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IEEE SYSTEMS JOURNAL 1
Resilience and Cost Trade Space for
Microgrids on Islands
Ronald E. Giachetti , Douglas L. Van Bossuyt, William W. Anderson, Jr., and Giovanna Oriti, Senior Member, IEEE
Abstract—This article examines the trade space between the
resilience and cost of an island microgrid. The article presents
two models for the resilience and the cost of the microgrid. The
resilience model considers the invulnerability and recoverability
of the microgrid and represents the power balance of the micro-
grid, energy storage, and maintenance policies. The cost model
adapts the levelized cost of energy measure to the context of island
microgrids. We conduct experiments to investigate two microgrid
architecture decisions of how much excess generation capacity and
redundancy to provide. The experiments show that redundancy of
generative sources provides greater resilience for similar cost, and
resilience improves quickly as excess power capacity is added while
the cost grows more slowly. Case studies for island microgrids show
how a redesign of the microgrid can improve resilience without
increasing costs. The article contributes to the literature a model
for decisions makers to evaluate the tradeoffs between resilience
and cost for island microgrids that must depend on their own
distributed energy resources.
Index Terms—Cost of energy, island, microgrid, recoverability,
resilience, trade space.
I. INTRODUCTION
THE US Department of Defense (DoD) is the largest energy
consumer in the USA with energy consumption classified
as either installation for the bases and facilities or operational for
powering military vehicles, planes, and ships. In response to var-
ious laws and regulations, the US DoD has been increasing the
efficiency of energy usage and reducing overall energy costs [1].
However, the US military’s energy policy goes beyond energy
efficiency. The US military wants to increase energy security
defined as the secure and reliable provision of energy to meet
mission needs [2]. Energy security is composed of resilience and
reliability in addition to the aforementioned efficiency. Reliabil-
ity describes the ability to deliver needed energy, and resilience
Manuscript received January 25, 2021; revised June 16, 2021; accepted
August 7, 2021. This work was supported in part by the Office of Naval
Research and the Navy Shore Energy Technology Transition and Integration
(NSETTI) program managed by Naval Facilities Engineering and Expeditionary
Warfare Center in Port Hueneme, CA, USA. (Corresponding author: Ronald E.
Giachetti.)
Ronald E. Giachetti and Douglas L. Van Bossuyt are with the Systems
Engineering, Naval Postgraduate School, Monterey, CA 93043 USA (e-mail:
regiache@nps.edu; douglas.vanbossuyt@nps.edu).
William W. Anderson, Jr. is with the Naval Facilities Engineering Systems
Command Port, Hueneme, CA 93043 USA (e-mail: bill.anderson1@navy.mil).
Giovanna Oriti is with the Electrical and Computer Engineering, Naval
Postgraduate School, Monterey, CA 93043 USA (e-mail: goriti@nps.edu).
Digital Object Identifier 10.1109/JSYST.2021.3103831
describes the ability to anticipate, adapt, and react quickly to
changing conditions and disruptions to normal operations.
The US military operates bases on islands and elsewhere,
where the base is not connected to the utility power grid. These
bases generate power locally, currently mainly by diesel gensets
connected directly to the loads they serve. The logistics and
costs of delivering diesel to remote island locations create a vul-
nerability to energy security of these facilities. For this reason,
among others, the US military wants to diversify their energy
sources away from an over-reliance on diesel gensets. While our
motivation stems from the US military case, energy security is a
wider concern shared by many diverse entities including island
nations, regions, as well as businesses. Returning to our focus on
islands, providing energy is difficult and expensive. Most islands
have relied on diesel, and given the fuel logistics, storage, and
other issues, many islands pay high rates for electricity [3].
Many islands have already, and many others are looking into
switching from primarily diesel generators (DGs) to microgrids
with significant amounts of renewable energy sources such as
wind and solar. In fact, the US Navy has set a goal for 25% renew-
able energy sources [4]. Microgrids are system solutions to the
energy generation and distribution problem because it involves
the design of sufficient energy generation, storage, and controls
to deal with the intermittent generation of renewable sources as
well as balancing load and supply across the network [5]. The
diversification away from diesel should also make the energy
infrastructure more resilient to natural as well as man-made
disasters. Resilience is the ability of a system to withstand
external disruptions and, if damaged, to recover quickly from
the damage. Resilience is especially important to the military be-
cause of the need for energy to sustain operations. Additionally,
military installations are not only concerned with disruptions
due to natural events but to attacks on the infrastructure from
adversaries.
The military uses the resilience concept to describe a system
that is trusted and effective in a wide range of mission contexts,
is easily adapted to operational and environmental changes
through reconfiguration and/or replacement, and has predictable
and graceful degradation of function [6]. In this article, we define
the energy resilience of a military installation as the ability
of the base to avoid disruption to its energy supply and, if
disrupted, to minimize the impact and duration of the disruption.
We explore the establishment of a microgrid on the base as the
means to provide energy resilience. We consider both microgrid
design factors as well as operational capabilities and policies
contributing to energy resilience.
U.S. Government work not protected by U.S. copyright.
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2IEEE SYSTEMS JOURNAL
The Navy designs microgrid systems using a top-down, mul-
tiphase process of architecture design followed by detailed de-
sign [5]. The microgrid architecture describes the structure of the
microgrid in terms of its components, how they are configured
and related to each other as well as the environment, and how
the microgrid balances the competing stakeholder requirements.
