Distributed Energy-Resource Design Method to Improve
Energy Security in Critical Facilities †
Petros Siritoglou 1, Giovanna Oriti 2,* and Douglas L. Van Bossuyt 3,*
Citation: Siritoglou, P.; Oriti, G.; Van
Bossuyt, D.L. Distributed
Energy-Resource Design Method to
Improve Energy Security in Critical
Facilities. Energies 2021,14, 2773.
Academic Editor: Emilio
Received: 1 March 2021
Accepted: 1 May 2021
Published: 12 May 2021
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1Hellenic Navy, Athens, 18648 Attica, Greece; email@example.com
2Department of Electrical Engineering, Naval Postgraduate School, Monterey, CA 93943, USA
3Department of Systems Engineering, Naval Postgraduate School, Monterey, CA 93943, USA
*Correspondence: firstname.lastname@example.org (G.O.); email@example.com (D.L.V.B.)
† This paper is an extended version of our paper published in 2020 IEEE International Conference on
Environment and Electrical Engineering and 2020 IEEE Industrial and Commercial Power Systems Europe
(EEEIC/I&CPS Europe), 9–12 June 2020; pp. 1–6.
This paper presents a user-friendly design method for accurately sizing the distributed
energy resources of a stand-alone microgrid to meet the critical load demands of a military, commer-
cial, industrial, or residential facility when utility power is not available. The microgrid combines
renewable resources such as photovoltaics (PV) with an energy-storage system to increase energy
security for facilities with critical loads. The design method’s novelty complies with IEEE Standards
1562 and 1013, and addresses resilience, which is not taken into account in existing design methods.
Several case studies simulated with a physics-based model validate the proposed design method
and demonstrate how resilience can be included in the design process. Additionally, the design and
the simulations were validated by 24 h laboratory experiments conducted on a microgrid assembled
using commercial off-the-shelf components.
energy security; off-grid; stand-alone; photovoltaics; solar; batteries; microgrid; dis-
tributed energy resources; IEEE Standards
Energy security is of great strategic importance for facilities where critical loads are
present. When the utility grid suddenly malfunctions, the energy security of a facility
is threatened, and the use of microgrids with distributed energy resources (DERs) can
improve the situation [
]. According to [
], “a succinct way to approach energy security is
through the four As: availability, affordability, accessibility (to all), and acceptability (from
a sustainability standpoint)”. Back-up diesel generators are typically available in critical
facilities and are generally turned on to power critical loads when the utility power grid is
down. However, diesel generators are not sufﬁcient to ensure the resilience of a critical
facility because the diesel-fuel supply may not be guaranteed for the time, for instance,
during which critical loads must be powered. To further improve the resilience of a critical
facility, a back-up microgrid including at least one renewable-energy source and energy
storage is proposed in this paper.
The U.S. Department of Defence (DOD) relies on energy in the age of network-
centric warfare to carry out critical missions at military bases in the USA and around
. Outages of grid-supplied energy to bases are a major concern to DOD and
have caused signiﬁcant losses in mission capability in some instances [
]. While high-level
guidance exists related to how long a load that is critical to mission success must continue
to be powered after the start of a grid outage (between 7 and 14 days depending on military
service branch guidance) [
], there is a gap in providing sufﬁcient direction and tools
to properly size a stand-alone microgrid for events of speciﬁc concern to the DOD [
Further, there is a gap in the DOD understanding of events that may cause some or all
Energies 2021,14, 2773. https://doi.org/10.3390/en14102773 https://www.mdpi.com/journal/energies
Energies 2021,14, 2773 2 of 20
of a stand-alone microgrid’s generation capacity to become unavailable. For instance, a
hurricane may cause initial grid outage, followed by another hurricane several days later,
which can damage a PV array, thus reducing its generation capacity [
]. Because of the
criticality of national defence to a country’s well-being, a design process to account for
such “one-two punches” to mission critical power supplies is needed.
This paper proposes a design methodology that follows the guidelines in IEEE Stan-
dards 1562 [
] and 1013 [
] to size the combination of a renewable-energy source, such as
a photovoltaic (PV) array, and energy storage to develop a microgrid. The microgrid is
explicitly a secondary or redundant microgrid that has the goals of (1) improving the
resilience of a critical facility, and (2) boosting energy security to allow for full-time mission
support when the utility grid is down and fuel delivery is interrupted.
