distribution network state estimation time ...distribution network state estimation, time dependency...
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DISTRIBUTION NETWORK STATE ESTIMATION, TIME DEPENDENCY AND
FAULT DETECTION
Mehdi Shafiei B.Sc and M.Sc in Electrical Engineering
A Thesis Submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
Electrical Engineering and Computer Science School
Science and Engineering Faculty
Queensland University of Technology
Queensland, Australia
2019
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Introduction 1
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2 Chapter 1: Introduction
Keywords
Medium voltage distribution networks, Low voltage distribution networks, Photovol-
taic energy, State estimation, Distribution state estimation, Forecasting-aided state es-
timation, Conditional multivariate complex Gaussian distribution, Spatial-temporal
correlation, Pseudo measured data, Kalman filter, Augmented complex Kalman filter,
Customer loads aggregation, Multi-layer distribution state estimation, Fault detection,
Quantile regression, Instantaneous and define time thresholds.
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Introduction 3
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4 Chapter 1: Introduction
Abstract
In the traditional power networks, electricity is generated in power plants and
through transmission and passive distribution networks, it is delivered to customers.
However, due to environmental concerns, carbon emissions and energy crisis, govern-
ments are considering incentive policies to install PV rooftops, and for investors to
finance grid connected renewable farms projects.
Brisbane, the capital of Queensland is the third most populous city in Australia.
For Brisbane, PV energy is considered as the most propitious kind of renewables with
the average of 261 sunny days in a year, estimating to 2884 yearly hours of bright
sunshine.
The transition from a passive distribution network to an active one increases un-
certainty and variability in both PV generation and customer load sides. This problem
can potentially introduce various planning and operational concerns. Monitoring node
voltages, branch currents, and real data are the initial requirement for any further anal-
ysis and evaluations for any sound and stable planning and operation. However, due
to significant cost and infrastructure investment requirements for upgrade in distribu-
tion networks, installing monitoring devices is not a practical solution. Hence, consid-
ering the technical issues and the nature of requirements at distribution level, an accu-
rate and fast estimating model for distribution networks with low number of monitor-
ing devices can be a very cost effective and useful alternative.
In the last two decades, distribution state estimation (DSE) algorithms have been
applied to distribution networks estimating the states of unmonitored nodes. However,
most available approaches have mainly focused on the snapshot algorithms at a single
time instant using the pseudo measurements to approximate the customer loads. The
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Introduction 5
main shortcoming of snapshot algorithms is ignoring the high time dependency factors
that exist in both customer loads and PV generations. Inclusion of this time depend-
ency of the measuring data will improve the accuracy of DSEs. Another important
factor in designing DSE algorithm is the computational time. Distribution networks
with considerable number of customer loads require DSE algorithms with low compu-
tational process time to estimate the states for different applications.
In order to consider the impact of time based data correlation in DSE formulation
two DSE algorithms with low computational time are developed in this thesis, which
account for the time dependency information of the measurement to improve the ac-
curacy of the estimated states. Inclusion of this approach for higher accuracy may in-
crease the computational time, while distribution networks require fast DSE algo-
rithms for online control and monitoring purposes. Therefore, additionally, customer
loads aggregation and layering structure are considered in the developed DSE algo-
rithms in this research thesis to decrease the estimation process time. Layering struc-
ture, divides distribution network into one main layer and several sub layers, where
customer loads in each layer are aggregated and it is seen like a large load by the main
layer. The aggregated loads in the main layer have lower variability and higher spatial
correlation that increase the accuracy of estimated states.
The anticipated high time dependency in the customer loads can also provide
DSE with enough information for the developed short-term forecasting algorithm to
detect faults in LV distribution networks. In active distribution networks, it is not cost
effective to clear fault from power substations, while distributed generating sources
are connected to the network. Furthermore, the conventional protection schemes are
not accurate enough for the future active distribution networks. For instance, as the
renewable power and load profiles considerably vary during the day and seasons, the
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6 Chapter 1: Introduction
overcurrent relays with fixed fault current thresholds may not detect faults especially
in cases when the fault current is far lower than the nominal load consumption. Hence,
it is required to continuously update the fault current thresholds in each time step based
on the state and time dependency of the system to correctly differentiate the limit be-
tween the normal operations and the faulty conditions. This necessitates predicting the
future expectation of normal conditions of the system. As it is highly unlikely to get
zero forecast error using deterministic forecasts and due to the high accuracy required
for fault detection algorithms, it is more pragmatic to use probabilistic forecast to ob-
tain an estimation of forecast errors. Probabilistic forecast is used in this study to pre-
dict the likely ranges of the future values of the load. Then, the probable ranges are
compared with the real-time measurements to detect faults highly accurately.
Different frequency sampling rates in the measurement devices are required for
different load models in DSEs. In the presence of low frequency sampling rate, cus-
tomer loads are modelled as composite loads. In contrast, considering the forthcoming
high frequency sampling rate measurement devices in the future, it would be essential
to consider the dynamic behaviour of customer loads. Induction motors as the main
dynamic loads have a different behaviour from other type of loads. Hence, a new dy-
namic load modelling approach is required for distribution networks, which can give
a better understanding about customer loads for both state estimator and foreseeable
protection algorithms.
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Introduction 7
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8 Chapter 1: Introduction
Table of Contents
Keywords ................................................................................................................................. 2
Abstract .................................................................................................................................... 4
Table of Contents ..................................................................................................................... 8
List of Figures ........................................................................................................................ 10
List of Tables .......................................................................................................................... 13
List of Abbreviations .............................................................................................................. 16
Statement of Original Authorship .......................................................................................... 19
Acknowledgements ................................................................................................................ 21
Chapter 1: Introduction .................................................................................... 22
1.1 Background and Motivation ......................................................................................... 22
1.2 Amis and objectives of the thesis ................................................................................. 24
1.3 Significance of this research ........................................................................................ 25
1.4 Key innovations of the research ................................................................................... 26
1.5 Structure of the thesis ................................................................................................... 29
Chapter 2: Literature Review ........................................................................... 35
2.1 Introduction .................................................................................................................. 35
2.2 State Estimation and forecasting allgorithms ............................................................... 36
2.3 Distribution network protection ................................................................................... 41
2.4 Load Modelling ............................................................................................................ 46
2.5 Summary ...................................................................................................................... 48
Chapter 3: Conditional Multivariate Complex Gaussian Distribution State Estimator 53
3.1 Introduction .................................................................................................................. 53
3.2 Spatial-Temporal Correlation....................................................................................... 54
3.3 Spatial-temporal distribution state estiamtion: BASICS and formualtion ................... 61
3.4 Simulation resutls ......................................................................................................... 69
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Introduction 9
3.5 Conclusion .................................................................................................................... 81
Chapter 4: Augmented Complex Kalman Filter Distribution State Estimation 84
4.1 Introduction .................................................................................................................. 84
4.2 Forecasting-aided Complex State Estimator: Basics and Formulation ......................... 85
4.3 Multi-Layer State Estimation ....................................................................................... 92
4.4 Simulation Results ........................................................................................................ 97
