Pilot Study on Residential Measures against
Unpredictable Outages with Batteries andPhotovoltaics Considering Necessary Loads
Masashi Matsubara, Masahiro Mae, Ryuji Matsuhashi
Department of Electrical Engineering and Information Systems
The University of Tokyo
Tokyo, Japan{matsubara, mae, matu}@enesys.t.u-tokyo.ac.jp

Abstract—Sudden natural disasters such as earthquakes sometimes cause a sudden blackout in the power grid, and households
suffer unpredictable outages. This paper aims to determine residential measures against unpredictable outages using batteries
and photovoltaics (PVs). This paper focuses on the effect of the
SoC margin that the battery keeps its state-of-charge (SoC) highin the normal state, and the operation of the battery is simulatedby an optimization problem considering the predictability ofoutages. This paper also introduces three resilience indices toquantify the duration, the maximum power, and the weighted
energy of a supply shortage. As a result, the SoC margin reduces
a supply shortage of important demand during an outage, anda 40% SoC margin reduces the outage cost by half in a 24-hour
unpredictable outage. The SoC margin also improves the worst
5% value of resilience indices, especially in the weighted energyof a supply shortage, by half with a 40% SoC margin. However,
the yearly electricity cost increases by 16% with a 40% SoC
margin, so the SoC margin has an economic tradeoff.
Index Terms—Battery, Photovoltaics, Resilience indices, SoC
margin, Unpredictable outage

I. I NTRODUCTION
Power grids suffered from severe disasters, and large blackouts caused people anxiety. In Japan, typhoons, heavy rains,and earthquakes yearly damage the transmission and distribution systems. In particular, direct earthquakes suddenly damage many transmission, distribution, and substation facilities.
As a result, these disasters sometimes cause extensive andlengthy blackouts. Thus, the resilience of the grid becomes
important to keep the function normal during extreme situations such as disasters. The measure to improve resilience
attracts the attention in the power system.
Grid owners and operators take measures against disasters
to prevent, mitigate, and recover the damage to the grid. In
prevention, the hardening equipment plan reduces the risk ofdamage, considering the future demand and climate trends [1],[2]. In mitigation, grid operators minimize the load shedding
by separating the damaged nodes [3], [4]. In recovery, theoptimal dispatch of mobile generators and repair crews reduces
the total load shedding [5]. However, the grid operators
cannot prevent all blackouts. Some households will suffer from979-8-3503-8174-0/24/$31.00 ©2024 IEEE

outages until the grid restoration. Thus, the demand-side selfprotective measures mitigate inconvenience during outages andimprove the overall resilience of the power system.
Residential systems that supply electricity during outages
contain power generation resources and backup energy storage.
Photovoltaics (PVs) are potent as a generation resource dueto their low environmental burden. The PV-battery system
improves self-sufficiency and shaves the peak of residential
demand [6]. The PV-battery-diesel system is demonstrated
in India [7], but the duration of considered outages is short(up to 3 hours). Cooperation among households improves
resilience [8], but outages are considered predictable. [9]analyzes the self-sufficient duration during outages but does
not focus on the operation in the normal state. The PV-battery
system can be a cost-effective solution to frequent outages indeveloping countries [10]. [11] proposes the model predictive
control-based operation method with battery degradation indeveloping countries, but outages are considered periodical
and predictable. The PV-battery sizing problem is consideredin [12], [13] using stochastic optimization. The sizing problem[12], [13] considers the risk of outages but does not propose aproactive operation. [14] simulates the PV output during pasthurricanes in the US. [15] compares the resilience of the PVbattery system among household types, regions, and outage
causes. [16] proposes the method to calculate residential reliability without simulations. However, the cause of outages does
not include earthquakes. In Japan, several large earthquakes
suddenly caused an extensive and lengthy blackout in thegrid. The operation of the PV-battery system should consider
unpredictable outages.
Sudden earthquakes sometimes cause lengthy and unpredictable outages in households. The measures in the grid
reduce the damage from disasters, but self-protective measuresin households can also mitigate damage. Although previous
research simulates the PV-battery systems [7], [8], [10]–[13], [15], unpredictable outages and measures are yet to beanalyzed. This paper aims to mitigate the damage caused byunpredictable outages by the PV-battery system in households.
The optimization problem, considering unpredictable outages,
decides the operation of the battery to minimize the supply