The microgrid architectural decisions include the type and quan-
tity of distributed energy resources and energy storage systems
in the microgrid to meet the loads’ power demands. The subse-
quent detailed design phase addresses the power and electrical
engineering issues of microgrid control, frequency regulation,
voltage regulation, and so forth.
This article focuses on the microgrid architectural design
phase and the architectural decisions of the type, number,
and power rating of distributed energy resources to include
in a microgrid architecture. The architect must balance the
military’s requirements for resilience and efficiency (cost) of
power delivery. This article contributes to the literature on
microgrid resilience two models to analyze the tradeoff between
resilience and cost during the architectural design phase. We use
the model to explore two design strategies commonly used on
these islanded Naval bases. The first design strategy is simply
to have excess energy generation and storage capacity. The
second design strategy is to decentralize and distribute energy
sources or to have redundancy in the energy generation. Both
excess capacity and redundancy are well-known architecture
heuristics [7].
The article is organized as follows. Section II defines re-
silience in the context of microgrids. Section III reviews the
literature and finds gaps in understanding resilience of island
microgrids and in exploring the trade space between resilience
and cost. Section IV presents the model of resilience and the
levelized cost of energy (LCOE) demanded. Section V presents
the method to assess resilience and cost. Section VI presents
experiments of excess capacity, redundancy, and maintenance
policies. Section VII applies the model and method to case
studies of island bases operated by the Navy. Section VIII
summarizes the article and draws conclusions.
II. RESILIENCE
Resilience describes a system that can resist and recover
quickly from disruptions. Resilience is multidimensional, con-
textual, and dependent on the time frame considered [8]. We
limit our context to microgrids. The literature defines resilience
with respect to system performance [9]. In the energy domain,
most research measures performance as delivered power [10].
The dimensions of resilience can be traced to the states
shown in Fig. 1. A microgrid can anticipate, prepare, and take
precautions against disruptions during the predisturbance phase.
The time frame for such preparation is typically long and, for our
study, out of scope. We focus on the resilience dimensions once
a disruption occurs. Once a disruption affects the microgrid, the
important resilience dimension is the microgrid’s invulnerability
or ability to resist a degradation in performance. The microgrid
operation prefers either none or as small as possible drop in per-
formance resulting from a disruption. Following a disruption, the
Fig. 1. Resilience curve showing power performance behavior before, during,
and recovering from a disruption.
microgrid must stabilize itself and recover from the disruption.
The second measure of interest is the microgrid’s recoverability
or ability to quickly return to required performance. Clearly, the
faster the recovery, the more resilient the system.
Resilience is also threat dependent [10], [11], and we model
it as such. Resilience to hurricanes, tsunamis, and other extreme
weather events is different than resilience to intentional attacks
on the system such as cyber attacks on the microgrids control
system or even destruction of parts of the microgrid infrastruc-
ture such as transformers or DGs. For example, transmission
lines over poles are more vulnerable to hurricanes (the disrup-
tive event) than transmission lines buried underground. While
burying transmission lines will improve resilience with respect
to hurricanes, it does nothing against other disruptions such as
cyber attacks.
The provision of a system’s resilience depends on both design
and operational policies. We can design systems in such a
way that they are less vulnerable and able to quickly recover.
From an architectural perspective, engineers have long used
functional redundancy because different distributed energy re-
sources will likely have different vulnerabilities and ability to
recover to different disruptions [8]. Similarly, excess capacity or
overdesigning the microgrid increases the overall resilience [8].
Likewise, from an operational perspective, policies for mainte-
nance, training, and logistics affect system resilience. Maintain-
ing equipment, having trained personnel, and readily available
spares all enhance the microgrid’s resilience.
III. LITERATURE REVIEW
Measuring resilience is a first step to assessing and improving
the resilience of a system. Multiple survey papers review quan-
titative measures of resilience from different perspectives such
as long-term and short-term aspects of large power grids [12], a
design perspective [13], or with respect to certain threats [14].
The measures reviewed mostly are based on the resilience curve
(shown in Fig. 1) with many attempting to capture resilience
in a single measure. Gholami et al. [15] describe the two main
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GIACHETTI et al.: RESILIENCE AND COST TRADE SPACE FOR MICROGRIDS ON ISLANDS 3
resilience measures as the ratio of the area defined by normal op-
erational performance and the actual operational performance,
which is the trapezoidal area of Fig. 1. Alternatively, researchers
have defined components of resilience. Francis and Bekera [16]
as well as Vugrin et al. [17] include absorption capacity, which
we label invulnerability, as the initial drop in performance.
How quickly the system can recover is an important aspect.
Renschler et al. [18] describe measures for this aspect of re-
silience. The US Aid program measures recoverability as the dif-
ference between nominal and actual system performance. They
also measure how much manpower effort goes into recovering
the microgrid [19].
Quantitative measures are important to support resilience
analysis. However, the resilience measures must be incorporated
into a larger model and/or method to support an overall assess-
ment of resilience. Several tools in use by government agencies
to assess resilience take the approach of a broad-based assess-
ment using questionnaires without quantitative measures of the
resilience. The US DoD uses the Energy Security Assessment
Tool (ESAT), a spreadsheet application, in which the user enters
data on power loads and infrastructure as well as answering
questions about the base’s mission and facilities. The Energy
Resilience Assessment Methodology helps clients identify risks
and vulnerabilities, analyze those risks, and develop a strategy to
mitigate and/or avoid the risks [20]. The resilience analysis pro-
cess for the DOE uses measures of outage magnitude in terms of
customer days, recovery costs, and community impact that could
be used to generate Pareto frontiers of resiliency improvement
costs vs. power outages [17]. Their outage magnitude measure
is very similar to System Average Interruption Duration Index
and is more a measure of reliability than resilience.