4.5 Protection scheme using ACKF-DSE ......................................................................... 106
4.6 Conclusion .................................................................................................................. 112
Chapter 5: Stochastic Fault Detection ........................................................... 116
5.1 Introduction ................................................................................................................ 116
5.2 Methodology ............................................................................................................... 117
5.3 Simulation Results ...................................................................................................... 124
5.4 Conclusion .................................................................................................................. 137
Chapter 6: Dynamic Load Modelling Using High Frequency Measuring Data in Distribution Network – for future work ................................................. 140
6.1 Introduction ................................................................................................................ 140
6.2 Dynamic load modelling............................................................................................. 141
6.3 Induction motor identification .................................................................................... 152
6.4 Conclusion .................................................................................................................. 156
Chapter 7: Conclusions ................................................................................... 159
7.1 Conclusion .................................................................................................................. 159
7.2 Future work recommendations ................................................................................... 163
Bibliography ........................................................................................................... 169
Appendices .............................................................................................................. 178
Appendix A ........................................................................................................................... 178
Appendix B List of publications ........................................................................................... 181
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10 Chapter 1: Introduction
List of Figures
Figure 1.1. Distribution networks with various distributed generations .................... 29
Figure 2.1. Distribution networks with various distributed generations [2]. ............. 35
Figure 2.2. Typical SE Algorithm. ............................................................................. 37
Figure 2.3. The proposed fault detection method in [55]. .......................................... 44
Figure 3.1. Impact of customer numbers on spatial correlation (a) Newmarket, (b) Pecan street, and on temporal correlation (c) Newmarket, (d) Pecan street. ................................................................................................. 57
Figure 3.2. Impact of mean and snapshot values on (a) Spatial correlation, (b) Temporal correlation .................................................................................... 58
Figure 3.3. Visualization of the correlation matrix for five groups of loads and PV generations, 5×5 matrix, and black to white colors represent the highest to lowest correlation; (a) PV outputs correlation, (b) customer loads correlation, (c) net loads correlation. .................................................. 61
Figure 3.4. Spatial-temporal correlation in CMCGD. ................................................ 67
Figure 3.5. The flowchart of the spatial-temporal CMCGD state estimator. ............. 68
Figure 3.6. A six-bus distribution network. ............................................................... 70
Figure 3.7. Visualization of correlation matrix for case study 1. ............................... 71
Figure 3.8. Real-time daily load profile for case study 1. .......................................... 72
Figure 3.9. Average voltage errors for scenario 1 and 3. ........................................... 75
Figure 3.10. IEEE 123 node test feeder [103]. ........................................................... 77
Figure 3.11. Schematic of an Australian residential distribution network. ................ 78
Figure 3.12. Three phase voltage magnitudes profile at bus 8. .................................. 79
Figure 3.13. Three phase voltage magnitudes profile at bus 23. ................................ 80
Figure 4.1. Kalman gain in one day. .......................................................................... 88
Figure 4.2. (a) One step difference of the injected current, (b) Temporal correlation. ................................................................................................... 90
Figure 4.3. A typical multi-layer representation of a distribution network. ............... 93
Figure 4.4. Contribution percentage (a) individual customer, (b) group of customers. .................................................................................................... 95
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Introduction 11
Figure 4.5. The flowchart of the layered state estimator. ........................................... 96
Figure 4.6. A six-bus distribution network. ............................................................... 98
Figure 4.7. Five areas voltage magnitudes in Case Study 1. .................................... 100
Figure 4.8. The estimated voltages, real and imaginary parts (a) area 1, (b) area 4. ................................................................................................................. 102
Figure 4.9. A MV/LV unbalanced distribution network. ......................................... 103
Figure 4.10. A three-layer state estimation representation. ..................................... 103
Figure 4.11. Three phase voltage magnitudes at bus 10. ......................................... 105
Figure 4.12. Three phase voltage magnitudes at bus 23. ......................................... 105
Figure 4.13. (a) Corrective error for the current measurement, (b) Corrective error in the form of histogram with fitted normal distribution. ................. 107
Figure 4.14. Examples of fault detection in (a) 3:20 am, (b) 3:20 pm and (c) 11:20 pm. ................................................................................................... 110
Figure 4.15. Corrective errors (a) Phase A, (b) Phase B and (c) Phase C................ 112
Figure 5.1. Quantiles of a typical Gaussian distribution. ......................................... 119
Figure 5.2. Measurements, and quantile 99.9% along with 17 prediction quantiles with probability level ranging from 1% to 97% in 6% increments (from the lightest to the darkest). ............................................ 122
Figure 5.3. Flowchart of the developed fault detection algorithm. .......................... 123
Figure 5.4. A six-bus distribution network. ............................................................. 125
Figure 5.5. Pavetta distribution network. ................................................................. 125
Figure 5.6. Comparison between pick up fault current and the developed IFT for (a) Case 1 (b) Case 2A, Phase A, (c) Case 2B, Phase A. ........................ 128
Figure 5.7. Examples of fault detection for Case 2A, Phase B, 30% increase in load (a) Normal condition, (b) Fault is detected by DTT, (c) Fault is detected by IFT. ......................................................................................... 132
Figure 5.8. Empirical versus Gaussian distributions fitted to the data. (a) aggregated current in Case 1, (b)-(f) the groups 1 to 5, from the lowest values to the highest values. The red and the dotted green curves represent the Gaussian distributions and the empirical distributions, respectively. ............................................................................................... 134
Figure 5.9. DTT logic .............................................................................................. 137
Figure 5.10. IFT logic .............................................................................................. 137
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12 Chapter 1: Introduction
Figure 6.1. Frequency responses of active power-angle transfer functions. ............ 142
Figure 6.2. Frequency responses of active power-voltage transfer functions. ......... 144
Figure 6.3. Frequency responses of active power-angle transfer functions. ............ 145
Figure 6.4. Frequency responses of active power-voltage transfer functions. ......... 146
Figure 6.5. Active power with respect to angle step change. ................................... 147
Figure 6.6. Frequency responses of active power-angle transfer functions. ............ 148
Figure 6.7. Frequency responses of active power-voltage transfer functions. ......... 149
Figure 6.8. Frequency responses of active power-angle transfer functions. ............ 150
Figure 6.9. Frequency responses of active power-voltage transfer functions. ......... 151
Figure 6.10. Case Study 1, with three induction motors. ......................................... 153
Figure 6.11. Case Study 2, with two induction motors and one fixed load. ............ 155
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Introduction 13
List of Tables
Table 3.1. Pseudo measured injected current at 100% loading condition ................ 71
Table 3.2. Comparative results from Case study 1, scenario 1 – for three time steps and three loading levels ...................................................................... 73
Table 3.3. Comparison results for scenario 2 – for three time steps with a decrease and an Increase in loading ............................................................. 74
Table 3.4. Comparison results for scenario 3 with two measurement points and three Time steps ........................................................................................... 75
Table 3.5. Comparison results for case study 2, with decreasing load ..................... 77
Table 3.6. Voltage error in case study 3.................................................................... 80
Table 3.7. Voltage error in case study 3 with higher R/X ratio ................................ 81
Table 4.1. Voltage magnitude error in case study 1 ................................................ 100
Table 4.2. Voltage angle error in case study 1 ........................................................ 100
Table 4.3. Magnitude voltage error in case study 2 ................................................ 104
Table 4.4. Voltage magnitude error and computational time in case study 2 ......... 104