1.1. Literature Review
Optimal sizing of DER, including PV and batteries, is addressed in many papers,
such as [
], and a comparison of optimization algorithms is presented in [
these papers propose several complex methods and algorithms to optimize for cost when
introducing renewable-energy sources into a microgrid, none of the proposed design
methods allows for design to maximize resilience. Furthermore, the vast majority of papers
focuses on optimizing battery sizing to reduce some costs, with most papers analyzing
grid-connected microgrids, and fewer studying stand-alone microgrids with
An optimization-parameter alternative to cost is the environmental impact of hybrid and
grid-connected microgrids, as presented in [
], where CO
minimization was one of
Reliability and resilience were very recently addressed in the microgrid litera-
with complex iterative sizing and energy-management methodologies that
require much time and operator knowledge to yield the promised results. A thorough
review of the literature on microgrid resilience up to 2018 was presented in , in which
the authors indicated that recovery, scheduling, and operational solutions were the fo-
cus of previous work, and that a gap existed on DER sizing when unplanned islanding
occurs. Their paper focused on the islanding time window, proposing a complex model
and numerical method to minimize cost without providing experimental validation of
batteries were sized to limit load shedding in islanded microgrids in
the event of cyber attacks; however, PV sources were not included. The novelty of [
in the new deﬁnitions that the authors introduce to estimate resilience in power systems
such as capacity accessibility and capacity adequacy. Although the paper presents several
numerical examples, no physics-based modeling or experimental validation was included
to support their claims. In the most recent paper [
], another extensive literature review
was presented where the authors ﬁrst identiﬁed a gap in sizing PV and batteries to improve
the resilience of a household; the focus on resilience from utility-grid failure did not account
for other possible damage types to the diesel generator or other DERs.
Many design programs are available to size, optimize, and run sensitivity and eco-
nomic analyses of DERs. The most popular are the hybrid optimization model for electric
renewables (HOMER) [
], the system advisor model (SAM) created by the National Re-
newable Energy Laboratory (NREL) [
], the microgrid design toolkit (MDT) developed by
Sandia National Laboratories (SNL) [
], and Xendee [
]. A recent report by the Interna-
tional Energy Agency [
] presented a comprehensive lists of all available tools that were
mostly focused on designing grid-tied power systems with emphasis on cost minimization.
Although some tools can be used to design stand-alone microgrids, several require a signiﬁ-
cant amount of time to run due to multiple iterations and sensitivity analyses implemented
in their algorithms; they also require that users have a detailed knowledge of microgrids
and their components. Most importantly, all of these tools aim at sizing for cost or the most
efﬁcient use of solar resources.
The above literature review identiﬁed a few gaps when looking for early-design
sizing methodology with focus on resilience. One gap is DER sizing to support critical
Energies 2021,14, 2773 3 of 20
loads for the required 14 days to ensure the resilience of a military operation, as deﬁned
by the facility’s energy manager. A second gap is DER design in compliance with IEEE
], but extends beyond lead-acid batteries to encompass other technologies
(e.g., lithium and ion). Furthermore, these authors could not ﬁnd in the literature a design
procedure validated by a physics-based model and by experimental measurements on a
generic commercial off-the-shelf (COTS) microgrid.
1.2. Novel Contribution and Paper Organization
This paper ﬁlls the above-identiﬁed gaps by presenting a design methodology for
sizing the DERs of a stand-alone microgrid, including PV arrays as a power source and
batteries as energy storage. This novel design method can assist energy managers in
the early design stages of back-up microgrids to improve the energy resilience of their
facilities, as it is a method based on worst-case analysis rather than an optimization method.
