# Assessing the Reliability Benefits of Energy Storage as a Transmission Asset

David Sehloff, Jonghwan Kwon, Mahdi Mehrtash, Todd Levin, Benjamin F. Hobbs

###### Abstract

Utilizing energy storage solutions to reduce the need for traditional
transmission investments has been recognized by system planners and supported
by federal policies in recent years. This work demonstrates the need for
detailed reliability assessment for quantitative comparison of the reliability
benefits of energy storage and traditional transmission investments. First, a
mixed-integer linear programming expansion planning model considering
candidate transmission lines and storage technologies is solved to find the
least-cost investment decisions. Next, operations under the resulting system
configuration are simulated in a probabilistic reliability assessment which
accounts for weather-dependent forced outages. The outcome of this work, when
applied to TPPs, is to further equalize the consideration of energy storage
compared to traditional transmission assets by capturing the value of storage
for system reliability.

###### Index Terms:

Transmission expansion planning, joint resource and transmission expansion,
co-optimization, energy storage as transmission, reliability

##  I Introduction

New electricity transmission infrastructure and energy storage installations
are recognized as key enablers of meeting decarbonization goals while
maintaining the reliability of power systems. Traditionally, the services
these assets can provide have been treated as distinct, but recently, energy
storage has been considered as a potential source of transmission services.
Storage operated as a transmission asset may offer preferable capital costs
and construction timelines compared to traditional transmission solutions,
while bringing unique advantages for supporting the system and enhancing both
reliability and resilience.

The development of regulatory guidelines for this application of energy
storage is evolving in the United States. In 2017, the Federal Energy
Regulatory Commission (FERC) issued a policy statement allowing dual use of
energy storage assets, that is, cost recovery through both the regulated
transmission planning practices (TPPs) and participation in competitive
markets [1]. Between 2020 and 2023, FERC issued orders accepting proposals
from three independent system operators defining a new class of asset,
”Storage as Transmission-Only Asset” (SATOA). A storage installation of this
type may be selected through TPPs provided that it addresses a specific
transmission system need and follows other requirements ensuring it provides
only transmission services [2, 3, 4]. As a result, the Midcontinent
Independent System Operator considered a SATOA in its TPP and identified it as
superior to a transmission line, or _wires_ , solution, leading to its
selection and plans for permitting and construction [5]. Despite this movement
toward consideration of energy storage for transmission services, existing
TPPs have barriers and disincentives which make them inadequate for evaluation
of energy storage solutions [6], one of which is evaluation of the reliability
contributions of energy storage compared with traditional wires solutions.

The co-optimization of transmission and energy storage planning has been
assessed under various distinct perspectives. One common perspective is the
centralized co-planning of transmission and storage to avoid the need for new
transmission installations, thereby reducing investment costs [7, 8, 9, 10,
11]. Variations of this perspective include incorporation of security
constraints and high renewable penetration [12]. Konstantelos and Strbac
included additional flexible network and non-network solutions in this
centralized planning approach and demonstrated the value of these solutions in
reducing risk under uncertain evolution of system capacity [13]. Go et al.
took the perspective of co-planning generation, transmission, and energy
storage, showing the benefits of a co-optimization approach to reduce
investment costs while meeting renewable portfolio standard constraints [14].
Dvorkin et al. considered transmission and energy storage co-planning from the
perspective of a merchant energy storage owner in a multi-level framework
finding maximum energy storage system profit with centralized least-cost
transmission expansion decisions [15]. Aside from these approaches considering
avoided costs and profits, Zach and Auer compared transmission and energy
storage investments with a welfare maximization approach [16]. Kwon et al.
introduced a framework for optimal sizing and siting of energy storage as a
transmission asset in order to satisfy specific needs identified in TPPs [17].
However, previous studies primarily focus on the economic value of
transmission and storage investments, lacking consideration of the reliability
contributions of these investments.

Many approaches for assessing the reliability of power systems have been
applied to transmission expansion planning. The expected unserved energy (EUE)
is commonly used to capture the energy shortfall, for example in [18, 19], and
metrics such as loss of load expectation (LOLE) and loss of load hours (LOLH)
can provide additional insights into the temporal nature of shortfalls [20].
Similar probabilistic metrics have been introduced, such as loss of load cost
(LOLC) [21]. An alternative to probabilistic reliability metrics is to ensure
robustness to a defined set of transmission and generation contingencies
through $N-1$ [22] or $N-k$[23, 24] security constraints. The 2022 IEEE
Composite Power System Reliability report [25] highlights the need to develop
composite system reliability methods which incorporate storage, common and
dependent mode failure models, and weather conditions into composite system
reliability analysis. Sundar et al. [26] applied temperature-dependent forced
outage rates to natural gas combined cycle and hydropower plants for resource
adequacy assessment, not considering the transmission network. Other studies
including [27, 28] have considered uncertainty from renewable generation and
included representation of the transmission system, but they do not model
weather-dependent or correlated generation outages.

Means for assessing the reliability value of energy storage have been a
subject of much recent work, as briefly reviewed in [29]. Stephen et al.
demonstrated that the approach by which storage dispatch is modeled can have a
large impact on resource adequacy metrics [30], particularly whether system
reliability (as in [31, 32, 33, 34]) or economic performance (as in [35]) is
the assumed dispatch objective. However, these studies focus on resource
adequacy with limited or no modeling of the transmission system and do not
take into account the concept of SATOA in assessing the reliability values.

This study considers the viewpoint of a system operator co-optimizing
transmission and energy storage for least-cost investment and operations and
introduces a framework to quantify the reliability contribution that energy
storage as a transmission asset provides at a system level and to compare
these benefits with those of transmission upgrades.

This study is the continuation of the conference paper [36], which was
presented at the Texas Power and Energy Conference (TPEC 2023). The main
contribution of [36] was to show the advantage of joint resource and
transmission expansion planning in comparison with the resource-only expansion
planning and project-by-project screening of expansion plans considering
different future scenarios representing uncertainties that exist in emission
reduction policies and forecasted demand. This article significantly extends
the authors’ previous work [36] by conducting a comparative analysis of
reliability outcomes stemming from various investment strategies: focusing
solely on transmission, solely on storage, or permitting investments in both.
The aim is to gain comprehensive insights into the reliability contributions
offered by SATOA and traditional transmission lines.

The contributions of this paper are the following:

  * •

An analysis framework that supports the assessment of the economic and
reliability value of both SATOA and traditional transmission assets.

  * •

A composite reliability assessment model considering weather-dependent
correlated generator outages, pre- and post-contingency operations including
storage as a transmission only asset, and the transmission network represented
with a DC power flow model

  * •

A case study demonstrating this framework for a representative high-renewable,
limited-transmission system, including findings highlighting the importance of
capturing reliability contributions of transmission assets including storage
in transmission planning, demonstrating that SATOA can offer comparable
benefits to transmission line investments.

The remainder of the paper is organized as follows. Section II presents the
methodology for the transmission and energy storage expansion planning and the
probabilistic reliability assessment and their coupling, Section III presents
a case study on a simplified ERCOT-like system, and Section IV concludes.

##  II Methods

This section presents an overview of the two-stage analysis framework, as
shown in Fig. 1, employed in this study. In the first stage, the Johns Hopkins
Stochastic Multi-stage Integrated Network Expansion (JHSMINE) model was
utilized for optimal planning of transmission and storage expansion. In the
second stage, the expansion decisions derived from JHSMINE are passed to the
Argonne Low-carbon Electricity Analysis Framework (A-LEAF) for a comprehensive
probabilistic reliability assessment.

Figure 1: Overview of the analysis framework. The expansion planning process,
described in subsection II-A, selects optimal size and location of storage and
transmission assets, and the probabilistic reliability assessment, described
in subsection II-B, simulates operations under random generation outage
scenarios and computes reliability metrics.

###  II-A Transmission and Storage Expansion

JHSMINE is a cost-minimizing capacity expansion planning tool that considers
several significant aspects of the expansion planning models such as unit
commitment, linearized power flow, renewable energy policies and energy
trading credits, etc., and has been used in several projects [37, 36, 38]. In
this paper, JHSMINE is used to find expansion planning solutions with three
different cases. In the first case, only the transmission investment option is
active. In the second case, storage investment is the only available option.
Lastly, in the third case, both transmission and storage investments are
considered as investment options. It is intuitive that conducting joint
storage and transmission expansion planning reduces costs relative to the
cases that allow either transmission-only or storage-only expansion planning.
However, assessing all three of these cases allows us to evaluate the
contribution of each individual technology to system reliability. Although
JHSMINE is capable of running a stochastic multistage expansion planning
model; here we apply its deterministic expansion planning mode for a single
planning horizon.

The objective function of JHSMINE is to minimize the probability-weighted of
total system cost as represented by (1). The objective function consists of
two terms: investment cost and operation cost, and both are realized at the
scenario tree node $(s,y)$, where $s$ and $y$ are indices for scenarios and
years, respectively. JHSMINE discounts the investment cost back to the
beginning of the planning horizon using $D_{y}$, where $\delta$ is the
interest rate. JHSMINE assumes that the operation condition (e.g., load,
policies, fuel price, etc.) of operation node will repeat until the next
operation simulation interval. All cash flows for operations are assumed to be
end-of-year flows, and the discounting formulas are defined accordingly as
$DA_{y}$.