Increasing the resilience of an installation will likely incur a
cost above what is needed to provide energy, absent any dis-
ruptive events. The decision of whether to make the investment
usually depends on a cost–benefit analysis. Lambert et al. [21]
describe an optimization model to design microgrids to meet
power load requirements using net present value to cost the
microgrid design. Measuring benefits is the more difficult part
of the analysis. Anderson et al. [20] use the value of lost load
(VoLL) metric defined as the price consumers are willing to
pay for uninterrupted power. VoLL varies by customer, time of
day, and both the extent and duration of power loss. Shroeder et
al. [22] compiled data from 21 VoLL studies conducting mainly
in Europe and the USA and found VoLL ranged widely from a
few dollars per MWh to over $100 per MWh. VoLL is relevant
for businesses but less so for military installations because they
are not profit-making ventures and instead are concerned with
mission accomplishment. For this reason, Peterson proposes a
mission index to measure the ability of a base to continue its
mission [23].
Closely related studies of resilience of islands and military
microgrids include the work of Anderson et al. [24] who formu-
late a mixed integer linear programming to minimize life-cycle
costs with meeting the loads one of the constraints. They find that
the addition of photovoltaic (PV) to a grid-connected microgrid
that only had diesel gensets for backup power can double the
duration the loads could be supported when disconnected from
the main power grid. They further note that the renewables pro-
vide energy throughout their life and, therefore, have economic
benefit besides increasing resilience. Other studies have shown
the cost of enhancing microgrids with renewable energy sources
and storage can often only be justified if resilience is valued [25].
Judson et al. [26] evaluate that the resilience of a military base is
in the context of a disruption causing loss of the connection to the
power grid. The authors visited military bases and observed that
most have diesel gensets as backup power to individual buildings
and/or loads. Among their recommendations is centralization
of DGs to serve multiple loads. Rocky Mountain Institute [27]
presents ten case studies of actual island microgrids including
their capacity, generation profile, and cost per kWh. They report
several findings such as adding renewables improves resilience,
islands need energy storage, and efficiency is important. Peter-
son [23] studies the resilience of microgrid for a military base by
analyzing what happens when each component of the microgrid
fails.
The literature on microgrid resilience and architecture design
highlights several areas worthy of further research, which this
article addresses. First, most research on microgrid resilience
considers the scenario of a microgrid connected to the larger
electrical grid and the disruptions are usually limited to discon-
nection from the grid. Or, as in Peterson [23], the researchers
ask what if a particular microgrid component fails? We have not
found any research where the models consider the probability
of damage given a disruption, which, as we will show later,
helps us analyze and compare microgrid architectures with
excess capacity and/or redundancy. Second, the literature has not
explicitly considered the tradeoffs involved, nor has the literature
examined how to quantify the trades in a format amenable for
decisions makers. We view the microgrid resilience through the
lens of an architectural design problem, in which a decision
maker must trade off resilience with the cost of power provision.
This reflects how many military microgrids are designed first in
an architecture design phase and then in a detailed design phase.
The architectural context allows us to analyze two common
resilience design principles of excess capacity and redundancy,
which has not received much attention in the literature.
IV. MICROGRID RESILIENCE AND COST MODEL
We want to support the microgrid system’s architecture design
phase with a model to trade off the cost of energy with the
resilience of the microgrid. We model resilience as how well
a given microgrid architecture can avoid being affected by dis-
ruptions, but if the disruption causes damage, then how quickly
can the microgrid recover from the disruptive event. Second,
we want to know the cost of the microgrid architecture over the
planning horizon. We present the information to the decision
maker as a trade space between resilience and cost, which are
two of the components of energy security for military bases (the
third one being reliability) [2]. To generate the trade space, we
use two separate models: 1) a cost model to estimate the cost of a
microgrid architecture and 2) a resilience model to estimate the
invulnerability and recoverability of the microgrid architecture.
The models are stochastic because they include distributions for
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4IEEE SYSTEMS JOURNAL
Fig. 2. Notional microgrid architecture.
probability of damage to a resource, given a disturbance and
the time to repair a resource. The models deal with the initial
microgrid architecture decisions and the microgrid’s resilience
with respect to delivering power. The model time step is 1 h,
and, consequently, the model ignores issues that happen more
quickly than 1 h such as frequency and voltage issues important
to the control of microgrids (see [28] for a description of these
issues). The following sections describe the formulation of the
resilience and cost models and how we use them to generate the
trade space.
A generic microgrid architecture for an island is shown in
Fig. 2. The microgrid consists of three types of power sources:
DGs, wind turbines (WTs), and PV panels. A particular island
microgrid may have zero, one, or more of each of the power
source types. The microgrid has a battery for energy storage.
All the power sources and loads are connected to a power
distribution bus. An important component of a microgrid is a
controller; however, we do not model or analyze any control
issues because it is out of scope for the architecture decisions we
analyze. Also not shown are all the inverters from dc to ac power
and other power network elements necessary for a microgrid.
We assume that the microgrid has these components as well
as suitable controllers. For the microgrid architecture shown,
the architectural decisions we focus on are: How many of each
generation source to have? and How much power generation
capacity for each source?
