Towards Fast and Semi-supervised Identification of Smart
Meters Launching Data Falsification Attacks
Shameek Bhattacharjee

Aditya Thakur

Sajal K. Das

Missouri University of Science andTechnology, Rolla, USA
shameek@mst.edu

Missouri University of Science andTechnology, Rolla, USA
astvd3@mst.edu

Missouri University of Science andTechnology, Rolla, USA
silvestri@cs.uky.edu

ABSTRACT
Compromised smart meters sending false power consumption data
in Advanced Metering Infrastructure (AMI) may have drastic consequences on the smart grid’s operation. Most existing defense
models only deal with electricity theft from individual customers(isolated attacks) using supervised classification techniques that do
not offer scalable or real time solutions. Furthermore, the cyber andinterconnected nature of AMIs can also be exploited by organizedadversaries who have the ability to orchestrate simultaneous data
falsification attacks after compromising several meters, and also
have more complex goals than just electricity theft. In this paper,
we first propose a real time semi-supervised anomaly based consensus correction technique that detects the presence and type ofsmart meter data falsification, and then performs a consensus correction accordingly. Subsequently, we propose a semi-supervisedconsensus based trust scoring model, that is able to identify thesmart meters injecting false data. The main contribution of the
proposed approach is to provide a practical framework for compromised smart meter identification that (i) is not supervised (ii)enables quick identification (iii) scales classification error rates better for larger sized AMIs; (iv) counters threats from both isolated
and orchestrated attacks; and (v) simultaneously works for a variety of data falsification types. Extensive experimental validation
using two real datasets from USA and Ireland, demonstrates theability of our proposed method to identify compromised meters innear real time across different datasets.

CCS CONCEPTS• Security and privacy → Trust frameworks; Intrusion detection systems; • Theory of computation → Semi-supervised
learning; • Hardware → Smart grid;

KEYWORDS
Data Falsification; Advanced Metering Infrastructure; Smart Grid
Security; Anomaly Detection; False Data Injection; Cyber-Physical
System Security

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ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea© 2018 Association for Computing Machinery.
ACM ISBN 978-1-4503-5576-6/18/06. . . $15.00
https://doi.org/10.1145/3196494.3196551

ACM Reference Format:
Shameek Bhattacharjee, Aditya Thakur, and Sajal K. Das. 2018. Towards Fast and Semi-supervised Identification of Smart Meters Launching Data Falsification Attacks. In ASIA CCS ’18: 2018 ACM Asia Conference on Computer and Communications Security, June 4–8, 2018,
Incheon, Republic of Korea. ACM, New York, NY, USA, 13 pages.
https://doi.org/10.1145/3196494.3196551

1

INTRODUCTION

Advanced Metering Infrastructure (AMI) is one of the building
blocks of the smart grid technology, responsible for collecting dataon loads and consumer’s electricity consumption [16]. Such data
are usually collected by smart meters installed on the customer site,
and are expected to play a pivotal role in current and future smart
grids. For example, AMI data will be at the basis of critical tasks
such as automated billing and pricing, demand response, forecast,load adjustments [31], and management of daily and critical peakshifts. Hence, the integrity of AMI data is of utmost importance.
However, data falsification attacks target the integrity of AMI data.
In the literature, defense against the falsification of electricity consumption data, has been mostly focused on electricity
theft, [9, 13, 14, 23], where individual customers are the primary
adversaries, who report lower than actual usage for lesser electricity bills. Since the actually measured reading of power consumption is reduced, such an adversarial strategy is a deductive modeof data falsification. Such attacks from individual rogue customers
are usually uncoordinated and we term them as isolated attacks.
However, it is recognized that the cyber and interconnectednature of AMIs can be exploited by more organized adversaries,(e.g., organized criminals [30] and business rivals [10, 27]), who
are more equipped to bypass cryptographic defense, compromise
several smart meters, and alter a large or small amounts of data
simultaneously, thereby significantly impacting the smart grid’s
operations [10, 13, 30]. We term such attacks as orchestrated attacks. Orchestrated physical attacks tampering the meter hardware
to produce false data was reported in [29, 30]. Thus, cryptography
or network intrusion alone cannot protect against this threat.
The goals of organized adversaries may not be restricted to monetary benefits on the customer billing side resulting from electricity theft. As an example, higher than actual power consumption
can be reported by a meter as a byproduct of static and dynamic
load altering attack [17] or hardware tampering affecting both customers and utilities. Such an attack is termed as an additive modeof data falsification. An additive attack launched by a utility on its
rival company’s meters, may induce loss of business confidence by
the customers of the victim company, due to higher bills. The expected future use of AMI data for demand response, forecast andload planning may induce additive attacks to benefit customers by