Unpredictable outage

Grid

Time

InterruptFirst
optimization

Household

Changing operation

Taking over state

Secondoptimization

BatteryPV

Considering outage

Fig. 2. Optimization sequence with an unpredictable outage.
Fig. 1. Household model.
Power supply rate

shortage with the importance of demand. This paper also
analyzes how effective keeping the state-of-charge (SoC) of
the battery high in the normal state is from both normal andoutage perspectives. In addition, this paper introduces three
indices to quantify residential resiliency and describes theoutage mitigation.

D

max
PshortG

II. S IMULATION AND R ESILIENCE E VALUATION M ETHOD

Outage lengthTime

A. Household Model
Fig. 1 shows the household model. The household is supplied electricity from the grid. However, it is suddenly interrupted by blackouts in the grid, which causes an outage. The
household has a battery and a PV and uses the generation of
the PV. The PV supplies electricity in both normal and outage
states. The battery can charge and discharge electricity fromthe grid and PV. The battery also charges excess electricity
from the PV during the outage.
B. Optimization and Outage Model
The optimization problem simulates the operation of thebattery. The objective is to minimize the sum of electricity
and outage costs, as shown in Equation (1).
X
min. T C =(Celec,t × Egrid,t
(1)
t
′
′
+ Cshort × Eshort,t + Cshort× Eshort,t).
′Egrid denotes the energy from the grid. Eshort and Eshortdenote the supply shortage of important demand and unimportantdemand, respectively. Celec denotes the electricity price. Cshort′and Cshortdenote the outage unit costs, which correspond to
the important and unimportant demand, respectively. t denotes
the number of time slots, and the resolution is 5 minutes.
The optimization problem describes the outage in theconstraints on the balance of supply and demand and the
maximum power from the grid. Equations (2) and (3) show
the balance of supply and demand, and the maximum powerfrom the grid, respectively.
′
Egrid,t + EBTd,t + EPV,t + Eshort,t + Eshort,t= Edem,t + EBTc,t .
max
Egrid,t ≤ (1 − BINoutage,t ) × Egrid.

Fig. 3. Relation between proposed resilience indices and resilience curve.

(BINoutage = 1), the energy from the grid becomes zero. The
battery and the PV can supply electricity during the outage.
′
The supply shortage (Eshort and Eshort) happens when the
demand exceeds the supply.
The optimization problem includes the constraints on the
SoC margin. The SoC margin limits the minimum SoC in thenormal state as it is higher than the actual minimum SoC.
The gap between the actual minimum and the minimum inthe normal state is called the SoC margin. The battery has theactual minimum and maximum SoCs (10 % and 90 %) to avoid
over-discharging and over-charging. The battery is prohibitedfrom violating this minimum SoC even during the outage. The
minimum SoC in the normal state can be larger than the actual
minimum SoC to measure unpredictable outages. This paper
externally defines the SoC margin as constant over time.
This paper proposes multiple optimizations to describe thechange of the operation after an unpredictable outage. The
scheme of multiple optimizations is shown in Fig. 2. At first,
the household decides on the operation without being aware of
the outage. The first optimization assumes that any outage does
not occur (BINoutage,t = 0 for all t) to reflect the awarenessof unpredictable outages. Immediately after the outage occurs,
the household adjusts the operation to endure the outage.
The second optimization decides again the operation after theoutage occurs, including the outage state.

(2)
C. Resilience Indices(3)

EPV , Edem , EBTc , and EBTd denote the energy of the PV,
electricity demand, and battery’s charge and discharge, respectively. BINoutage denotes the outage state. During the outage

The resilience indices can evaluate the improvement of residential resilience by the measures against outages. Resiliencecurves [3] and resilience triangles [17] are widely used todescribe the system’s state affected by a large disturbance.

