Designing Reactive Power Control Rules for Smart Inverters using Machine Learning

78 Pages·2017·1.42 MB·English

Designing Reactive Power Control Rules for
Smart Inverters using Machine Learning
Aditie Garg
Thesis submitted to the Faculty of the
Virginia Polytechnic Institute and State University
in partial fulfillment of the requirements for the degree of
Master of Science
in
Electrical Engineering
Vassilis Kekatos, Chair
Virgilio A. Centeno
Jaime De La Reelopez
May 1, 2018
Blacksburg, Virginia
Keywords: smart inverters; support vector machines; kernel-based learning; voltage
regulation; power loss minimization; linearized distribution flow model
Copyright 2018, Aditie Garg
Designing Reactive Power Control Rules for
Smart Inverters using Machine Learning
Aditie Garg
(ABSTRACT)
Due to increasing penetration of solar power generation, distribution grids are facing a
number of challenges. Frequent reverse active power flows can result in rapid fluctuations
in voltage magnitudes. However, with the revised IEEE 1547 standard, smart inverters
can actively control their reactive power injection to minimize voltage deviations and power
losses in the grid. Reactive power control and globally optimal inverter coordination in real-
time is computationally and communication-wise demanding, whereas the local Volt-VAR
or Watt-VAR control rules are subpar for enhanced grid services. This thesis uses machine
learning tools and poses reactive power control as a kernel-based regression task to learn
policiesandevaluatethereactivepowerinjectionsinreal-time. Thisnovelapproachperforms
inverter coordination through non-linear control policies centrally designed by the operator
on a slower timescale using anticipated scenarios for load and generation. In real-time,
the inverters feed locally and/or globally collected grid data to the customized control rules.
Thedevelopedmodelsarehighlyadjustabletotheavailablecomputationandcommunication
resources. The developed control scheme is tested on the IEEE 123-bus system and is seen
to efficiently minimize losses and regulate voltage within the permissible limits.
Designing Reactive Power Control Rules for
Smart Inverters using Machine Learning
Aditie Garg
(GENERAL AUDIENCE ABSTRACT)
The increasing integration of solar photovoltaic (PV) systems poses both opportunities and
technical challenges for the electrical distribution grid. Although PV systems provide more
power to the grid but, can also lead to problems in the operation of the grid like overvoltages
and voltage fluctuations. These variations can lead to overheating and burning of electri-
cal devices and equipment malfunction. Since the solar generation is highly dependent on
weather and geographical location, they are uncertain in their output. The uncertainity in
the solar irradiance can not be handled with the existing voltage control devices as they
need to operate more frequently than usual which can cause recurring maintenance needs
for these devices.
Thus, to make solar PV more flexible and grid-friendly, smart inverters are being devel-
oped. Smart inverters have the capability of advanced sensing, communication, and control-
lability which can be utilized for voltage control. The research discusses how the inverters
can be used to improve the grid profile by providing reactive power support to reduce the
power losses and maintain voltages in their limits for a safer operation.
Acknowledgments
I would first like to thank my thesis advisor Dr. Vasillis Kekatos for his patience,
motivation, enthusiasm, and immense knowledge. The door to his office was always open
whenever I ran into a trouble spot or had a question about my research or writing. He
consistently steered me in the right the direction whenever he thought I needed it.
I wish to thank Dr. Virgilio Centeno and Dr. Jaime De La Ree for creating a nur-
turing environment at the power systems laboratory. Dr. Centeno additionally, has always
motivated me to pursue work in the direction of my passion and I wish to stand by this
inspiration for the rest of my life. I would also like to express my appreciation towards all
members of the power systems laboratory at Virginia Tech for their constant support and
healthy interactions.
I would like to extend my heartfelt thanks to my dear friends, Megha Ravishankar
Rao and Manik Aggarwal. All our fun get-togethers revitalized me. Finally, I would like to
thank my parents Dinesh Kumar and Alka Gupta without whose sincere efforts and constant
guidance I would not have been able to experience my present life.