$\displaystyle\begin{aligned} \hbox to0.0pt{$\min\quad
obj=\sum_{\left(s,y\right)}{SP_{s,y}}\left(D_{y}\cdot invc_{s,y}+DA_{y}\cdot
oprc_{s,y}\right),$\hss}&\\\ \quad&D_{y}=1/(1+\delta)^{y-y_{origin}},\\\
\quad&DA_{y}=D_{y}\cdot
P\left(1,Y_{y},\delta\right)=D_{y}\left(\sum_{t=1}^{Y_{y}}\frac{1}{\left(1+\delta\right)^{t}}\right)\end{aligned}$
(1)

JHSMINE calculates the investment cost of new facilities using (2), which
includes the expansion costs of facilities that are newly expanded and the
salvage revenue for facilities that are newly retired.

$\displaystyle invc_{s,y}\\!$
$\displaystyle=\\!GEXC_{s,y,k}\\!\cdot\\!gincexp_{s,y,k}$
$\displaystyle\hfill-\sum_{\mathclap{\left(s^{\prime},y^{\prime}\right)}}\\!{GSAL_{s,y,k}\\!\cdot\\!gincret_{s,y,k}}+LEXC_{s,y,l}\\!\cdot\\!lincexp_{s,y,l}$
$\displaystyle\hfill-\sum_{\mathclap{\left(s^{\prime},y^{\prime}\right)}}\\!{LSAL_{s,y,l}\\!\cdot\\!lincret_{s,y,l}}+EEXC_{s,y,j}\\!\cdot\\!eincexp_{s,y,j}$
$\displaystyle\hfill-\sum_{\mathclap{\left(s^{\prime},y^{\prime}\right)}}\\!{ESAL_{s,y,j}\\!\cdot\\!eincret_{s,y,j}}$
(2)

JHSMINE calculates the operation cost using (3), which is composed of seven
terms: the fixed operation and maintenance (O&M) cost of generation and
storage facilities represented by (4); the variable O&M cost of generation and
storage operations modeled by (5); the fuel cost of generation and storage
operations shown in (6); the start-up cost from generation unit commitment
represented by (7); and finally the value of lost load modeled by (8).

$\displaystyle oprc_{s,y}=fomc_{s,y}+vomc_{s,y}+stuc_{s,y}+voll_{s,y}$ (3)
$\displaystyle fomc_{s,y}=\sum_{k}{GFOM_{k}\cdot GNPL_{k}\cdot gstat_{s,y,k}}$
$\displaystyle\hfill+\sum_{j}{EFOM_{j}\cdot EGCP_{j}\cdot estat_{s,y,j}}$ (4)
$\displaystyle
vomc_{s,y}=\sum_{rp,h}\\!RPW_{y,rp}\\!\Bigg{(}\\!\sum_{k}\\!{GVOM_{k}\\!\cdot\\!gopt_{s,y,rp,h,k}}$
$\displaystyle\hfill+\sum_{j}{EVOM_{j}\cdot edis_{s,y,rp,h,j}}\Bigg{)}$ (5)
$\displaystyle
fuelc_{s,y}=\sum_{rp,h}RPW_{y,rp}\Bigg{[}\sum_{f}FC_{s,y,f,rp,h}$
$\displaystyle\hfill\\!\cdot\\!\left(\\!\sum_{k\in
K_{f}}\\!{\\!GHR_{k}\\!\cdot\\!gopt_{s,y,rp,h,k}}\\!+\\!\sum_{\mathclap{j\in
J_{f}}}\\!{EHR_{j}\\!\cdot\\!edis_{s,y,rp,h,j}}\\!\right)\\!\Bigg{]}$ (6)
$\displaystyle stuc_{s,y}=\sum_{rp,h}RPW_{y,rp}$
$\displaystyle\hfill\cdot\left(\sum_{k}{GSUC_{k}\cdot GNPL_{k}\cdot
gsup_{s,y,rp,h,k}}\right)$ (7) $\displaystyle
voll_{s,y}=\sum_{rp,h}{RPW_{y,rp}\\!\cdot\\!VOLL\left(\sum_{i}{nload_{s,y,rp,h,i}}\right)}$
(8)

The feasibility space of JHSMINE is constructed by a set of equality
constraints and a set of inequality constraints. Among the equality
constraints are nodal power balances in the system, DC power flow
representation, energy balances for storage, etc. The set of inequality
constraints includes thermal limits of transmission lines, output power limit
of generating units, energy storage representations, etc. [29], [30]. The unit
commitment constraints in JHSMINE are expanded based on the “Tight Relaxed
Unit Commitment” (TRUC) Constraints in [39], For classic unit commitment
without generation expansion, readers are referred to [40] and [41]. Under
TRUC, unit commitment variables, i.e., operating status, start-up, and shut-
down variables, can be relaxed; in the meanwhile, each unit commitment
constraint is still physically meaningful. For the power flow representation,
a disjunctive version of the DC Optimal Power Flow (DCOPF) is modeled in
JHSMINE. The detailed model formulations of JHSMINE, including the set of
constraints, can be found in [42].

###  II-B Probabilistic Reliability Assessment

A-LEAF is an integrated power system simulation framework that includes a
suite of generation and transmission capacity expansion, unit commitment, and
system reliability assessment models111https://www.anl.gov/esia/a-leaf. In
this paper, we employ the probabilistic reliability assessment model in
A-LEAF, which conducts Monte Carlo simulations to quantify the risk of
unserved energy (i.e., the system’s reliability level) and calculates various
reliability metrics. Furthermore, the reliability assessment model was
enhanced to specifically consider the operation of SATOA.

Inputs to the reliability assessment model include the generation portfolio,
generator and storage characteristics, transmission topology, and time series
data for load, temperature, and variable renewable energy availability. The
model first generates outage scenarios for each generating asset in the system
using a two-state Markov model. This model captures the dynamic evolution of
individual unit-level outage states over time. During each distinct time
period, the availability state of each generating asset is stochastically
determined, taking into account the unit’s state transition probabilities. In
this study, we utilized weather-dependent state transition probabilities that
are calculated using the methodology outlined in [43]. After generating outage
scenarios, the model conducts a Monte Carlo simulation with a two-stage
structure, as shown in Fig 2. In the first stage, the model solves an economic
dispatch problem for each operating day to obtain steady-state dispatch
setpoints for all the resources. The model does not dispatch the SATOA
resources in the first stage because, by definition, these resources should
maintain their full state-of-charge (SOC) levels to be used when the system
has contingencies. In the second stage, for each outage scenario, the model
solves a post-contingency system re-dispatch problem to assess the system’s
ability to handle generator outages and determine expected unserved energy.
The transition between the steady-state dispatch schedule and the post-
contingency redispatch is constrained by both available headroom and the ramp
rate of individual assets. In addition, the second stage simulates the post-
contingency cases in a myopic way, meaning that it performs hour-by-hour
simulations without anticipating future outages in the redispatch algorithm.
The outcomes from all trials are then used to compute reliability metrics,
such as EUE and LOLH. In this paper, we present the second stage model
formulation in (9)-(28). The second stage model solves the following
optimization problem for each time period during a post-contingency event.

$\displaystyle\min$
$\displaystyle\quad\sum_{it}{\left({MC}_{i}\left(d_{it}^{up}+d_{it}^{dn}\right)+\sum_{nt}{\left(VOLL\cdot{ens}_{nt}\right)}\right)}$
(9)
$\displaystyle-\left(\sum_{k\left(n,\right)}f_{kt}-\sum_{k\left(,n\right)}f_{kt}\right)+\quad\sum_{\mathclap{i,Bus\left(i\right)=n}}g_{it}\quad-\qquad\sum_{\mathclap{i,Bus\left(i\right)=n,i\in\mathrm{\Psi}_{ES}}}{chg}_{it}$
$\displaystyle\hfill+{ens}_{nt}-D_{nt}=0,\qquad\forall n\in N$ (10)

$\displaystyle f_{kt}$ $\displaystyle=\sum_{n}{PTDF_{kn}\cdot p_{nt}^{inj}},$
$\displaystyle\forall k\in K$ (11) $\displaystyle p_{nt}^{inj}$
$\displaystyle=\sum_{\mathclap{i,Bus\left(i\right)=n}}g_{it}\,-\quad\sum_{\mathclap{i,Bus\left(i\right)=n,i\in\mathrm{\Psi}_{ES}}}{\left({chg}_{it}\,+{ens}_{nt}-D_{nt}\right)},$
$\displaystyle\forall n\in N$ (12) $\displaystyle-F_{k}^{+}$
$\displaystyle\leq f_{kt}\leq F_{k}^{+},$ $\displaystyle\forall k\in K$ (13)