800
100
90

500

80

400

70

300

60

200

50
40

100

30

0

20

-100

Grid PowerPV Generate
Battery Discharge

700

Battery SoC [%]Electric Energy [Wh/5min]600

Supply Shortage
Battery Charge
Battery SoC

10

600

Supply Shortage
Battery Charge
Battery SoC

100
90

500

80

400

70

300

60

200

50
40

100

Battery SoC [%]Grid PowerPV Generate
Battery Discharge

700

Electric Energy [Wh/5min]

800

30

0

20

-100

10

-200
0
01/21 08:00 01/21 20:00 01/22 08:00 01/22 20:00 01/23 08:00 01/23 20:00 01/24 08:00 01/24 20:00-200
001/21 08:00 01/21 20:00 01/22 08:00 01/22 20:00 01/23 08:00 01/23 20:00 01/24 08:00 01/24 20:00

Fig. 4. Power supply around a 24-hour unpredictable outage without an SoC
margin.

Fig. 5. Power supply around a 24-hour unpredictable outage with a 40 %SoC margin.

They show the transition of functionality around the disturbance. The concept of resilience includes a time dimension[18], so defining one index to describe resilience is difficult.
For example, Panteli et al. [3] propose four indices. They
describe the speed and amount of dropping functionality, thedegraded state’s duration, and the restoration speed. Chatterji
et al. [13] also propose the indices for residential resilience.
They include the average, maximum, and duration of load
sheddings, aggregating the different outage scenarios.
This paper introduces resilience indices that describe themitigation of outages in a household. Households can prepare
and mitigate outages but cannot remove the cause of outages.
Thus, the indices mainly focus on how long and large thesupply can be kept during the outage. This paper proposes
three indices as below.
• D, which denotes the cumulative duration of supply
shortages.
max• Pshort , which denotes the maximum power of supply
shortages.
• G, which denotes the ratio of the total supply shortage
with the measure to the one without the measure.
These indices correspond to the duration and amount ofdegradation and the area of the resilience curve, as shownin Fig. 3. When they get smaller, the residential system gets
more resilient. Only G includes the importance of demand. For
calculating G, the weight for important demand is five, and theweight for unimportant demand is one. This ratio equals the
proportion of outage unit costs (Section III-A). The proposed
indices are similar to the ones in [13], but our indices aredefined in each outage scenario.

to the Japanese wholesale market price in 2023. In Section
III-A, the unpredictable outage occurs during the day withlittle generation of the PV. The outage duration is 24 hours,
based on the 50 % recovery time after the blackout due to the
Hokkaido Eastern Iburi earthquake in Japan 2018.
The operation of the battery depends on the importantdemand during outages. There are surveys on the type ofimportant demand [15], [19]. Refrigerators, cell phone chargers, and televisions have higher needs during the outage
by a large earthquake [19]. In the outage simulation, [9]considers that the important demand is half the demand during
the outage. This paper assumes that the important demandduring the outage is half the demand the household would
use without the outage. The outage unit cost, or the value oflost load, is estimated by surveys. The unit cost depends on
the regions and outage situations, but the representative value
is around 100 JPY/kWh to 1000 JPY/kWh [20]–[22]. This
paper assumes that the outage unit costs are 500 JPY/kWhfor the important demand [23] and 100 JPY/kWh for theunimportant demand.
First, we compare costs and resilience indices with different
SoC margins. The total costs and outage costs with different
SoC margins are shown in Table I. The resilience indices withdifferent SoC margins are shown in Table II. From 0 % to40 %, the SoC margin reduces the outage cost by around 1200
JPY per 20 % point increase in the SoC margin. The decreasein the outage cost also reduces the total cost. However, thetotal cost at an 80 % SoC margin is higher than at a 40 %SoC margin. With a very high margin, the electricity cost
increases more than the decrease in the outage cost. The SoC
margin improves the indices, especially G, which describes theweighted energy of the supply shortage. Compared to no SoC
margin, a 40 % SoC margin does not reduce D but reducesmax
Pshortby 33 % and G at half.
Next, we show the operation around the outage. The power
supply around the unpredictable outage without the SoC
margin and with a 40 % SoC margin is shown in Figs. 4 and 5,
respectively. For comparison, the power supply around a 24hour predictable outage is shown in Fig. A1 (see Appendix).
When the outage is predictable, the battery refrains from

