Sayon MS Thesis Presentation Draft-4

Measuring and Enabling Resiliency in Distribution
Systems With Multiple Microgrids
Sayonsom Chanda
Major Advisor: Dr. Anurag K. Srivastava
1

Presentation Outline
– Problem Statement
• Concept of Resiliency applied to power systems
– Literature Review
• What has been done so far and what are the research gaps?
– Computation of Resiliency Metrics
• mathematical formulation
– Enabling resiliency
• Using multiple microgrids
– Simulation and Results
• On real and standard test feeders
– Conclusions
2

– Conclusions
3

Vulnerabilities of power distribution system
4
High impact,
Low frequency events
Smart Grid has
information flow
as critical to its
operation: increasing
Vulnerability to getting
hacked.
Level of servicing,
OH/UG Construction
Mitigation Schemes
Protective relays Enough resources to
meet demands?
Energy security
issues.
Acts of terrorism.
PROBLEM STATEMENT
Focus of the thesis: for any extreme event, analysis of resiliency.

Background: Effect of weather on continuity of power supply
400% increase in number of weather
related power outages over the last 20
years, in US .
In 2012, Superstorm Sandy left more than
8.5 million customers without power
Economic Benefits of Increasing Electric
Grid Resilience to Weather Outages
estimates the average annual cost of
weather-related power outages to be
between $18 and $33 billion over the past
decade
To reduce these losses and avert
discontinuity of power supply during
unfavorable weather events, we must
re-engineer our existing systems to be
resilient to weather changes.
Weather-related outages in US between 1992-2012
Picture: Region-wise most financial losses as a result of
power interruption due to weather-related events.
Source: National Climatic Data Center
PROBLEM STATEMENT 5

– Conclusions
6

Concept of resilience applied to power systems
• Resilience of networks [social networks, water networks,
airport networks] is well-studied. However, resilience of power
distribution system is a new topic of interest.
• Multiple definitions of resiliency
– US PPD-21: reducing the risk to critical infrastructure by physical
means or defense cyber measures to intrusions, attacks, or the
effects of natural or man-made disasters.
– NARUC: robustness and recovery characteristics of utility
infrastructure and operations, which avoid or minimize interruptions
of service during an extraordinary and hazardous event.
– Dominion Power Virginia: ability to reduce the magnitude and/or
duration of a disruptive event
– SNL – Resiliency is the ability of system to respond and remain
functional during an event X, given there is a threat Y of it happening.
7LITERATURE REVIEW

• Resiliency has been studied from several perspectives, for both long and short time
scales.
Interest in resiliency power system research has increased over the years.
LITERATURE REVIEW
Summary of literature review
Database: IEEExplore Digital Library
Keyword: Power System Resiliency
Database: Google Scholar
Keyword: Resiliency Metrics
• Metrics can evaluate both Operational and Planning resiliency, or deal with them
separately.
• No formal resiliency metric for power distribution system
8

Power System resilience has been studied from complex network point of
view.
Fig: European Power Grid
• 3,000 Nodes, 150,000 mi of HV network
• Resiliency of this network has been studied by
Pagani (’12), Solé (’08), Rosas-Casals(’07),
Albert(’04), Crucitti(’04)
For the US Power Grid:
• Watts(’99)- studied US Power Grid resiliency in his
book.
• Holmgren(’07)- compared US Grid resiliency to
Nordic Grid Resiliency
• Wei(’10), Chen(’07)- Vulnerability Evaluation
Models
• Wang(’10)- NYISO-2935 bus system, WECC
system
• Bompard(’10), Dwivedi(’10), Pahwa(’10)- complex
network analysis of IEEE Systems
9LITERATURE REVIEW

Differences between Reliability and Resiliency
Resiliency
• Measured in anticipation of some
form of threat
Reliability
• Measure of operational consistency
and good performance of Utility
towards its customers over long time
period.
• Priority of critical loads is
considered
• No classification load is reflected in
measurement of reliability
• Resiliency is an indication of
preparedness of a network to
withstand or avert damage coming
from outside the power system [like
weather]
• Reliability accounts for only power
lost due to operational or equipment
damages, over which Utility has
control. It doesn't consider external
factors
• No formal metrics • SAIDI, SAIFI, MAIFI, etc
10LITERATURE REVIEW

LITERATURE REVIEW
Approaches towards studying Resiliency
System A and System B show different
resiliency based on what reconfiguration
algorithms are there in the DMS [ RAND]
Sandia National Lab Conceptual Framework for deriving Resiliency
Metrics as a PDF. Higher Resiliency is shifting the peak to the left.
Resiliency Metrics Computation and Enabling
Framework proposed by Panteli et al
11