Table 4.5. Fault detection result in case study 1 ..................................................... 108
Table 4.6. Fault detection results for Case study 2 ................................................. 112
Table 5.1. Fault detection results for Case 1 ........................................................... 130
Table 5.2. Fault detection results for Case 2A ......................................................... 130
Table 5.3. Fault detection results for Case 2B ......................................................... 130
Table 5.4. Fault detection results for Case 1 with Gaussian assumption ................ 135
Table 5.5. Coordination of protection areas in percent (%) .................................... 136
Table 6.1. The Induction Motors Parameters .......................................................... 142
Table 6.2: Active power-angle transfer functions, zeros, poles and gains ............... 143
Table 6.3: Active power-voltage transfer functions, zeros, poles and gains ............ 144
Table 6.4: Active power-angle transfer functions, zeros, poles and gains ............... 145
Table 6.5: Active power-voltage transfer functions, zeros, poles and gains ............ 146
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14 Chapter 1: Introduction
Table 6.6: Active power-angle transfer functions, zeros, poles and gains ............... 148
Table 6.7: Active power-voltage transfer functions, zeros, poles and gains ............ 148
Table 6.8: Mars Overhead Cable Parameters ........................................................... 149
Table 6.9: Active power-angle transfer functions, zeros, poles, gains and Busbars voltages ........................................................................................ 150
Table 6.10: Active power-voltage transfer functions, zeros, poles, gains and Busbars voltages ........................................................................................ 151
Table 6.11: Active power-angle transfer functions, zeros, poles, gains and Busbars voltages ........................................................................................ 152
Table 6.12: Active power-voltage transfer functions, zeros, poles, gains and Busbars voltages ........................................................................................ 152
Table 6.13: Active power-angle/voltage transfer functions, zeros, poles and gains ........................................................................................................... 153
Table 6.14: Active power-angle/voltage transfer functions, zeros, poles and gains ........................................................................................................... 155
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Introduction 15
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16 Chapter 1: Introduction
List of Abbreviations
AAVE Average Angle Voltage Error
ACKF Augmented Complex Kalman Filter
AMVE Average Magnitude Voltage Error
AVE Average Voltage Error
BIBC Bus-Injection to the Branch-Current
CDF Cumulative Distribution Function
CMCGD Conditional Multivariate Complex Gaussian Distribution
COV Covariance
CR Correlation
CS Conditional Multivariate Complex Gaussian Distribution Spa-
tial
CST Conditional Multivariate Complex Gaussian Distribution Spa-
tial-Temporal
DER Distributed Energy Resource
DLF Direct Load Flow
DSE Distribution State Estimation
DSE-MACKF Multi-layer Distribution State Estimation based on Aug-
mented Complex Kalman Filter
DTT Definite Time Threshold
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Introduction 17
FASE Forecasting-aided State Estimation
IFT Instantaneous Fault Threshold
KDE Kernel Density Estimation
KF Kalman Filter
LV Low Voltage
MAVE Maximum Angle Voltage Error
MMVE Maximum Magnitude Voltage Error
MV Medium Voltage
MVE Maximum Voltage Error
PDF Probability Distribution Function
PV Photovoltaic
RC Residential Community
RMSE Root Mean Square Error
SD Standard Deviation
SE State Estimation
VAR Variance
WLS Weighted Least Square
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18 Chapter 1: Introduction
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Introduction 19
Statement of Original Authorship
The work contained in this thesis has not been previously submitted to meet re-
quirements for an award at this or any other higher education institution. To the best
of my knowledge and belief, the thesis contains no material previously published or
written by another person except where due reference is made.
Signature: QUT Verified Signature
Date: January 2019
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20 Chapter 1: Introduction
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Introduction 21
Acknowledgements
It is my pleasure to thank those who support me during the period of my PhD.
My foremost gratitude goes toward my principal supervisor, Dr. Ghavameddin Nour-
bakhsh for his admirable supervision, encouragement and guidance. I also wish to
extend my sincere appreciation to my associate supervisors, Prof. Gerard Ledwich and
Dr. Ali Arefi for their invaluable support and advice throughout my PhD. It was my
honour to work under their supervision and to be a part of their research team.
Furthermore, I would like to convey my sincerest thanks to my QUT colleagues
and friends, especially Associate Prof. Geoff Walker, Dr. Adriana Bodnarova and Mr.
Samuel Cunningham-Nelson for their support and encouragement.
I gratefully acknowledge Queensland University of Technology (QUT) for
providing my QUTPRA scholarship, which has given me this opportunity to develop
my teaching and learning skills. Also, I would like to thank QUT Research Student
Centre Staff members, especially Ms. Janelle Fenner and Ms. Judy Liu, and staff mem-
bers of EECS School especially Ms. Joanne Kelly, Ms. Joanne Reaves and Ms. El-
lainne Steele for their support during my PhD period.
Special thanks to my lovely family, my parents, my sister and my brother in law,
for their constant encouragement and support in whole my life.
Last but not least, I would like to thank my wife Faranak for her love and con-
stant support, for all the late nights and early mornings, and for giving me hope over
last eight years. Without your everlasting encouragement, patience and pure love this
research has not been able to take this place. Thank you for always being my best
friend. I owe you everything.
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22 Chapter 1: Introduction
Chapter 1: Introduction
1.1 BACKGROUND AND MOTIVATION
Environmental concerns and incentive-based policies supported by the network
operators have led to a rapid increase in renewable energy penetration in distribution
networks. However, a high PV penetration with intermittent generation increases the
complexity of distribution networks and calls for new control and monitoring algo-
rithms.
Although in the recent years, several methods are proposed to control and mon-
itor of medium voltage (MV) distribution networks, the challenges and the potential
solutions with the modern low voltage (LV) distribution networks are yet to be inves-
tigated. Most of the current monitoring and protection schemes rely on considerable
number of measurement and communication devices in distribution networks, which
is not feasible from the imposed cost perspective.
In order to achieve a cost-effective monitoring method, distribution state estima-
tions (DSEs) are employed to estimate the states of the unmonitored nodes. This re-
quires using pseudo data instead of measurements to make the DSE algorithms ob-
servable. Pseudo data is the historical data provided by the temporary measurement
devices or the electricity bills. The accuracy of the pseudo data affects the performance
of the DSEs. However, the problem is that the pseudo data in LV distribution networks
with unpredictable behaviour of customer loads are low in accuracy. This calls for new
methods to refine the data such that they improve the accuracy of the estimated states.
Several methods are proposed in literature for updating pseudo data based on spatial
correlation. However, temporal correlation is not well-addressed in the literature,
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Introduction 23
though it provides further information for updating pseudo data to improve the accu-
racy of estimated states.
Iterative-based nature of most of the current DSE algorithms is an important
drawback of DSE algorithms. In general, the iterative-based algorithms impose a high
computational burden, which makes them inefficient for large distribution networks
with a considerable number of customer loads, while the active distribution networks
with high sampling rate measured data, rooftop PVs and storages require fast and ac-
curate state estimator for control and monitoring applications. Furthermore, in the cur-
rent literature, the real and imaginary parts of the states are estimated independently.
However, this approach can introduce inaccuracy as it ignores the interactions between
the real and imaginary parts of the states. Therefore, it is highly desirable to devise a
method that can directly include states as complex values.
In general, DSE algorithms can be divided into two main categories as snapshot
estimators and forecasting-aided state estimators (FASEs). Snapshot state estimator is
mainly used in transmission networks for balancing between different measurements
devices, while FASE algorithms are more suitable for real-time applications in distri-
bution networks. In FASE algorithms, the impact of time dependency is considered
for estimating the current states. Furthermore, through FASE, the error of estimation
can be employed to detect the abnormalities, specifically faults in distribution net-
works.
In this thesis, not only two new DSE methods are developed, but also the im-
portance of DSE algorithm in fault detection is studied. One of the main reason of
importance of DSE algorithm in fault detection is that fixed fault current thresholds in
conventional protection schemes may not be accurate at detecting high impedance
faults in LV distribution networks, where the load profile varies considerably during
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24 Chapter 1: Introduction
the day. Hence, it is expected that using customer loads time dependency for dynami-
cally updating fault thresholds increase the accuracy of fault detection in such net-
works. FASE algorithms employ a corrective error to refine the estimated states, in
consecutive time intervals. This error signal can be used to detect faults in LV distri-
bution networks, where a large increase in corrective error can indicate a potential
abnormality in distribution networks. An alternative approach is to use probabilistic
forecasts to generate the likely ranges with probability levels for the future values of
loads. The predicted ranges can be compared with real-time measurements to detect
faults.
