networks (DNs), it is becoming more and more complex to develop and maintain models of these networks. Currently, most TSOs are only able to determine reduced models of limited portions of DNs including aggregated production models based on different distributed production technologies (wind, solar, hydro and thermal etc.) to be used in their grid management functions [10].

The limitations in terms of synthesizing reduced models are due to the lack of network observability (too few measurements at the distribution level), insufficient network modeling information, and challenges with model information management (that are coupled with computational issues when handling increasingly complex models). Current methods used by TSOs to determine reduced models require a detailed model of the network to be reduced [40] and often make assumptions, such as “pure loads”, that are no longer valid for ADNs (with the increased generation sources at lower voltage levels). In some cases, detailed modeling of a few portions of DNs, where there are voltage instabilities issues, is performed. However, the models are typically updated yearly and cannot be updated automatically [71]. PMU measurements from multiple locations in the DN can be exploited to be used for model synthesis of the DN.

36 CHAPTER 3 STEADY STATE MODEL SYNTHESIS

Model synthesis methods for power systems has been extensively discussed in the literature [62], [72]–[91]. In [76]–[79], various methods are presented to obtain dynamic equivalent models of ADNs.

Steady state model synthesis of power system has been investigated in the past [72]–[75], [80]–[82], mainly focusing on transmission systems, where DNs represented by pure loads. The synthesized models presented in the literature, including only positive sequence networks, cannot be used to represent unbalanced systems such as DNs. In [72], the Radial Equivalent and Independent (REI) equivalents are presented and in [73] reduced equivalent models are derived with LTC Transformers. Note that in both [72] and [73] reduced models are derived assuming that a detailed model of the system is available, which is uncommon (particularly for DNs). Moreover, both in [72] and [73], methods’ application for real-time model synthesis is not considered.

In [62] and [83], the topology of the system is assumed to be unknown and the equivalents are calculated based on state estimation techniques. In [84] and [85], Ward equivalents are used for synthesizing the reduced models of the detailed power network. The issue with these equivalents is that the physical behavior of the internal system is accurate whereas the behavior of the external system is approximated, hence limiting their ability to retain the characteristics of the entire system. The methods, proposed in [74], [75], [86], can use real-time PMU measurements, making them suitable for real-time applications; however, they are restricted to acquire PMU measurements from a single location, making them unable to synthesize models for multiple sections of power networks.

In [87], a method is proposed for the reduction of DNs with voltage dependent loads and generators, however, such approach requires the knowledge of external network topology and DGs control schemes. In [88], a method is proposed to obtain equivalent models for DNs to be used in reliability studies. In [89], an offline transmission analysis is performed by using a reduced equivalent of the DN. In [90], a method is presented for estimating series impedance parameters of DN using advanced metering infrastructure (AMI). In [91], a generic reduced equivalent model for DN is used for calculating voltage driven reinforcement cost for LV feeder under 3-phase imbalances. Although, the proposed model, presented in [91], incorporates the effect of mutual impedances, however, the model’s parameters may not be updated in real-time.

The works presented above lacks a method that can synthesize steady state equivalent models of ADNs in real-time. Hence, there is clearly a need to develop such a method. This thesis presents an application that performs real-time steady state model synthesis (SSMS) for multiple sections of unbalanced DNs by acquiring real-time measurements from multiple PMUs. The proposed approach is generic and can be applied to any section of a DN with any feeder

3.2 METHODOLOGY 37

configuration, generation sources or load types. Although having more PMUs provides better observability and allows the SSMS application to determine more detailed models, the developed SSMS application does not put any requirement in terms of the number of installed PMUs.

3.2 Methodology

TSOs need to determine reduced models of DNs to be used in their grid management functions and to have more insight over DNs. Currently; some TSOs are able to determine reduced models of limited portions of the DNs however the models are updated yearly. Also, available models have assumptions, such as pure loads, that are no longer valid for ADNs.

Assuming that PMU measurements are available at any single or more buses in a DN and they measure all three-phase voltage and current phasors, a three phase steady state equivalent model can be synthesized for the portion of the DN that is located between the installed PMUs. As the operating conditions of the system changes, the parameters of the equivalent model can be updated accordingly.

3.2.1 Model Synthesis Based on Two PMU Measurement Points at the Distribution Network

Fig. 3.1 shows an arbitrary section of the DN, bounded by two buses with PMU measurements. As the figure shows, the bounded section may include any kind of feeder structure with an arbitrary combination of loads and generation sources. The three-phase voltage and line current synchrophasor measurements, provided by the PMUs, can be utilized to derive the reduced steady state model. As Fig. 3.1 depicts, the model consists of a parallel branch, including an impedance in series with a voltage source to represent the net balance of generation/load in the selected section, and two series impedance to represent the power loss in the feeders of the selected section. The model is synthesized in three phase to capture the unbalance between the three phases of the DN.

PMU measurement points provide three phase voltage and current phasors (shown in red in Fig. 3.1) which are the known entities in the model. The impedance of the series and parallel branches, and the magnitude and the angle of the voltage sources are the unknown parameters of the model.

Applying a KVL equation on phase ‘a’ of the series branch of the model yields (3.1).

( )( )1 1 2 2 1 1 2 2

a aa a a a a a a aV V R jX I Id d j j - = + - (3.1)

Separating real and imaginary parts of (3.1) and converting them to


rectangular form yields (3.2) and (3.3), resulting in a system of two linear equations with two unknowns.

Fig. 3.1 Synthesized model based on two PMU measurement points.

Solving (3.2) and (3.3) the value of aR and

aX can be obtained.

( ) ( )1 2 1 2 1 2

a aa a a a a a

r r r r i iV V R I I X I I- = - - - (3.2)

( ) ( )1 2 1 2 1 2

a aa a a a a a

i i i i r rV V R I I X I I- = - + - (3.3)

where a

rV , a

iV , a

rI , and a

iI are the real and imaginary parts of the voltage

and current phasors, respectively. Note that as indicated in Fig. 3.1, the model is assumed to have equal impedances in the series and in the parallel branches.

As ( )0 0 1 1 1 1

a aa a a a a aV V R jX Id d j = - + and 0 0 1 1 2 2a a a a a aI I Ij j j = + , the

equivalent voltage source of the parallel branch can be obtained from (3.4).

3.2 METHODOLOGY 39

( )0 0 0 0

a aa a a a a aE V R jX Id d j = - + (3.4)

Separating real and imaginary parts of (3.4) yields (3.5) and (3.6), which can

be solved to obtain the value of aE and a .

0 0 0

a aa a a ar r r iE V R I X I= - + (3.5)

0 0 0

a aa a a ai i i rE V R I X I= - - (3.6)

where a

rE and a

iE are the real and imaginary parts of the voltage source

phasor, respectively.

Applying the same work-flow, explained through equations (3.1) to (3.6), the

parameters of the other phases, i.e., bR ,

bX , cR ,

cX ,bE , b ,

cE , and c can be derived similarly. Therefore, by utilizing the synchrophasor

measurements belonging to the same time instant (i.e. syncrophasor snapshot), the parameters of the model can be calculated through equations (3.1) to (3.6). Note that the calculated values are valid only for the specific time instant to which the measurements belong to. Hence, they should be updated in real-time by using the incoming real-time PMU measurements, which are processed by the KF.

An important implication of updating the parameters in real-time is that the synthesized model reproduces the voltage drop between the two PMU

measurement points, i.e. 1 2V V

, simultaneously. This means that the proposed

model considers not only the voltage drop caused by the phase current but it also takes into account the induced voltage drop due to the mutual couplings between the phases. In order to clarify this matter, let’s consider synthesizing phase ‘a’ of a simple branch, shown in Fig. 3.2. As the figure shows, the voltage drop across the branch can be derived from (3.7). Note that the subscript ‘act’ refers to the “actual value” of the parameters to differentiate them from the values in the synthesized model.

( )( )( )( )

1 1 2 2 1 1 2 2

1 1 2 2

1 1 2 2

a aa a a a a a a aact act

ab b b b bact

ac c c c cact

V V R jX I I

jX I I

jX I I

d d j j

j j

j j

- = + -

+ -

+ - (3.7)

The voltage drop, derived in (3.7), can be calculated by (3.8) using the estimated model parameters.