$\displaystyle g_{it}\leq S_{it}{CAP}_{i},$ $\displaystyle\forall i\in
I\in\mathrm{\Psi}_{VRE}^{FIX}$ (14) $\displaystyle 0\leq{soc}_{it}\leq
SOC_{i}^{+},$ $\displaystyle\forall i\in I\in\mathrm{\Psi}_{ES}$ (15)
$\displaystyle{soc}_{it}\\!-\\!{\bar{SOC}}_{i,t-1}\\!-\\!\epsilon_{i}^{C}{chg}_{it}\\!+\\!\frac{1}{\epsilon_{i}^{D}}g_{it}\\!=0,$
$\displaystyle\forall i\in I\in\mathrm{\Psi}_{ES}$ (16) $\displaystyle
g_{it}={\bar{G}}_{it}+d_{it}^{up}-d_{it}^{dn}$ $\displaystyle\forall i\in I$
(17)
$\displaystyle\sum_{i}{C_{cit}(g_{it}-chg_{it})}-\sum_{i}{C_{cit}\left({\bar{G}}_{it}-{\bar{CHG}}_{it}\right)}$
$\displaystyle\hfill\leq\sum_{i}{({1-C}_{cit})}({\bar{G}}_{it}-{\bar{CHG}}_{it})$
(18) $\displaystyle g_{it}\leq C_{cit}{CAP}_{i}$ $\displaystyle\forall i\in I$
(19) $\displaystyle{chg}_{it}\leq C_{cit}{CAP}_{i}$ $\displaystyle\forall i\in
I$ (20) $\displaystyle d_{it}^{up}\leq{CAP}_{i}R_{i}^{10}$
$\displaystyle\forall i\in I$ (21) $\displaystyle
d_{it}^{dn}\leq{CAP}_{i}R_{i}^{10}$ $\displaystyle\forall i\in I$ (22)
$\displaystyle{chg}_{it}-{\bar{CHG}}_{it}\leq{CAP}_{i}R_{i}^{10}$
$\displaystyle\forall i\in I$ (23)
$\displaystyle{-chg}_{it}+{\bar{CHG}}_{it}\leq{CAP}_{i}R_{i}^{10}$
$\displaystyle\forall i\in I$ (24) $\displaystyle
g_{it}-{\bar{G}}_{it-1}\leq{CAP}_{i}R_{i}^{H}$ $\displaystyle\forall i\in I$
(25) $\displaystyle{\bar{G}}_{it-1}-g_{it}\leq{CAP}_{i}R_{i}^{H}$
$\displaystyle\forall i\in I$ (26)
$\displaystyle{chg}_{it}-{\bar{CHG}}_{it-1}\leq{CAP}_{i}R_{i}^{H}$
$\displaystyle\forall i\in I$ (27)
$\displaystyle{\bar{CHG}}_{it-1}-{chg}_{it}\leq{CAP}_{i}R_{i}^{H}$
$\displaystyle\forall i\in I$ (28)

The objective function (9) minimizes the cost of load shedding and the
redispatch of generators. System operating constraints are enforced through
the system balance equation (10) and PTDF-based power flow constraints
(11-13). The scheduling of variable renewable energy assets is bounded by the
hourly generation profiles in (14). The model tracks the SOC of energy storage
assets with upper and lower bounds in (15-16). The generation redispatch in
each hour of a post-contingency event is constrained by equations (17-28).
Specifically, generation redispatch is represented as deviations from the
steady-state dispatch setpoint in (17). Constraint (18) ensures that the total
amount of generation redispatch is less than the total generation lost,
considering the potential of load shedding. Asset availability during the
post-contingency is captured in (19) and (20) by the generator availability
status, $C_{cit}$, which has a value of one if an asset is available. The
deviations from the steady-state setpoints are restricted by ramp rate
constraints in (23-24). Lastly, the inter-temporal constraints between the
current and previous periods are enforced by equations (25-28).

Figure 2: Overview of the Monte Carlo simulation in the reliability assessment
model. The black box represents the steady-state system operation for each
hour, while the red box illustrates the post-contingency system re-dispatch
phase

##  III Case Study

This section presents a case study demonstrating the framework on an
aggregated version of the Texas power system.

###  III-A Description

The network used in this case study is a simplified representation of the
Electric Reliability Council of Texas (ERCOT) system, aggregated to seven
zones as shown in Fig. 3. These zones are balancing areas defined in [44],
from which we source our zonal load and wind and solar resource data. Table I
gives the non-coincident peak values for each zone.

Figure 3: The network used in the case study, an aggregated ERCOT system which
preserves individual generator units.

Generation units and parameters are also taken from [44], which is based on
published data for real units. Each generation unit in the system is assigned
to a zone but still modeled individually in both the simulation of outages and
the optimization of dispatch. Table I gives the total capacity by zone and by
resource type. The type “NG” includes natural gas simple cycle combustion
turbine and combined cycle plants, and “OGS” represents any oil or gas steam
plants.

TABLE I: Generation capacity and peak load by zone. Zone | Capacity by Resource Type (MW) | Peak Load (MW)
---|---|---
Coal | Hydro | NG | Nuclear | OGS | Solar | Storage | Wind | Total
1 | 2,514 | 0 | 8,956 | 0 | 1,163 | 480 | 110 | 0 | 13,223 | 19,381
2 | 0 | 0 | 1,317 | 0 | 0 | 2,311 | 184 | 9,710 | 13,523 | 1,179
3 | 3,231 | 37 | 7,734 | 2,560 | 1,739 | 521 | 311 | 8,413 | 24,546 | 12,897
4 | 7,047 | 124 | 15,060 | 2,400 | 5,298 | 3,158 | 150 | 3,168 | 36,405 | 30,673
5 | 1,615 | 315 | 6,386 | 0 | 1,443 | 197 | 11 | 0 | 9,967 | 8,547
6 | 0 | 0 | 2,109 | 0 | 0 | 2,478 | 86 | 2,563 | 7,236 | 1,840
7 | 0 | 58 | 0 | 0 | 0 | 3,036 | 4 | 5,927 | 9,025 | 1,838
Total | 14,407 | 534 | 41,562 | 4,960 | 9,642 | 12,181 | 856 | 29,782 | 113,923 | -

The transmission network used in this case study is an aggregated, synthetic
network that is based on the existing transmission lines in the ERCOT system.
The network is constructed by estimation of topology and line parameters using
publicly available geographic data from the Homeland Infrastructure
Foundation-Level Data [45] and aggregated to a zonal DC power flow model using
the methods introduced in [46]. Each inter-zonal link is represented by its
reactance and thermal capacity, as shown in Table II.

TABLE II: Aggregated transmission link parameters. From Zone |  To Zone |  Reactance (p.u.) |  Thermal Capacity (MW)
---|---|---|---
1 |  3 |  0.0042 |  5,294
1 |  5 |  0.0024 |  5,109
2 |  4 |  0.0018 |  14,463
2 |  6 |  0.0036 |  6,610
2 |  7 |  0.0016 |  3,497
3 |  5 |  0.0010 |  10,478
3 |  7 |  0.0115 |  283
4 |  5 |  0.0015 |  9,731
4 |  7 |  0.0177 |  3,384
5 |  7 |  0.0126 |  3,164
6 |  7 |  0.0033 |  2,928

###  III-B Transmission and Storage Expansion

The JHSMINE transmission and storage expansion model is applied to this system
to find optimal expansion decisions for each of three cases: transmission
expansion (TEP), battery storage expansion (BEP), and joint battery storage
and transmission expansion (BTEP). The single peak load hour of each day is
considered, for a total of 365 unique operating conditions. Due to this daily
resolution, generator ramp constraints and battery charging and discharging
ramp constraints are not modeled in the expansion problem, but they are
considered in the detailed reliability assessment. The TEP problem represents
a TPP scenario in which the interface between Zone 3 and 7 has been identified
as a limiting constraint, and planners seek the optimal sizing of the upgrade
based on a least-cost expansion formulation. This link may be upgraded to
increase its thermal capacity at a cost of 1.6 thousand USD per MW-mile, with
the MW increase modeled as a continuous variable between 0 and 3,000 MW. The
BEP problem represents an alternative approach which considers energy storage
as candidate upgrades throughout the system. We consider a generic four-hour
duration battery energy storage system (BESS) that can be installed in any
zone in 400 MW increments up to 1,200 MW total, with an investment cost of
0.35 million USD per MWh. The BTEP problem represents a combination of the TEP
and BEP, allowing co-optimization of link 3-7 upgrade and storage investments.

Table III shows the optimal expansion results of each problem. The TEP
resulted in an upgrade to increase the capacity of this link by 1,495 MW, at a
cost of 80.46 million USD, resulting in very large operational cost savings.
The reason for this is that the alleviation of this severe transmission
constraint allows the renewable production in Zone 7 to be sent to other
zones, significantly reducing curtailment of these resources. No storage
solution in this example was able to offer this benefit, or any operational
benefit outweighing the investment cost, as the results of the BEP show no
storage investments. The BTEP result further shows that no storage investment
resulted in a net benefit, even if coupled with the transmission upgrade. It
is important to note that no load shedding is observed throughout the 365
periods of operation in the expansion analysis with JHSMINE.

TABLE III: Expansion planning results. Case |  BTEP |  BEP |  TEP
---|---|---|---
Annual operation cost (B$) |  4.337 |  6.657 |  4.337
Line investment cost (M$) |  80.46 |  0 |  80.46
Storage investment cost (M$) |  0 |  0 |  —
Selected lines |  3-7 (1,495 MW) |  0 |  3-7 (1,495 MW)
Selected storage |  — |  — |  —

###  III-C Assessing Reliability Benefits of Potential Expansion Decisions

Next, the reliability is assessed using A-LEAF. To better understand the
reliability contributions associated with SATOA additions, ten candidate
storage installations are examined in Zone 3, including two- and four-hour
systems with capacities ranging from 300 MW to 1500 MW. To assess the
reliability, we first generate a set of 1,000 random generator outage
scenarios for each hour of the year, then we simulate operations under each of
the configurations for each outage scenario. Finally, for each configuration,
we compute the EUE and LOLH from the outcomes of all scenarios. The
reliability assessment model simulates system dispatch across all 8,760 hourly
periods in the year. The inclusion of these operational details and
contingency modeling enables the reliability outcomes under each configuration
to be captured with greater accuracy.