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea
drawing undue incentives during demand response [1]. Note that,an organized attacker may also perform a balancing additive anddeductive attacks to evade detection methods that use mean aggregates, which are termed as camouflage mode of data falsification.
Previous works on orchestrated or isolated attacks have many
disadvantages. Classification based techniques use computationally expensive Multi-Class Support Vector Machines (SVMs) [8, 9],
Neural Networks [7] and only focus on retrospective identification (takes 6 months to 2 years), lacking the possibility of detecting the attacks or compromised meters before serious damages.
Other works [1, 11] utilize a complete supervised approach by
maintaining continuous fine grained meter specific historical evidence which is impractical and error prone for large scale AMI networks, and requires separate training for particular attack types.
State based detector needs special hardware which is very costly
as elaborated in Section 2. Some consensus based approaches
use traditional measures of central tendency such as median andmean [14, 22, 23] or their variants. Such consensus measures geteasily affected by larger margins of false data or larger fractions ofcompromised meters (when using instantaneous consensus metrics). They also fail under camouflage attacks (typical in orchestrated attacks), may lead to larger error rates (when using historicalconsensus metrics), since the mean aggregate of power consumption data readily changes (proved later by real datasets).
In this paper, we propose an anomaly based consensus correction scheme and a semi-supervised learning based trust scoringmodel, that detects occurrence as well as the specific type of falsification of power consumption data (referred to as attack context),
and then identify the compromised meters injecting such false data
in an AMI, regardless of isolated or orchestrated attacks. Specifically, we propose a novel metric based on harmonic to arithmetic
mean ratios of daily power consumption to detect anomalies andinfer the attack context. Based on the inferred attack context, we
calculate a resilient mixture mean and standard deviation as an approximate consensus measures that weaken the alterations causedby the false data from orchestrated attacks. Subsequently, a set of
discrete rating levels is associated to each meter over time using
the proximity of its reported data to this resilient mixture mean.
Then, a Folded Gaussian distribution based weighing procedure isused to assign weights to each of the discrete rating levels. Basedon rating levels and weights observed over a time window, a trust
value is calculated per meter that classifies compromised meters.
We validated our model through extensive experiments on real
datasets acquired from two different AMI infrastructures withvarying sizes and regions. Results show that our proposed method
is able to detect and decipher additive, deductive, and camouflage
attacks launched by organized adversaries in real time. We demonstrate that our method is robust to a high fraction of compromised
meters (upto 75%), is able to identify compromised meters from
non-compromised ones over margins of false data, thus making it
scalable for large sized AMI. Additionally, our method identifies
against isolated attacks from individual meters. We compare ourresults with three existing works to show improvement.

2 LIMITATIONS OF RELATED WORK
Existing works on AMI data falsification can be classified into
Classification based, State Estimation based, and Consensus based

Bhattacharjee et al.
methods. Classification based approaches [7–9] require extensive
training phases and multi-class SVMs for each customer separately,in order to detect electricity thefts. They are computationally complex and only allow retrospective identification. A study comparing classification methods [7] concluded that the accuracy of mostof these models are only 60% to 70%, although they suffer fromprivacy intrusion and complexity issues.
State based detection techniques [6, 12, 13] in contrast, require
additional monitoring hardware deployed at various points acrossthe AMI and distribution network for consistency checks. Additional hardware requirement is costly to the extent that it has beenrecognized as a practical deterrent for utility providers to use such
solutions in scale. Some works monitor non-technical loss (NTL)at the transformer meter. However, in [7] it is observed that NTL
could vary due to large number of factors other than attacks (e.g.,
legitimate changes due to unexpected weather) and hence suffersfrom high number of false alarms. Moreover, the NTL approachcannot detect for camouflage or load altering induced attacks.
Consensus based methods [14, 22, 23] use smoothened moving
average of median or mean power consumption for detection, followed by information theory to identify meters. Most works except [14] assume isolated electricity theft from a small number ofmalicious meters that does not greatly bias the consensus. But thisassumption on unbiased consensus may not hold for organizedadversaries with higher attack budgets launching orchestrated attacks. Some works such as [22, 23], use historical mean/median
power consumption for comparison of bad behavior. However, themean power consumption varies readily due to contextual factors
such as weather, customer habits etc. as shown later from studies
with our real datasets. Some works [1, 11] use a supervised learning of historical proximity patterns of each meter with instantaneous consensus, but fails for higher fractions of compromised meters (≥ 40%). Additionally, supervised approaches become cumbersome for large scale grids due to large training sets and requirelabels which may not be available or accurate. Another major limitation these methods, is that the assumed margins of false data
per meter are usually fixed and are also typically very high (600W1500W), which favors easier detection. As shown later, the mean
consumption can easily get affected by both larger margins offalse data or legitimate consumption changes (e.g., sudden weatherchanges), which increases errors. This is evident from [14, 22],
where fine grained monitoring still yields accuracy of about 62%.
Note that cryptography based approaches are not enough sincephysical attacks can also cause data falsification [29, 30].