A. Resilience Model
We measure two aspects of resilience: 1) invulnerability (I)
describing the ability of the microgrid system to resist power
loss immediately following a disturbance and 2) recoverability
(R) describing the ability of the microgrid system to repair
generation resources and meet the full demand.
We measure invulnerability in a manner similar to [16]
and [17] as the drop in power generated immediately after the
disruption, which is given by the ratio of power generated to
load demand
I=Pt
Dt
.(1)
The term Ptdenotes the power delivered at time t, and not the
total rated power available. This is an important distinction for
the island microgrids we are investigating because they all have
excess power generation capacity. For example, we analyzed
one island naval installation with five times more generation
capacity than needed. The installation could lose two of its five
generators and still be able to meet the demand. Rather than
using the total rated power available and allowing I>1,we
use the actual power delivered. Consequently, Pt<=Dtand
I∈[0,1].
We define recoverability, referring to Fig. 1, as the ratio
of the area bounded by the demand and the postdisturbance
power generated between the time of the disturbance and full
recovery [19]. The area represents what proportion of demand
goes unmet and for how long
R=1−tr
t=tdDt−Pt
tr
t=tdDt
.(2)
We only determine recovery when Ptdecreases less than
Dt. The recoverability measure R∈[0,1] with 0 representing a
microgrid that never recovers and 1 representing a microgrid in
which power generation never decreases less than the demand.
The two dimensions of invulnerability and recoverability for
resilience can be combined to obtain an overall metric with ω∈
[0,1] to weigh one dimension more than the other
ξ=ωI +(1−ω)R. (3)
In the face of a disturbance scenario Sk, such as a hurricane
or cyber attack, power is lost when one or more resources are
damaged. Let the conditional probability P(di|Sk)denote the
probability of damage to a resource idue to disruptive event
Sk. The conditional probability of damage allows us to capture
differences in the vulnerability of various power generation
resources to each disturbance type because, for instance, WTs
will exhibit differences in damaged experienced from PV panels.
Hence, we model resilience to specific types of threats because,
as previously said, resilience is threat dependent [11].
Each resource has an associated control authority, which is a
binary variable with values defined as
μα
it =1,iff power source iof type αin time tis on
0,otherwise
where the type αcan be DG, PV cells, WT, or battery (BAT).
The model assumes that a resource is either damaged or not
damaged. To model partial damage, at the expense of extra
computations, we can take a single resource such as PV and
partition it into multiple resources, each with their own condi-
tional probabilities and control authority variables.
1) Power Balance: The power balance constraint, given by
(4), ensures for each time period tthe power generated equals
the loads and any necessary load shedding. The summation adds
up all the power sources (diesel, solar, and wind) multiplied by
their control authority μα
it to determine if they are operational
during the time period. The power generated by solar and wind
is intermittent and dependent on the solar irradiance and wind
speed, which is governed by the model data inputs. The diesel
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GIACHETTI et al.: RESILIENCE AND COST TRADE SPACE FOR MICROGRIDS ON ISLANDS 5
gensets have the additional variable of the loading denoted by
Lit. The battery is either discharging or charging; consequently,
only one of PC
tor PD
tis nonzero. The variable LStdenotes any
necessary load shedding, and Pload
tdenotes the total loads
N
i=1
(μDG
it LitPDG
i+μPV
it PPV
it +μWT
it PWT
it )
−ηcPC
t+PD
t/ηd+LSt=Pload
t∀t=1,...,T. (4)
The DGs provide dispatchable power and must operate within
their minimum and maximum loading limits, typically between
0.3 and 0.9. The minimum loading for the DG prevents prema-
ture aging and failure due to wet stacking [29]
Lmin
i≤Lit ≤Lmax
i.(5)
The fuel consumed by the DGs must be less than the fuel
available. Diesel fuel consumption is a function of the loading
factor and the maximum fuel consumption rate fimeasured as
gallons per hour
T
t=1
N
i=1
(μDG
it Litfi)≤F. (6)
2) Energy Storage: A microgrid with renewable energy
sources typically incorporates energy storage, usually a battery,
for multiple reasons such as frequency and voltage regulation.
However, here, we are only concerned with the storage capacity
to sustain loads for a desired time duration when the renewable
energy sources are unavailable. In determining the appropriate
size of backup storage for a particular application, one generally
selects the energy rating on the basis of the period of time one
expects to have to support the load in the event of a failure of the
primary supply [30]. A straightforward physics-based approach
to sizing the battery is found in [31].
The battery has three states of charging, discharging, or nei-
ther. We assume that the battery is fully charged at the start of
a disruption. The energy in the battery at time tis the energy in
the previous time period plus any energy charged or discharged
into the battery during the time interval Δt(taken as 1 h) and is
given by
EBAT
t=EBAT
t−1+Δ
tηcPC
t−ΔtPD
t/ηd(7)
where ηcand ηddenote the charging and discharging efficien-
cies, respectively, and PC
tand PD
tdenote the charging and
discharging power, respectively.
The battery is constrained by its rated energy capacity and
maximum charge and discharge rates
EBAT
min ≤EBAT
t≤EBAT
max (8)
PC
t≤PCmax (9)
PD
t≤PDmax.(10)
3) Maintenance: The model mostly considers how micro-
grid design decisions affect resilience. However, resilience is
achieved not only through design but also by operational policies
concerning the microgrid. Studies have shown that preventive
and routine maintenance can mitigate against damage as well
as contribute to quicker repair of realized damages. Moreover,
the availability of spares can greatly increase the ability to
quickly repair and restore power. Consequently, more and better
maintenance, training, logistics, and inventory policies improves
both invulnerability and recoverability.