In contrast to the expansion model, unserved load is observed under each
configuration. Fig. 4 shows the EUE by zone for each configuration. The TEP
result gives a significant improvement compared to the reference case. The
energy storage investments demonstrate improvements which increase with
storage capacity, from a slight improvement over the reference case with a 2
hour, 300 MW system, to a large improvement with a 4 hour, 1500 MW system. The
storage investments do not outperform the transmission expansion planning
results, however. Table IV shows the EUE values for the reference, TEP, and
three of the storage configurations in greater detail. The values in the table
are in MWh, followed by the relative change compared to the reference case as
a percentage in parentheses. In the reference and storage cases, the EUE in
Zone 3 is the largest of any zone. The TEP result completely eliminates the
unserved energy in Zone 3, though several other zones experience increases in
EUE. This demonstrates that transmission upgrades may lead to significant
changes in the patterns of generation dispatch and power flow through a
network, potentially influencing the distribution of reliability throughout
the network.

TABLE IV: Annual expected unserved energy by zone under the reference, transmission expansion, and three storage cases. | Annual Expected Unserved Energy (MWh)
---|---
Zone | Reference | TEP (_Relative_) |  Storage(4h 1500MW) (_Relative_) |  Storage(4h 600MW) (_Relative_) |  Storage(2h 600MW) (_Relative_)
1 | 138.4 | 201.9  (+45.8%) | 100.3  (-27.6%) | 125.9  (-9.0%) | 130.8  (-5.5%)
2 | 5.5 | 399.9  (+7197.5%) | 6.9  (+25.1%) | 6.5  (+19.1%) | 5.7  (+3.5%)
3 | 5717.1 | 0.0  (-100.0%) | 1552.6  (-72.8%) | 3423.0  (-40.1%) | 4267.3  (-25.4%)
4 | 0.0 | 27.3  — | 0.0  — | 0.0  — | 0.0  —
5 | 0.0 | 0.0  — | 0.0  — | 0.0  — | 0.0  —
6 | 0.0 | 14.2  — | 0.0  — | 0.0  — | 0.0  —
7 | 3.4 | 282.9  (+8264.5%) | 1.7  (-49.3%) | 2.4  (-28.3%) | 3.0  (-11.9%)
Systemwide | 5864.4 | 926.2  (-84.2%) | 1661.4  (-71.7%) | 3557.9  (-39.3%) | 4406.7  (-24.9%)

Similarly, Fig. 5 shows the LOLH by zone for each configuration, and Table V
gives additional detail. The TEP again gives the best performance under this
metric. The storage solutions result in relative improvements in LOLH which
are quite similar to their improvements in EUE. The TEP solution also results
in similar relative improvements in LOLH as it does in EUE.

TABLE V: Annual loss of load hours by zone under the reference, transmission expansion, and three storage cases. | Annual Loss of Load Hours (h)
---|---
Zone | Reference | TEP (_Relative_) |  Storage(4h 1500MW) (_Relative_) |  Storage(4h 600MW) (_Relative_) |  Storage(2h 600MW) (_Relative_)
1 | 0.34 | 0.54  (+57.4%) | 0.27  (-21.3%) | 0.32  (-6.7%) | 0.33  (-3.5%)
2 | 0.03 | 0.65  (+2492.0%) | 0.03  (+8.0%) | 0.03  (+20.0%) | 0.03  (+12.0%)
3 | 5.79 | 0.00  (-100.0%) | 1.62  (-71.9%) | 3.61  (-37.6%) | 3.96  (-31.5%)
4 | 0.00 | 0.03  — | 0.00  — | 0.00  — | 0.00  —
5 | 0.00 | 0.00  — | 0.00  — | 0.00  — | 0.00  —
6 | 0.00 | 0.03  — | 0.00  — | 0.00  — | 0.00  —
7 | 0.01 | 0.25  (2644.4%) | 0.00  (-55.6%) | 0.01  (-44.4%) | 0.01  (0.0%)
Systemwide | 6.16 | 1.49  (-75.8%) | 1.93  (-68.8%) | 3.97  (-35.7%) | 4.33  (-29.7%)
Figure 4: Annual expected unserved energy (EUE) in each zone under the
Transmission Expansion (TEP), Battery Expansion (BEP, by zone in which the
battery is installed), and Reference cases. Figure 5: Annual loss of load
hours (LOLH) in each zone under the Transmission Expansion (TEP), Battery
Expansion (BEP, by zone in which the battery is installed), and Reference
cases.

The lost load events which make up the annual metrics in Tables IV and V occur
on a relatively small number of days. This can be seen in Fig. 7, which shows
the EUE by zone in the TEP, BEP, and Reference cases on the four days with the
highest lost load. August 2nd and 1st experience the most severe shortfalls,
accounting for 53% of the yearly EUE in the reference case. The behavior
exhibits a similar pattern across the four days.

Figure 6: Example of a single sample outage scenario on August 2. Each plot
shows the generation, demand, and unserved energy. The rows represent each
zone, and the columns represent the Reference, storage (4 h 1500 MW), and TEP
configurations. Figure 7: Expected unserved energy (EUE) in each zone by day,
for the four days which have the highest EUE under the Transmission Expansion
(TEP), Storage in Zone 3, and Reference cases.

Fig. 6 shows the hourly dispatch by generation type for one sample outage
scenario on August 2nd. The rows of the figure make up the results for all the
zones, and the columns represent the results under the Reference, BEP in Zone
3, and TEP configurations, respectively. The realization of the stochastic
characteristics in this single sample are identical between the three
configurations; any differences across the three columns are only the result
of the storage or transmission additions. Overlaid on each plot are the hourly
demand profiles in black, along with a red area representing any unserved
energy in the zone. The system outcomes shown in Fig. 6, though only
representing a single sample on a single day (Aug. 2nd) are illustrative of
several observed across reliability metrics. In the storage configuration, the
new storage installed in Zone 3 is discharged in hours 12 through 16,
contributing to a decrease in unserved energy in this zone. The reduced
curtailment of wind and photovoltaic generation in Zone 7 can be seen in the
TEP solution, as well as the unserved load event that occurs in hour 15 in
that zone.

###  III-D Cost and Reliability

In order to compare the reliability outcomes between the expansion
configurations, we compute the cost of reduction of both expected unserved
energy and loss of load hours by dividing the annual investment costs shown in
VI by the reduction in each metric compared with the reference case. Fig. 8
shows these costs for the storage configurations in Zone 3 and for the TEP
configuration. The TEP configuration offers the lowest cost of reliability
improvements in both EUE and LOLH. The costs of reliability improvements under
the storage options are slightly higher in this case. The smaller storage
units, however, give more comparable costs of improvement and offer lower
capital costs, potentially allowing more to be placed throughout the network
in situations where more distributed application is advantageous. Note that
this comparison does not include other values, such as operational cost
savings, that could result from these investments. Operational savings may
often present an advantage of transmission investments compared to SATOA
investments, since SATOA must reserve its capacity for essential transmission
services.

Figure 8: Capital cost of reduction of expected unserved energy and loss of load hours under the BEP configurations with a battery in Zones 3 and 5 and the TEP configuration. TABLE VI: Annualized cost of each upgrade. Upgrade | Cost (M$/annum)
---|---
Storage: 2h, 300MW | 19.8
Storage: 2h, 600MW | 39.6
Storage: 2h, 900MW | 59.5
Storage: 2h, 1,200MW | 79.3
Storage: 2h, 1,500MW | 99.1
Storage: 4h, 300MW | 39.6
Storage: 4h, 600MW | 79.3
Storage: 4h, 900MW | 118.9
Storage: 4h, 1,200MW | 158.6
Storage: 4h, 1,500MW | 198.2
TEP | 80.7

##  IV Conclusions

This paper presents a two-stage analysis framework to quantify the reliability
benefits of transmission assets, including SATOA. The framework consists of an
optimal storage and transmission expansion planning methodology formulated as
a mixed integer linear program using a DC power flow representation, along
with a probabilistic reliability assessment methodology that simulates system
operations under stochastic generator outage scenarios.

This framework is used to demonstrate that transmission and storage each may
be identified as appropriate solutions for different aspects of reliability
needs. Traditional least cost expansion tools provide valuable insights but
may not capture factors which influence reliability, such as correlated
generator outages, and they need to be coupled or integrated with detailed
reliability assessment to quantitatively evaluate of the reliability benefits
of storage as a transmission asset. The case study presented here demonstrated
that the upgrade of a severely constrained transmission corridor connecting a
zone with excess renewable generation to a high-load zone with poor
reliability was optimal from a least-cost expansion perspective and also
provided significant reliability benefits. Storage as a transmission asset was
not able to outperform the reliability contributions of the transmission
upgrade in this scenario, but large storage installations achieved nearly
comparable improvements of 71.7% in EUE and 68.8% in LOLH, compared to the TEP
solution’s 84.2% and 75.8%, respectively. In addition, smaller storage
additions showed capital costs per unit improvement of 25.1 thousand USD/MWh
EUE reduction and 21.9 million USD/h LOLH reduction, compared to 16.3 thousand
USD/MWh and 17.3 million USD/h, respectively, under the TEP solution. Given
the lower total cost and potentially greater feasibility of installation,
storage solutions for incremental improvements may offer advantages in certain
cases. This underscores the need for planning tools which accurately assess
both the economic and reliability contributions of both traditional
transmission and storage as transmission only solutions for quantitative
comparisons of which solution best meets the planning needs at hand.