Thus, a resilient distribution system should be able to:
W
R
A
P
Withstand any sudden inclement weather or human attack
on the infrastructure.
Respond quickly, to restore balance in the community as
quickly as possible, after an inevitable attack.
Adapt to abrupt and new operating conditions, while
maintaining smooth functionality, both locally and globally.
Predict or Prevent future attacks based on patterns of past
experiences, or reliable forecasts.
12LITERATURE REVIEW

– Conclusions
13

Need for Resiliency Metric & Computation Framework
Resiliency Metrics can help
• justify DMS control actions
• cost-benefit analysis of microgrids
• mitigate loss and inconvenience through
proactive action in anticipation of storm
• improve the network through feedback
• impact economics of power exchange
between grid to consumers in microgrids
Computing Resiliency is a complex
decision making problem.
• ANL proposed an infrastructure survey based
approach, viz, RMI
• LBNL follows a modeling based optimization
approach to compute resiliency (below)
• Resiliency Metric should reflect redundancy
and restoration efforts of the network.
14FORMULATING RESILIENCY METRICS

Procedure to compute resiliency metric
• Topological Resiliency (RT)
– Percolation Theory
• Weather Factor (WF), Cyber-attack threat
• Age of Equipments/Maintenance Levels (λ)
• Control Systems and DMS Response
– Restoration schemes by operating switches
– Load flow in damaged network.
• Multi-criteria decision making
– Many approaches possible.
– Chose Analytical Hierarchical Process (AHP)
FORMULATING RESILIENCY METRICS
Fragility Model
Restoration &
Recovery
Computation
15

Approaches to determine Topological Resiliency
(i) Using Complex Network Analysis
(ii) Using path redundancy as a criteria (direct approach)
However, the first step is to convert the
power systems into a graph
B1
B6
B2 B3
B4
B5
1
2
3
4
5
6
Bus → Node (N)
Branch → Edge (E)
Generator → N/A
Load → N/A
G=(N,E)

Important Graph Theory Parameters

Properties of Distribution System Topology
• Dist. Sys. modeled as a graph G(N,E) with N nodes and E edges.
• Average Degree <k> is a measure of how many nodes are
connected to one node on an average. Higher value indicates
greater fragility.
• Ratio of first moment and second moment of average degree
distribution should tend to zero for less fragile network.
• Determines the most important nodes of a network. Computed as
where nk --> nl,ni = 1 if the shortest path between nk and nl passes
through ni, and 0 otherwise. It is computed through all nodes.
• It is an indicator that captures the fact that the higher the value of
second smallest eigenvalue of Laplacian matrix of the network the
network is more resilient
Degree
Betweenness
Centrality
Algebraic
Connectivity

During a forceful disruptive event, nodes have high and random probability of
getting damaged.
• Nf  Largest component of the damaged network
• N0  Largest component of the undamaged network
• f  fraction of damaged nodes
For each distribution system a different plot is obtained. So direct conclusion about
resiliency cannot be made.

Percolation theory is used to flow of information/mass in networks with
uncertainties in path of propagation.
• pc  percolation threshold [it’s a value of probability between 0 to 1]
• p  Probability of each node being functional despite an unfavorable event
• <σ>  Average size of the clusters (i.e. no. of nodes in an island) prior to
reaching the percolation threshold
• Percolation Theory is easy to
find a path from a source to a
sink, or check its feasibility.
• It can be used to determine a
condition in the distribution
system – such that no matter
how many nodes are damaged
there is at least one path from a
sink to a source. That condition
is called Percolation
Threshold.

Simplistic Study of Percolation Threshold
• Percolation Threshold is useful in networks where all loads are critical, or
when we are focusing only on critical loads of a network.
[so, if a percolation threshold is known, we can know that up to what probability of node damage,
we can be sure that at least one critical load will be safe. It gives an insight into network
extremities.]
• Probability of each node being functional post-
contingency = p
• Probability of finding a functional node during an
contingent situation is p*(z-1)
• At percolation threshold we know: pc(z-1)=1
• So, pc for such network is 1/(z-1)
• Putting z=3, we get pc=0.5. It means there will be
an infinite path in the network even when
probability of each node being damaged is as
high as 50%
For each network, pc can be determined.