( )( )1 1 2 2 1 1 2 2

a aa a a a a a a aV V R jX I Id d j j - = + - (3.8)

By equating (3.7) and (3.8), the modeled impedance will be obtained as:

( )( ) ( ) ( )1 1 2 2 1 1 2 2 1 1 2 2

1 1 2 2

a a ab aca a a a b b b b c c c cact act act acta a

a a a a

R jX I I jX I I jX I IR jX

I I

j j j j j j

j j

+ - + - + - + =

-

(3.9)

which clearly shows that the calculated per phase impedance is a function of voltage drops caused by both the self- and the mutual impedances. For example,

any change in 2

bI

will affect the phase ‘a’ impedance a aR jX+ through the

mutual impedanceab

actX .

Fig. 3.2 Model synthesis for a three-phase branch with mutual couplings.

3.2 METHODOLOGY 41

3.2.2 Model Synthesis Based on ‘N’ Number of PMU Measurement Points at the Distribution Network

The modeling approach, followed in the previous section, can be extended to model a portion of the DN that is bounded by multiple PMUs. Fig. 3.3 shows the model synthesis of phase ‘a’ of such a portion. As shown in the figure, addition of each PMU results in addition of an extra series branch to the synthesized model.

Equations (3.1) to (3.6) are still valid to determine the impedance of the parallel branch and the series branches between PMU 1 and PMU 2, i.e. a aR jX+ , and also to determine the voltage source phasor a aE , except

that the current is calculated as 0 01

Na a a a

k kk

I Ij j=

= å .

The impedance of the other series branches, i.e. , can be determined by (3.10).

( )( )

1 1 1 1

2 2

a aa a a a a ak k

a a a ak k k k

V V R jX I

R jX I

d d j

j- -

- = +

- + (3.10)

where 3,4,...,k N , representing the branch number. Separating real and

imaginary parts of (3.10) yields two linear equations from which the two

unknown, 2

a

kR

and 2

a

kX

, can be determined.

Note that, when applying this method, PMU 1 and PMU 2 are the two PMUs that have the smallest impedance between them among any other pair of the PMUs. This is to ensure that the impedances, to be calculated for the other series

branches i.e. 2 2

a a

k kR jX

, do not become negative. Hence, in order to select

the correct pair of PMUs as PMU 1 and PMU 2, the impedance R jX should

be evaluated through equation (3.1) for any pair combination of the N PMUs. The two PMUs having the smallest R jX will be selected as PMU 1 and

PMU 2.


Fig. 3.3 Synthesized model based on ‘N’ number of PMU measurement points.

3.2.3 Model Synthesis Based on One PMU Measurement Point at the Distribution Network

For a single PMU measurement point, i.e. N=1, the PMU has to be installed at the end of one of the distribution feeders. As Fig. 3.4 shows, the proposed method needs to utilize a single transmission level PMU, installed at the high voltage side of the point of common connection substation, so that the two PMUs4, i.e. the transmission level PMU and the distribution level PMU bound the whole DN.

4 This is because the proposed SSMS method requires at least 2 PMUs to calculate the unknown

parameters of the reduced equivalent model.

3.3 HIL EXPERIMENTAL TEST SETUP FOR SSMS LABVIEW REAL-TIME APPLICATION 43

As indicated in Fig. 3.4, the synthesized model will be the same as a Thevenin equivalent model covering the whole DN starting from the transmission side of the substation, i.e. where the transmission level PMU is installed.

Fig. 3.4 Synthesized model based on one PMU measurement point at distribution network

3.3 HIL Experimental Test Setup for SSMS LabVIEW Real-Time Application

This section describes the HIL real-time simulation setup in which the SSMS method, developed in this thesis (as presented in section 3.2) is validated.

As shown in Fig. 3.5, two measurement locations have been specified on a grid model that is simulated by the OPAL-RT real-time simulator [65]. The measured voltages and currents are fed to PMUs through the analogue output


ports of the OPAL-RT simulator. As indicated in the figure, the PMUs used in this setup are Compact Reconfigurable IO systems (CRIO) from National Instruments Corporation, programmed with LabVIEW graphical programming tools to perform phasor calculations [67].

As the figure shows, the current signals are passed through the current amplifiers before being fed to the PMUs. Syncrophasors are then sent to a Phasor Data Concentrator (PDC) [69], which streams the data over TCP/IP to a workstation computer holding SmartGrid’s Synchrophasor Development Kit (S3DK) [70]. The S3DK serves as a real-time data mediator, parses the PDC data stream and makes it available to the KF application in the LabVIEW environment. Note that the PMU data is processed (mainly to extract quasi-steady state component) by the KF application, which is implemented based on “the modified KF” method, described in Section 2.4.2. The output of the KF application is stored in a reconfigurable data buffer, from which the SSMS application in LabVIEW, reads the data. The SSMS application estimates the unknown parameters of the proposed equivalent model and updates them in real-time.

PDC Stream

SEL-PDC 5073

Gri

d m

od

el is

si

mu

late

d in

rea

l-ti

me

S3DK real-time data mediator

Node 1 Node 2

Raw PMU Data

Filtered PMU data

Kalman Filter LabVIEW Application

SSMS LabVIEW Application

SSMS Algorithm

Reconfigurable data buffer

KF Algorithm

data buffer

Estimated Equivalent Model


V1 I1


V2I2

Phase Unwrapping

Opal-RT Simulator

Fig. 3.5 Hardware-in-the-Loop (HIL) real-time simulation setup.

3.4 CASE STUDIES 45

3.4 Case Studies

3.4.1 Reproduction of the Equivalent Model Parameters in Real-Time

A simple equivalent model as shown in Fig. 3.1, is included in a power system model (not shown here) and is simulated for 100 s with known parameters to reproduce the values of the parameters by the SSMS application. Using the HIL setup, shown in Fig 3.5, the PMU measurements were available on both buses of the model. The true values of the parameters on phase ‘a’ of the model are

0.128aR p.u. , 0.126aX p.u. , 1aE p.u. , and 1.1591a rad . In

this example, it has been assumed that there is no mutual coupling between the phases.

Two events were created in the simulation: 1) A load of (0.2+j0.1) p.u. is connected at t = 40 s in the right side of PMU 2 (event occurs outside the section

bounded by the PMUs) and, 2) A step increment of 10 % is introduced ina

E at t = 70 s (the event occurs inside the bounded section by the PMUs). Fig. 3.6 shows the reproduced model parameters for phase ‘a’ of the model by the implemented SSMS application. It is evident from Fig. 3.6 that for event 1 there are no noticeable changes in the model parameters as it was outside the boundary

Fig. 3.6 Reproduction of the parameters of phase ‘a’ of the equivalent model by LabVIEW SSMS Application.


of the two PMUs; whereas a

E is updated accordingly for event 2 (see top right of Fig. 3.6).

3.4.2 Incorporating the Effect of Mutual Inductances

In this example, it is shown how the existence of the mutual coupling between the phases will affect the estimated value of the model parameters. For this example, three different models are simulated:

Model 1: Equivalent model without any mutual inductance between the phases (same as in section 3.4.1)

Model 2: Same as Model 1 with addition of mutual inductance between the phases. The values of the mutual inductances are 0.0066 . .abX p u ,

0.0092 . .acX p u , and 0.0079 . .bcX p u .

Model 3: The parameters of Model 2, estimated by the SSMS application, are inserted to an equivalent model, shown in Fig. 3.1. The voltages and currents at the PMU measurement points of Model 2 are then compared with those of the Model 3 for the purpose of validation. Note that Model 2 is the “true” model with mutual coupling whereas Model 3 is a synthesized model of Model 2.

Fig. 3.7 shows the estimated values of the parameters of phase ‘a’ of Model 2.

0.1227-

0.1226-

0.1225-

0.1224-

0.1223-

0.1222-

1.002-

1-

0.998-

0.996-

0.994-

0.992-

0.99-

Ra

(p.u

.)X

a (p

.u.)

Ea

(p.u

.)δ

a (p

.u.)

Time(Sec) Time(Sec)

30 50 70

0.103-

0.102-

0.101-

0.115-

0.1-

0.0995-

Load conencted

on phase ’b’

-1.155-

-1.156-

-1.157-

-1.158-

-1.159-

-1.16-

-1.61-30 50 70

Load conencted

on phase ’b’

Load conencted

on phase ’b’

Load conencted

on phase ’b’

Fig. 3.7 Estimation of the parameters of phase ‘a’ of Model 2.

3.4 CASE STUDIES 47

As shown in Fig. 3.7, the estimated values of the per-phase parameters, i.e.aR , aX , aE and a , are different from the real values due to the existence of

the mutual coupling between the phases. Also, in order to better show the effect of mutual coupling, a load consuming active and reactive power of (0.2+j0.1) p.u. is connected to phase ‘b’ at t = 40 s. As shown in Fig. 3.7, although the event is taking place on phase ‘b’, it impacts the values of the parameters on phase ‘a’ due to the existence of the mutual coupling.