This work also points to several important future directions. The inability of
SATOA to bring operational savings due to its exclusion from market
participation may be a barrier to its adoption. The reliability implications
of allowing partial market participation should be studied. In the case study,
the aggregated network obscures detailed power flow constraints and therefore
potentially underestimates transmission congestion and its reliability
impacts. A finer network resolution would more accurately capture whether the
reliability benefits of storage are primarily realized locally or
alternatively whether they can be allocated across the system via existing
transmission infrastructure. Incorporating a forced outage model for
transmission lines would also improve the characterization of the reliability
benefits of each transmission asset. Future work includes the application of
the framework with more detailed transmission network models to reflect these
complex effects of congestion as well as the incorporation of models of
weather-dependent transmission outage behavior. Additional future work will
examine the participation of energy storage both as a transmission and market
asset, identifying operational constraints which can enable this dual use
while maintaining reliability benefits.

## Nomenclature

### JHSMINE Sets and Indices

$F$

Fuel types, index $f$.

$G$

Generation technologies, index $g$.

$H$

Hours within a representative period (e.g., 24 hours), index $h$.

$I$

Buses, index $i$.

$J$

Energy storages, index $j$.

$K$

Generators, index $k$.

$L$

Transmission lines, index $l$.

$RP$

Representative periods, index $rp$.

$S$

Scenarios, index $s$.

$T$

Hours of a planning period (e.g., 8760 hours), index $t$.

$W$

States/Provinces, index $w$.

$Y$

Years, index $y$.

### JHSMINE Parameters

$CTAX_{s,y,w}$

Carbon price or tax of state $w$ in the scenario tree node $(s,y)$, unit $/ton
CO2e.

$D_{y}$

Discounting factor of year $y$ to the beginning of the planning horizon.

$DA_{y}$

Accumulative discounting factor of year $y$ to the beginning of the planning
horizon.

$EER_{j}$

Emission rate of the storage facility $j$, unit ton CO2e/MWh.

$EEXC_{s,y,j}$

Expansion cost of the storage facility $j$ in scenario tree node $(s,y)$, unit
M$.

$EFOM_{j}$

Fixed O&M cost of the storage $j$, unit $/MW-year.

$EHR_{j}$

Heat rate of the storage $j$, unit MMBTU/MWh.

$ESAL_{s,y,j,s^{\prime},y^{\prime}}$

Salvage revenue of storage facility $j$ if expanded in the scenario tree node
$(s^{\prime},y^{\prime})$ and retired in node $(s,y)$, unit M$.

$EVOM_{j}$

Variable O&M cost of the storage $j$, unit $/MWh.

$FC_{s,y,rp,h,f}$

Price of the fuel $f$ at hour $h$ of representative period rp in scenario tree
node $(s,y)$, unit $/MMBTU.

$GER_{k}$

Emission rate of the generator $k$, unit tonCO2e/MWh.

$GEXC_{s,y,k}$

The expansion cost of the generator $k$ in scenario tree node $(s,y)$, unit
M$.

$GFOM_{k}$

Fixed operating and maintenance cost of the generator $k$, unit $/MW-year.

$GHR_{k}$

Average heat rate of generator $k$, unit MMBTU/MWh.

$GNPL_{k}$

Nameplate capacity of the generator $k$, unit MW.

$GSAL_{s,y,k,s^{\prime},y^{\prime}}$

The salvage revenue of the generator $k$ if it is expanded in scenario tree
node $(s^{\prime},y^{\prime})$ and retired in the node $(s,y)$, unit M$.

$GSUC_{k}$

Start-up cost of generator $k$ per unit of the capacity, unit $/MW.

$GVOM_{k}$

Variable operating and maintenance cost of the generator $k$, unit $/MWh.

$LEXC_{s,y,l}$

Expansion cost of the transmission line $l$ in the scenario tree node $(s,y)$,
unit M$.

$LSAL_{s,y,l,s^{\prime},y^{\prime}}$

Salvage revenue of the transmission line $l$ if it is built in the scenario
tree node $(s^{\prime},y^{\prime})$ and retired in the node $(s,y)$, unit M$.

$RACP_{w}$

Alternative compliance penalty for RPS of state $w$, unit $/MWh

$RPW_{y,rp}$

# of periods represented by representative period $rp$ in year $y$.

$SP_{s,y}$

Scenario probability, unitless.

$VOLL$

Value of lost load, unit $/MWh.

### JHSMINE Variables

#### Expansion and Retirement

$eincexp_{s,y,j}$

Storage incremental expansion, 1 if the storage $j$ becomes commissioned in
$(s,y)$, binary, unitless.

$eincret_{s,y,j}$

Storage incremental retirement, 1 if the storage $j$ is decommissioned in
$(s,y)$, binary, unitless.

$gincexp_{s,y,k}$

Generator incremental expansion, 1 if the generator $k$ becomes commissioned
in $(s,y)$, binary, unitless.

$gincret_{s,y,k}$

Generator incremental retirement, 1 if the generator $k$ is decommissioned in
$(s,y)$, binary, unitless.

$lincexp_{s,y,l}$

Transmission line incremental expansion, 1 if the transmission line $l$
becomes commissioned in $(s,y)$, binary, unitless.

$lincret_{s,y,l}$

Transmission line incremental retirement, 1 if the transmission line $l$ is
decommissioned in $(s,y)$, binary, unitless.

#### Operations

$edis_{s,y,rp,h,j}$

Discharge of the storage $j$ at the hour $h$, nonnegative, unit MW.

$gopt_{s,y,rp,h,k}$

Power output of the generator $k$ at the hour $h$, nonnegative, unit MW.

$gsup_{s,y,rp,h,k}$

Start-up action of the generator $k$ at the beginning of the hour $h$, binary,
unitless.

$nload_{s,y,rp,h,i}$

Load shedding at bus $i$ at the hour $h$, nonnegative, unit MW.

$nrps_{s,y,rp,h,w}$

Non-compliance with RPS policy, unit MW, nonnegative.

#### Objective Function

$obj$

Objective function, unit $.

$invc_{s,y}$

Investment cost occurs at the scenario tree node $(s,y)$, unit $.

$oprc_{s,y}$

Operation cost occurs at the scenario tree node $(s,y)$, unit $.

$fomc_{s,y}$

Fixed O&M cost occurs at the scenario tree node $(s,y)$, unit $.

$fuelc_{s,y}$

Fuel cost occurs at the scenario tree node $(s,y)$, unit $.

$vomc_{s,y}$

Variable cost occurs at the scenario tree node $(s,y)$, unit $.

$stuc_{s,y}$

Start-up cost occurs at the scenario tree node $(s,y)$, unit $.

$ctax_{s,y}$

Carbon tax payment occurs at the scenario tree node $(s,y)$, unit $.

$voll_{s,y}$

Lost load cost occurs at the scenario tree node $(s,y)$, unit $.

$rpsc_{s,y}$

Cost of renewable portfolio standards non-compliance penalty, occurs at the
scenario tree node $(s,y)$, unit $.

### A-LEAF Sets and Indices

$d\in D$

Set of representative day groups.

$i\in I$

Set of generator technologies.

$h\in H$

Set of hour periods.

$t\in T$

Set of sub-hour periods.

$c\in C$

Set of risk scenario.

$k\in K$

Set of transmission lines.

$n\in N$

Set of buses.

$\mathrm{\Psi}_{ES}\in I$

Set of energy storage generators.

$\mathrm{\Psi}_{VRE}^{FIX}\in I$

Set of variable renewable energy generators with fixed generation profiles

### A-LEAF Parameters

$C_{cit}$

Generator availability status (1: available, 0: unavailable)

$CAP_{i}$

Power capacity, index $i$, unit MW

${\bar{CHG}}_{it}$

Steady-state energy storage charging, unit MW

$D_{nt}$

Power demand, indices $n$,$t$, unit MW

$\epsilon_{i}^{C}$

Energy storage charging efficiency, index $i$

$\epsilon_{i}^{D}$

Energy storage discharging efficiency, index $i$

$F_{k}^{+}$

Transmission capacity, index $k$, unit MW

${\bar{G}}_{it}$

Steady-state generator dispatch setpoint, indices $i,t$, unit MW

${MC}_{i}$

Marginal variable cost, index $i$, unit $

$PTDF_{kn}$

Power transfer distribution factor, indices $k$,$n$

$R_{i}^{10}$

10 mins ramp capacity, index $i$, unit MW

$R_{i}^{H}$

Hourly ramp capability, index $i$, unit MW

$S_{it}$

Renewable generation profile, indices $i$,$t$, unit MW

$SOC_{i}^{+}$

Maximum state-of-charge, index $i$

$VOLL$

Value of lost load, unit $/MWh.