3

SYSTEM ARCHITECTURE AND DATASETDESCRIPTION

We consider a set of N smart meters reporting power consumption data to a data concentrator periodically. Let the i-th smart meter report a datum Pti at the end of time slot t. We model Pti as
the realizations of a random variable (r.v.) P i denoting the power
consumption distribution of the i-th smart meter. A Neighborhood
Area Network (NaN), formed by a collection of houses is governedby a NaN gateway node, that may act as data concentrators collecting data from multiple smart meters in an area. Multiple NAN
gateways may be connected to form a Field Area Network (FAN),Semi-supervised Identification of Smart Meters Launching Data Falsification
governed by a FAN gateway, which in turn is connected to the Utility Wide Area Network (WAN).
Decentralized defense models are deployed at either NAN or
FAN gateways while centralized detection frameworks are deployed at the WAN [3]. Since the datasets did not reveal the actual topology, we show results on smaller subsets of meters and asa whole, to mimic both deployment possibilities and understandperformance scalability with varying micro-grid size N .

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Koreaλ (d )λ −1d (λ) = 
 l n (d )0.03

λ = argmax f (d,λ∗ )λ ∈Rwhere f (d,λ∗ ) is the logarithm of the likelihood function given by:

0.025

Probability

400

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. Using Eqn. 1, any P i can be converted
such that d¯(λ) = i =1n
to obtain an approximate gaussian distributed r.v. denoted as p i .
For Texas dataset, we found λ = −0.03, which is closer to zero.
Therefore, to simplify implementation, we used effective λ = 0
for the transformation of both datasets in this paper. Note that our
proposed model does not require the data to be perfectly Gaussian.
We performed the above procedure for 3 subsets of smart meter
population sizes (see Fig. 3(a)) to prove topology invariance on theGaussianity. Hence, we validate the claim that, power consumption of meters in a micro-grid can be approximated by a Gaussian distribution. We also denote pti = ln(Pti + 2) as the effective
power consumption report from each i on a power transformed
scale (since λ = 0) at any time slot and pmix denotes the aggregate mixture. The transformation is done to exploit certain statistical properties exhibited by the Gaussian distributions. The extent
of Gaussianity is depicted through a Q-Q plot in Fig. 3(b). While
the Gaussian approximation resulted in 67% and 69% of the datapoints to be within the first standard deviation (for texas and irish
datasets), the distributions remain unbalanced around the mean
with 64% of the total datapoints on the left and 36% on the right ofthe mean on average. This asymmetry contributes to unique observations under orchestrated attacks as discussed in Section 5.1.1.

(b)Figure 1: Texas Dataset: (a) All Houses, (b) Mixture
Frequency of Power Value

 n

n
X
n  X [d i (λ) − d¯(λ)]2 f (d , λ) = − l n + (λ − 1)l n (d i )2  i =1
n

i =1


Quantiles of Input Sample

Frequency of Power Value

500

(1)

where λ is an appropriate transformation parameter chosen froma possible set λ∗ ∈ R, such that

3.1 Dataset Description
To study the distribution of P i , we investigated hourly (i.e., tslotted hourly) reported real power consumption datasets of 700
houses from Austin, Texas [25] and 5000 houses from Dublin,
Ireland [26] that belong to residential customers. We observedthat each P i follows an approximate lognormal distribution in the
Texas dataset. We also observed that all such log-normal distributions are clustered close to each other such that the variance
between them is not arbitrarily large. The evidence is shown in
Fig. 1(a). Given this observation, we claim that the combination of
the individual lognormals can be well approximated by a mixture
distribution which is also log-normal (as evident from Fig. 1(b)). We
denote P mix as the random variable with approximate lognormal
mixture distribution considering all houses in the grid. The trends
from Texas dataset, also matches with trends from the same experiments over the Irish dataset with similar results on consumption
for a different population for different years as shown in Figs. 2 (a)and 2(b), proving generality of observations.

if λ , 0;if λ = 0

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(a)