The time to repair resource iis given by a lognormal dis-
tribution with mean trepair
iand standard deviation σi[32]. The
model considers three operational policies for maintenance of
none, medium, and full level of preventative maintenance. The
full level is when the base follows the manufacturer’s suggested
maintenance schedule, has trained maintenance staff, and avail-
able spares. The mean time to repair (MTTR) for no and medium
maintenance levels is 1.5 and 2.5 times greater than the MTTR
when the installation follows the full maintenance policy.
When a resource is damaged, the model calculates the time
to repair and sets the corresponding control authority for that
resource (i.e., μα
i) to 0 for the duration of the time to repair.
Upon reaching the time to repair, the resource is repaired and
the control authority is set to 1, making its power generation
available to the microgrid.
B. Cost Model
The LCOE is a common means to determine the price of
energy in order to recover all the costs of installing and operating
the energy system [33].1The LCOE calculates the net present
value of all the costs and divides it by the energy generated
to provide the unit cost per kWh. The LCOE assumes that all
the energy generated can be used and/or sold back to the power
grid. Islands do not have a larger power grid to sell power to, and
any excess energy beyond their storage capacity goes unused.
Consequently, the LCOE would underestimate the actual cost of
energy used.
To address this issue, we revise the LCOE to account only for
actual energy usage called the levelized cost of energy demanded
(LCOED).
The net present value of the costs of energy production are
given by
NPVcosts =T
t=1 N
i=1(It+Mt+Ft−HT
i)
(1 + r)t.
The numerator captures all the costs of investment (It), main-
tenance (Mt), and fuel (Ft) minus the residual remaining value
(HT
i) of any equipment iwith useful life past the planning
horizon T, in which the planning horizon is set equal to the
expected life of the Distributed Energy Resource (DER) com-
ponent with the shortest expected economic life. The total costs
are discounted by the discount rate r. The fuel cost for the DGs
in time tis
Ft=
i∈I
(cgfiLitμDG
it )∀t∈T(11)
where cgdenotes the price of diesel in $/gal.
The maintenance cost depends on the level of maintenance the
base commander determines for the equipment. Maintenance
1The LCOE is usually applied to a single energy source for the purposes of
comparing it against other alternatives.
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6IEEE SYSTEMS JOURNAL
cost is a function of the power rating of the equipment. Con-
sequently, the model assumes that the maintenance cost is the
same for two 500-kW rated diesel gensets as for one 1000-kW
genset.
The net present value of the energy actually used by the
microgrid is
NPVenergy =T
t=1 Dt
(1 + r)t.
The LCOED is calculated as the costs per unit energy
LCOED =NPVcosts
NPVenergy
.(12)
The denominator calculates the total energy consumed over
the planning horizon. Both the costs and energy used are dis-
counted by the marginal rate of return r. The LCOED provides
cost per unit energy ($/kWh), which we use to compare micro-
grid architectures in much the same way that LCOE is used to
compare individual energy generation sources.
V. R ESILIENCE ASSESSMENT METHOD
We solve the models using a scenario-based approach in
which each scenario is a disruptive event with the potential to
cause damage to the microgrid. Many of the threats a military
installation wants to protect against are rare and, in some cases,
have not ever occurred but can be imagined. Such events are
called high-impact, low-probability (HILP) events. The like-
lihoods and impacts of HILP events remain difficult to pre-
dict [34]. Our approach is to say, “what if low-probability event
koccurs?” Our reason is that we are not so much concerned
with trying to estimate the occurrence of the event but rather
understanding the resilience of the microgrid in case the event
occurs.
We apply the following steps:
1) Collect input data. The model requires input of a power
demand profile, solar irradiance, and wind speed—all
by hour of the day. The data for the solar and wind is
converted into power generation by those DER sources.
For some island installations, historical data of solar and
wind generation is available and was used directly.
2) Identify and characterize threats. The threats include nat-
ural events such as extreme weather as well as disruptions
caused by adversaries such as a cyber attack. For each
threat scenario k, the probabilities of damage P(di|Sk)
must be estimated by either historical data or subject
matter expert (SME) estimation. Quantification of expert
judgment is common in risk analysis, especially in defense
contexts [35],[36] and can be performed using the method
of [37].
3) Generate microgrid architecture alternatives. A microgrid
architecture specifies the number, type, and rating of each
generative resources. By varying each factor, we can gen-
erate a trade space.
4) Evaluate the resilience and cost of each architecture alter-
native for each threat scenario.
TAB LE I
SCENARIO PROBABILITY OF DAMAGE P(di|Sk)
TAB LE I I
COST DATA FO R ALL EXPERIMENTS
1) The resilience model determines the invulnerability
and recoverability of each design. The time step tis set
to 1 h. We use the Monte Carlo method and determined
7500 simulations provided a 90% confidence interval
for the results [38]. The mean results are combined
across all scenarios.
2) The cost model determines the LCOED for each archi-
tecture alternative.
5) Generate graphs depicting the trade space between cost
and resilience for the architectures.
VI. EXPERIMENTS
This section presents experiments conducted on the model
using the assessment method. All experiments use the data in
Table I derived from multiple sources [39]–[43].
In all the experiments, the weighing factor ωbetween invul-
nerability and recoverability is 0.5. The decision maker can,
through adjustment of the weighing factor, evaluate only invul-
nerability (ω=1) or only recoverability (ω=0). The planning
horizon is 10 years with a discount rate of 7.5%, and fuel is $2.60
per gallon. Table II shows the cost data for each DER [44], [45].