Fig. 3.8 compares the voltage and current magnitude and angles of PMU 2 for all the three models. As shown in the figure, the voltage phasor is noticeably different if the effect of the mutual couplings is not considered (compare Model 1 with Model 2/Model 3). Also, the figure shows that Model 3 reproduces the voltage and current phasors of Model 2 quite accurately, which validates the accuracy of the parameters of Model 3 that is estimated by the SSMS application.

Fig. 3.8 Estimation of the parameters of phase ‘a’ of Model.

3.4.3 Model Synthesis of a Sample Active Distribution Network

In this section, the SSMS application is applied on an ADN. The network has been adopted from an ADN model, presented in [64] with some model components taken from [92]. Fig. 3.9 depicts the single-line diagram of the

30 35 40 45 50 55 600.86

0.88

Va

(p

.u.)

30 35 40 45 50 55 60

0.3

0.32

Ia (

p.u

.)

Model1

Model2

Model3

30 35 40 45 50 55 60

-0.88

-0.86

-0.84

a (p

.u.)

30 35 40 45 50 55 60

-1.3

-1.25

Time (sec)

a (

p.u

.)


network. PMU measurements were made available by connecting the Opal-RT simulator in HIL, similarly as in Fig. 3.5, on Node 814 and Node 852. Two events were created in the simulation: 1) A lateral MV feeder disconnects from Node 834 at t = 40 s, and 2). A wind farm generating 1 MW (0.2 p.u.) disconnects from Node 854 at t = 70 s. The equivalent model parameters for phase ‘a’, estimated by the SSMS application, are shown in Fig. 3.10.

Fig. 3.9 Single line diagram of the sample network.

As the figure shows, the disconnection of the lateral feeder (event 1) mainly

impacts the value of aR and

aX . This is because when the lateral feeder disconnects, the currents flowing through all three phases of the main feeder reduce accordingly which, in turn, decreases the voltage drop induced on all phases through the mutual couplings. In case of event 2, the disconnection of the wind farm, located inside the bounded section of the two PMUs, causes voltage to drop from 0.982 p.u. to 0.93 p.u.

In order to validate the equivalent model parameters, estimated by the SSMS application, the bounded section of the sample network has been replaced by an equivalent steady state model, as shown in Fig. 3.11. The same events, performed on the sample network, have been simulated on the network, shown in Fig. 3.11.

3.4 CASE STUDIES 49

Fig. 3.10 Estimation of the parameters of phase ‘a’ of the sample network.

Fig. 3.11 Single-line diagram of the network with the equivalent model.


During the simulation, the parameters of the equivalent model have been updated5. Fig. 3.12 and Fig. 3.13 compare the voltage and current phasors, provided by PMU 1 and PMU 2 in the sample network, with those of the network containing the equivalent model. Note that the oscillations in the phasor signals are due to the sinusoidal variation6 embedded in the static load models of the simulated network. As the figure shows, the reproduced voltage and current phasors are quite similar to those of the sample network, which shows the validity of the developed SSMS application. In order to analyze the difference between the true values and the reproduced values, the mean error is calculated for each sections of the simulation i.e. e1 for the part the signal before event1, e2

for the part of the signal between event 1 and event 2, and e3 for the part of the signal after event 2. The calculated errors are shown in Fig. 3.12 and Fig. 3.13.

As shown in Fig 3.12 and Fig 3.13, for both PMUs, the maximum error of voltage magnitudes, current magnitudes, voltage angles, and current angles are 0.00068 p.u., 0.0119 p.u., 0.0162 rad., and 0.017 rad., respectively.

40 50 60 70 80 90 100

0.95

1

Va

(p

.u.)

40 50 60 70 80 90 100

0.2

0.3

0.4

Ia (

p.u

.)

true

reproduced

40 50 60 70 80 90 100

-1.2

-1.15

a (

rad

)

40 50 60 70 80 90 100

-2.5

-2

-1.5

Time (sec)

a (

rad

)

Fig. 3.12 True phasors versus reproduced phasors for PMU 1.

5 The parameters are updated at the start of each event and held constant up to the next event. 6 The sinusoidal variations are considered to exhibit a realistic behavior of the loads.

3.5 SUMMARY 51

40 50 60 70 80 90 1000.9

0.95

1

Va

(p

.u.)

40 50 60 70 80 90 100

0.3

0.35

Ia (

p.u

.)

true

reproduced

40 50 60 70 80 90 100-1.25

-1.2

-1.15

a (ra

d)

40 50 60 70 80 90 100-2.2

-2

-1.8

Time (sec)

a (

rad

)

Fig. 3.13 True phasors versus reproduced phasors for PMU 2.

3.5 Summary

This chapter has presented a novel methodology to perform steady state model synthesis (SSMS) in real-time for multiple sections of unbalanced DNs using synchronized phasor measurement data. It has been shown that the proposed SSMS technique can produce accurate models for any feeder configuration located between the installed PMUs.

The proposed approach is generic and can be applied to any section of a DN with any feeder configuration, generation sources or load types. Although having more PMUs provides better observability and allows the SSMS application to determine more detailed models, the developed SSMS application does not put any requirement in terms of the number of installed PMUs.

If the system configuration changes, the parameters of the synthesized model will automatically update in real-time. Also, the updated parameters can be sent to TSOs in real-time to improve their energy management functions.

Chapter 4

4 Test jkkj

Sensitivity Analysis of the SSMS Method

4.1 Introduction

Sensitivity analysis is the study of how the uncertainty in the output of a mathematical model or system can be distributed to different sources of uncertainty in its inputs [93]. A related practice is uncertainty analysis, which has a greater focus on uncertainty quantification and propagation of uncertainty. Ideally, uncertainty and sensitivity analysis should run in tandem.

Sensitivity analysis of a method can be performed by recalculating its outputs for a considerable number of times under different assumptions and then analyzing how their accuracy is impacted. This study is useful for a variety of purposes including but not limited to the following:

Testing the robustness of the outputs in the presence of various uncertainties.

Identifying the method’s inputs that cause substantial uncertainty in the outputs and should therefore be considered for enhancing robustness.

Searching for different types of errors in the outputs.

54 CHAPTER 4. SENSITIVITY ANALYSIS OF THE SSMS METHOD

In chapter 3, a steady state model synthesis (SSMS) method is introduced, which synthesizes a three-phase steady state equivalent model of the DN. Although a performance analysis of the method is presented in chapter 3 using hardware-in-the-loop (HIL) simulation setup, yet there was a need to perform a detailed sensitivity analysis of the proposed SSMS method to know how sensitive the output of the method is to the changes in its inputs.

The application of sensitivity analysis in power system has been extensively discussed in literature [94]–[96]. In [94], sensitivity analysis is applied to evaluate the variation of total generation cost with respect to change in reactive power, for determining the optimal location of the capacitor banks in the network. The influence of parameter perturbations on power system stability limit has been discussed in [95]. In [96], a sensitivity analysis on the accuracy of different DC power-flow models is presented.

This chapter presents a comprehensive sensitivity analysis of the SSMS method. A detailed methodology is proposed to perform sensitivity analysis on PMU data-based applications such as the proposed SSMS method.

4.2 Methodology for Sensitivity Analysis of the SSMS Method

The main outputs of the SSMS method (presented in chapter 3) are the voltage and current phasors reproduced by the synthesized model. This section presents a methodology to analyze how the accuracy of these outputs is influenced by different inputs of the SSMS method.

4.2.1 End-to-End Total Vector Error (TVE)

The accuracy of the SSMS outputs can be measured using an extended revision of the TVE concept introduced in [28]. This extended revision, called end-to-end TVE in this study, is defined as the measure of the difference between the theoretical phasor value of the signal being measured and the reproduced version of the same phasor, as shown below:

2 2

2 2

ˆ ˆ( ( ) ( )) ( ( ) ( ))( )

( ) ( )r r i i

end to end

r i

V n V n V n V nTVE n

V n V n- -

- + -=

+ (4.1)

4.2 METHODOLOGY FOR SENSITIVITY ANALYSIS OF THE SSMS METHOD 55

ˆ ( )rV n =

( )rV n =

ˆ( )iV n =

( )iV n =

where

Real part of the reproduced voltage

Real part of the true (actual) voltage

Imaginary part of the reproduced voltage

Imaginary part of the true (actual) voltage As illustrated in Fig. 4.1, the end-to-end TVE consists of the following two TVEs: (a) PMU TVE

PMU TVE is defined as the difference between the “true” phasor (in our case, existed in the simulation environment) and the phasor estimated by the PMU as shown in Fig. 4.1. This TVE can occur due to the phase angle error that is the product of instrumentation channels and improper timing sources of the PMU [97]. In our experimental setup (explained in Section 4.3), the real-time simulator and the PMUs have different dynamic ranges on voltage and current ratings. This can also contribute as a source of PMU TVE. In addition, the current amplifiers are sources of phase angle errors, which in turn may cause PMU TVE.