1.2 AMIS AND OBJECTIVES OF THE THESIS
This work develops original solutions based on customer loads time dependency
for control and monitoring in LV distribution networks with a low number of meas-
urement devices. Two DSE algorithms are established to estimate the network states
with a low number of measurement devices. Additionally, this work develops two
methods to increase the accuracy of the pseudo data. To develop a new fault detection
scheme in LV distribution networks, it is recommended to consider DSE corrective
error to determine fault thresholds. Furthermore, the quantile regression as a nonpara-
metric distribution [1] is deployed to determine the dynamic fault current thresholds
to detect faults with low fault currents. In order to achieve the main objective of this
thesis, which is improving the monitoring and protection of LV distribution networks,
the following research studies are conducted:
Developing DSE algorithms catered for distribution networks with limited
number of measurement devices. The DSE formulations are desired to esti-
mate the states in complex forms.
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Introduction 25
Developing a FASE algorithm for real-time studies, which is able to refine
the estimated states, gradually.
Developing a new formulation for updating pseudo data considering the im-
pact of spatial and time correlation.
Investigating the impact of load aggregation on the accuracy of DSE algo-
rithm.
Developing a new fault detector algorithm based on FASE approach as an
application of DSE methods.
Determining dynamic fault current thresholds by employing short-term prob-
abilistic forecasting.
Proposing a new dynamic load modelling for distribution networks.
1.3 SIGNIFICANCE OF THIS RESEARCH
The fast growing integration of renewable energies in distribution networks has
made these networks active. Renewables cause voltage and flow violations in distri-
bution networks. This calls for fast monitoring and protection methods to maintain the
reliability and consistent delivery of the electricity. For monitoring purposes, the high
cost of widespread monitoring installations such as measurement devices and commu-
nication platforms is not economically viable. In this regard, state estimation can play
an important role using limited measuring devices at nominated nodes while employ-
ing pseudo data for the remaining unmonitored nodes. However, usually the accuracy
of the pseudo data is very low, which decreases the accuracy of the estimated node
voltages and branch currents states in distribution network. Therefore, new methods
are needed to update and refine the pseudo data in order to obtain highly accurate re-
sults from DSE algorithms.
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26 Chapter 1: Introduction
As an application for the developed method, FASE is employed in distribution
networks for high impedance fault detection. High impedance faults in distribution
networks will often increase the current slightly, which the conventional overcurrent
relays with fixed current thresholds may not be able to detect them. Hence, advanced
state estimation with forecasting algorithms are required to update the fault current
thresholds in each time step to increase the accuracy of the fault detection algorithms.
1.4 KEY INNOVATIONS OF THE RESEARCH
The main contribution of this research is to develop new fast DSE algorithms
with acceptable performance for distribution systems and in particular for LV net-
works with low number of measurement devices. Additionally, this work develops
new approaches for updating the pseudo data to increase the accuracy of DSEs. More-
over, two methods are proposed for fault detection for LV distributing networks. In
order to achieve the main objectives of this research, the following innovative research
developments are accomplished in this thesis and are described and listed as:
1. Customer loads show a very high time dependency, and similar load types
in different locations are highly correlated. Based on this observation, the
first innovation of this thesis is to incorporate spatial-temporal correlation
to develop a new method for updating pseudo data in MV and LV distribu-
tion networks. Conditional multivariate complex Gaussian distribution
(CMCGD) is used to characterize the spatial-temporal correlations among
consumer loads to refine the estimated states.
2. The investigations in this thesis show that the injected currents of the cus-
tomer loads can be considered as the integration of white noise. Therefore,
the novelty of the second chapter of this thesis is mainly to develop a new
DSE method based Augmented Complex Kalman Filter (ACKF) to refine
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Introduction 27
the estimated states continuously. The ACKF in literature needs to update
2 states, while in this thesis the developed algorithm updates states to have a time efficient DSE algorithm.
3. The study performed in this thesis shows that the phase adjacent aggregation
not only decreases the number of estimated states, but also increases the
cross correlation between aggregated loads. One of the key contributions of
this thesis is to divide a large distribution networks into one main-layer and
several sub-layers. The customer loads in sub-layers are aggregated and act
like a large customer load seen by the main-layer. Through load aggregation,
a higher cross correlation among aggregated loads is achieved and this cor-
relation information is employed to update the pseudo data, leading to a sig-
nificant increase in the accuracy of the established framework.
4. A new probabilistic forecasting algorithm is developed to consider the time
correlation for the injected currents to predict upper limits with probability
guarantees for them. The developed framework is able to predict the upper
limits or the so-called quantiles without any restrictive assumption on the
probability distribution of the injection current. A framework is established
to link the concept of the upper limits with probability guarantees to two
fault thresholds for instantaneous and definite time tripping. One main ad-
vantage of the developed method is that it dynamically updates the fault
current thresholds for each next time step.
5. In the presence of measurement devices with higher frequency sampling in-
tervals, it is necessary to consider dynamic behaviour of induction motors
in the state estimation algorithms. The last innovative research contribution
of this thesis is to establish a new method to dynamically model a set of
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28 Chapter 1: Introduction
induction motors in the distribution network with a first order transfer func-
tion. The gain, zero and pole of the transfer function are employed to infer
the size of the induction motors and their distance from the measurement
devices.
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Introduction 29
The summery of the main contributions of each chapter is provided in Figure
1.1.
Figure 1.1. Distribution networks with various distributed generations
1.5 STRUCTURE OF THE THESIS
This thesis is presented in six chapters.
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30 Chapter 1: Introduction
Chapter 1. Introduction:
In this chapter an overview of the thesis along with background, motivations,
significance and contributions of the work are outlined.
Chapter 2. Literature Review:
This chapter provides a comprehensive literature review towards an introduction
to snapshot and real-time DSE algorithms, load modelling and fault detection in dis-
tribution networks.
Chapter 3. Conditional Multivariate Complex Gaussian Distribution State
Estimation:
This chapter uses a model of the time correlation of loads to formulate a set of
pseudo measurements, this time correlation reduces the effective noise in the esti-
mates. In the first part of this chapter a comprehensive study on the significance of
spatial-temporal correlation is provided, which mainly focuses on:
Impact of loads aggregation on spatial-temporal correlation between two
residential communities (RCs).
Impact of two time intervals (Snapshot and mean measurement types) on
spatial-temporal correlation.
Impact of PV penetrations on spatial-temporal correlation of net customer
loads.
In the second part of chapter 3, conditional multivariate complex Gaussian dis-
tribution (CMCGD) is formulated based on spatial-temporal correlation between cus-
tomer loads to increase the accuracy of pseudo data. Finally, a new one-iteration DSE
algorithm is established to estimate the states of distribution networks. The perfor-
mance of the developed method is evaluated based on three case studies, including an
unbalance LV distribution network.
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Introduction 31
Chapter 4: Augmented Complex Kalman Filter Distribution State Estima-
tion:
This chapter represents the time model of the loads as an explicit state equation
which means that state estimates have cumulative corrections. Due to the fact that the
states of distribution networks are complex values, chapter 4 is mainly focuses on aug-
mented complex Kalman filter to formulate a fast complex FASE algorithm. In chapter
4, a typical distribution network is divided into several estimation layers, with series
and parallel levels to decrease the computational time. In the main estimation layer,
the customer loads in sub layers are aggregated and act like a large load with low
variations. This allows for an increase in the accuracy of the estimated states. Low
variations and high correlation between aggregated loads comparing to the individual
loads, increase the accuracy of the developed scaling factors as the contribution of the
consumed power in each sub layer to the measured current on the LV transformer. This
helps to decrease the error of updated pseudo data. Finally, the corrective error of Kal-
man filter consecutively and continuously refines the estimated states.