### A-LEAF Variables

${chg}_{it}$

Storage charging, indices $i$,$t$, unit MW

${ens}_{nt}$

Energy not served, indices $n$,$t$, unit MWh

$f_{kt}$

Power flow, indices $k$,$t$, unit MW

$g_{it}$

Power output, indices $i$,$t$, unit MW

$p_{nt}^{inj}$

Net power injection, indices $n$,$t$, unit MW

$d_{it}^{up}$

Generator redispatch up, indices $i$,$t$, unit MW

$d_{it}^{dn}$

Generator redispatch down, indices $i$,$t$, unit MW

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# Unsupervised Change Detection Based on Image Reconstruction Loss

Hyeoncheol Noh
Hanbat National University
<EMAIL_ADDRESS>equal contribution Jingi Ju 11footnotemark: 1
Hanbat National University
<EMAIL_ADDRESS>Minseok Seo 11footnotemark: 1
Hanbat National University
<EMAIL_ADDRESS>Jongchan Park
Lunit Inc
<EMAIL_ADDRESS>Dong-Geol Choi
Hanbat National University
<EMAIL_ADDRESS>
###### Abstract

To train the change detector, bi-temporal images taken at different times in
the same area are used. However, collecting labeled bi-temporal images is
expensive and time consuming. To solve this problem, various unsupervised
change detection methods have been proposed, but they still require unlabeled
bi-temporal images. In this paper, we propose unsupervised change detection
based on image reconstruction loss using only unlabeled single temporal single
image. The image reconstruction model is trained to reconstruct the original
source image by receiving the source image and the photometrically transformed
source image as a pair. During inference, the model receives bi-temporal
images as the input, and tries to reconstruct one of the inputs. The changed
region between bi-temporal images shows high reconstruction loss. Our change
detector showed significant performance in various change detection benchmark
datasets even though only a single temporal single source image was used. The
code and trained models will be publicly available for reproducibility.

##  1 Introduction

In earth vision, change detection is a task to detect semantic changes in two
high spatial resolution (HSR) images from different times and the same area
(i.e. bi-temporal images). Change detection is a very important task in the
field of earth vision used for urban expansion, urban planning, environmental
monitoring, and disaster assessment [15, 32].

However, the manual comparison and change detection between two HSR images is
a very labor-intensive and costly job. To solve this problem, recent deep
learning-based change detection methods [5, 11] have been proposed and the
results are promising. Due to the data-driven nature of deep learning methods,
a large-scale training dataset of bi-temporal images and corresponding change
labels is essential for supervised approaches [5, 11]. The challenge lies in
the expensive dataset: Collecting the correctly registered bi-temporal HSR
images is expensive, and annotating the changes between them is more costly
than general semantic segmentation [28] or object detection datasets [31].
Another challenge is the imbalanced dataset: The change detection dataset
requires two images taken at different times in the same area, and in real-
world scenarios, changes are rare, so it is more difficult to collect a change
detection dataset in which changes exist (e.g. class balanced).

Figure 1: Qualitative comparison of unchanged bi-temporal pair images and
changed bi-temporal pair images and pseudo-unchanged pair images. (a) and (b)
are actual bi-temporal pair images, (c) is a pseudo-unchanged pair created by
photometric transform.

To solve this data collection problem, various unsupervised change detection
(UCD) methods [14, 10, 25, 21] have been proposed. UCD approaches effectively
solve the problem of expensive annotations in change detection, but they still
require correctly registered bi-temporal HSR images, or the performance was
low compared to supervised learning methods.

In the existing UCD setting, because it does not explicitly train change and
unchange, the prediction result is noisy both when the change occurs and when
the change does not occur. To solve this problem, most UCD methods use post-
processing. However, they do not disclose how to post-processing, or they are
overfitting for specific situations. (e.g. pixels with small area are removed)

Inspired by the study of unsupervised anomaly detection [20, 13], we rethink
the UCD setup. In both change detection and anomaly detection, change/anomaly
situations are rare in the real world. The unsupervised anomaly detection
methods [20, 13] train the image reconstruction model with only normal data,
and the model is fitted to the normal distribution. During inference, normal
inputs will be well reconstructed, as they fall in the normal distribution; on
the other hand, anomaly inputs will have high reconstruction error, as they
fall outside the normal distribution. Can UCD use reconstruction errors like
unsupervised anomaly detection? Since unchanged pairs can be generated
synthetically, we can train an image reconstruction model that trains normal
distributions. For example, if the change detector is trained on the unchanged
area by pairing $X^{t1}$ with itself, it can be trained on the unchanged area
without $X^{t2}$ images or changed labels.

In this paper, we propose unsupervised change detection based on image
reconstruction loss (CDRL) using only unlabeled single-temporal single source
images. The proposed method explicitly solves the challenges of data
collection in change detection, as it does not require expensive bi-temporal
HSR images, expensive annotations, nor balanced datasets with sufficient
changes. CDRL is trained to reconstruct the original source image by receiving
the source image and the photometrically transformed source image as a pair.
The purpose of photometric transformations is to create pseudo-unchanged pairs
that mimic unchanged pairs, as shown in Fig. 1-(a) and Fig. 1-(c). In the
unchanged pairs, there are no structural changes by definition, but only style
changes or photometric changes. The pseudo-changed pairs can be used to train
CDRL instead of changed pairs. Similar to unsupervised anomaly detection, CDRL
receives only (pseudo-)unchanged pair images during training and is trained to
reconstruct the original source image, so if untrained cases (changed pair
Fig. 1-(b)) are input during inference, the reconstruction loss is high for
that area.

However, unlike existing unsupervised anomaly detection studies, change
detection usually receives two images, so there are two major problems. First,
the image reconstruction models should be able to reconstruct the original
source image by receiving two pair images. Second, the reconstruction models
should focus more on the structure information of the photometrically
transformed source image. To solve this problem, we propose an image
reconstruction model using generative adversarial networks based on encoder-
decoder. CDRL consists of a shared encoder to extract features from each
image, and a decoder to fuse the features from the two images for image
reconstruction. To pay attention to the structure information of the
photometrically transformed source image, spatial attention was performed only
on the photometrically transformed source image.

To validate the efficacy of our proposed CDRL, we evaluated it on LEVIR-CD [6]
and WHU-CD [22]. Even though CDRL does not use bi-temporal pairs or pre-
trained weights, CDRL outperforms the existing UCD method using bi-temporal
pairs and the UCD method using pre-trained weights by a large margin.

Figure 2: Overview of the overall framework of CDRL. CDRL is trained to
reconstruct $X^{t1}$ by receiving a pseudo-unchanged pair during training, and
when a changed bi-temporal pair that is not learned during training is input
during inference, the reconstruction loss is large in the region with large
structure change.

To sum up, our major contributions are as follows:

  * •

We propose CDRL, a method to train a change detector on a single-temporal
single source image in UCD. To the best of our knowledge, this is the first
time to use a single-temporal single source image in UCD.

  * •

We propose an encoder-decoder-based generative adversarial network that
receives paired images as input.

  * •

We evaluate CDRL on various change detection datasets, and CDRL outperforms
previous UCD methods by a large margin.

##  2 Related Work

The problem we are trying to solve is ① obtaining a matched bi-temporal image
including a changed area is more difficult than obtaining a general single-
temporal image ② pairwise annotation is very expensive and time consuming.
Therefore, this section focuses on the problems encountered by existing change
detections, and finally briefly introduces the field of anomaly detection that
we have been inspired by.

###  2.1 Supervised Change Detection (SCD)

Supervised change detection is largely divided into a method that uses only
single-temporal information and an approach that performs temporal information
modeling or different modeling [33]. A change detector that uses only single-
temporal information, called post-classification comparison (PCC), trains a
semantic segmentation model during training [33, 34]. After that, the semantic
segmentation model predicts the change area through the xor operation of the
results obtained by predicting images from two different times during
inference. PCC has the great advantage of not requiring coregistrated pair
images, but this method only simply treats the change detection task as the
semantic segmentation task and ignores the temporal information modeling, thus
significantly decreasing the performance.

To solve this problem, change detection methods [5, 11] were proposed for
temporal information modeling between pair images taken at different times in
the same area. All of these methods achieved high performance, but the
generalization performance of these models was not guaranteed because of the
small size of the change detection benchmark datasets [19, 27, 18, 7, 9, 8,
12, 4, 1]. The reason why the change detection benchmark datasets are small is
that collecting bi-temporal pair images is much more difficult than collecting
single-temporal images, and pairwise annotation is very expensive and time-
consuming.

Since our proposed CDRL performs UCD using only unlabeled single-temporal
single source images, it can alleviate the problem of collecting bi-temporal
pair images and the cost and time-consuming problems of labeling.

###  2.2 Unsupervised Change Detection (UCD)

UCD is usually divided into a method [30, 26, 3, 16] based on the concept of
Change Vector Analysis [23] (CVA) or a method [25] based on a Generative
Adversarial Network (GAN) using an unlabeled bi-temporal pair image. However,
because they use pre-trained weights without direct training on the dataset,
the performance is low, or large-scale unlabeled bi-temporal pair images are
required to train the GAN model.

Our proposed CDRL can be explicitly trained on an unchanged area and can be
trained without bi-temporal pair images.

###  2.3 Unsupervised Anomaly Detection

The anomaly detection study we are inspired by is a reconstruction-based
method [2, 24]. Reconstruction-based methods typically utilize generative
models like auto-encoders or generative adversarial networks to encode and
reconstruct the normal data. These methods hold the insights that the
anomalies can not be reconstructed since they do not exist at the training
samples. These unsupervised anomaly detection methods achieved AUROC
performance of over 95 in various benchmark datasets [2], even without
explicitly training the anomaly data.

We also applied the fact that only unchanged pair (normal) images are trained
during training like this reconstruction-based anomaly detection, and that
when a changed pair (anomaly) is input during inference, the reconstruction
loss is high.