Among other features, the design method allows for the designer to verify that the sizing
of energy storage is sufﬁcient based on potential PV failures in the context of improving the
resilience of a microgrid to a variety of disruptions. Additionally, the design method was
implemented on a MATLAB-based experimentally validated software platform featuring a
user-friendly interface and less than 1 s processing time. The software could run in manual
or automated mode, allowing for use with no knowledge of DER components’ datasheets
The paper is organized as follows: in Section 2, the design methodology is presented,
including all equations and assumptions, with emphasis on the key parameters on which
an energy manager should focus for resilience. Five design examples are presented in
Section 3to demonstrate the functionality of the proposed method and software using a
scaled 24 h load proﬁle. In each case, load power requirements were met by the microgrid
with DERs sized by the proposed tool. In Section 4, the design equations and physics-based
model are validated by experimental measurements on a microgrid setup with commercial
off-the-shelf (COTS) components.
2. DER Design Methodology and Software Implementation
The design method is ﬁrst described in this section through a series of equations that
have user preferences as inputs, and the sizes of PV panels and batteries as outputs. The
equations were adapted from IEEE Standards 1562 [
] and 1013 [
]. The method and
equations were implemented in a software tool by reading the user’s inputs from a graphic
user interface (GUI) and then solving the equations.
2.1. Design Methodology and Equations
The ﬁrst step in the proposed design methodology is to calculate the appropriate
battery capacity, which was computed with Equations
, given the critical AC
Load power demand in MWh/day, the inverter’s efﬁciency, and the DC bus voltage Vbus.
DC Load [MWh/day] = AC Load
Inverter0s E f f ici ency (1)
Load [Ah/day at DC Bus] = DC Load
To further enhance the resilience of the critical loads, an autonomy period is taken
into account. This is the number of days when the critical load must be entirely supported
by the fully charged battery bank without receiving power from the PV array. The most
important out of many considerations that should be made to determine the autonomy are
the criticality of the load application, system availability, and solar-irradiance variations
of the area of interest throughout the day or season. This feature allows for an energy
manager to account for the performance requirement of critical loads when using this
Energies 2021,14, 2773 4 of 20
design tool to size the batteries. The unadjusted battery capacity is given by multiplying the
load demand at the DC bus (Ah/day) by the autonomy period (days) in Equation (3).
Unadjusted Batt Capacity [Ah] = Load ·Autonomy (3)
In addition to the battery voltage (Vbat) and its capacity (Capacity) in Ah, and depend-
ing on the selection of type of battery (deep cycle lead acid or Li–Ion), maximal depth
of discharge (MDOD), battery efﬁciency, and multicell recharge voltage are determined.
One of the factors that the design algorithm also considers is temperature since it affects
available battery capacity. Battery capacity is adjusted by speciﬁc temperature-correction
factors (TCFs) for lead acid [
] and Li–Ion batteries [
]. For lead acid batteries, the TCF
drops with temperature, going from 1 at 25
C (and higher) to 0.95 at 15
C, and down
to 0.65 at
C. For Li–Ion batteries, the TCF is 1 for temperatures down to 5
then drops to 0.95 at
C and 0.77 at
] as the capacity of Li–Ion batteries is less
impacted by temperature than the capacity of lead acid batteries is.
Battery capacity is further adjusted for the MDOD, which is a parameter that should
be selected from resilience-oriented life-cycle cost analysis. A design margin (M) of 10%
) is also taken into consideration to maintain system availability, and for uncertain-
ties in load determination, as in Equation (4).
Nominal Battery Capacity [Ah] =
M·Unadjusted Battery Ca pacity
In order to size the batteries, IEEE standard 1562–2007 refers to the system voltage
range, mentioning that it should be accordingly deﬁned [
]. Speciﬁcally, the standard
as the lowest maximal voltage and
as the highest minimal voltage be-
tween which all loads operate properly. According to [
], the number of series-connected
batteries is determined by
Battseries(rounded down) = Vmax
where the multicell charging voltage (
) is given by the product of the voltage of
the individual cell and the number of cells in the battery, as is shown in Equation
the number of cells computed in Equation (7) for lead acid and Li-Ion batteries.
Vmul ticell [V] = Vcell ·Ncell s (6)
2, for Lead Acid Batteries
3, for Li-Ion Batteries.
An alternative to Equation
was introduced for two reasons: (i) the difﬁculty of
recording the maximal and minimal voltages at which each DC load is operating, and
(ii) determining the number of series-connected batteries using the recharge voltage in some
cases results in lower voltage during the periods when the batteries are mostly depleted.