Date

III. C ASE S TUDY
A. Situation and Battery Operation
Based on the household’s actual data, this paper simulates
the proposed measure against an unpredictable outage. The
demand are based on the actual demand for a detached housein the Kansai region in Japan. This paper focuses on thewinter because the PV generates less power. The power andcapacity of the battery are 3 kW/13.5 kWh. The capacity of
the PV is 3 kW at peak. The electricity price is connected

Date

SoC margin
0%
20 %
40 %
80 %

Total cost [JPY]
12570
11450
10470
10610

Outage cost [JPY]
4550
3330
2120
610

TABLE IIR ESILIENCE INDICES WHEN A 24- HOUR UNPREDICTABLE OUTAGEOCCURS AT 08:00 IN THE SUNLESS DAY.
SoC margin
0%
20 %
40 %
80 %

D [min]
1440
1440
1440
920

max [kW]
Pshort
1.93
1.82
1.29
0.97

G [%]
90.8
66.5
42.3
12.1

discharging before the outage. In contrast, when the outage
is unpredictable, the battery does not charge before the outage
because the operation before the outage is defined without
being aware of it. Thus, there is little SoC in the case without
the SoC margin (Fig. 4). There is a large supply shortage forimportant demand without the SoC margin because of little
energy from the battery and the PV. In contrast, the battery
has some energy before the outage with a 40 % SoC margin(Fig. 5). Thus, the battery can supply electricity to importantdemand until around 22:00. In conclusion, unpredictable outages are an important factor in the operation of the battery. In
particular, setting the SoC margin can mitigate the damage ofsuch unpredictable outages.
B. Multiple Scenarios of Outages
Since the damage of an outage depends on its occurrence
timing, the effectiveness of outage measures should be discussed based on multiple outage scenarios. In each scenario,
a 24-hour unpredictable outage occurs during the optimization
time (14 days). The timing of outage occurrence in the firstscenario is 6 hours later than the start of optimization tosimulate the normal operation before the outage. The occurrence timing in each scenario is different at 30 minutes. The
occurrence timing in the last scenario is 30 hours before theend of optimization to avoid the violation of constraints. The
number of the scenarios is 601 (= (24×14−36)×(60/30)+1).
The scenarios includes severe and mild ones because eachscenario differs in demand and PV output during the outage
and the SoC at the outage occurrence.
Fig. 6 shows the sorted distribution of G with different SoC
max
margins. The sorted distributions of D and Pshort
are shown in
Figs. A2 and A3 (see Appendix). Table III shows the worst 5 %value of proposed indices. Supply shortage happens in mostscenarios, even with the SoC margin. However, the SoC margin decreases the index G, showing resilience improvement.
At the worst 5 % values, the index G decreases much with
the SoC margin. The battery with the SoC margin supplies
the important demand with priority. Thus, G decreases a lot
because it is calculated by the supply shortage weighted by

100

Shortage Energy Rate [%]TABLE IT OTAL AND OUTAGE COSTS WHEN A 24- HOUR UNPREDICTABLE OUTAGEOCCURS AT 08:00 IN THE SUNLESS DAY.

No Margin
20% Margin

80

40% Margin
80% Margin

60
40
20
0

0

100

200

300

Cases

400

500

600

Fig. 6. Ratio of the total supply shortage (G) in descending order in themultiple outage scenarios.