Chapter 5: Stochastic Fault Detection:
The time variation of loads is limited due to system variance for residential loads,
this enables faults to be detected as an abnormal change in measured loading. The aim
of chapter 5 is to present a new fault detector algorithm for LV distribution networks
when the fault current is low, referring to high impedance fault. In this chapter it is
shown that conventional protection scheme of overcurrent relays is not accurate
enough for fault detection in LV distribution networks. Hence, quantile regression is
employed to forecast the quantiles of the current at the next time step. The forecasted
quantiles are used to continuously update the developed fault current thresholds. In
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32 Chapter 1: Introduction
this chapter, the behaviour of the measured current in LV distribution networks is stud-
ied and it is concluded that it does follow a Gaussian distribution. The developed
framework is evaluated using data from a real distribution network with 169 houses.
The results suggest that the developed model can be very promising for LV residential
distribution networks.
Chapter 6: Dynamic Load Modelling Using Measured Data in Distribution
Networks:
In the presence of measured data with a high frequency sampling intervals, it is
necessary to consider dynamic load models as the part of domain load prediction in
the state estimation algorithms. The aim of chapter 6 is to develop a new dynamic load
modelling and identification framework as initial step for future research work on its
own. Induction motors as the main dynamic loads in the distribution networks can be
modelled as a first order transfer function that gain, pole and zero can be considered
to infer the size of induction motors. The developed method can be employed in the
state estimation algorithm where the estimated states represent the dynamic behaviour
of the LV distribution network for control and protection studies. This chapter repre-
sents the first step toward dynamic load modelling for monitoring, control and protec-
tion purposes for future LV distribution networks.
Chapter 7: Conclusions and Future Works:
Conclusion drawn from this thesis along with the future work directions are pro-
vided in this chapter.
1.5.1 Thesis road map
The aim of this thesis is to develop new solutions for monitoring distribution
systems and particularly LV networks with a low number of measurement devices.
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Introduction 33
The analysis in this thesis show that customer loads have high time dependency, and
the temporal correlation information can be used to design highly accurate monitoring,
control and protection algorithms for the LV distribution networks. For LV distribu-
tion networks with limited number of measurement devices, pseudo data are employed
for the unmonitored nodes to give information about customer loads. However, pseudo
data often comes with a high error rate, which decreases the accuracy of the state esti-
mator algorithms. Therefore, a new method based on CMCGD is developed to incor-
porate time and spatial correlation information to update the pseudo data. To increase
the spatial-temporal correlation, load aggregation is considered, where increasing the
number of aggregated customer loads leads to an increase in the accuracy of estimated
states. In this method, spatial correlation of the measured data at time t as well as its
temporal correlation with the previous time steps increases accuracy of the pseudo
data. In the developed method, in each time step a combination of the measured data
at t and a window of previous measured data are employed to update the pseudo data.
In the first developed DSE method, the corrective error of each window of meas-
ured data is independent from other corrective errors. Therefore, an alternative DSE
method that considers the possibility of continuously refining the estimated states is
established in this thesis. Investigations show that the differences between injected
current in two successive time steps act like a white noise. Therefore, injected currents
are considered as the states in a new established DSE based ACKF algorithm, which
refines the estimated states gradually.
In order to study the practicality of the developed method in the protection ap-
plications, the Kalman filter corrective errors are considered to determine the fault
current thresholds. It is shown that fault conditions in the distribution networks will
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34 Chapter 1: Introduction
cause a considerable jump in the corrective error. For a network without historical data
the error of ACKF can be used to determine the fault thresholds.
In the presence of historical data from few measurement points, a new probabil-
istic forecasting algorithm is established to capture the high time dependency in the
injected currents and develop a model to predict upper limits with probability guaran-
tees for the injected currents. The instantaneous and definite time thresholds are deter-
mined based on the predicted upper limits. In the established method, the upper limits
are predicted continuously and the fault thresholds are updated dynamically for each
next time step. One significant advantage of the established method is that it is distri-
bution-free. Hence, there is no restrictive assumption about the probability distribution
of the injected currents. This is important because the empirical investigations pro-
vided in this thesis show that the inject current does not follow a Gaussian distribution.
All the developed methods in this research are designed in such a way that they
work efficiently in applications with low sampling frequencies such as one-minute
sampling interval. With the low frequency sampling data, the particular characteristic
of induction motor loads is lost and appear like any other composite loads. By increas-
ing the sampling frequency, the dynamic behaviour of these loads can be observed and
can impact the load modelling in distribution systems. Therefore, in chapter 6, a new
framework to model the dynamic load behaviour for customer loads is established.
This framework is a significant first step for the design of state estimator algorithms
for the future distribution networks equipped with new measurement devices capable
of high frequency sampling rate.
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Literature Review 35
Chapter 2: Literature Review
2.1 INTRODUCTION
The phrases Renewable Energy Resources (RERs) and distributed generations
(DGs) are commonly used for local supplied generation such as photovoltaic panels,
wind turbines, fuel cells and gas engines which are connected to the distribution net-
works as shown in Figure 2.1, [2].
Figure 2.1. Distribution networks with various distributed generations [2].
Increasing penetration of RERs and DGs in distribution networks introduces new
challenges for monitoring of these networks. The problems relating to the protection
of these networks are:
1- In distribution networks it is not cost effective to have measurement points in
all nodes. Consequently, the new monitoring methods should be based on a
few measurement points for control and monitoring.
2- Active distribution networks require efficient monitoring method for the fast
decision making required in designing the control and protection algorithms.
3- Conventional protection schemes with fixed threshold currents may not be
accurate enough for fault detection in distribution networks.
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36 Chapter 2: Literature Review
In this chapter a comprehensive literature review is provided to address:
1- State Estimation in distribution networks: In section 2.2, a comprehensive
review of state estimators in distribution networks are provided. Recent stud-
ies in both snapshot and forecasting-aided state estimators are provided in
this section. Furthermore, in the last part of this section, a study about short
term forecasting algorithm is provided, to report the effectiveness of the de-
veloped method for distribution networks.
2- To have state estimators in distribution networks with low number of real
measurements, the load models play an important role. Hence, in section 2.3,
dynamic and static load modellings are introduced based on the results of
several articles.
3- It is tried to give an overview about distribution networks protection algo-
rithms in section 2.4. To explain the fundamental concepts and developments
in the areas of protection schemes, several methods based on conventional
protection algorithms, communication based fault detectors, state estimators
and forecasting algorithms are studied and reviewed in this section.
2.2 STATE ESTIMATION AND FORECASTING ALLGORITHMS
Power system state estimation has been used extensively for transmission sys-
tems operation and control since its first introduction in 1970 [3-5]. As shown in Figure
2.2, the application of SE can be divided into three steps, namely; inputs, State Esti-
mation (SE) process and output [6], as follows:
Inputs:
Network Parameters
System Measurements
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Literature Review 37
Pseudo measurements
DSE Process
Processing the networks based on the first part
Analysis the Observability of the networks
DSE algorithm
Bad data identification
Output
Voltage magnitude of busbars
Voltage angle of busbars
Node injection current
Branch current
Figure 2.2. Typical SE Algorithm.
SE in distribution networks has become important in last decade, especially after
proposing networks with DERs. Distribution State Estimation (DSE) in comparison
with SE in transmission network has new challenges [6]. Firstly, the number of meas-
urements in distribution networks is limited for economic reasons. The type of meas-
urements is another difference between these two networks. In distribution networks,
the operators employ pseudo measurements data mainly for node voltages and current
Input SE Process Output
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38 Chapter 2: Literature Review
injections, while in transmission networks the operators have access to accurate meas-
urement data of various quantities. The third and the most important difference is the
diversity in distribution loads, which causes two problems [7-10]. Firstly, due to the
dynamic changes in distribution networks, the DSE algorithm requires low computa-
tional burden. Secondly, diversity in customer loads causes pronounced phase imbal-
ances, which should be considered in DSE algorithm. The early development of DSE
goes back to 1990 when the weighted least square (WLS) algorithm was designed and
applied to a distribution system [11]. Later in 1996, a DSE was designed and employed
as a real-time monitoring in distribution management system (DMS) for applications
such as volt/var control considering the impacts of DERs, feeder reconfiguration, bat-
tery storage management and protection [12, 13]. Multiphase DSE approaches suitable
for LV network in the presence of DERs are established in [14].