On the other hand, using nominal battery voltage is straightforward; therefore, the number
of series-connected batteries is determined by Equation (8) in the proposed design tool.
Batseries(rounded up) = Vbus
Energies 2021,14, 2773 5 of 20
The number of batteries connected in parallel is readily given by
Bat par allel (rounded up) = Nominal Battery Capacity
Battery (unit)Capacity (9)
The PV array was designed next. To properly design a sufﬁcient stand-alone power
system, it is recommended to use the peak sun hours (PSH) in kWh/m
of the month
with the lowest solar radiation for the desired location. This is a conservative assumption
to improve microgrid resilience. PSH data are available from the NREL’s national solar-
radiation database [
] including 25 years of solar-radiation data and several other factors
such as wind and temperature.
System losses (SL) that should be taken into consideration include battery efﬁciency,
wire losses, dust, aging of the PV array, and other parasitic losses. A fair assumption of
15% total system losses was considered to be the default value in the design tool, and
this is updated by adding the complement of the round-trip battery efﬁciency (battery
SL =0.15 + (1−Bate f f )(10)
Considering that the PV array was designed to recharge the batteries that are sup-
plying power to the load, the output voltage of the PV array should be greater than the
battery-bank recharge voltage. The equation that is proposed by IEEE Standard [
taken a step further by determining the number of PV modules that should be connected
in series by Equation
, where the
is the voltage at the maximal power point of the
used PV module.
MPPT charge controllers are often used to improve the PV efﬁciency. The use or
absence of MPPT controllers is a choice for the user in the input window of the proposed
design tool. The design tool accounts for a derating voltage factor of 80% when the PV
array is directly connected to the battery bank to ensure that the knee of the maximal power
point is well above the battery-recharge voltage. On the other hand, if MPPT controllers
are used, the derating factor is set to 95% to account for any variations of high ambient
temperatures and power-conversion losses of the MPPT. A speciﬁc temperature-correction
factor was not included in Equation
, and will be included in future version of the
PVseries (rounded up) = Vmul ticell ·Batseries
Vmp ·(Derating Voltage Factor)(11)
An additional considered parameter for the determination of the number of PV panels
that should be connected in parallel is the PV array-to-load ratio
. The user can
select the desired A:L according to their location and the loads’ performance requirements,
which is typically 1.1 to 1.2 for noncritical loads and areas with high and consistent solar
radiation, and 1.3 to 1.4 for critical loads or areas with low solar radiation. The number of
PV modules that should be connected in parallel is determined by Equation
Imp is the current at the maximal power point of the used PV module.
PVparal lel (rounded up) = Load[Ah/day]·(A:L)
(1−SL)·Imp ·PS H (12)
2.2. Design Software
The above method and equations were used to create design software with a user-
friendly GUI in MATLAB, where the user could either select manual mode and input the
PV characteristics and batteries that they choose or select automatic mode and pick among
a variety of commercially available DERs. The window with the inputs in manual mode is
shown in Figure 1. The window in automatic mode (not shown) has several pull-down
menus in the “Parameters of the Elements Used” section for users who do not have PV and
battery data sheets available, and want to use those available in the preloaded database of
the software tool. The window with the outputs is shown in Figure 2for design example 1,
Energies 2021,14, 2773 6 of 20
presented in Section 2. These outputs were obtained when the inputs were as shown in
The peak power consumption of critical AC loads and DC loads (if there are any) is the
first input to the design tool, which is used by the software to compute
Equations (1) and (2)
“Required Usable Storage” is assigned to the
variable in Equation
used to compute Equation
. The rest of the inputs can mostly be obtained from
data sheets, except the array-to-load-ratio, which is a parameter that affects resilience as
described in the previous subsection.
Additional details on the software implementation of the design method, including
the GUI and commercial DERs used in automatic mode, can be found in .
Figure 1. Input user interface in manual mode—Design Example 1.
Energies 2021,14, 2773 7 of 20
Figure 2. Output GUI from design software—Design Example 1.