##  3 Method

This section describes the components of the CDRL in detail. First, the
training pipeline will be briefly described in Sec. 3.1, and then, a method of
performing photometric transform based on a single-temporal single source
image will be described in Sec. 3.2. Sec. 3.3 describes the reconstructor that
receives pair images and is trained as an objective to reconstruct the
original source image. Finally, Sec. 3.4 describes the entire objective
function of the CDRL including the GAN model.

###  3.1 Overall Pipeline

CDRL performs photometric transform to create a pair image as a single-
temporal single source image. Photometric augmentation of simple rules such as
brightness control and channel shuffling does not sufficiently express the
style change of the corresponding bi-temporal pair image in the real-world
unchanged area. Therefore, in order to express the style change of the
corresponding bi-temporal pair image of the unchanged area of the real-world,
we perform photometric transform by style transfer using CycleGAN [35].

After that, the generated pair image as shown in Fig. 2 is input to the U-Net-
based original source image reconstructor during training. For our purpose, to
train the original source image reconstructor with high reconstruction loss
for the region where the change has occurred, we need to pay attention to the
channel information in the original source image and pay attention to the
spatial information in the photometric transformed image. To achieve this
purpose, we applied spatial attention to the photometric transform image and
channel attention to the original source image using the CBAM [29].

Despite these efforts, the original source image reconstructor has a problem
of overfitting the original source image too easily during training.
Therefore, to prevent overfitting, we made a discriminator and conducted
adversarial training with the image reconstructor.

###  3.2 Photometric Transformation

The purpose of photometric transform for training CDRL is to create a natural
style change while maintaining the structure like an actual unchanged bi-
temporal pair image as a single-temporal single source image. In order to
achieve this purpose, we adopted CycleGan [35], which receives unpaired images
and changes the style while maintaining the structure. In the existing
CycleGan, when there are two domains $\\{x_{1},x_{2},...,x_{n}\\}\in X$ and
$\\{y_{1},y_{2},...,y_{n}\\}\in Y$, it receives two samples $x_{i}$ and
$y_{j}$ and is trained to optimize the parameters of two mapping functions
$G:X\rightarrow Y$, $F:Y\rightarrow X.$ However, since we need to perform
unpaired style transfer in one domain, we train a function that maps two
randomly selected samples $x^{t1}_{i}\in X^{t1}$ and $x^{t2}_{i}\in X^{t2}$ in
one domain $X$. Therefore, when there is discriminator $D_{t2}$ for mapping
function $G:X^{t1}\rightarrow X^{t2}$ and discriminator $D_{t1}$ for
$F:X^{t2}\rightarrow X^{t1}$, our objective function is as follows:

$\displaystyle L(G,F,D_{t1},D_{t2})=L_{GAN}(G,D_{t2},X^{t1},X^{t2})$ (1)
$\displaystyle+L_{GAN}(F,D_{t1},X^{t2},X^{t1})+\lambda L_{cyc}(G,F),$

where $\lambda$ controls the relative importance of the two objectives.

###  3.3 Pair Image-based Source Image Reconstructor

The pair image-based Source Image reconstructor $R(.)$ is trained to
reconstruct $X^{t1}$ by receiving the pseudo unchanged pair image $X^{t1}$,
$X^{t2}$ previously created in Sec. 3.2 as an input. To achieve this purpose,
the pair image-based source image reconstructor consists of a shared encoder
and a decoder that concats and fuses each feature map of the pair image output
from the encoder. $R$ is trained to optimize the objective function as
follows:

$\displaystyle L_{mae}(R)=MAE(R(X^{t1},X^{t2}),X^{t1}),$ (2)

where ${MAE}$ is the mean absolute error between the reconstructed image and
the source image.

A source image reconstructor trained only on pseudo unchanged pair images
during training should have a high reconstruction loss when a changed pair
image is received during inference. However, if the source image reconstructor
reconstructs by relying only on the structure information of the source image
regardless of the photometrically transformed image, the reconstruction loss
is low even when a changed pair image is input. To alleviate this problem, we
modified the CBAM structure to perform spatial attention on the photometric
transformed image and channel attention on the original source image. Through
this process, the source image reconstructor is trained by paying attention to
the structure information of the photometric transformed image and paying
attention to the style information in the source image. Figure 3 shows our
attention structure modified from the CBAM structure. As shown in the figure,
channel attention is performed on the $X^{t1}$ image and spatial attention is
performed on the $X^{t2}$ image, which is then added and concatenated to
train.

Figure 3: Our proposed pseudo-pair CBAM structure. Channels are applied to the
$X^{t1}$ image, and spatial attention is applied to the $X^{t2}$ image

###  3.4 GAN for detailed structure reconstruction

As in the [17] study, if only the $MLE$ loss is used, the reconstruction image
does not reconstruct the structure well and is blurry. If the reconstruction
result is blurry, the performance of the CDRL is degraded because it is
insensitive to structure changes. Therefore, we use GAN as in [17] to solve
this problem. So, given the discriminator $D_{r}$, the objective function of
the discriminator is:

$\displaystyle L_{gan}(R,D_{r},X^{t1},X^{t2})=log(D_{r}(X^{t1}))$ (3)
$\displaystyle+log(1-D_{r}(R(X^{t1},X^{t2}))),$

where $R$ tries to reconstruct images $R(X^{t1},X^{t2})$ that look similar to
images from $X^{t1}$ , while $D_{r}$ aims to distinguish between translated
samples $R(X^{t1},X^{t2})$ and original source image $X^{t1}_{i}$. $R$ aims to
minimize this objective against an adversary $D_{r}$ that tries to maximize
it, i.e., $min_{R}max_{D_{r}}L(R,D_{r},X^{t1},X^{t2})$.

The final objective function of the source image reconstructor that combines
the GAN loss and the MAE loss is

$\displaystyle L_{total}=L_{gan}+\lambda L_{mae}$ (4)

where $\lambda$ controls the relative importance of the two objectives. We use
$\lambda$ as 100 in all experiments.

##  4 Experiments

In this section, CDRL is evaluated on two HSR remote sensing change detection
datasets. Section Sec. 4.1 describes the experimental setting in detail, and
section Sec. 4.2 describes the loss analysis experimental results in detail.
Also, in Sec. 4.3, pixel level change detection, which is the same as the
existing change detection experimental settings, and in Sec. 4.4, we describe
the patch level change detection results suitable for our proposed change
detector application situation. Finally, in Sec. 4.5, qualitative results, and
in Sec. 4.6, the results of the ablation study are described in detail.

###  4.1 Experimental Setting

#### Datasets

Two HSR remote sensing change detection datasets were used to train and
evaluate the performance of object change detection.

  * •

LEVIR-CD [7]. The LEVIR-CD dataset contains 637 bi-temporal pairs of HSR
images and 31,333 change labels on building instances. Each image has a
spatial size of 1,024 $\times$ 1,024 pixels with a spatial resolution of 0.5
m. The change labels provide information about the construction of new
buildings and the disappearance of existing buildings. This dataset provides
an official split of 445 training, 128 validation, and 64 test pairs. The
evaluation results are computed in the test pair set.

  * •

WHU building change detection [18]. The WHU dataset has one pair of aerial
images of size 15,354 $\times$ 32,507 pixels obtained in 2012 and 2016 at the
same area. It provides 12,796 and 16,077 building instances labels,
respectively, and changed labels across the pair. We will use the change
labels later to evaluate change detectors. Training, validation, and test sets
are given specific areas containing 4,736, 1,036, and 2,416 tiles
respectively.

#### Implementation details

CycleGAN was used to generate pseudo unchanged pairs for training of CDRL. The
two datasets $X^{t1}$ and $X^{t2}$ of CycleGAN are randomly divided into
datasets $X$. All implementation details strictly follow the official CycleGAN
code111https://github.com/junyanz/pytorch-CycleGAN-and-pix2pix. For the data
augmentation, RandomRotate90, HorizontalFlip, VerticalFlip, Transpose,
RandomBrightnessContrast, and Sharpen of albumentations
222https://github.com/albumentations-team/albumentations were used, and the
probability $p$ of almost all applications is $0.3$.

We trained the source image reconstructor using the Adam optimizer with beta
values equal to (0.5, 0.999). The learning rate set to 0.0002 and batch size
of 1 to train the model. evaluation is using both the LEVIR-CD and WHU dataset
validation (or test) sets. Our all models are implemented on PyTorch and
trained using a single NVIDIA Quadro RTX 8000 GPU. The detailed structure of
the network will be available soon on our project page.

#### Evaluation Metrics

  * •

Pixel Level Change Detection. We use the common metrics in pixel-by-pixel
binary classification tasks and object change detection tasks: intersection
over union (IoU), recall, precision score. Because our goal is also to
classify whether it has changed or not at the pixel level.

  * •

Patch Level Change Detection. We used classification AUC for patch level
change detection. Note that if all of the output mask values of the change
detector are 0, it is set to unchanged, if at least one is 1, it is set to
change

Figure 4: Sample images divided into unchange, small change, and large change
for reconstruction loss analysis. Figure 5: Qualitative analysis of CDRL. The
top 3 lines are the qualitative results of CDRL in the region where the change
has occurred, and the bottom line is the qualitative result of CDRL in the
unchanged pair. It can be seen that CDRL localizes the area where the change
occurred.