The residual value is estimated as Ii(n−T)/n. Battery storage
is priced per kWh at $270/kWh and operational and maintenance
costs annually of $1500 and batteries have an economic life of
10 years. More thorough discussion of the data can be found
in [46].
A. Sensitivity Analysis
Some of the inputs depend on SME judgement and/or quanti-
ties difficult to measure precisely. For this reason, we conducted
extensive sensitivity analysis of the output on variations in
the input variables. A full sensitivity analysis can be found in
Anderson [46]. Here we highlight those inputs to which the
model output is highly sensitive.
Fig. 3 shows how changes of +/– 50% to the input variables
affects the LCOED. The LCOED is most sensitive to changes in
the DG’s fuel consumption rate and fuel cost. Fortunately, these
are two variables that are well known in the case studies we did.
Figs. 4 and 5 both show how changes of +/– 50% to the input
variables affect invulnerability and recoverability. Recovery is
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GIACHETTI et al.: RESILIENCE AND COST TRADE SPACE FOR MICROGRIDS ON ISLANDS 7
Fig. 3. Sensitivity of LCOED to input variables.
Fig. 4. Sensitivity of invulnerability to input variables.
Fig. 5. Sensitivity of recoverability to input variables.
very dependent on the MTTR given by λ. Invulnerability is
sensitive to the SME estimates of the probability of damage;
however, even being off by 50% on the input, the output measure
is not off by more than 10%.
B. Excess Capacity
The first set of experiments we conduct investigate the re-
silience and cost of having excess capacity. A microgrid with a
power generation rating much greater than the power demand
it serves, and especially when the microgrid uses a diverse and
redundant set of power generative sources, will have greater
resilience than a microgrid in which its power rating is more
or less equal to demand. The reason is that in the face of a
disturbance, extra power is an obvious buffer to partial losses
of power generation. Of course, having excess power will lead
to higher costs. The decision is to determine the best tradeoff
between increased resilience for increased costs.
Fig. 6 shows the resilience and LCOED versus the ratio of the
microgrid’s total power generation rating to the peak demand
experienced during the year. The power ratio varies from a
value of 1.25 to a value of 5. Fig. 6 shows how resilience
initially improves quickly and then tapers off as excess capacity
increases. Meanwhile, cost increases linearly as excess capacity
increases.
Fig. 6. Effect of excess capacity on resilience and cost.
Fig. 7. Effect of excess capacity on invulnerability and recoverability.
Fig. 8. Maintenance and excess capacity effects on recovery.
We show how each component of resilience responds in Fig. 7.
Both invulnerability and recoverability increase with excess ca-
pacity, but invulnerability increases more rapidly and to a higher
level than recoverability because recoverability also depends on
the maintenance level. Fig. 8 shows how better maintenance
influences the time to recover when there is little excess capacity,
but as the microgrid has more excess capacity, the maintenance
level becomes irrelevant.
C. Redundancy
We define redundancy as having multiple smaller power gen-
eration sources instead of a single large power generation source.
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8IEEE SYSTEMS JOURNAL
Fig. 9. Effect of redundancy on resilience and cost.
The term “no” means there is no redundancy or only a single
source is present, while the terms double, triple, quadruple, and
quintuple mean there are 2, 3, 4, and 5 sources, respectively. In
the redundancy experiments, if a single diesel genset is rated at
2000 kW, then double redundancy has two diesel gensets rated
at 1000 kW each, triple has three rated at 666 kW each, and so
forth. Therefore, the microgrid’s total power generation capacity
remains unchanged in the experiments, with only how the power
generation capacity is divided among sources. In the experiment,
the total power generation rating was 4 mW and the maximum
load was less than 4 mW.
Having redundant power generation sources distributed
throughout the microgrid improves the resilience of the micro-
grid for the same overall cost of delivery. Fig. 9 shows modest
but measurable improvements in resilience as redundancy in-
creases from no redundancy to double with decreasing returns
on redundancy. At the same time, LCOED remains constant.
Fig. 10 shows the time to recover for different redundancy
levels and either full or no maintenance. There is little difference
on the LCOED because the maintenance cost is small compared
to the investment and operating costs. Maintenance has a larger
effect when there is no redundancy as shown by the difference
between the no-maintenance and full-maintenance recovery
times for a single resource. Once there is some redundancy, the
effect of maintenance levels decreases rapidly such that there is
no difference in time to recover between quadruple and quintuple
redundancy.
VII. CASE STUDY
The purpose of the model is to serve as a decision support
for base commanders to explore the trade space of investment
decisions concerning microgrids and the impact on resilience
and costs. This section presents an examination of a Naval
base, which currently has a single, large diesel genset rated at
Fig. 10. Redundancy effects on time to recover.
TABLE III
COMPARISON OF THREE ARCHITECTURES FOR THE ISLANDED NAVA L
INSTALLATION CASE STUDY
1.25 mW as backup power to a critical facility with an average
load of 200 kW. The diesel genset is extremely oversized for the
expected load and, consequently, operates well below its power
rating causing extreme inefficiencies due to wet stacking (i.e.,
inability to burn all the fuel supplied).