3. Design Examples and Simulated Outputs
The proposed methodology implemented in the design software described in the pre-
vious section feeds its outputs into a physics-based model, so that the designed microgrid’s
power ﬂow can be veriﬁed through simulations. In this section, we present ﬁve examples
to demonstrate the functionality of the proposed design methodology. The physics-based
model was implemented in Simulink/MATLAB for a microgrid architecture including
PV arrays, energy storage, and equivalent DC load. The architecture of the microgrid is
shown in Figure 3, which is also the circuit schematics of the COTS microgrid assembled in
the laboratory for experimental validation. This architecture was chosen for two reasons:
(1) it is simple to assemble with the use of widely available COTS components, and
more reliable than more complex architectures are because it requires a minimal number
Figure 3. Architecture of commercial off-the-shelf (COTS) microgrid.
The physics-based model uses the PV and battery ratings determined by the design
tool, as is shown in Figure 2, with the 24 h load proﬁle [
] shown in
. The area
of the load proﬁle over the 24 h period is DC load in Ah/day. The software scales the
load-demand curve on the basis of the user’s input data. The design examples presented
here demonstrate that the proposed design tool allows for the user to size the DERs of a
microgrid for resilience, and simulate hours, days, or months of stand-alone operation to
verify that the critical load is serviced at all times in different scenarios.
Energies 2021,14, 2773 8 of 20
PV current = 0; load and battery currents were identical for the ﬁrst simulated scenario
3.1. Design Example 1: 24 h Autonomy without Sunlight
In this example, we designed the energy-storage component to support the critical
loads for 24 h without receiving power from the PV array. The inputs to the design tool
are shown in Figure 1, including Li–Ion batteries Relion RB48V200 [
] and SunPower
X22-360-COM PV panels [
]. With these inputs, the output of the design tool is shown in
Figure 2, in which the “Run Simulation” button is visible that could be clicked to run the
time-domain simulation for this design example. The simulated results in
Figures 4and 5
show that the batteries supplied the total load current demand, since the output of the PV
array was zero, simulating a failure of the PV or a cloudy day. The key result of this design
example is shown in Figure 5, which indicates that the batteries were not depleted at the
end of the 24 h. This conﬁrmed that the energy-storage system could support the system
load without receiving power from the PV array for the period of autonomy set by the user.
The SOC never dropped lower than the complement of the MDOD of the batteries.
3.2. Design Example 2: 24 h Autonomy with Sunlight
With the same inputs as that in Example 1, in this scenario, the PV output in Ah was
simulated using a step proﬁle imitating a parabola to approach hourly solar irradiance [
This proﬁle was scaled according to the output of the PV array that was calculated by the
design tool, as is shown in Figure 2.
The simulated PV current proﬁle is shown in Figure 6. With this PV current, and with
the input parameters in Figure 1, the plots shown in Figures 6–8were obtained in which
the PV array output current supplied power to the load from 06:00 until 21:00. Up until
08:00, load demand was higher than the output of the PV array; thus, the battery current
was still positive and delivered most of the power to the load. Beginning at 08:00, when
the PV array output became higher than the load demand, it charged the batteries until
about 14:30, when they were fully charged. Lastly, at 19:00, when the solar irradiation was
signiﬁcantly reduced, the batteries supported the load until the end of the day, at which
point they reached an SOC of 93.79%.
Energies 2021,14, 2773 9 of 20
Figure 5. Battery SOC in scenario without sunlight.
Figure 6. Load and PV currents for scenario with sunlight.
Energies 2021,14, 2773 10 of 20
Load and battery currents in scenario with sunlight.
was positive coming out of the
battery, and negative when charging the battery.
Figure 8. Battery SOC in scenario with sunlight.
3.3. Design Example 3: Impact of A:L Parameter
A variation on the design example shown above is presented here to show the inﬂu-
ence of the A:L ratio on the microgrid design. The user inputs were identical to those in the
previous scenarios except for the A:L ratio, which was increased from 1.1 to 1.3. The output
of the design tool was unchanged for the batteries; however, the number of PV panels
Energies 2021,14, 2773 11 of 20
changed from 3591 to 4239. The plots in Figure 9show that the increased A:L resulted in
approximately 30% faster battery charging. This scenario also resulted in PV array output
that was 20% higher, as expected. This example demonstrates that this tool could assist
in the ﬁne-tuning of the DER sizing to improve energy security. The ﬁfth design example
expands on this concept.