Molloy-Reed Criteria for Percolation Threshold
• In an uncorrelated network with degree distribution P(k), the probability that
an undamaged section is connected to an functional node of degree k is given
by kP(k)/<k> - Molloy et al(’95), Cohen et al(’00), Arisi(’13).
• The percolation threshold is possible if and only if any two nodes, ni and nj of
the infinite path is also connected to another node.
• In a network, percolation threshold can occur only when k2 = 2<k>, where
k2 is the second moment of degree distribution, and <k> is the first moment of
degree distribution.
– The second moment provides the variance measuring the spread in the degrees. Its
square root is the standard deviation.
– The first moment is the average degree of the nodes in the distribution system
By comparing p with pc we can comment on the resiliency of system with respect to the
threat. According to work by Essam(‘80), average cluster size can be determined using
percolation threshold for each threat. This would enable us to get a preliminary idea about
adequacy of redundant resources.

Using Molloy-Reed Criteria to determine Critical Fraction
• fc  fraction of damaged nodes/undamaged nodes critically sufficient to
sustain a critical load. [This is an important criteria to determine the resiliency
metric]
Since <k> and <k2
> are easy to determine from basic properties of the graph, the critical
fraction of the network to sustain at least one important load no matter what the
contingency, can be determined.

• The critical ratio of damaged to undamaged nodes in a network that
sustained damages, is dependent on the ratio of variance and
average degree distribution of the network configuration under
configuration.
• Resilience of a distribution system configuration is dependent on the
heterogeneity of the network.
– In highly heterogeneous networks, <k2
>  ∞ consequently, fc  1, which
which indicates theoretically infinite resiliency of the distribution system
system network to any sort of damages.
– So, the more resilient design (or re-design) of the distribution system is such
system is such that the variance in its degree distribution be maximized.
Since <k> and <k2
> are easy to determine from basic properties of the graph, the critical
fraction of the network to sustain at least one important load no matter what the
contingency, can be determined.
Some insights:

Other metrics that give insight into topological resiliency
• The metrics introduced are mainly divided into two groups: (i)
statistical metrics, and (ii) spectral metrics.
• Statistical metrics are used to quantify the constructional
properties.
• Spectral metrics are derived from analysis of eigenvalues of
finite sets.
• Thus the first step of a more accurate analysis is determining
the most important nodes from the weighted adjacency matrix
A(G) of the graph.

Insights from Adjacency Matrix
• The centrality vector of A(G) can be used to determine the most important node of the
network, which leads to most fragmentation.
• The centrality vector computes the importance of the node in terms of degree, betweenness,
closeness or eigenvectors.
• The elements of the dominant eigenvector of the adjacency matrix represent the nodes
whose functionality is crucial to the resilience of the network.
• Centrality vector of the previous system is C(A(G)) = [0.11, 0.48.0.69.0.46, 0.15, 0.15], which
suggests that the third node C is the most important node of the network as well.
Adjacency Matrix
Spectral Gap
Algebraic
connectivity
Programming ease
of other network
parameters

Identifying critical nodes of a distribution system from Adjacency Matrix
27
Data from R1-12.47 PNNL Prototypical Feeder-1

Determining Topological Resiliency
• Metrics such as ‘Algebraic Connectivity’ and ‘Spectral Gap’ are
often used to quantify the ‘strength of connectedness’ of the
network.
28
Topological Resiliency Vector
• It includes the different criteria that can be
used to determine topological resiliency.
• These multiple criteria is used for a
complex decision making process that
computes the resiliency metric.

Computing Resiliency Metrics
• Used in complex decision making problems
• Used in computation of resilience of water distribution networks [Pandit '2014]
• Using all the factors affecting resiliency a decision making matrix is created as follows,
where we are evaluating between n distribution system scenarios, and there are m
evaluation criteria.
• xij gives the raw score of performance of one scenario over another.
• The relative importance of each criterion is denoted by a one- dimensional weighing
vector W which contains m weights, with wj denoting the weight assigned to the jth
criterion.
Goal is to assign a Resiliency Metric, a single numerical measure of an dist. sys. op.
condition relative to the other op. condition; to each decision option by defining a utility
function ui=f(X,W), where U={u1, u2, ... un}

Computing Topological Resiliency Metrics
• Weights are assigned based on a relative interaction
between all the resiliency indicator metrics using fractions
a through u in the interval (0, 1].