A high penetration of DERs in a distribution network on one hand, and unpre-
dictable customer loads behaviour, on the other hand, require fast and accurate DSE
methods for online generation/load demand considerations and planning [15-18].
However, a high number of customer loads and a huge amount of measured data from
smart meters make centralized DSE algorithms complicated and computationally de-
manding [19]. An enhanced form of DSE with a significant reduction in measurement
points, while retaining accurate estimations, can be an attractive alternative. Generally,
decreasing the number of measurement points leads to an under-determined system,
meaning that the measurements cannot provide sufficient information required for an
accurate state estimation algorithm [20]. This problem is resolved using pseudo meas-
urements for unmeasured buses, satisfying the distribution network observability con-
ditions [21]. Pseudo measurements can be obtained from advanced metering infra-
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Literature Review 39
structure (AMI), historical data or customers’ billing data [22], or they can be calcu-
lated based on the nominal customers’ load power, consumed power and daily load
profiles [23]. Although the use of pseudo measurement has become an essential part
of the DSE algorithms, the associated error with this type of measurement data is still
substantial, leading to DSE with low accuracy and reliability. Spatial correlation in-
formation between real measured and unmeasured points is deployed to improve DSE
accuracy in [24]. In [25], spatial correlation between loads are used to further increase
the accuracy of the estimated injected currents in unmeasured buses. Similarly, in [26],
spatial dependencies is modelled to determine pseudo load profile for unmeasured cus-
tomers where the essential load patterns are extracted from the smart meters data using
clustering techniques.
Although, the impact of incorporating spatial correlation information on the ac-
curacy of DSE is addressed in the literature, there is no developed DSE formulation
capable of including temporal dependency or spatial-temporal dependencies. This is
while customer loads in general show high correlations in successive time steps. The
temporal correlation can offer a measure for the similarity of load(s) variations in time,
greatly enhancing estimation quality. Recently, in the forecasting literature, the great
potential of involving spatial-temporal dependencies in improving PV power predic-
tion performance has been verified [27]. Also, spatial-temporal correlations is consid-
ered for load growth forecasting and load demand in electrical vehicles (EVs) charging
patterns [28]. A Vector Auto-Regressive (VAR) model is considered in [29] to inte-
grate time and space correlations present in measured data into a DSE algorithm. In
this article WLS as an iterative algorithm is employed for state estimation in presence
of several phasor measurement units. The iterative based algorithms with the large
amount of required data in a distribution network makes these estimation processes
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40 Chapter 2: Literature Review
computationally time-consuming, while an active distribution network with DERs re-
quires fast and accurate state estimators, updating data in less than one second [30].
To deal with a large amount of measured data, a new algorithm based on compressed
measurements is developed in [31]. However, the iterative DSE algorithm developed
in [31] computationally is highly demanding.
Traditionally, SE algorithms are formulated with a static nature in which states
are estimated based on single instantaneous measurements, and previous measured
values are incorporated in the estimation. However, due to high cross-correlations,
valuable information can be extracted from previous measured data to be used in fore-
casting-aided SE (FASE) methods. In general, FASE algorithms are used to detect
unexpected variation in the system states for control and protection analysis, network
configuration errors and bad data detection [32]. For instance, in the security and con-
trol analysis, a recursive FASE method based on measurements is reported in [33], and
also a comprehensive study of this method is detailed in [32, 34]. In [35], it is shown
that Kalman filter as the most common time series forecasting-aided state estimator
[36] has a better performance compared with WLS for distribution networks. In [37],
two decoupled FASE algorithms are established for estimating voltage magnitude and
voltage angle independently. These algorithms are not efficient due to their high com-
putational cost and ignoring the dependencies between magnitude and angle estima-
tion noises [38]. A complex formulation for the state estimator can potentially improve
the accuracy of estimation [39].
Distribution networks contain an extremely large number of customer nodes, and
it is not computationally efficient to process state estimation in a single layer. Instead,
the network can be divided into several subareas, where DSE is carried out in sequence
-
Literature Review 41
or parallel [40]. In a multi-layers state estimation approach, several factors can be con-
sidered to determine the boundaries of the subareas such as overlapping buses, coor-
dination and synchronization [41]. A multi-layers DSE is presented in [16, 17] consid-
ering parallel and series zones [14, 18]. In parallel zones, DSE is employed for several
zones simultaneously allowing for a lower computation time. Similarly, in series
zones, network schematic matrix reduction leads to a higher computational efficiency.
Although this multi-layers state estimation method reduces the computational time, it
requires a significant number of real measurements, making them economically unat-
tractive and computationally inefficient for real distribution networks.
2.3 DISTRIBUTION NETWORK PROTECTION
In the past decade, distribution networks have witnessed rapid changes in local
generation and network monitoring, control and operation. Distribution networks in
the presence of local DERs have become more complex to monitor and operate. This
necessitates development of more advanced protection frameworks tailored for the
specific limitations and structure of distribution networks.
Protection and smart switch devices play an important role in active distribution
networks. Protection devices identify faults and send commands to smart switches to
isolate a fault, while other switches may facilitate alternative route of power supply to
reduce outages. The role of protective devices and smart switches become more im-
portant as penetration of renewable energy resources increase in distribution networks
[42].
Protection is a critical aspect of future distribution network operation. In partic-
ular that; DERs with power electronics interface, bidirectional fault currents, and high
vulnerability factor of network devices require new protection schemes in comparison
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42 Chapter 2: Literature Review
with the traditional distribution networks. Furthermore, for operating in both grid-con-
nected and islanding modes new reliable protection schemes should be designed [43].
In [44] the problems associated with the protection in active distribution networks are
presented, mostly related to the operation of protection relays as well as the behaviour
of distribution networks in fault situations. In the noted article, it has been shown that
traditional protection schemes are not applicable in distribution networks with DERs.
Therefore the authors in [45] have established digital relays with a communication
scheme for distribution networks protection. For the high fault current protection, [46]
recommends to isolate DGs from the network even in the situation with the faults in
the remote area. In [47, 48] a novel idea is presented to detect and discriminate fault
based on the measured three-phase current and voltage waveforms when faults occur
in the power transmission network. In this approach, Negative-sequence components
of the three-phase current and voltage quantities are employed in order to have fast
online fault detection.
In some other approaches, multilevel wavelet transform, principal component
analysis, support vector machines (SVM), and adaptive structure neural networks are
employed at the same time for fault detection. In [49] wavelet is employed for fault
detection based on the comparison between the nominal values and extracted positive
and negative sequence components of the voltage. It is of vital importance to limit the
ground current in distribution networks due to power electronics interface, hence in
[50] a grounding electrode system is applied to limit grounding current. In [51] Dijks-
tra’s method is developed to find the relay hierarchy and thereby update new settings
due to the operation condition of distribution networks. Dijkstra’s method is a search
algorithm which finds the shortest path between nodes. Based on the condition of
switches (close or open), this algorithm models distribution networks as a graph which
-
Literature Review 43
relays represent nodes and connections consider as edges. Consequently, the relays
settings are coordinated based on the distances between the nodes.