Fig. 4.1 Types of TVEs

True Phasor

Estimated Phasorby Field Application

Estimated Phasor by PMU

PMU TVE

Field Application TVE

End‐to‐End TVE


(b) Field Application TVE

The difference between the phasor estimated by the PMU and the phasor reproduced by the synthesized model of the SSMS application is defined as Field Application TVE. This type of TVE is mainly the product of the SSMS application estimation errors.

4.2.2 Methodology of calculating End-to-End TVE

The end-to-end TVE can be calculated by running the SSMS application in a HIL simulation setup (explained in Section 4.3). The HIL setup is used for real-time simulation of the grid model whose synthesized reduced model is of interest. As shown in Fig. 4.2, through the HIL setup, the estimated voltage and current phasors at the boundary buses of the grid model are fed to the SSMS application which estimates the parameters of the reduced equivalent model. These parameters are sequentially updated in real-time as soon as any change in the operating point of the system occurs. The resulting array of the parameters is fed to a reduced equivalent version of the grid model. The reduced model is then simulated to reproduce the corresponding voltage and current phasors. The reproduced voltage and current phasors are then compared to their true values in order to calculate the end-to-end TVE using (4.1).

Fig. 4.2 Methodology for calculating end-to-end TVE

4.3 HIL REAL-TIME TESTING SETUP 57

Note that as indicated in Fig. 4.2, the sensitivity analysis is performed by calculating the end-to-end TVE versus different inputs, such as, the location of PMUs, system operating points and occurrence of different disturbances.

4.2.3 End-to-End TVE as Evaluation Metric

As mentioned before, the end-to-end TVE is selected as the evaluation metric for the sensitivity analysis of the results produced by the SSMS method.

We have defined a 3 % mean error requirement for the end-to-end TVE7 in this study. In other words, we would like the SSMS outputs, i.e. the reproduced phasors, to have limited sensitivity to the changes in the SSMS inputs (i.e. location of PMUs, system operating points, and occurrence of different disturbances) such that the end-to-end TVE remains within 3 %. The basis of this requirement is as follows:

DC Power flow models available in literature can have more than 15.7 % error [96].

As SSMS is a method to synthesize steady state models of the ADN, having 3 % end-to-end TVE for estimated parameters still provides much better accuracy of the reduced equivalent models than power flow models.

3 % is an acceptable value because end-to-end TVE contains PMU TVE, which is not related to the performance of the target application. Specifically, in our case, the amount of phase angle error generated by instrumentation and difference in dynamic range of the ratings of different equipment increase the end-to-end TVE.

4.3 HIL Real-Time Testing Setup

This section describes the HIL real-time simulation setup for accessing the performance of SSMS method. As shown in Fig. 4.3, a grid model is simulated using the OPAL-RT real-time simulator. The measured voltages and currents are fed to PMUs through the analogue output ports of the OPAL-RT simulator and the amplifiers. As the figure shows, Syncrophasors are sent to a Phasor Data Concentrator (PDC) which streams the data over TCP/IP to a workstation computer holding SmartGrid’s Synchrophasor Development Kit (S3DK) [70]. S3DK serves as a real-time data mediator that parses the PDC data stream and makes it available to the SSMS application in LabVIEW environment. As shown in Fig. 4.3, different types of TVEs explained in Section 4.2.1 can be visualized.

7 Observe that requirements in terms of each type of TVE defined could be imposed and assessed.

However, such work would require additional experimental tests, and can be a potential future work in this area.


SSMS Application

Grid model simulated in

real-time

PMU 1

PMU 2

SEL-PDC 5073

S3DK real-time data mediator Field Applications

PMU TVE Field Application TVE

End-to-End TVE

PDCStream

Opal-RT Simulator

Voltage & Current Amplifier

V1

I1

V2

I2Voltage & Current

Amplifier

Fig. 4.3 HIL simulation setup showing different types of TVEs.

4.4 Sensitivity Analysis of the SSMS Method

Fig. 4.4 shows a single diagram of a grid network model, which has been adopted from an ADN model presented in [64]. The grid model is taken as benchmark model to perform different case studies to demonstrate how sensitive the output of the SSMS method is with respect to the changes in its inputs. In chapter 3, SSMS method is validated by the grid model, shown in Fig 4.4. Therefore, any changes in the grid model can be considered as the inputs to the SSMS method.

Three variable inputs are considered in this study: change in the system operating point, occurrence of different disturbances in the grid network, and change in the location of the PMUs installed in the network. For case study 1, the experiment is repeated 125 times (for each step decrease in wind power). Whereas, for case study 2 and case study 3, the experiment is repeated 40 times each. Table 4.1 contains the summarized information about the location of PMUs and disturbances for different case studies corresponding to the node number in Fig 4.4.

4.4 SENSITIVITY ANALYSIS OF THE SSMS METHOD 59

Fig. 4.4 Single line diagram of a sample network.

TABLE 4.1

Location of PMUs and disturbances for different case studies (Corresponding to the node numbers in Fig 4.4)

Case study Node Number in Fig 4.4

PMU 1 PMU 2 Disturbance 1 814 852 854 2 814 852 834 & 854

3 LS1 814 852

854 LS2 800 834 LS3 800 840

4.4.1 Case Study 1: Change in system operating point

This case study shows how sensitive the output of SSMS method is with respect to changes in the system operating point. The changes are realized by applying a power decrease of 0.35 MW (16 % of the total load) in 5 steps (0.075 MW in each step) to the wind turbine connected at node 854 in Fig. 4.4. The sensitivity of the output of the SSMS method is evaluated by calculating the mean, maximum and minimum values of the end-to-end TVE for each step decrease in the wind power generation. The results are summarized in Table 4.2. The largest mean value of the end-to-end TVE for all the voltage and current phasors is 2.3723 %. Note that, as mentioned in Table 4.1, the PMUs are installed at nodes 814 and 852.


TABLE 4.2 End-to-end TVE for Case Study 1

(Number of trails=125 for each step decrease in wind power)

Phasors End-to-end TVE (%)

Mean Max Min SD

V1 0.1184 0.1564 0.1034 0.0143

I1 2.3723 3.7165 1.6429 0.4644

V2 1.6486 1.7288 1.5818 0.0416

I2 1.4972 1.6172 1.4026 0.0559

The standard deviation (SD) is calculated for each voltage and current phasor. The maximum value of SD of end-to-end TVE is 0.4644 %, which shows the uncertainty in the output of the SSMS method is small. The probability distributions for the end-to-end TVE for both voltage and current phasors, for both PMU 1 and PMU 2, are plotted and are shown in Fig. 4.5. The top plots correspond to the voltage phasors and the bottom plots are for the current phasors.

Fig. 4.5 Probability distribution of end-to-end TVEs for case study 1.

0.08 0.1 0.12 0.14 0.16 0.180

10

20

30

40

50

60

70

80

90

TVE for V1 (%)

Pro

bab

ility

Den

sity

TVE for Voltage Phasor for PMU 1

1 1.5 2 2.5 3 3.5 4 4.50

0.5

1

1.5

2

2.5

3

3.5

4

TVE for I1 (%)

Pro

babi

lity

Den

sity

TVE for Current Phasor at PMU 1

1.5 1.55 1.6 1.65 1.7 1.75 1.80

5

10

15

20

25

30

35

40

TVE for V2 (%)

Pro

bab

ility

Den

sit

y

TVE for Voltage Phasor at PMU 2

1.3 1.4 1.5 1.6 1.70

5

10

15

20

25

30

TVE for I2 (%)

Pro

bab

ility

Den

sity

TVE for Current Phasor at PMU 2

4.4 SENSITIVITY ANALYSIS OF THE SSMS METHOD 61

4.4.2 Case Study 2: Occurrence of Disturbances

The sensitivity of the output of the SSMS method is analyzed by applying two types of disturbances in the grid model (shown in Fig. 4.4). The following two events were created:

Event 1: Disconnection of a lateral feeder at bus 834. Event 2: Loss of 1 MW wind generation at bus 854. The end-to-end TVE is calculated for three different time periods (listed in

Table 4.3), to analyze the sensitivity of the SSMS output with respect to these two events.