Figure 9. Battery SOC (A:L = 1.1 vs. A:L = 1.3).
3.4. Design Example 4: 14 Day Autonomy with Prolonged Partial PV Disruption
Analysis up to this point considered a microgrid that must sustain itself over 24 h either
with or without PV generation through adequate energy storage. However, microgrids
may encounter generation disruptions lasting longer than 24 h or partial disruptions
in generation that could result in insufﬁcient energy storage and dropped critical loads.
For instance, storms may damage PV installations [
], attacks on power infrastructure
may occur [
], or equipment failures may happen [
]. We focus on PV disruption
to investigate battery and PV array sizing from the perspective of sustaining the load
throughout the disruption.
While many definitions and measures of resilience exist across many domains, we con-
sider resilience to be the ability of the system to continue to function against a disturbance [
Within the resilience framework that Madni and Jackson proposed , microgrid design
elements over which we can have inﬂuence correspond to (1) withstand—have sufficient
battery capacity to ride through a PV disruption—and (2) recover from a disruption—time to
recharge battery before next potential disruption. Most resilience measures focus on the dura-
tion of a disruption and the ensuing recovery, and on the consequence of a disruption [
with a wide variety of variations in formulations and various aspects of the involved
systems taken into account. In the instance of the microgrid in the second design example,
it is most useful to evaluate (1) if the battery-charge state reaches zero, which represents
withstanding a disruption, and (2) the time it takes to return to a full charge state, which
represents recovering from a disruption. In the above scenarios, we demonstrated battery
sizing based on 100% PV loss over a 24 h period. We now extend our modeling efforts
to investigate (1) PV disruptions that are not complete (e.g., losing part of a PV array
Energies 2021,14, 2773 12 of 20
due to storm damage or debris coverage), and (2) the restoration of PV capacity after a
maintenance and repair window, and the resulting battery recharge.
Using the same microgrid system as that in the second design example, we induced a
failure of 50% of the PV capacity into a 14 day analysis period, which represents required
days of autonomy of some military microgrids when offsite power is lost. The 50% PV
capacity reduction could represent, for example, storm damage. After 3 days, full recovery
to 100% PV capacity was achieved. The battery sized for one day of full autonomy was
sufﬁcient to ride out the disruption caused by the reduced PV capacity. It took 4.6 days to
return to a nominal battery charge state. Figure 10 shows the battery state of charge over
the 14 day analysis period.
Battery state of charge over 14 day period with 50% PV disruption occurring on Day 1
and PV returning to full capacity occurring on Day 4. Battery regained full charge state at 4.6 days
after PV returned to full capacity.
While many simple and complex measures of resilience exist in the literature, it is
sufﬁcient for this level of design and analysis to simply simulate a variety of potential
disruptions and verify that the microgrid design is sufﬁcient to (1) withstand the disruption
and (2) recover from the disruption in an acceptable period of time. Sizing a battery for
the expected duration of a partial PV disruption requires a system designer to hypothesize
about the types of disruptions that may occur. For instance, the initial disruption that
disconnects a critical load from grid-connected power and disrupts fuel availability for a
backup diesel generator, which in turn initiates usage of the microgrid, could be caused
by a hurricane disrupting grid-scale energy generation and transmission 100 km away.
The hurricane may then impact the microgrid some hours or days later, causing partial
disruption of the PV array either through damage to panels or damage to cabling and
other associated components. In such a situation, and where the critical load is sufﬁciently
important, a standby reserve of PV panels and other requisite hardware may be available
Energies 2021,14, 2773 13 of 20
to be installed to bring the PV array back to full capacity. The process of repairing a PV
array may take several days to complete.
3.5. Design Example 5: 14 Day Autonomy with Prolonged Partial PV Disruption and Increased
The recovery time to a fully recharged battery from initial microgrid disruption
includes both the time to repair and bring the PV array back to full capacity, and the time
to recharge the battery once the PV array is fully restored. The amount of time it takes to
return to a predisruption charge state is important if the hypothesized disruption could
occur more than once in a relatively short period of time. For instance, the 2017 Atlantic
hurricane season had both Hurricane Irma and Hurricane Maria spaced two weeks apart,
which impacted the US Virgin Islands [
]. Other similar disruptive weather events such
as intense thunderstorms and tornadoes in the Midwest of the United States can occur
with regularity. While the 8.6 day recovery time from initial disruption to a full charge
state (4 days of 50% PV capacity and 4.6 days of recharge time) shown in Figure 10 may
be sufﬁcient, a shorter period may be desired, in which case a large PV array is required.