In [52] an overcurrent relay is employed to detect the fault and limit the output
of DERs and finally reclose the breakers after fault clearance. Furthermore, the over-
load relays are considered in the developed protection scheme to limit the output power
of DERs, when several loads are out of service during fault conditions. In [45] numeric
relays are employed to implement differential protection scheme in a distribution net-
works. Furthermore, the authors proposed a new method to simulate high impedance
fault to test their proposed protection algorithm. In this method, the magnitude of fault
resistance is randomly changes between 50 and 1000 Ω. The fault duration also varies
between 10µs and 5ms. With this method a true model for high impedance fault is
simulated. In [53] time-frequency transform algorithm is employed to retrieve the
spectral energy of the fault current at both ends of the feeder. Differential algorithm is
considered to find the threshold difference and thereby send a command to the breaker
soon as fault is detected. In this paper the results shows that the established method
can be useful in both radial and mesh network and can identify high impedance faults
as well. Islanding detection is one of the most important issues in active distribution
networks. Several methods have been reported in research literature regarding island-
ing detection. For example; in [54] the authors concluded that positive feedback (PF),
voltage unbalance and harmonic distortion are the most valuable islanding detection
methods. However, normally there are several DERs exit in a distribution network and
therefore they can contribute to frequency and voltage errors, consequently PF method
could destabilize the network. In [55] the authors proposed to divide the network into
small segments, containing transformers, line segments and circuit breaker at the
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44 Chapter 2: Literature Review
boundary between each segment, as shown in Figure 2.3. Although this method can be
useful, the cost of allocating relays for each segment may not be acceptable.
Figure 2.3. The proposed fault detection method in [55].
Several papers proposed communication platforms in active distribution net-
works for monitoring and control purposes [56], [57]. Power Line Communication
(PLC) is considered as an attractive communication system for distribution network
operators due to its low investment cost [58]. In [59], a new fault detection and location
algorithm is proposed using PLC devices installed at the beginning point of the Me-
dium Voltage (MV) distribution line. In this method, the deviations in detection met-
rics related to the network impedances and frequencies are used to detect the high
impedance faults. Although the developed method alleviates the shortcoming of the
conventional overcurrent protection schemes for the case of detecting high impedance
faults, it is not cost effective approach in LV distribution networks due to its large
range of required measurement devices and communication platforms.
In the distribution networks with insufficient communication platforms, fore-
casting-aided state estimators can be employed for real-time applications [60]. Kalman
-
Literature Review 45
filter as the most common real-time state estimator is considered to formulate a new
fault detector in [61]. In this article, the Kalman filter in the time domain estimates
the amplitude, phase and frequency of fundamental components of the traveling waves
to detect the singularity points. However, the method requires investment in installing
highly accurate Phasor Measurement Units (PMUs) in distribution networks, while the
high cost of PMUs limits the scale of their widespread installation. The measurement
data is employed in Bayesian and Gaussian prior distribution frameworks to identify
outages in the power networks. Bayesian inference is also employed in [62] to form
posterior distribution condition for voltage dip state estimation caused by the presence
of DERs.
In the distribution networks using conventional measurement devices with low
sampling rates, forecasting algorithms in both regression and classification processes
play an important role to reduce the operation costs and to improve the reliability.
SVM as a statistical data classification method is employed in [63] and [64], while
voltage disturbances and fault current signals are considered in SVM as independent
variables. Different fault scenarios are classified by SVM to detect and identify faults
in a power system. The problem with fault classification algorithms is that they require
protection relay, and disturbance or event recorder data in different fault conditions,
which are not available in LV distribution networks. In LV distribution networks,
model-based fault detectors can be used to continuously monitor the difference be-
tween the measured data and the model-predicted outputs [65]. In [66], the output of
deterministic load forecasts and the hypothesized fault conditions are compared with
the measured line flows to detect outages in a distribution network. However, highly
intermittent generation and consumption profiles in a distribution network can easily
cause non-negligible prediction errors in deterministic forecasts. While the probability
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46 Chapter 2: Literature Review
of getting zero forecast errors in deterministic forecasts is zero, it is more reasonable
to use probabilistic forecasts to provide an estimation of forecast errors. Probabilistic
forecasts can output likely ranges with probability guarantees for the future values of
the load. The probable ranges can be compared with real-time measurements to detect
faults. Bayesian quickest change detection and statistical process control methods are
recommended in literatures [67-70] as probabilistic short-term forecasting algorithms
to detect unpredicted changes in the behaviour of the system. As part of these two
methods, there are parameters that are determined based on Gaussian assumption and
it can be difficult to determine those parameters where the underlying distribution is
non-parametric. The pattern of the changes in injected currents in distribution networks
in the presence of renewable resources does not fit to any probability distributions.
Hence, a distribution free algorithm is required for short term forecasting to detect
faults in distribution networks.
2.4 LOAD MODELLING
The utilities are responsible for careful design, adequate planning and safe oper-
ation of their current distribution networks with renewable generation resources. Part
of this responsibility is to have advance techniques and technologies in place to mini-
mise customer outages while managing the network with minimum permissible quality
issues. However, considering the extensive distribution networks, it is not cost effec-
tive for utilities to upgrade their networks with the current traditional standard protec-
tion devices. All these changes and the consequent challenges and constraints need to
be addressed properly. One of the critical problems arises in such networks is the pro-
tection, where renewable resources with different types of static and dynamic loads
are present.
-
Literature Review 47
Load modelling can be introduced as active and reactive power changes to volt-
age and frequency changes [71]. Although identifying the accurate load modelling is
important for analysing the power system network, several factors reduce the accuracy
of load modelling such as: diversity of load modelling, uncertainty of load behaviour
for each costumer in each day, lack of information in distribution networks [72].
Static and dynamic load modelling can be employed for power system analysis.
It is worth to note that the static type of load modelling can be employed to approxi-
mate the components of dynamic load modelling [73]. For dynamic load modelling a
set of nonlinear equations are considered as described in [74].
Dynamic and static load modelling play an important role in power system anal-
ysis, because the characteristics of loads have a major effect in power systems espe-
cially the stability of inter-area modes [75]. In [76] dynamic load modelling is em-
ployed to study the effect of active and reactive loads on the oscillation of multi ma-
chine power system. Placement of the dynamic loads in the network is the topic of
[77], which influences the damping of inter-area oscillation. In this paper, the authors
claim that dynamic load model can affect the parameters of Power System Stabilizer
(PSS).
Also, Load modelling is important in stability analysis. Characteristic of dy-
namic load modelling is employed in power system analysis in [78]. In this paper,
evolutionary algorithm is used to identify the parameters of load modelling. The load
modelling is applied in [79] for analysing voltage stability. In this paper, both active
and reactive powers have been modelled as constant current and constant impedance
respectively. Furthermore, induction motors are considered as dynamic loads which
obviously affect the voltage stability. Induction motors cause changes in dynamic be-
haviour of the network. In dynamic study of induction motor, inertia ( ) and torque
-
48 Chapter 2: Literature Review
damping factor ( ) should be considered. In [80], the authors estimate these parame-
ters based on the measured data from the Phase Measurement Unit (PMU). To estimate
these parameters the transfer function between the changes in active power and fre-
quency is considered.
The next step after load modelling in power system study is load aggregating. In
[81] constant impedance and constant power loads are considered as static loads, while
induction motors are considered as a dynamic loads of an aggregated load model. The
authors of [82] claimed that the induction motors in a network can be modelled by one
or two aggregated induction motors. In [83] it is claimed that based on the measure-
ments on the busbars, the induction motors can be divided into three groups: small,
medium, large induction motors. Least square algorithm is employed to identify the
percentage of small, medium and large induction motors and constant impedance and
constant power loads based on the measurements on busbars.