TABLE 4.3 Different time periods in Case Study 2

No. Details of the Sections

1 Before Event 1

2 Between Event 1 & Event 2

3 After Event 2

For each time period, mean, maximum and minimum values of the end-to-end TVE for each voltage and current phasor were calculated. Note that in this case study the PMUs are installed at nodes 814 and 852. The results are summarized in Table 4.4. As shown in the table, the largest mean value of the end-to-end TVE is 3.0549 % for all the voltage and currents phasors for both PMUs. Moreover, SD is calculated for each phasor for both PMUs. The maximum value for SD of the end-to-end TVE, for all phasors of both PMUs is 0.4349 %. The results from Table 4.4 show that the end-to-end TVE remains in the permissible range despite the occurrence of the two disturbances.


TABLE 4.4

End-to-end TVE for Case Study 2 (Number of trails=40)

Phasors Sections End-to-end TVE (%)

Mean Max Min SD

V1

1 0.1267 0.1633 0.1 0.0251 2 0.1382 0.1672 0.1051 0.0218 3 0.1186 0.1486 0.0896 0.0193

I1

1 2.5192 2.9901 2.1016 0.2804 2 3.0549 3.6330 2.3176 0.4349 3 1.3455 1.6704 1.0952 0.1632

V2

1 1.6448 1.6830 1.611 0.0239 2 1.6259 1.6650 1.6004 0.0211 3 1.7326 1.7592 1.7024 0.0163

I2

1 1.4878 1.5671 1.4390 0.0265 2 1.7434 1.7843 1.7063 0.0237 3 1.5624 1.5862 1.5442 0.0120

4.4.3 Case Study 3: Change in PMU Location

In this case study, the location of each pair of PMUs (used in the SSMS method) is varied, as shown in the grid model in Fig 4.4. This is to investigate how sensitive the SSMS output is with respect to the measurement points, that is the PMU location.

In this case study, the following Location Sets (LS) are selected:

Location Set 1: PMU 1 at node 814 PMU 2 at node 852 Location Set 2: PMU 1 at node 800 PMU 2 at node 834 Location Set 3: PMU 1 at node 800 PMU 2 at node 840

For each PMU location set (LS), mean, maximum and minimum values of end-to-end TVE for voltage and current phasors for both PMU 1 and PMU 2 were calculated. The results are summarized in Table 4.5. As shown in the table, the largest mean value of the end-to-end TVE is 2.5192 % for all the voltage and currents phasors for both PMUs. Moreover, SD is calculated for each LS for the voltage and the current phasors for both PMUs. The maximum value for SD for all the phasors for both PMUs is 0.2804 %.

The results from Table 4.5 show that the end-to-end TVE does not change much by changing the PMU location set in the network, which indicates that the output of SSMS method is impervious to different PMU locations in the network.

4.5 SUMMARY 63

TABLE 4.5 End-to-end TVE for Case Study 3

(Number of trails=40)

Phasors PMU

Location Set

End-to-end TVE (%)

Mean Max Min SD

V1

1 0.1267 0.1633 0.1 0.0251

2 0.0533 0.0609 0.0407 0.0056

3 0.0355 0.0383 0.03412 0.0013

I1

1 2.5192 2.9901 2.1016 0.2804

2 2.4842 2.8366 1.8817 0.2727

3 1.6148 1.74208 1.54582 0.0630

V2

1 1.6448 1.6830 1.611 0.0239

2 1.6164 1.6623 1.5837 0.0243

3 1.5254 1.67248 1.64415 0.00833

I2

1 1.4878 1.5671 1.4390 0.0265

2 1.4667 1.4825 1.4476 0.01218

3 - - - -

4.5 Summary

This thesis has presented a sensitivity analysis of a method that performs steady state model synthesis (SSMS) of ADNs using synchronized phasor measurement data. The original TVE concept was extended (end-to-end TVE) to serve as an evaluation metric in the sensitivity analysis. A methodology for sensitivity analysis of the SSMS application was presented and performed through three different case studies. The presented results show that the method’s output adjusted to the changes in operating point of the system well. Moreover, the results provided acceptable values for the end-to-end TVE before and after the disturbances. In addition, it was shown that the end-to-end TVE does not change much by changing the location of the PMUs in the grid. In summary, the results of the case studies show that the output of the SSMS method is quite impervious to the changes in its inputs, which indicates the robustness of the method.


Chapter 5

5 Test jkkj

Experimental Validation of the SSMS Method

5.1 Introduction

The steady state model synthesis (SSMS) method has been proposed in Chapter 3, where measurements from phasor measurement units (PMUs) from multiple locations in a distribution network were exploited for synthesizing a three-phase steady state equivalent model of the observed network. Synthesized PMU measurements were used, using a hardware-in-the-loop (HIL) simulation setup at KTH SmarTSLab. In Chapter 4, a detailed sensitivity analysis of the SSMS method was presented in order to investigate how sensitive the output of the method is to changes in its inputs. Although, Chapter 3 and Chapter 4, presents the theoretical background of the SSMS methodology and its performance validation in a laboratory environment, yet, there is a need to test the validity of the SSMS method using the data from real PMUs installed on real ADN.

In this context, successfully testing the SSMS methodology on real systems, not only demonstrates its applicability, but also shows the practical feasibility of the method. This adds a significant value to the method itself and facilitates its implementation on real systems.

66 CHAPTER 5. CONCLUSIONS

With this background, this chapter has the following contributions:

An HIL experimental validation method of the PMU-based SSMS application.

A performance assessment of the SSMS application using “real” PMU data from a distribution feeder.

A detailed analysis of the parametrization of the SSMS application w.r.t. model parameter estimation update rate.

The contributions summarized are further explained in the subsequent section. In this chapter, an extensive experimental validation of the SSMS method is performed. The syncrophasor measurements [98] were acquired from the real PMUs installed at an actual active distribution feeder at EPFL’s campus, Lausanne, Switzerland [30], [99]. The extended version of the Total Vector Error (TVE) concept (first introduced Chapter 4) and power flow comparisons at the PMU buses were used as performance evaluation metrics.

In this thesis, a detailed performance assessment of the SSMS method is conducted by testing the method extensively under different conditions using a real-time hardware-in-the-loop simulation setup at Distributed Energy System Laboratory (DESL), EPFL [100]. The method was tested by utilizing the PMU data for the days of the year when the targeted distribution feeder at EPFL campus was mostly active (i.e. with a surplus of PV generation) and for the time when it was mostly passive (i.e. with minimal PV generation). Moreover, the partial solar eclipse event of 2015 that occurred in Switzerland [47] was analyzed in order to investigate its impact on the performance of the SSMS method.

Additionally, a comprehensive analysis is presented, which might help power system operators to configure a target application based on the SSMS method. It is shown how the performance of the SSMS method varies by varying the update rate of the target application. The tradeoff between estimation accuracy (tracking) and update rate (speed) is determined.

5.2 The EPFL Campus Active Distribution Network

As shown in Fig. 5.1, the power distribution network of EPFL campus [30] includes all the components of an ADN. The lines are short, and the load demand is variable as a function of the time of the day and weather conditions. Moreover, active power injections are present as 2 MWp of photovoltaic (PV) generation together with 6 MW of combined heat and power generation units. Due to the variable demand and the extensive use of power electronics, the voltage and current profiles contain the typical dynamics of ADNs, which make the EPFL campus network an ideal testing venue to validate the SSMS application.

5.3 METHODOLOGY 67

The monitored network is composed of 5 electrical substations i.e. EL-A, EL-E, EL-G, EL-L and PC-2 as shown in Fig. 5.1. PV panels inject active power at EL-A, EL-E, EL-G and EL-L. The lines in the network are underground cables with parameters as reported in the Appendix A. A class-P PMU prototype [67] based on the NI cRIO 9068 hardware [101] is installed in each substation to estimate voltage and current syncrophasors. A stationary GPS unit (NI-9467 [102]) is used for the synchronization to the UTC-time.

Fig. 5.1 Network topology of the power distribution feeder overlaid on top of a map of the EPFL campus.

5.3 Methodology

5.3.1 Data Acquisition

The PMU measurements were acquired from specified locations as shown in Fig. 5.1. A single line diagram of the active distribution feeder network at the EPFL campus is shown in Fig. 5.2. The purpose of Fig. 5.1 and Fig. 5.2 is to show how to obtain a reduced equivalent model of the detailed EPFL campus network. The reduced model is shown in Fig. 5.3.