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Figure 2: Irish Dataset: (a) All Houses, (b) Mixture

3.2 Gaussian Approximation of the Data
With an aim to ease mathematical tractability and exploit certain
known properties of Gaussian distributions, we seek to convert theapproximate lognormal distributions to an approximate Gaussian
distributions. For this, we use a (NIST recommended) power transformation procedure [2] which is described by the following:
Given a data set d = {d 1 ,d 2 · · · ,d n }, where n denotes the total
number of data points, the power transformation of d is given byd (λ) = {d 1 (λ), · · · ,d n (λ)}, such that:(b)

Figure 3: pmix for Texas Data: (a) Various N , (b) QQ-Plot

3.3 Time Domain Granularities
While real data is collected hourly (known as time slots t), we calculate various consensus/anomaly detection metrics at the end of
a finite ‘time window’ (denoted by T ), that is a collection of l timeslots. Here, l depends on how fine or coarse grained monitoring isdesired. Let Tr e be the average time taken by customers to react
to the environmental factors that may trigger sudden legitimatechanges in power consumption in houses. For example, in warmer
sunny days during winter season, it is expected that most houses
would reduce heaters within some time Tr e < l. Sufficient research
exists to show that using l = 24 hour window is reasonable [9].

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

In this section, we elaborate on four factors characterizing the adversarial strategy, namely, fraction of compromised meters, attack
types, falsification margins, and falsification distributions that canbe employed by organized or isolated adversaries. To the best of
our knowledge, we have ensured that the numbers quantifying
the adversarial strategy do not favor or suit the proposed defense
mechanism. Since real malicious data samples are not available, we
generated the malicious samples by applying the following four aspects of adversarial strategy over the real dataset:
Fraction of Compromised Meters: Power consumption datafrom smart meters can be sabotaged by an organized adversary or
isolated rogue customers [13]. Let organized adversaries compromise M meters based on their attack budget and control a certain
fraction M
N = ρmal ∈ [0, 1) of the N smart meters. For example,
ρmal = 0.50, means 50% of the total number of meters is compromised. Note that ρmal could be very high in decentralized microgrids, where N is typically smaller. Unlike most existing works,
we explore the full possible spectrum of ρmal varying from 1%
to 90% for varying network sizes N , while studying performance.
Although the defense model is focused on an orchestrated attack
with larger ρmal , we show in Section 6, that our trust model is also
identifies small scale isolated attacks from lone ‘rogue meters’.
Attack Types: The organized adversaries falsify data from multiple compromised meters simultaneously using one of falsification
attacks deductive, camouflage, additive, based on its objective andintent. Falsification of data is achieved by accordingly changing theactual power consumption value Pti by some amount δ t . For example, for deductive falsification, the actual power consumption data
Pti from the i-th compromised meter at time t is modified as Pti −δ t .
Similarly, for additive falsification, the modified attack sample isPti + δ t from a compromised meter. For camouflage falsification,
half of the compromised meters launch additive falsification while
the other half launches deductive falsification with the same average value of δ t . The δ t amount of false data is chosen randomly
from within a margin (δmin ,δmax ) according to some falsification
distribution with a strategic average falsification margin δ avд .
Average Falsification Margin: We denote δ avд as the averagemargin of false data for each compromised meter. The strategic
value of δ avд by a rational adversary is some value that ensuressome minimum revenue but also prevents easy detection. Unlike
existing works, which either do not clearly articulate the exact
δ avд (such as [14]) or achieve good performance for high δ avд
values such as 1200W-1500W [11], 600-900W [1], 400W-430W [9],we explore δ avд values ranging from as low as 50W upto 2000W, toshow the classification performance over a broad range of possibleδ avд values. The micro-grid sizes of 200, 800 and 5000 are used toshow the scalability of performance error rates with relative sensitivity to δ avд . We report improved performance on different parameters for δ avд > 350W that is compared to existing works, andderive conclusions on δ avд required to evade detection.
Falsification Distribution: Additionally, we argue that the distribution of δ t within (δmin ,δmax ) should be some variant of uniform

0.03

0.015

0.025
Additive Data

0.01

Probability

4 ATTACK MODEL AND IMPLEMENTATION

distribution such that the resultant shape of power consumption
distribution remains unchanged, making it a smarter and less obvious attack. In contrast, the effect of normally distributed δ t on
the resultant shape is quite apparent. A comparison between normally and uniformly distributed δ t is shown in Figs. 4(a) and 4(b).
Note that, while our defense model works under both cases the results mostly consider variants of the uniformly distributed strategy.
Apart from this (a) Random strategy, the following falsification distributions are also possible: (b) Periodic: Targeting the dynamicor time of use (TOU) electricity pricing [11], where attacks arelaunched on specific times when the price/demand of electricity
is high. We implemented a periodic strategy where attacks happen on every 12 hours in a day,(c) Incremental: Instead of immediately attacking with the intended δ avд , the adversary increases
its average falsification margins by a minuscule amount dδ on every time slot till it reaches its intended δ avд . We implemented
an incremental strategy where dδ = 2W updated 4 hourly. (d)Omission: No data reaches the utility since communication/data
is jammed/dropped. This is implemented by replacing data withnull values from a subset of meters.