2.5 SUMMARY
As reviewed in this chapter, enhancing state estimation and forecasting ap-
proaches are proposed in several articles for monitoring distribution networks. In ac-
tive distribution networks with DERs, the focus of most articles has been placed on
fast control and monitoring algorithms. In order to design accurate control and moni-
toring algorithms, a considerable number of measurement devices are required. In-
stalling measurement devices with communication platforms is not cost-effective in
distribution networks. Hence, DSEs can be very effective to estimate the states of un-
measured nodes in distribution networks. The state estimation methods currently avail-
able in literature have the following drawbacks:
1- The snapshot algorithms such as WLS as the common approach to estimate
the states of the distribution networks consider the states in each time step
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Literature Review 49
independent of the previous time steps [7-10, 84-86]. This is while in the
distribution networks with low number of measurement points, incorporating
the impact of time dependency can improve the accuracy of the estimated
states. Consequently, the time dependency can be deployed in the FASE al-
gorithms such as Kalman filter [39] or recursive least square to refine the
estimated states.
2- For complex states, in various articles [14-18, 87] the estimation is designed
via two formulations, to estimate the magnitude and the phase separately.
These iterative methods are practical for high and medium voltage networks,
in presence of long transmission lines with considerable angle difference be-
tween node voltages. In contrast, the low voltage distribution networks do
not have long overhead lines or underground cables that can cause significant
angle difference between node voltages. Therefore, a linear complex state
estimation formulation can be considered to estimate states in a single itera-
tion and in a complex format. Non-iterative complex state estimation algo-
rithm decreases the computational time for real time monitoring or control
applications.
3- Complex regressive least square methods exist in the literature [38, 88, 89]
for state estimation. However, these methods do not consider the relative
certainty between the measured data and estimated states. In the developed
complex state estimation formulation in this thesis, the gains are considered
to represent the relative gain between current measured data and the esti-
mated states, and can be tunned based on the value of the corrective error. If
there is a high confidence in the measurement relative to the covariance of
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50 Chapter 2: Literature Review
the propagated state, the gain places more weight on the most recent meas-
ured data, and force the estimated states to follow the measured data more
responsively. Otherwise, the estimated states follow the pattern of estimation
process more closely and do not change this pattern.
Due to the high uncertainties in both customer loads and DERs in distribution
networks, conventional protection algorithms with fixed fault thresholds may not be
sensitive enough for fault detection, especially with low fault currents. Therefore, new
distribution network fault detectors are proposed in the literature to detect faults with
low short circuit currents. Communication based protection algorithms are proposed
in several articles [45, 51, 58, 59, 90]. However, the main issues related to these meth-
ods are the cost and the security of these methods. To have a cost benefit and accurate
protection schemes, DSEs and forecasting algorithms are considered as a basis for de-
veloping new protection schemes. In these methods, measured data, pseudo data and
the disturbance of protection relays in different fault scenarios are considered to clas-
sify different fault scenarios, for fault detection and identification.
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Literature Review 51
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Conditional Multivariate Complex Gaussian Distribution State Estimator 53
Chapter 3: Conditional Multivariate Com-plex Gaussian Distribution State Estimator
3.1 INTRODUCTION
The increasing complexity of distribution networks calls for advancement in
DSE to monitor the operating conditions more accurately. A sufficient number of
measurements is imperative for a reliable and accurate state estimation. The limitation
on the measurement devices is generally tackled using the so-called pseudo measured
data. However, the errors in pseudo data by current techniques are quite high leading
to a poor DSE. As customer loads in distribution networks show high cross-correlation
in various locations and over successive time steps, it is plausible that employing the
spatial and time dependencies can improve the pseudo data accuracy and estimation.
Although, the role of spatial dependency in DSE has been addressed in the literature,
one can hardly find an efficient DSE framework capable of incorporating temporal
dependencies present in customer loads. Consequently, to obtain a more efficient and
accurate state estimation, a new non-iterative DSE framework is developed to involve
spatial-temporal dependencies together. The spatial-temporal dependencies are mod-
elled by conditional multivariate complex Gaussian distributions and are studied for
both static and real-time state estimations, where information at preceding time steps
are employed to increase the accuracy of DSE. The efficiency of the established ap-
proach is verified based on quality and accuracy indices, standard deviation and com-
putational time.
This chapter is organised as follow: Firstly, the spatial-temporal correlation is
introduced. This is followed by introducing the formulation of state estimation based
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54 Chapter 3: Conditional Multivariate Complex Gaussian Distribution State Estimator
spatial-temporal correlation; then three case studies are considered to evaluate and val-
idate the performance of the developed DSE algorithm.
3.2 SPATIAL-TEMPORAL CORRELATION
Correlation is a statistical relationship between two random variables. Spatial
correlation is computed based on the data from different locations, while temporal cor-
relation represents the degree of similarities between data in different time steps [91].
The temporal and spatial correlation coefficients are usually defined as [92]:
, ∗, var x
(3.1)
where , and denote covariance, standard deviation and variance, respec-
tively. For spatial correlation, and represent two sets of data from two different
geographic locations, while temporal correlation describes the dependency at a given
location and between time intervals of and . In this section, the aim is to
study the spatial-temporal correlation strength between net loads in a distribution sys-
tem based on two important factors:
1. The number of loads in customer communities (RCs),
2. Time interval for which load data is averagely available,
3. Presence of DERs at load buses.
3.2.1 Spatial-temporal correlation-Impact of the number of loads in RCs
To study the first factor, two RCs is considered, while the number of customers
are gradually increased in each community. The spatial and temporal correlation coef-
ficients are computed and shown in Figure 3.1. For the analysis, one-minute active
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Conditional Multivariate Complex Gaussian Distribution State Estimator 55
power data of two real datasets from Newmarket suburb in Brisbane, Australia in
summer season, and Pecan street, Texas, USA in winter season is considered [93]. The
spatial correlations are calculated for the aggregated load in each community over the
course of 7 days. The temporal correlation coefficients represent the correlation
strength between successive time steps of the aggregated loads. According to Figure
3.1, as the number of customers increases, the spatial correlation between the aggre-
gated loads in two RCs increases. This happens due to smoothing effects of aggrega-
tion. As one observes in Figure 3.1 (a) and Figure 3.1 (b), the spatial correlation coef-
ficient between two individual houses is less than 20% and it increases to more than
80% when the number of houses in each RC rises to 25. The temporal correlation in
Figure 3.1 (c) and Figure 3.1 (d) shows a similar trend. Note that; in Figure 3.1 (c), the
irregular jump at the case with two houses is accidental and does not imply to be a
general trend.
(a)
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56 Chapter 3: Conditional Multivariate Complex Gaussian Distribution State Estimator
(b)
(c)
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Conditional Multivariate Complex Gaussian Distribution State Estimator 57
(d)
Figure 3.1. Impact of customer numbers on spatial correlation (a) Newmarket, (b) Pecan street, and on temporal correlation (c) Newmarket, (d) Pecan street.
3.2.2 Spatial-temporal correlation-Impact of time interval
The second statement is the time interval of available data. Some applications
require the correlation calculation between loads’ average values over longer time in-
tervals. Whereas other algorithms are using the correlation of snapshot values. In order
to show the impact of time interval, three sample load buses, each with twenty house-
holds are considered. Figure 3.2 (a) shows the spatial correlation between load bus 1
and other two buses, for two time intervals of thirty minutes (Snapshot) and half an
hour (Mean of thirty one minute samples). The load data for half an hour time interval
obtained by averaging 30 one-minute data. As seen, the spatial correlation has changed
slightly, for example from 0.77 to 0.80 for one minute and half an hour time intervals,
between bus 1 and 2.
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58 Chapter 3: Conditional Multivariate Complex Gaussian Distribution State Estimator
(a)
(b)
Figure 3.2. Impact of mean and snapshot values on (a) Spatial correlation, (b) Temporal correlation
RC1-RC2 RC1-RC3
0.75
0.85
0.95Mean Instantaneous
Corr(t,t-30) Corr(t,t-60)
0.75
0.8