Fig. 5.2 Targeted EPFL Campus active distribution feeder.

Fig. 5.3 Reduced equivalent network of the targeted EPFL campus feeder.

5.3.2 Detailed Validation Model

Procedure 1:

(a) The acquired PMU data is replayed in a Real Time Simulator (RTS) as shown in Fig. 5.4.

(b) Active power (P) and reactive power (Q) are calculated based on the acquired PMU data and given to the RTS load models.

5.3 METHODOLOGY 69

TV

TI

MI

P

MV

Fig. 5.4 Detailed Validation Model.

(c) A simulated EPFL PMU model estimates the phasors at bus 5 and bus 2,

i.e. TV , TI . The simulated PMU is based on a syncrophasor extraction

(SE) algorithm presented in [67], which is both compliant with the accuracy requirements of the IEEE Std. C37.118 [28] and deployable into a RTS platform [103]. The PMUs installed at the EPFL network, and the simulated PMUs in the RTS, use the same SE algorithm. The SE algorithm, its implementation and validation have been described in details in [67]. Moreover, integration of the simulated PMU into OPAL-RT eMEGASIM RTS [65] has been experimentally validated in [103].

(d) MV , MI are sent to a Phasor Data Concentrator (PDC), i.e. SEL-PDC-

5073 [69]. (e) PDC streams the data over TCP/IP to a workstation computer holding

SmartGrid’s Syncrophasor Development Kit (S3DK) [70], which serves as a real-time data mediator and parses the PDC data stream and makes it available to the SSMS application in LabVIEW environment.

(f) A LabVIEW SSMS application estimates the parameters of the reduced equivalent model of the detailed EPFL network.

5.3.3 Equivalent Model

Procedure 2:

(a) - (c) are the same as in procedure 1.

(d) M estV , M estI

are the syncrophasor estimated by the simulated PMU for

the reduced equivalent model as shown in Fig. 5.5.


TV

TI

M estV

M estI

P

Fig. 5.5 Equivalent Model.

(e) The pre-processed parameters P (explained in Section 5.3.4), obtained

from ( P ) in procedure 1, are replayed in the reduced model.

The synchrophasors MV , MI ,M estV and

M estI

as shown in Fig. 5.4 and 5.5 are

used for the performance analysis.

5.3.4 Pre-Processing of P for use in the RTS

For validation purposes, the estimated parameters require some pre-processing as shown in Fig 5.6.

(a) The raw estimated parameters i.e. P have an update rate of 0.5 sec. A sample-and-hold functionality is applied to P , i.e. the output holds its sampled value until a new estimate is produced.

(b) PMU measurements have a refresh rate of 20 m sec, whereas, the LabVIEW SSMS application estimates the parameters with an inherent update rate of 2 estimates / second (i.e., every 0.5 sec). Therefore, a uniform up-sampling is performed on the estimated parameters P to get *P , to synchronize the sampling rate of the PMU measurements to the estimated parameters.

(c) As the P and Q of loads in the detailed network (Fig. 5.4) and in the equivalent network (Fig. 5.5) were interpolated to simulate both networks in the RTS at a relatively small time-step, (i.e. 100 µsec), the up sampled parameters were interpolated.

(d) The pre-processed parameters P are replayed in the equivalent model.

5.4 PERFORMANCE EVALUATION METRICS 71

P

*P

P

*P

Fig. 5.6 Pre-processing of the estimated parameters.

5.4 Performance Evaluation Metrics

5.4.1 End-to-End Total Vector Error (TVE)

In this thesis, end-to-end TVE is used as one of the performance evaluation metrics for the SSMS application. The end-to-end TVE, initially introduced in Chapter 4, is defined as the difference between the actual phasor value of the signal being measured and the reproduced version of the same phasor, as shown in (4.1).

5.4.2 Power Flow Comparison

The other metric used for the performance evaluation of the SSMS application is the comparison of power flow for the active power P and the reactive power Q at the PMU buses for both the actual and the reduced equivalent network, defined as:

kl k lij ij ijP P P

kl k lij ij ijQ Q Q (5.1)

where ‘k’ represents the true value and ‘l’ the reproduced values of P and Q in the line between nodes ‘i’ and ‘j’.


5.5 Case Studies and Experimental Validation Results

In this section, PMU data from the EPFL campus feeder network is used to perform experimental validation of the SSMS application using several case studies. Following the methodology described in Section 5.3, the metrics defined in Section 5.4 are analyzed.

5.5.1 Case Study 1: A Typical Load Profile

In this case study, a typical load profile from the installed PMUs at the EPFL campus feeder is considered. PMU data [98] for 1st of September 2014 between 13:00-13:01 is fed to the SSMS application. The equivalent model parameters for phases a, b and c estimated by the SSMS application, are shown in Fig. 5.7. The figure shows that the parameters are updated automatically with the changes in the system operating conditions.

Fig. 5.7 Estimation of the parameters of phases a, b and c of the reduced EPFL network model.

Fig. 5.8 and 5.9 compare the voltage and current phasors provided by PMU 1 and PMU 2 measured in the actual EPFL feeder network, with those of the equivalent network. As the figures show, the reproduced voltage and current phasors are similar to those measured in the actual network. In order to analyze the difference between the measured values and the reproduced values, the average absolute error is calculated. As shown in Fig. 5.8 and Fig. 5.9, the average absolute estimation error is at most 0.2746 % for all the voltage and current phasors.

5.5 CASE STUDIES AND EXPERIMENTAL VALIDATION RESULTS 73

Fig. 5.8 Measured phasors versus reproduced phasors of phase ‘b’ for PMU 1.

Fig. 5.9 Measured phasors versus reproduced phasors of phase ‘b’ for PMU 2.


The sensitivity of the output of the SSMS application is evaluated by calculating the mean, maximum and minimum values of the end-to-end TVE using (4.1). The results are summarized in Table 5.1. The standard deviation (SD) is calculated for each voltage and current phasor. The end-to-end TVE and the SD for both the voltage phasors is small, whereas for current phasor of PMU 1 the values are higher with the largest mean end-to-end TVE of 2.1705 %.

TABLE 5.18

End-to-end TVE for Case Study 1

Phasors End-to-end TVE (%)

Mean Max Min SD

V1 0.0019 0.0275 1.88e-5 0.0022

I1 2.1705 30.4209 0.0190 2.5520

V2 0.0032 0.0297 1.77e-4 0.0025

I2 0.0523 1.3033 2.63e-4 0.0796

Top part of Fig. 11 and Fig. 12 compare the active power at PMU 1 and PMU 2 measured in the EPFL feeder network, with those of the reproduced equivalent network. As the figures show, the reproduced active power matches the true actual power with sufficient accuracy. Average absolute mismatch (error) in the active power for PMU 1 and PMU 2 are plotted in the bottom part of Fig. 5.10 and Fig. 5.11 respectively.

8 Error plots of the data used to compile this table are shown in Appendix B. 9 At t=53 sec, sudden rise in current magnitude causes this high value of error for only 0.4

seconds. The value is marked with a red circle in Fig B.1 in Appendix B.


Fig. 5.10 Active power comparison of phase ‘b’ for measured and reproduced network for PMU 1. 10

Fig. 5.11 Active power comparison of phase ‘b’ for measured and reproduced network for PMU 2.

10 The outliers in the error are due to improper tracking of the active power during a short period

when sudden variations occur in the active power.


In addition to that, a comprehensive error analysis is performed for the active power (P) and the reactive power (Q) for each phase for both PMU 1 and PMU 2. The results for the error analysis of P and Q are given in Table 5.2 and Table 5.3 respectively. As the tables show, the maximum error in P and Q for both PMU 1 and PMU 2 are 1.344 % and 11.82 %, respectively.

TABLE 5.2

P & Q comparison for PMU 1

P P & Q comparison for PMU1

Average error in P (W)

Average error in P (%)

P1a 687.84 1.344

P1b 599.39 1.120

P1c 575.12 1.023

Q Average error in

Q (var) Average error in

Q (%)

Q1a 860.11 7.84

Q1b 850.94 11.82

Q1c 948.42 7.90

TABLE 5.3 P & Q comparison for PMU 2

P P & Q comparison for PMU2

Average error in P (W)

Average error in P (%)

P2a 7.2210 0.0285

P2b 7.0766 0.0282

P2c 5.0682 0.0208

Q Average error in

Q (var) Average error in

Q (%)

Q2a 19.31 1.805

Q2b 15.62 1.541

Q2c 17.51 1.488


5.5.2 Case Study 2: Active Network Conditions (A Summer Weekend)

In this case study, a PMU data set is selected for the time of year of 2015 when the EPFL campus feeder network was mostly active, i.e. a significant amount of active power was injected by the PVs. Fig. 5.12 shows a power profile for two days of the active power intake by the EPFL feeder from 23rd May to 25th May, 2015. The figure shows two dips in the power profile which corresponds to the time of day when the PVs were injecting a significant amount of power. During this time, the active power intake from the grid reduces (less external power is needed to feed the local loads). On the other hand, during night time when PV production falls, a significant amount of active power is drawn from the grid.