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Contents
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Prior Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Linear Regression and Kernel Methods 8
2.1 Linear Regression Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Regularized Least Squares . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Kernel Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.1 Dual Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Constructing Kernel . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 RKHS and Representer’s Theorem . . . . . . . . . . . . . . . . . . . 16
3 Grid Modeling and Problem Formulation 20
3.1 Grid Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
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4 Prior Works 27
4.1 Local Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 Optimal Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Affine Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.3.1 Affinely Adjustable Robust Control Policies . . . . . . . . . . . . . . 35
4.3.2 Probabilistic Control Policies . . . . . . . . . . . . . . . . . . . . . . 38
4.4 Proposed Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5 Methodology 41
5.1 Control Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5.2 Learning Policies from Scenarios . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
5.3 Optimal Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.3.1 Voltage Drop and Power Loss Minimization . . . . . . . . . . . . . . 47
5.3.2 Power Loss Minimization under Voltage Constraints . . . . . . . . . . 49
5.4 Implementing Reactive Control Policies . . . . . . . . . . . . . . . . . . . . . 51
6 Numerical Tests 53
6.1 Tests for Voltage Drop Minimization . . . . . . . . . . . . . . . . . . . . . . 55
6.2 Tests for Power Loss Minimization under Voltage Constraints . . . . . . . . 59
7 Conclusions 63
Bibliography 65
vi
List of Figures
1.1 Solar generation from Pecan street data [1]. . . . . . . . . . . . . . . . . . . 2
1.2 Bus voltage profile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.1 Line n feeding bus n from its parent bus π . . . . . . . . . . . . . . . . . . . 22
n
4.1 Apparent Power of the inverter. . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.1 Control rules design and real time operation. . . . . . . . . . . . . . . . . . . 50
6.1 IEEE 123-bus feeder [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.2 Voltage drop minimization for each scenario with local inputs . . . . . . . . 57
6.3 Voltage drop minimization for each scenario with global inputs . . . . . . . . 58
6.4 Average voltage drop vs power loss for power loss minimization under voltage
constraints for 100% penetration . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.5 Average voltage drop vs power loss for power loss minimization under voltage
constraints for scenarios (a) 20% and 50% penetration . . . . . . . . . . . . . 62
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List of Tables
6.1 Reactive power control for voltage drop minmimization ∆ (qg) λ = 1 Per-
s
centage improvement (%) relative to no reactive power support qg = 0 (LI)=
With local inputs only, (GI)= With local and global inputs. . . . . . . . . . 56
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Chapter 1
Introduction
1.1 Motivation
Electricity is an inevitable and integral part of life in today’s world. In the past carbon fossil
fuels were the main conventional sources of producing electricity. These sources were not
environmentalfriendly, involvedemissionofgreenhousegasesanddepletionofnon-renewable
sources such as coal, petroleum and natural gas which have limited availability. But, with
increased awareness of the harmful effects of the gases, governments in many countries are
assigning topmost priority to improve energy efficiency and reduce our carbon footprint on
the planet [3].
In addition, to limited sources of generation, there is an increase in peak consumption
with the increase of demand on basis of rising per capita kWh consumption [4]. Thus,
1
2
the gap between generation and consumption capacities of the grid is reducing, leading to
increased pressure on the grid [4]. Increase in demand and limited amount of generation
resources makes the grid highly dynamic and vulnerable to voltage fluctuations [5]. Thus,
finding new sources of energy has become very essential. Renewable generation is one of the
key solutions used to provide electricity and stability to the grid.
Figure 1.1: Solar generation from Pecan street data [1].
Themostcommonrenewableenergyresourcesusedinthepresentworldarephotovoltaic
and wind energy. Increased penetration of renewable sources into the grid provides a logical
solution to handle the environmental issues. Since solar energy is locally available near
the load, it is easy to harness. Nevertheless, with increasing quantum of these renewable
sources results in more problems for the grid, such as reverse power flow, voltage regulation
etc. For example, a solar farm connected at the end of a long rural feeder can introduce
voltage regulation problems to all the residential buses along the feeder. Moreover, frequent
power flow reversals due to remote injection of renewable energy, strain the apparent power