Computing Resiliency Metrics (Cont'd)
• In order to develop a Resiliency Metric (Ri) for each topology of the distribution
system, the comparison scores (xij) for each criterion need to be transformed to
a unit less value score (pij).
• Then a linear transformation is taken to convert xij to pij as shown above.
– Higher value indicates higher resiliency.
• AHP is used to determine relative weights W between all factors that affect
resiliency as mentioned earlier. The most dominant eigenvector has the form
• where A, B, . . . , G are the derived weights of importance of the metric in its
suffix.
• Overall topological resiliency metric

Other Factors that impact resiliency of distribution
system
• Distribution system is more complicated than simple networks.
So several parameters must be considered
• Power Flow Feasibility [PFF]
• Inclusion of Distributed Generators on topological resiliency
[LNLF]
• Influence of Weather [WF]
• Influence of quality of power distribution equipment [λeqp]
• Influence of restoration strategies being used at DMS level.
[LNLF]
• Microgrids
It is possible to add other factors into composite resiliency
computation.

Power Flow Feasibility
• It is possible to design a distribution network with great topological resilience, but
impossible to sustain power system wise due to physical constraints.
If a is the vector of independent terms
and b is the vector of dependent terms,
then the power flow solution of the
system is: F(a,b)=a+F(b)=0
For power flow to be
feasible, Op. Point must
be within here
If power flow is feasible, PFF=1
33
• All faulted paths need to eliminated and power flow criteria must be satisfied.

– Conclusions
34

Enabling resiliency with Microgrids
35ENABLING RESILIENCY OF MICROGRIDS

Determining Load Not Lost during an extreme event
• Modified Depth-First Search algorithm is used to compute Load not Lost Factor (LNLF).
• After, topological resiliency, weather factor, power
flow feasibility, LNLF  AHP is used to compute
the Composite resiliency, just as topological
resiliency was computed.

Summary of steps to compute composite resiliency metrics
Evaluate Composite Resiliency
Consider several other
factors that impact the
overall resiliency of the
network
Check how many loads
remain connected
Verify Power Flow
Feasibility
Use Multi-criteria decision
making to come up with a
single value of Composite
Resiliency
Evaluate Topological Resiliency
Use AHP to assign weights to different
constructional parameters of the network
Linearize all parameters to a single composite value
of topological resiliency
Modeling the distribution system as a graph
Evaluate Network
Parameters
Determine Percolation
Threshold
Determine Critical Fraction
of nodes that can be
damaged

– Conclusions
38

Test System - 1
• IEEE Distribution Feeder System
39SIMULATIONS AND RESULTS

Resiliency Results of IEEE Comprehensive Distribution System

Test System - 2
• South Pullman (SPU) Feeders in Avista’s Pullman distribution system
Feeder 1 (F1) F1Topological Resiliency Analysis Results
F1 Composite Resiliency Analysis Results
Variation of Composite Resiliency with node failure
probability (p)

Pullman Analysis (Cont’d)
F2, F3, F4, F5 & F6 Topological Resiliency
Analysis Results
F2, F3, F4, F5 & F6 Composite Resiliency
Analysis Results
• Resiliency of whole Pullman is higher than
individual feeders.
• Availability on DGs affected composite
resiliency.
• Nodes with higher betweenness centrality are
located proximal to each other.
Whole Pullman Visualization of Critical
Nodes
42
F-2
F-3
F-4
F-5
SIMULATIONS AND RESULTS

Test System – 3: Multiple Microgrids based on CERTS
Concept
CERTS Multiple Microgrids Topological Resiliency
Analysis Results
CERTS Multiple Microgrids Composite Resiliency
Analysis Results
43ENABLING RESILIENCY OF MICROGRIDS

CERTS Multiple Microgrid Analysis (Cont’d)
Microgrid 1 Islanded Microgrid 1 & 2 IslandedMicrogrid 2 Islanded
• Thus with two microgrids, over all system resiliency can be improved.
• Direct correlation of topological resiliency with betweenness centrality can be
observed above.
• Additional Distributed Generators increase the resiliency of the system.

– Conclusions
45

Conclusions
• Provided a literature review to identify
state-of-the-art in resiliency metrics in
distribution systems.
• Developed a resiliency metric for power
distribution systems.
• Modified previously developed
reconfiguration algorithm for enabling
the resiliency of the distribution system.
• Tested and validated developed
resiliency metric on industry-standard
and real distribution systems.
• Sensitivity of the metric depends on all the factors that
affect resiliency. However, how much change occurs
due to variation of a single parameter keeping others
constant – is a future work.
• Compare the resiliency metrics with other formulations
based on path redundancy method.
• Possible to include more Smart Grid algorithms and
technologies like VVC, Look-ahead and Robust
Controller, Demand Response, V2G and other
methods of enabling resiliency.
• Alternative path based simple resiliency metric
Future Work
46