PMU data from 23rd May 2015 between 10:43-10:45 (when the network was mostly active), as shown in the encircled part (bottom left) of Fig. 5.12, was selected for analysis and is shown in Fig. 5.13.

Fig. 5.12 Active power intake from the grid (a weekend-day in summer, 2015).


Fig. 5.13 Active power intake under network active conditions ((10:43-10:45), 23rd May 2015).

Fig. 5.14 and Fig. 5.15 compare the voltage and current phasors, measured by

PMU 1 and PMU 2 in the EPFL feeder network, with those of the reproduced equivalent network. As the figures show, the reproduced voltage and current phasors accurately match those of the actual network. Moreover, the average estimation error (as shown in 5.14 and Fig. 5.15) is quite small for both the voltage and current phasor for both PMUs. The maximum estimation error is 0.3899 % for all the voltage and current phasors.


Fig. 5.14 Measured phasors versus reproduced phasors of phase ‘b’ for PMU 1 (active network conditions).

Fig. 5.15 Measured phasors versus reproduced phasors of phase ‘b’ for PMU 2 (active network conditions).


5.5.3 Case Study 3: Passive Network Conditions (A Winter Night)

In this case study, PMU data is selected from 2015, when the EPFL campus feeder network was passive, i.e. minimum active power injected by the PVs. Fig. 5.16 shows a power profile for two days of the active power intake from 22-24 January 2015. The two peaks shown in the figure corresponds to the time of day when the active power intake from the grid was at its maximum. PMU data is selected from January 22nd, 2015 between 10:03-10:05 (when the network was mostly passive), as shown in the encircled part (top left) of Fig. 5.16. The selected power profile is shown in 5.17.

Fig. 5.16 Active power intake from the grid (weekdays in winters 2015).

Fig. 5.17 Active power intake under passive network conditions (10:03-10:05, 22nd Jan 2015).


A comparison of the voltage and current phasors is performed; results are shown in Fig. 5.18 and Fig. 5.19. As the figures show, the maximum estimation error is 1.4808 % for all the voltage and current phasors.

Fig. 5.18 Measured phasors versus reproduced phasors of phase ‘b’ for PMU 1 (passive network conditions).

Fig. 5.19 Measured phasors versus reproduced phasors of phase ‘b’ for PMU 2 (passive network conditions).


5.5.4 Case Study 4: Solar Eclipse 2015

In this case study, PMU data is selected corresponding to the solar eclipse event occurred on 20th March 2015 which was partially observed in Lausanne, Switzerland. The solar eclipse reached its maximum obscuration of 69.63 % at 10:31, as shown in Fig. 5.20. The immediate effect of the solar eclipse on the EPFL campus feeder is an increase in the power intake from the external grid. This is due to the fact that the generation from the PV panels decreases due to the decreased amount of direct irradiance.

This impact can also be observed from Fig. 5.21, which compares the active power intake from the grid (1 minute averaged) during 09:00-12:00 for 5 days,

Fig. 5.20 Phases of the partial solar eclipse on 20th March 2015 in Lausanne [47].

Fig. 5.21 Active power intake from the grid between 09:00-12:00 during Solar Eclipse (1 minute averages).


i.e. 16th March until 20th March. The figure shows that the red line, which represents the day of the eclipse, is different from the responses for the other days. In particular, the peak (encircled in Fig. 5.21) corresponds to the period when the eclipse was at 69.63 % obscuration. A power profile for 6 minutes of the PMU data is selected from 20th March, 2015 between 10:29-10:35 (when the eclipse was at 69.63 % obscuration), as shown in the encircled part (top middle) of Fig. 5.21. The selected power profile is shown in Fig. 5.22.

Fig. 5.22 Active power intake from the grid during the obscuration (10:29-10:35, 20th Mar 2015).

Fig. 5.23 and 5.24 compares the voltage and current phasors during peak time of the solar eclipse (10:29-10:35). As the figures show, the maximum estimation error is 1.1977 % for all the voltage and current phasors as shown in Fig. 5.23 and 5.24. It is worth noticing that sudden variations in the active power intake during the eclipse caused frequent voltage dips. Note that the SSMS application is able to track these variations.


Fig. 5.23 Measured phasors versus reproduced phasors of phase ‘b’ for PMU 1 (during solar eclipse).

Fig. 5.24 Measured phasors versus reproduced phasors of phase ‘b’ for PMU 2 (during solar eclipse).

5.6 DISCUSSION 85

5.6 Discussion

The previous studies show that the SSMS application provides a reduced equivalent model with sufficient accuracy. In addition, it also shows that it is capable of tracking frequent variations due to local loads inrushes as well as PV power fluctuations. However, this ability has limitations that depend upon the update rate of the SSMS application. The update rate of the application is system dependent and needs to be determined for every system where the application is used.

In this section, case study 1 (presented in Section 5.5.1) is extended to perform a comprehensive analysis for evaluating the impact of different updates rates in the SSMS application. Fig. 5.25 shows the estimation of the reduced model parameter ‘Ra’ for different update rates of the SSMS application. The inherent update rate of the SSMS application is 0.5 sec. In this analysis, the SSMS application was configured to generate updates every 1 sec, 1.5 sec, 3 sec and 5 sec. As the figure shows, by slowing down the update rate, information can be lost. For instance, when updating the SSMS application every 1.5 sec or more, it could not track the dip in Ra at t=35 sec. On the other hand, slower update rates lead to faster estimation speed of the application.

Fig. 5.25 Estimation of “Ra” for different update rates.


Fig. 5.26 shows how the probability distribution of the estimated parameter ‘Ra’ changes while varying the update rate of the SSMS application. The figure shows that slowing down the update rate results in a reduced number of estimations. Fig. 5.27 compares the mean, maximum and minimum values of the estimated parameter ‘Ra’ for different update rates. The figure shows that different update rates have a limited impact in the mean value of the estimated parameter ‘Ra’. This shows that the SSMS application captures the quasi-steady state behavior for the update rates analyzed.

Fig. 5.28 shows how the SSMS application reproduces the active power at PMU 1 for different update rates. The figure shows that for an update rate of 1.5 sec or more, the SSMS application could no longer “track” the active power, in particular, a large peak in the active power at t=35 sec could not be accurately tracked. However, note that the quasi-steady state of the network (for which the application is built), is adequately captured.

Fig. 5.26 Probability density estimates of “Ra” for different update rates.

Pro

ba

bili

ty d

en

sit

y

Pro

bab

ilit

y d

ensi

ty

5.6 DISCUSSION 87

Min

Max

Mean

Fig. 5.27 Mean, maximum and minimum estimated values for “Ra” for different update rates.

Fig. 5.28 Active power at PMU 1 for different update rates of the SSMS application.


Fig. 5.29 compares the average error caused by the SSMS application in reproducing the active power at PMU 1 for different update rates. As the figure shows, increasing the update rate would lead to a higher average error in the reproduced active power, due to the loss of its tracking ability. Note that the error is low considering the simplicity of the reduced model.

Fig. 5.29 Average error in the reproduced active power at PMU 1 for different update rates.

5.7 Summary

This thesis has presented a comprehensive experimental validation of a PMU application for steady State Model Synthesis (SSMS) of active DNs. The validation is performed utilizing real PMU measurements at the DN of EPFL. The validity of the SSMS application has been shown by testing it extensively under various network operating conditions.

It was demonstrated that the SSMS application can produce accurate equivalent reduced models of the section of the network bounded by PMUs. The performance of the application was successfully validated for the case when the EPFL network was under active and passive operating conditions. In addition, the SSMS application was tested by utilizing PMU data during a solar eclipse event, which showed satisfactory performance. The maximum estimation error was 1.4908 % for all the voltage and current phasors for all the case studies.

0

0,5

1

1,5

2

2,5

3

3,5

4

0,5 1 1,5 3 5

5.7 SUMMARY 89

Ideally, the update rate of the application should automatically adapt to evolving network conditions. However, a method has to be developed, implemented and tested vigorously before such functionality can be used.