SMEs were employed to estimate the probability of damage,
given various scenarios including a tsunami among others. The
demand profile varies between 150 and 250 kW. Using Xendee
to design the microgrid, we developed a design with five 64-kW
diesel gensets (total 320 kW), five PV arrays (total 196 kW),
and five batteries with 383-kW power and capable of 760 kWh
of storage [47]. The architecture was guided by the desire for
greater usage of renewable energy sources as well as efficiency.
In the Xendee model, we interpret efficiency as the objective to
minimize the costs.
Table III shows the results for the current architecture, which
is the base case and two alternatives. The first alternative is sim-
ply replacing the single diesel genset with five smaller gensets
with equal total power rating, and the second alternative is
the Xendee generated architecture described above. The results
show that the redundancy as well as excess capacity of the
redundant case provides significantly improved resilience for
similar cost. The Xendee optimized alternative shows that the
diversity of multiple sources of diesel, PV, and battery provides
the same expected resilience but at a much lower cost because
less excess capacity is required.
1) Other Island Bases: We investigated the power resilience
and cost of three other island bases shown in Table IV with their
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GIACHETTI et al.: RESILIENCE AND COST TRADE SPACE FOR MICROGRIDS ON ISLANDS 9
TAB LE I V
THREE ISLAND BASES
Fig. 11. Trade space between resilience and LCOED for island DVB.
mean demand, peak demand, and power sources and ratings. All
three island bases enjoy excess capacity with, for example, DVB
having four times as much generation capacity as the peak load.
The LCOED for these islands is very high, especially com-
pared to worldwide average LCOE of $0.05 per kWh for natural
gas and $0.1–$0.2 per kWh for wind [48]. Several explana-
tions for the high cost include having far greater capacity than
required, meaning on DVB, for example, most of the diesel
gensets sit idle, representing large capital expenditures; yet, they
mostly go without generating any power. Additionally, islands
face higher costs of maintenance, fuel, and installation of the
distributed energy resources. Given the high costs, the base
commanders can benefit from tools to help them evaluate the
costs and benefits of microgrid architectures.
Fig. 11 shows the trade space for DVB for combinations
of WTs and diesel gensets. The WTs are all rated at 225 kW
each, and the diesel gensets are all rated at 1 mW each. The
graph shows that DVB could obtain similar resilience for a
much lower overall LCOED by having only two diesel gensets.
Additionally, the graph shows that the addition of WTs has
minimal improvement on resilience.
Additional information on the case studies is available in [46].
A. Discussion
Resilience is a complex, multidimensional measure of a sys-
tem’s ability to adapt to changing environments and disruptions
of which we only consider the two components of vulnerability
and recoverability. The experiments provide useful information
to a decision maker in determining how much they would want
to pay for greater resilience. Provision of excess capacity led to
a significant increase in resilience with diminishing returns as
more and more excess capacity was added. In the experiment
conducted, Fig. 6 showed that at a power-to-demand ratio of
1.25, resilience is 0.68, and at a power-to-demand ratio of 2.0,
the resilience is 0.83 with a corresponding increase in LCOED
of $0.12–$0.15 per kWh. Such information is very valuable
in evaluating microgrid architectures and how much excess
capacity to have.
The functional redundancy also improved resilience but to
a lesser extent. Having no redundancy gives a resilience of
between 0.84 and 0.86 depending on maintenance policies, and
having double redundancy improves the resilience to between
0.88 and 0.89. Incorporating some redundancy into a microgrid’s
architecture does not really cost anything; consequently, such
improvements are probably worthwhile in most cases.
The experiments varied the maintenance policies, and, in
general, we found that maintenance is most important at low
power-to-demand ratios when there is little excess power gener-
ation. The affect of no or little maintenance can be significant to
the time to recover. The results are reasonable because if a base
experiences damage to components and has to wait for spare
parts, technical support, etc., then it will take longer to return
the microgrid to full operation.
The purpose of the model is to support the early architectural
decisions in microgrid design, and the article presents the case
studies to illustrate how the model could be used. For the island
cases, we show how the model can generate the tradespace and
provide information for decisions makers to determine the mix
and number of distributed energy resources to have.
The model assumes independence in the probability of dam-
age to resources, but in the face of common cause failure events,
this would greatly underestimate the extent of damage. We do not
consider common cause failures. Additionally, the model does
not address all aspects of resilience. The concept of resilience
depends on the time frame under consideration. Our analysis did
not investigate the adaptability and/or ability of the microgrid
system to evolve to changing conditions over a longer time
frame.
VIII. CONCLUSION
This article describes two models and an associated method
for military decision makers to generate the tradespace between
resilience and cost for microgrids supporting island naval bases.
The first model represents the resilience of the microgrid across
two dimensions of invulnerability and recoverability. The model,
intended for the early microgrid architecture design, represents
the power balance of the microgrid including the distributed
energy resources, battery storage, and load. The second model
determines the LCOE adapted to island naval bases such that
the cost is only spread across the energy actually provided rather
than the total capacity available. A resilience assessment method
describes how to collect data and apply the two models to gen-
erate trade spaces for the decision maker to trade improvements
in vulnerability and recoverability with costs.
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10 IEEE SYSTEMS JOURNAL
This article makes several contributions to the literature on
microgrid resilience. First, the article adapts resilience and cost
metrics to the characteristics particular of island naval bases.
Second, the article shows how to use the two models to generate
a trade space between resilience and the cost of providing
that resilience. Third, the models consider how maintenance
policies affect the recoverability of the microgrid. In this way,
the models include both design and operational considerations
and their effect on resilience and cost. Lastly, the inclusion of the
conditional probability of damage, given a disruption, allows us
to examine through experimentation two common architecture
heuristics of installing excess power generation capacity and of
redundancy in the distributed energy resources.