Increasing the A:L ratio to 1.4 produces a recovery time from initial disruption to fully
recharged battery of 5.8 days, as shown in Figure 11.
Battery state of charge over 14 day period with 50% PV disruption and A:L = 1.4 occurring
on Day 1 and PV return to full capacity occurring on Day 4. Battery regained full charge state at
1.8 days after PV returned to full capacity. Recovery time was 5.8 days.
Oversizing the PV array from the original A:L = 1.1 to A:L = 1.4 decreased recovery
time in this scenario by 3 days. In certain scenarios, a 3 day reduction in recovery time
may make a signiﬁcant difference in the ability of a critical load to be maintained through
a second disruption event during a 14 day grid power outage and diesel-fuel interruption.
Resilience can be further improved by increasing battery size and/or PV array size on the
basis of scenarios that a facility reasonably expects to encounter.
Energies 2021,14, 2773 14 of 20
4. Experimental Validation of Design Method and Software
The proposed design method was used to size the COTS components of a small
microgrid that was assembled in the laboratory. Experimental measurements on the COTS
microgrid were compared to 24 h simulations without and with sunlight.
First, the design method was used to size the batteries of the COTS microgrid shown
in Figure 12, which was tested for 24 h without sunlight to simulate either a very cloudy
day or a situation where PV panels are damaged. With respect to the input data in
the AC load was reduced to 2.9 kWh/day, and the system and battery-voltage were both
set to 12 V. An 85% efﬁcient inverter with 12 V rated input and 120 V rated output was used
to interface the battery bank to the AC loads. Sealed deep-discharge lead-acid batteries
rated at 100 Ah were selected. The design tool output indicated that four batteries could
meet the user input’s speciﬁcations.
Table 1shows the measurements acquired during the 24 h experiment, demonstrating
the stable operation of the microgrid and the expected decrease in battery output voltage as
batteries were depleted. The experimental battery SOC was computed using the Coulomb
counting method [
], and it was plotted versus the SOC simulated with the proposed
tool in Figure 13. Matching the plot of the battery SOC in the simulation with the one
of the experiment validated the design tool. The Coulomb counting method estimates
the SOC by measuring the current that is discharged from the battery and integrates it
over time. This value is repeatedly subtracted from the initial SOC or, later, the previous
SOC value. The experimental SOC could also be obtained using the open-circuit voltage
] where the linear plot of the battery’s open-circuit voltage
and its SOC
can be determined from measurements of
at 100% SOC when the batteries are fully
charged, and the measured
at 0% SOC when the batteries are fully discharged. Then, it
is straightforward to ﬁnd the corresponding SOC for any measured Voc .
Laboratory experiment setup for the scenario without PV output. Major elements were
identiﬁed and included AC loads, inverter, batteries, and a variety of test hardware.
Table 1. Summary of laboratory measurements w/o sunlight.
Time (h:min) DC Current (A) AC Current rms (A) DC Voltage (V) AC Voltage rms (V)
1:20 11.23 0.999 12.54 119.8
9:30 11.56 0.999 12.29 119.8
19:00 12.04 0.999 11.88 119.6
23:00 12.24 1.002 11.70 119.9
Energies 2021,14, 2773 15 of 20
Figure 13. Comparison of simulated and measured battery SOC for scenario without sunlight.
Next, a COTS microgrid was built using the batteries of the previous setup, and
PV panels with 16 V MPP voltage and 6.25 A MPP current. AC load input was set to
, A:L to 1.1, and the design tool output indicated that 3 batteries and
panels were needed to meet the user requirements. The circuit schematic is shown in
, and the laboratory setup is shown in Figure 14. Maximal power-point track-
ing (MPPT) modules interfaced with the PV panels, and a 90 W halogen lamp was used
as constant load for the 24 h time period. Table 2shows the acquired current and volt-
age measurements during the 24 h experiment, demonstrating the stable operation of
The experiment was started at 21:00 to measure the lowest SOC that the battery bank
could reach before sunrise. The PV array output current was recorded and is plotted in
Figure 15. The battery input current had a similar shape because the outputs of the MPPT
modules fed the battery bank, as shown in Figure 3. Figure 16 contrasts the experimental
SOC plot with that obtained in simulations using the scaled PV proﬁle in Figure 6.