the demand importance. In contrast, the worst 5 % values ofmax
D and Pshort
do not decrease so much because there aresupply shortages of unimportant demand and scenarios thatthe battery’s SoC is short.
C. Cost Reduction in Normal State
The battery can reduce electricity costs by charging anddischarging at electricity prices. However, the SoC margin
restricts the discharge in the normal state. Thus, higher margins
increase the costs in the normal state. The yearly optimization
without outages simulates the normal operation of the battery
with the PV. We compare the costs in the normal state among
different SoC margins. The objective function and constraints
are the same as in Section II, but the resolution is 30 minutes
to reduce the computational burden.
The yearly costs with different SoC margins are shown in
Table IV. The cost does not include the outage and initial costsof the battery and PV. The battery cannot charge and discharge
at an 80 % SoC margin, so the cost at an 80 % SoC marginequals the cost without the battery. This cost is higher thanwhen the battery can charge and discharge. The SoC marginincreases the cost. A 40 % SoC margin increases the cost by
16 % (18300 JPY) compared to the case without a margin.
In addition, the cost increase accelerates with an increase in
the margin. The accelerating increase in the cost is because
the battery loses the opportunity to reduce the cost, such asdischarge at high electricity prices, with a high SoC margin. In
contrast, with a small SoC margin, the battery actively charges
and discharges when there are fluctuations in electricity prices.
The battery’s energy discharged is 2.58 MWh without an SoC
margin. However, it decreases to 1.73 MWh (33 % decrease)with a 40 % SoC margin and zero with an 80 % SoC margin. In
conclusion, the SoC margin mitigates the risk of unpredictable
outages but increases the cost in the normal state.
IV. C ONCLUSION
This paper simulates the operation of the battery to reduce the residential supply shortage through the optimization
problem considering unpredictable outages. The battery only
sometimes has enough energy before unpredictable outages,
but the SoC margin reduces the supply shortage of importantTABLE III
W ORST 5 % OF RESILIENCE INDICES IN THE MULTIPLE OUTAGESCENARIOS .
SoC margin
0%
20 %
40 %
80 %

D [min]
1440
1440
1440
1032

max [kW]
Pshort
1.93
1.69
1.29
0.97

G [%]
74.8
56.8
36.7
12.1

TABLE IVY EARLY TOTAL COSTS CALCULATED BY THE OPTIMIZATION WITHOUTANY OUTAGE .
SoC margin
0%
20 %
40 %
80 %

Total cost [JPY]115200121300133500188500Difference [JPY](base)+6100+18300+73300demand. In addition, the SoC margin mitigates the damageof unpredictable outages, quantified by the outage cost. Compared to no SoC margin, the outage cost decreases by half
(2400 JPY) in a 24-hour unpredictable outage with a 40 %SoC margin. However, a high SoC margin restricts discharge
in the normal state and increases the yearly electricity cost by
16 % (18300 JPY) at a 40 % SoC margin. It shows a tradeoff
between a measure against unpredictable outages to decrease
discomfort and an operation to reduce the electricity cost.
This paper proposes resilience indices representing a supply
shortage’s duration, maximum power, and energy during an
outage. The SoC margin, in particular, effectively reduces
the index describing the energy of a supply shortage (G). It
decreases by 50 % at a worst 5 % value with a 40 % SoC
margin because the battery supplies electricity to importantdemand. These indices help evaluate the residential resilience,
considering the importance of demand.
In this paper, the value of the SoC margin is constant in one
optimization problem. However, it may unnecessarily restrict
the operation of the battery to reduce electricity costs. The
variable SoC margin, which is low in moderate situations
and high in severe situations, may balance resilience andeconomic operation. The method to set optimal and variable
SoC margins is our future work. In addition, the probabilityof large earthquakes is very small (twice within the past 25
years). It may be reasonable not to set the SoC margin fromthe view of stochastic optimization. A comprehensive analysisof the cost and mitigation is our future work.
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A PPENDIX
800

Grid PowerPV Generate
Battery Discharge

600

Supply Shortage
Battery Charge
Battery SoC

100
90

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Battery SoC [%]Electric Energy [Wh/5min]

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01/21 08:00 01/21 20:00 01/22 08:00 01/22 20:00 01/23 08:00 01/23 20:00 01/24 08:00 01/24 20:00

DateFig. A1. Power supply around a 24-hour predictable outage without an SoC
margin.

Shortage Duration [min]

1920
1680

No Margin
20% Margin

40% Margin
80% Margin

300

500

1440
1200
960
720
480
240
0

0

100

200

Cases

400

600

Fig. A2. Duration of the supply shortage (D) in descending order in themultiple outage scenarios.

Max Shortage Power [kW]3.5

No Margin
20% Margin

3

40% Margin
80% Margin

2.5
2
1.5
1
0.5
0

0

100

200

300

Cases

400

500

600

max ) in descending
Fig. A3. Maximum power of the supply shortage (Pshortorder in the multiple outage scenarios.