Chapter 6

6 Test jkkj

Conclusions

This thesis focused on the design, development, implementation, analysis and

experimental validation of a synchrophasor based real-time application capable of performing steady state model synthesis of active distribution networks (ADNs). The thesis also presented the methodologies for pre-processing of PMU data to be fed to the developed model synthesis application.

The thesis is composed of five chapters, a list of references and conclusions. Chapter 1 presented background of how distribution networks are being transformed into active grids, research scope of the thesis, key potential challenges addressed in the thesis, and a brief summary of the main contributions of the thesis.

Chapter 2 provided a solution to process PMU data in the presence of grid dynamics and noise, which may impact the performance of the steady state model synthesis application. As the model to be synthesized is described by an equivalent AC circuit, this thesis developed two methods for PMU data pre-processing using the Kalman filter technique to extract the quasi-steady state components from the raw PMU signals. The proposed methodologies are also capable of reducing noise, compensating for missing data and filtering outliers from input PMU signals in real-time. It was shown that “the modified KF” method is more suitable for real time applications as it does not perform any data


windowing. Moreover, it has been demonstrated that “the modified KF” has the best performance in tracking the quasi-steady state, when a disturbance is applied.

In Chapter 3, the core method developed in this thesis is presented. It performs steady state model synthesis (SSMS) for multiple sections of unbalanced ADNs using measurements from multiple PMUs. The proposed approach is generic and can be applied to any portion of a distribution network with any feeder configuration. The performance and the effectiveness of the proposed method have been illustrated in details by using through RT-HIL simulations. It has been shown that the proposed SSMS technique can produce accurate models for any feeder configuration located between the installed PMUs. If the system configuration changes, the parameters of the synthesized model will automatically update in real-time.

Developing a method to synthesize steady state models of ADNs in real-time provides a first step towards satisfying the need of equivalent models of ADNs, which may help to improve the interactions between TSOs and DSOs. Reduced equivalent models of ADNs may potentially be used in energy management functions of TSOs, making it possible to exchange those models with TSOs in near real-time. To this end, an appropriate framework should be developed, and this thesis does not cover the development of such a framework. In addition, the question regarding how to use and integrate the SSMS application into current power system operation and planning tools is out of the scope of this thesis. Both of these aspects pose interesting research questions for future work.

Chapter 4 presented a comprehensive sensitivity analysis of the SSMS application. The End-to-end TVE was used as a metric to evaluate the sensitivity of the output of the application to the changes in its inputs. The analysis was performed through several case studies and show that the output of the SSMS method is quite impervious to the changes in its inputs, which indicates that the method is robust.

In Chapter 5, extensive experimental validation of the SSMS application is performed. Syncrophasor measurements were acquired from real PMUs installed at an actual active distribution feeder at EPFL’s campus, Lausanne, Switzerland. The validity of the SSMS application has been shown by testing it extensively under various network operating conditions. The performance of the application was successfully validated for the case when the EPFL network was under active and passive operating conditions. In addition, the SSMS application was tested by utilizing PMU data during a solar eclipse event, which showed satisfactory performance. The maximum estimation error was 1.4908 % for all the voltage and current phasors for all the case studies.

CHAPTER 6. CONCLUSIONS 93

Finally, a comprehensive study that can help power system operators to configure the SSMS application was performed. It is shown that the performance of the SSMS method, and hence the estimation error, vary depending on the update rate of the application. The tradeoff between estimation accuracy (tracking) and update rate (speed) is determined. Ideally, the update rate of the application should automatically adapt to evolving network conditions. However, to achieve this automatically, a method has to be developed, implemented and tested vigorously before such functionality can be used.

Appendices

Appendix A: EPFL network, line parameters corresponding to Fig 5.1.

length L in km, resistance R in Ω/km, reactance X in Ω/km, and susceptance B in S/km. The subscripts 0 and 1 stand for zero and positive sequence, respectively.

L R0 X0 B0 R1 X1 B1

Line 1 0.46032 0.159 0.113 1,3e-4 0.159 0.113 1,3e-4

Line 2 0.0728 0.159 0.113 1,3e-4 0.159 0.113 1,3e-4

Line 3 0.07168 0.159 0.113 1,3e-4 0.159 0.113 1,3e-4

Line 4 0.03472 0.159 0.113 1,3e-4 0.159 0.113 1,3e-4

Appendix B: End-to-End TVEs along with the mean values corresponding to Table 5.1.

Fig. B.1 Phases of the partial solar eclipse on 20th March 2015 in Lausanne [47].

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List of Publications

Journal Papers: 1. F. Mahmood, H. Hooshyar, J. Lavenius, A. Bidadfar, P. Lund and L.

Vanfretti, "Real-Time Reduced Steady-State Model Synthesis of Active Distribution Networks Using PMU Measurements," in IEEE Transactions on Power Delivery, vol. 32, no. 1, pp. 546-555, Feb. 2017.

2. F. Mahmood, H. Hooshyar, L. Vanfretti, “Extracting steady state components from synchrophasor data using Kalman filters,” MDPI Journal of Energies, vol. 9, no. 315, 2016. [Invited Paper].

3. F. Mahmood, L. Vanfretti, M. Pignati, H. Hooshyar, F. Sossan and M. Paolone, "Experimental Validation of a Steady State Model Synthesis Method for a Three-Phase Unbalanced Active Distribution Network Feeder," in IEEE Access, vol. 6, pp. 4042-4053, 2018.

4. H. Hooshyar, F. Mahmood, L. Vanfretti, M. Baudette, “Specification,

implementation, and hardware-in-the-loop real-time simulation of an active distribution grid,” Elsevier Sustainable Energy, Grids and Networks (SEGAN), Volume 3, September 2015, Pages 36-51.

5. S. R. Firouzi, L. Vanfretti, A. Ruiz-Alvarez, H. Hooshyar, F. Mahmood,

“Interpreting and implementing IEC 61850-90-5 routed-sampled value and routed-GOOSE protocols for IEEE C37.118.2 compliant wide-area synchrophasor data transfer,” Elsevier Journal of Electric Power Systems Research, vol. 144, pp. 255-267, March 2017.

Conference Papers:

1. F. Mahmood, H. Hooshyar, and L. Vanfretti, “A method for extracting steady state components from Syncrophasor data using Kalman Filters,” in 2015 IEEE 15th International Conference on Environment and Electrical Engineering (EEEIC), 2015, pp. 1498–1503.

2. F. Mahmood, H. Hooshyar, and L. Vanfretti, “Sensitivity Analysis of a PMU-Fed Steady State Model Synthesis Method for Active Distribution Networks,” in IEEE PES General Meeting 2017, Chicago, USA, 2017.

3. F. Mahmood, L. Vanfretti and H. Hooshyar, "Modeling of a detailed photovoltaic generation system for EMT-type simulation," in ENERGYCON 2014 - IEEE International Energy Conference, 2014, pp. 916-921.

4. H. Hooshyar, F. Mahmood and L. Vanfretti, "Specification and implementation of a reference grid for distribution network dynamic studies," in 2014 IEEE PES General Meeting | Conference & Exposition, 2014, pp. 1-5.

5. H. Hooshyar, L. Vanfretti, F. Mahmood, R. S. Singh, N. Singh, A. Bidadfar, S. R. Firouzi, “Synchrophasor applications facilitating interactions in transmission and distribution operations,” in Proc. IEEE PowerTech Conference, Manchester, UK, June 18-22, 2017. [Invited Paper for Special Session on Industry Perspective on Synchrophasor Technology].

6. S. R. Firouzi, L. Vanfretti, A. Ruiz-Alvarez, F. Mahmood, H. Hooshyar, I. Cairo, “An IEC 61850-90-5 gateway for IEEE C38.118.2 synchrophasor data transfer,” in Proc. IEEE PES General Meeting, Boston, MA, US, July 17-21, 2016.

Farhan Mahmood received his Master’s Degree in Electrical Power Engineering from KTH Royal Institute of Technology, Sweden in 2012. He is a PhD scholar at the Department of Electric Power & Energy Systems (EPE), School of Electrical Engineering and Computer Science (EECS) at KTH, Sweden. His thesis is titled: “Synchrophasors based Steady State Model Synthesis of Active Distribution Networks”. His research interests include integration of renewable energy, real-time digital simulation, power system analysis, smart grids and synchrophasor based applications for active distribution networks. Get in touch: Email: [email protected] Tel: + (46) 73- 893 6476

LinkedIn: LinkedIn/in/FarhanMahmoodPhD

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