Table 2. Summary of laboratory measurements with sunlight.
Time (h:min) DC Current (A) AC Current rms (A) DC Voltage (V) AC Voltage rms (V)
21:23 8.90 0.752 12.68 119.8
06:56 8.96 0.760 12.45 119.7
11:19 8.60 0.753 14.44 120.0
16:05 8.73 0.756 13.88 119.9
18:38 8.82 0.753 12.91 119.5
21:07 8.90 0.755 12.76 119.7
Energies 2021,14, 2773 16 of 20
Laboratory setup for 24 h with sunlight. (
) Major identiﬁed elements including AC
loads, inverter, batteries, MPPTs, and a variety of test hardware. (bottom) Deployed PV array.
Figure 15. PV array output current.
Energies 2021,14, 2773 17 of 20
Figure 16. Experimental and simulated battery SOC in scenario with sunlight using ideal PV current.
Although the two curves in Figure 16 are similar, differences are due to discrepancies
between the experimental PV proﬁle in Figure 15 and the standard PV proﬁle used in
simulation (Figure 6). The experimental PV current rapidly increased, but also decreased
very early on the day of testing instead of the gradual current changes of the default PV
proﬁle implemented in the Simulink model. Thus, an additional plot, shown in
was created by feeding the experimental PV current into the physics-based model to correct
Experimental and simulated battery SOC in scenario with sunlight using experimental
Energies 2021,14, 2773 18 of 20
The two experiments demonstrated that the design software output correctly sized
DERs to meet the user requirements. Furthermore, it output simulated plots that matched
those of a generic microgrid, assembled in the laboratory entirely with COTS components.
Thus, the implemented physics-based model in the design software was experimentally
This paper presented a novel methodology and design software to size DERs for
resilient stand-alone back-up microgrids. A design method based on the guidelines in IEEE
Standards 1562 [
] and 1013 [
] was presented with all the required equations to size
batteries and PV arrays given the user requirements. The method was implemented in a
user-friendly software program that can be operated with different levels of knowledge
on DER technical speciﬁcations, allowing for the timely design of a back-up microgrid
with focus on resilience. Critical-load requirements, autonomy, and array-to-load ratio
are the input parameters to the software tool that outputs the appropriate DER ratings
to obtain the desired performance by the facility’s energy manager based on speciﬁed
Several microgrid-design examples were presented to demonstrate how the proposed
method can be used to achieve the user’s resilience goals with a stand-alone microgrid.
Speciﬁcally, using the software tool, a facility energy manager can simulate potential
disruptions to verify that the design could allow for the microgrid to continue to operate
through one or multiple disruptions and recover in an acceptable period of time. Examples
included obtained simulations with a physics-based model that could run from the design
software’s output GUI. Two 24 h laboratory experiments on COTS microgrids validated
the design method and physics-based model.
The design software is fully editable and available to research groups for future
optimization. A team of engineers is currently conducting research on optimizing different
aspects of back-up microgrid design using this methodology, and is porting the design
software to Python in order to better provide resilience to critical facilities. The availability
of such a methodology and the open-source tool implementation offers a great advantage
towards achieving energy security.
Conceptualization, P.S. and G.O.; methodology, P.S., G.O., and D.L.V.B.;
software, P.S.; validation, P.S.; writing—original-draft preparation, P.S. and G.O.; writing—review
and editing, G.O. and D.L.V.B. All authors have read and agreed to the published version of
This research was funded by NAVFAC as part of the Naval Shore Energy Technology
Transition Program (NSETTI).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
This research is partially supported by the Naval Postgraduate School. Any
opinions or ﬁndings of this work are the responsibility of the authors, and do not necessarily reﬂect
the views of the sponsors or collaborators. Approved for Public Release; distribution is unlimited.
Conﬂicts of Interest: The authors declare no conﬂict of interest.
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