###  4.2 Loss Analysis Results

We planned a loss analysis experiment to check whether the source image
reconstructor has a high reconstruction loss in the part where the structure
is changed a lot.

We divided the dataset into unchange, small change (the changed part is less
than 30% of the total image), and large change as shown in Fig. 4. When the
dataset was split based on these criteria, the LEVIR-CD dataset was split into
8 unchanged pairs, 35 small change pairs, and 21 large change pairs. The WHU
dataset was split into 377 unchange pairs, 145 small change pairs, and 138
large change pairs.

Method | Dataset | Reconstruction Loss
---|---|---
|  | Un | Small | Large
CDRL (Aug) | LEVIR-CD | 24.79 | 36.81 | 44.91
CDRL (Pseudo Unchange Pair) | LEVIR-CD | 14.45 | 34.74 | 43.49
CDRL (Aug+Pseudo Unchange Pair) | LEVIR-CD | 10.15 | 31.41 | 38.53
CDRL (Aug) | WHU | 35.95 | 41.11 | 50.89
CDRL (Pseudo Unchange Pair) | WHU | 22.89 | 39.37 | 49.46
CDRL (Aug+Pseudo Unchange Pair) | WHU | 17.20 | 38.03 | 47.65

Table 1: Loss analysis results of CDRL in LEVIR-CD dataset and WHU dataset.

Table 1 shows the results of loss analysis of CDRL in the LEVIR-CD test
dataset and the WHU test dataset. As shown in the table, the loss of the
unchanged pair was the lowest in both the LEVIR-CD dataset and the WHU
dataset, and the loss of the large change pair was the highest. These
experimental results indicate that the source image reconstructor is not good
at reconstructing the source image when a pair with a large change in
structure is input during the test because only pseudo unchanged pairs were
input during training, as we intended. Also, the fact that the loss was low in
the unchanged pair indicates that our pseudo unchanged pair was generated at a
level similar to that of the actual unchanged pair.

However, if the source image reconstructor works perfectly as we intended, the
reconstruction loss should be close to 0 when an unchanged pair is input. As
shown in Table 1, the unchanged pair showed the lowest loss, but the value was
not small. The reason for this is that the LEVIR-CD dataset and the WHU
dataset are labeled as only changes in building, and in fact, the unchanged
pair includes many structural changes such as land becoming lakes, roads that
did not exist, and cars. A more detailed analysis result is described with an
example in Sec. 4.5.

Figure 6: Qualitative analysis result of unchanged bi-temporal images for
which CDRL showed high reconstruction loss. CDRL predicted that when roads,
lakes, and cars were created, it was all change.

###  4.3 Pixel Level Change Detection Results

We compared and analyzed the performance of CDRL with other UCD and SCD
methods. In order to compare our CDRL with the existing UCD methods, we
reproduced all [21, 10, 21] methods and tested them in LEVIR-CD and WHU. As
shown in Table 2, the existing UCD methods have high recall values and low
precision because prediction results are very noisy and vulnerable to small
structural changes. These experimental results indicate that our CDRL is
robust to small structural changes and also to style changes.

However, when compared with BIT, which is a state-of-the-art supervised change
detection, the performance of CDRL was low due to a large gap. This reason is
mainly analyzed for two reasons. First, unlike supervised change detections,
CDRL does not learn the pixel-level change area explicitly, so it can localize
only the approximate location. Therefore, compared to BIT, our CDRL has
similar recall value but clearly lower precision. Second, supervised change
detection can be explicitly trained on information about change objects of
interest, so it can explicitly learn that a car is created or a lake is
changed to be unchanged, but our CDRL predicts that they are all changed.

Method | Dataset | Supervision | Precision | Recall | IoU
---|---|---|---|---|---
NMCD [21] | LEVIR-CD | Unsup | 0.13 | 0.71 | 0.07
UCNN [10] | LEVIR-CD | Unsup | 0.16 | 0.79 | 0.09
UCDGAN [21] | LEVIR-CD | Unsup | 0.20 | 0.66 | 0.15
CDRL | LEVIR-CD | Unsup | 0.63 | 0.92 | 0.59
BIT [5] | LEVIR-CD | Sup | 0.89 | 0.89 | 0.80
NMCD [21] | WHU | Unsup | 0.07 | 0.96 | 0.03
UCNN [10] | WHU | Unsup | 0.07 | 0.95 | 0.03
UCDGAN [21] | WHU | Unsup | 0.09 | 0.93 | 0.08
CDRL | WHU | Unsup | 0.52 | 0.93 | 0.50
BIT [5] | WHU | Sup | 0.86 | 0.81 | 0.72

Table 2: Quantitative comparison results of CDRL and UCD, SCD methods. Note
that, since there are no post-processing implementation details of the
existing UCD methods, it was not applied.

###  4.4 Patch Level Change Detection Results

Many real-world applications that use change detectors do not rely solely on
change detectors. In these situations, the role of change detectors is to
reduce human labor intensity by providing information on the patch or area
where the change occurred among hundreds of patches. Considering this
application situation, we try to solve change detection with patch level
classification.

Dataset | AUC
---|---
LEVIR-CD | 83.52
WHU | 87.18
Table 3: Patch level binary classification results in the LEVIR-CD dataset and
the WHU dataset.

Table 3 shows the patch level change detection results for our CDRL in the
LEVIR-CD dataset and the WHU dataset. As shown in the table, high AUC was
achieved in both datasets despite using only single-temporal single source
images. Note that CVA-based methods predict that there is a change in all
patches because the output result is noisy.

###  4.5 Qualitative Results

CDRL was qualitatively analyzed on the LEVIR-CD dataset. As shown in Fig. 5,
it can be seen that the CDRL detects the changed part well because the
reconstruction loss is high in the part where the structure change is large.

Also, for the unchanged pair, even if the style change is large, since there
is no structure change, it can be seen that the reconstruction loss is low and
no change is predicted Therefore, it is thought that CDRL will be useful in
applications where it is important not to localize the exact location, but to
know the approximate location or whether or not changes have occurred in units
of patches.

Fig. 6 shows the qualitative analysis results for samples with poor CDRL
performance As shown in the figure, since CDRL cannot designate a specific
change object of interest, it predicts that a change has occurred when a car
is created, the ground becomes a lake, or a lake becomes the ground.
Therefore, the reason for the low IoU in all our experiments is dominant for
the above reasons.

###  4.6 Ablation Study

In order to compare and analyze the effect of the attention module and
adversarial training constituting the CDRL, we conducted an ablation study on
the LEVIR-CD dataset.

#### Attention Modules

Table 4 shows the patch level classification results of CDRL in the LEVIR-CD
dataset according to the existence of channels attention and spatial
attention. As shown in the table, performance was higher with CBAM than
without CBAM. Also, in our proposed CDRL, the pseudo-pair CBAM, which provides
channels attention to the $X^{t1}$ image and spatial attention to the $X^{t2}$
image, has the highest performance.

CDRL | AUC
---|---
w/o Attention | 77.38
w/ CBAM | 80.90
w/ Pseudo-pair CBAM | 83.52
Table 4: Patch level binary cleavage results of CDRL with or without attention
module.

#### Adversarial Training

We designed an experiment to check whether adversarial training solves the
blurry problem of reconstruction images like [17] in CDRL.

Figure 7: Qualitative comparison of reconstructed images with and without
discriminator.

Fig. 7 is a sample of the reconstructed image with and without discriminator.
As shown in the figure, it can be seen that the reconstructed image is blurred
when there is no discriminator. On the other hand, if there is a
discriminator, it can be seen that the boundary is reconstructed more clearly.
These results indicate that adversarial training is also effective in CDRL.

Table 5 shows the results of measuring the AUC of CDRL with and without
discriminator on the LEVIR-CD dataset. As shown in the table, it can be seen
that higher AUC was achieved with the discriminator. These experimental
results show that the sensitivity of the CDRL to the structure of the pair
image, like our design, helps the performance.

##  5 Discussion and Future work

In our work, we performed change detection with source image reconstruction
loss using only unlabeled single-temporal single source images. However, the
semantic change we are interested in can exist in a variety of ways, such as
buildings, seasons, cars, and trees. The prerequisite for CDRL is to make the
reconstruction loss appear high in the part where the structure change occurs
regardless of the style change. However, the semantic change that we are
interested in can be diverse, such as natural scenery, artificial objects,
weather, and environmental changes. Therefore, in future work, based on the
fact that CDRL has a significant performance improvement in UCD, we plan to
study semi-supervised change detection to efficiently detect changes of
interest (change of specific object)

CDRL | AUC
---|---
w/o discriminator | 69.09
w/ discriminator | 83.52
Table 5: Patch level binary cleavage results of CDRL with or without
discriminator.

##  6 Conclusion

In this paper, to solve the problem that it is difficult to construct a bi-
temporal pair dataset containing semantic changes, we propose a CDRL that
performs unsupervised change detection using only a single-temporal single
source image. In order to solve the unsupervised change detection problem as a
reconstruction-based unsupervised anomaly detection problem, CDRL defined
normal data as unchanged pairs and anomaly data as changed pairs. After that,
a change detector (reconstructor) that receives pair images was proposed. We
verified the CDRL on the WHU and LEVIR-CD datasets, and achieved significant
performance despite unsupervised change detection using single-temporal single
source images. We hope that CDRL will be widely used in real-world scenarios
where it is difficult to obtain labeled bi-temporal pair images.

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