Future Work: Alternative path based simple resiliency metric
47
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Resiliency of Path_Comb_without_Loop
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Impact of combination of
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Key References
• K. H. LaCommare and J. H. Eto, “Cost of power interruptions to electricity consumers in
the United States,” Energy, vol. 31, no. 12, pp. 1845–1855, 2006.
• R. J. Campbell, “Weather-related power outages and electric system resiliency,”
Congres- sional Research Service, Library of Congress, 2012.
• A. Kwasinski, “Technology planning for electric power supply in critical events considering
a bulk grid, backup power plants, and micro-grids,” IEEE Systems Journal, vol. 4, no. 2,
pp. 167–178, 2010.
• D. P. Chassin and C. Posse, “Evaluating North American electric grid reliability using the
Barabasi–Albert network model,” Physica A: Statistical Mechanics and its Applications,
vol. 355, no. 2, pp. 667–677, 2005.
• E. D. Vugrin, D. E. Warren, M. A. Ehlen, and R. C. Camphouse, “A framework for
assessing the resilience of infrastructure and economic systems,” in Sustainable and
Resilient Critical Infrastructure Systems, Springer, 2010, pp. 77–116.
• K. Sun, “Complex networks theory: A new method of research in power grid,” in
Transmission and Distribution Conference and Exhibition: Asia and Pacific, IEEE/PES,
2005, pp. 1–6.
• Y. Zhang and L. Guo, “Network percolation based on complex network,” Journal of
Networks, vol. 8, no. 8, pp. 1874–1881, 2013.
• R. Albert, I. Albert, and G. L. Nakarado, “Structural vulnerability of the North American
power grid,” Physical review E, vol. 69, no. 2, p. 025 103, 2004.

Publications
1. Chanda, S., Shariatzadeh, F., Srivastava, A., Lee, E., Stone, W., & Ham, J. “Implementation of non-intrusive energy saving estimation for Volt/VAr control of
smart distribution system”. Electric Power Systems Research, vol. 120, (pp. 39-46).
2. Shariatzadeh, F., Chanda, S., Srivastava, A. K., & Bose, A. “Real time benefit computation for electric distribution system automation and control” IEEE
Industry Applications Society Annual Meeting, 2014 (pp. 1-8)
3. Chanda, S., & Srivastava, A. K. “Quantifying Resiliency of Smart Power Distribution Systems with Distributed Energy Resources” 24th IEEE International
Symposium on Industrial Electronics, 2015
4. Chanda, S., Venkataramanan, V., & Srivastava, A. K. “Real time modeling and simulation of campus microgrid for voltage analysis” Proceedings of the
North American Power Systems Conference, 2014
49
Posters presented
1. Modeling & Analysis of Campus Microgrid Distribution Systems – IEEE PESGM 2013
2. Real-Time Energy Savings Calculations for Integrated Volt/VAR Control – ESIC Summit 2013
3. Developing Integrated Load Modeling Framework for Campus Microgrids with Large Buildings – IEEE T&D 2014
4. Distribution system resiliency with distributed generation and storage – ESIC Summit 2015
Awards
1. Best Graduate Student Poster Award (3rd prize) – IEEE PESGM (2013)
2. Best Graduate Student Poster Award (2nd prize) – IEEE T&D (2014)
3. Team Member of winning team, DOE Hydrogen Design Project (2014)
4. William R. Wiley Research Exposition Scholarship Recipient (2nd Prize for Best Oral presentation) – Washington State University (2015)
1. Chanda, S., & Srivastava, A. K. “Defining and Enabling Resiliency of Electric Distribution Systems with Multiple Microgrids” IEEE Transactions on Smart
Grid: Special Issue on Power Grid Resilience [Abstract Accepted]
2. Chanda, S., & Srivastava, A. K. “Application of Complex Network Theory to Evaluate Resiliency of Smart Distribution Systems”, IEEE Power And Energy
Technology Systems Journal
3. Shariatzadeh, F., Chanda, S., Srivastava, A. K., & Bose, A. “Real time benefit computation for electric distribution system automation and control” IEEE
Transactions on Industry Applications Society [Under Review]
4. Shariatzadeh, F., Chanda, S., & Srivastava, A. K. “Robust Look-Ahead Approach for Heat Ventilation and Air Conditioning Control Systems in Active
Distribution Systems” IEEE Transactions on Sustainable Energy.
5. Shariatzadeh, F., Chanda, S., & Srivastava, A. K. “Multilayer Architecture and Control of Active Distribution Systems” IEEE Transactions on Power Delivery
Upcoming Publications

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