An important finding is that redundancy can improve re-
silience at little to no cost under the assumption that costs are
proportional to kW. Adding excess capacity beyond the expected
total load initially leads to large increases in resilience and
then experiences diminishing improvements. The cost of power
generation is mostly linear, and it is for the decision makers
to determine how much resilience they want depending on the
costs.
The maintenance and logistical aspects such as availability
of spares, trained maintainers, and so forth are important con-
tributors to resilience. While our model made some simplify-
ing assumptions about the logistics, the model indicated that
maintenance is important to recoverability, especially when the
generative capacity is only slightly more than the load. Future
work should examine in greater detail the effects of logistics and
maintenance on resilience.
The intent of the model is to support base commanders in
determining the microgrid architecture and operational policies
for the microgrid. The article demonstrated through several case
studies of Navy installations on islands how the model would
support the decision maker through visualization of the trade
space.
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Ronald E. Giachetti received the B.S. degree in mechanical engineering from
Rensselaer Polytechnic Institute, Troy, NY, USA, in 1990, the M.S. degree in
manufacturing engineering from Polytechnic University, Brooklyn, NY, USA,
in 1993, and the Ph.D. degree in industrial engineering from North Carolina
State University, Raleigh, NC, USA, in 1996.
He is currently a Professor and Chair of the Systems Engineering Department,
Naval Postgraduate School, Monterey, CA, USA. He teaches and conducts
research in the design of enterprise systems, systems modeling, and system
architecture. He has authored or coauthored more than 50 technical articles on
these topics including a textbook on the Design of Enterprise Systems: Theory,
Methods, and Architecture. At the Naval Postgraduate School, he leads the
Systems Engineering Department consisting of 45 faculty and staff serving 400
students in resident and distance-learning programs. Prior to joining NPS, he
was an Associate Professor of Industrial and Systems Engineering with Florida
International University, Miami, FL, USA.
Douglas L. Van Bossuyt received the minor in business administration, the
H.B.A. in international studies, the H.B.S in mechanical engineering in 2007,
the M.S. degree in mechanical engineering in 2009, and the Ph.D degree in
mechanical engineering with a minor in industrial engineering in 2012, all from
Oregon State University, Corvallis, OR, USA.
He is currently an Assistant Professor with the Systems Engineering Depart-
ment, Naval Postgraduate School (NPS), Monterey, CA, USA. His research
focuses on the nexus of failure and risk analysis, functional modeling and
conceptual system design, tradeoff studies and decision-making, and resilient
systems. He has authored or coauthored more than 60 peer reviewed technical
journal articles and conference papers on these and related topics, and holds
two US patents. Prior to joining NPS, he was an Automation Engineer at a startup
company, an Assistant Professor of Mechanical Engineering with Colorado
School of Mines, Golden, CO, USA, and a Probabilistic Risk Assessment
Engineer with NuScale Power, Portland, OR, USA. He was a Visiting Scholar
with the University of Sydney Faculty of Architecture, Design, and Planning,
Sydney, Australia; a Space Grant Intern with the Jet Propulsion Laboratory
in Pasadena, CA USA; a DAAD-RISE Intern with the Karlsruhe Institute
of Technology, Karlsruhe, Germany; an IE3 Intern with the Centre d’études
maghrébines à Tunis in Tunis, Tunisia; and was a Research Diver with the
Oregon State University Research Dive Program.
William Anderson received the B.S. degree in mechanical engineering from
Virginia Military Institute, Lexington City, VI, USA in 1986, the M.S. degree in
civil engineering from UC at Berkeley, Berkeley, CA, USA in 1993, the second
M.S. degree in green technologies from University of Southern California, Los
Angeles, CA, USA in 2015, the MBA degree from the Claremont Graduate
School, Claremont, CA, USA in 2002, and the Ph.D. degree in systems engi-
neering from the Naval Postgraduate School, Monterey, CA, USA in 2020.
He is a Director of Energy and Utilities for Naval Facilities Engineering
Systems Command, Ventura, CA USA. He is responsible for energy security and
microgrid solutions for US Naval installations globally. Prior to this position,
he was a management consultant serving Fortune 100 companies in operations
and high tech sectors across multiple industries. He also completed a career as
a U.S. Naval Officer (Civil Engineer Corps) having led SEABEEs in support of
Special Forces (SEALs).
Giovanna Oriti (Senior Member, IEEE) received the Laurea (Hons.) and Ph.D.
degrees in electrical engineering from the University of Catania, Catania, Italy,
in 1993 and 1997, respectively.
She was a Research Intern with the University of Wisconsin-Madison, Madi-
son, WI, USA, for two years. After graduation, she joined United Technology
Research Center, East Hartford, CT, USA, where she developed innovative
power converter topologies and control. In 2000, she launched her own consult-
ing business developing physics-based models of power converters and drives
for electromagnetic interference analysis, stability analysis, and development of
control algorithms. In 2008, she joined the faculty of the Electrical and Computer
Engineering (ECE) Department, Naval Postgraduate School (NPS), Monterey,
CA, USA, where she is currently a tenured Associate Professor. Her research
interests include power electronic converters for electric ship systems, energy
management, microgrids, and renewable energy interface. She holds one U.S.
Patent and has coauthored more than 50 papers published in IEEE transactions
or IEEE conference proceedings.
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