Probability

Therefore, T has a daily time granularity. For confirming the presence of falsification, we calculate a cumulative average of anomaly
detection metric over a ‘sliding time frame’ of F time windows.

Bhattacharjee et al.

0.02

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Figure 4: Attack Distribution (a) Obvious, (b) Smarter

5

PROPOSED FRAMEWORKThe proposed framework has two major parts: (a) Anomaly-driven
consensus correction model, and (b) Trust scoring model. The consensus correction model provides robust consensus as inputs to the
proposed trust scoring model, which improves the classification.

5.1 Anomaly Driven Consensus Correction
The objective of the anomaly based consensus correction module
is to prevent the consensus measure (aggregate mean and standard
deviations) from getting too biased due to orchestrated attacks.
First, we show that the arithmetic mean is not a stable historicalinvariant for aggregate power consumption. Therefore, historicalmean cannot be used as a consensus measure, and instantaneous
mean cannot be used since distinguishing legitimate changes in themean from malicious changes is difficult. The consensus correction
module has four phases: (i) proposed detection metric training, (ii)inferring presence of organized falsification, (iii) detecting type offalsification, and (iv) calculation of resilient consensus (resilientmean and standard deviation (µ M R and σ M R ) in a time window.
5.1.1 Ratio of Harmonic to Arithmetic Mean. Now, weshow that the ratio of harmonic to arithmetic mean metric is better than other consensus/aggregate based measures for anomaly
detection and consensus correction due to: (i) Higher invarianceto legitimate changes in consumption, (ii) Pythagorean mean special asymmetry property facilitates attack detection.

Semi-supervised Identification of Smart Meters Launching Data Falsification

dow T (T is a daily window consisting of 24 time slots). Similarly,
let the average daily standard deviation be denoted as SD avд (T ) =P24
t =1 σt /24. Many prior works such as [14, 22, 24], propose theuse of arithmetic mean or its derived smoothening statistics (suchas Cumulative Sum/Moving Averages of AMavд (T )) for sequential
anomaly detection. Thereafter, they propose to use historical mean
as a consensus in the event of an attack or the mean prior to theattack detection. However, Fig. 5(a) shows how actual arithmetic
mean power consumption fluctuates for the same time windows
for three years [25] in the Texas dataset without showing any repeating historical pattern or a stable time series. Due to high fluctuations of the instantaneous arithmetic mean, the error residual
between the derived smoothening statistic and the actual mean islarge. Thus, it will be difficult to identify legitimate changes from amalicious one by monitoring the time series. It will also cause large
errors if historical arithmetic mean is used as a consensus. This isevident from the high rates of false alarms and missed detection
reported in [7, 9]. To circumvent this problem, we propose to use
the ratio of HMavд (T ) and AMavд (T ) as the detection metric by:r at ioQ av
д (T ) =H M av д (T )AM av д (T )(3)

We denote µ r at io and σr at io as the mean and standard deviationr at io (T ) observed in the dataset. Let us explain three reasonsof Q avд
for choosing Eqn. 3, as a metric for detecting presence of attacks.
(i) High Invariance to Legitimate changes: From our experir at io (T ) sammental study, we observed that the time series of Q avд
ples over different years and across multiple datasets is highly stable over time in contrast to the time series of arithmetic meanr at io (T ) overof power consumption. Fig. 5(b), shows the daily Q avд
three different years (2014, 2015, 2016) for the Texas dataset, whiler at io (T ) for six different meter popuFig. 6(a) shows the ratio Q avд
lations for a completely different AMI data set in Dublin, Irelandr at io (T ) isduring 2009-2010. Both, Figs. 5(b) and 6(a), prove that Q avд
a highly stable invariant metric across different data sets, as comr at io (T ) canpared to the aggregate arithmetic means. Note that, Q avд
not exceed 1, due to the HM ≤ AM property [18].
r at io (T ) also exhibits hisApart from the stability over time, Q avд
torical stability over different years, unlike arithmetic mean whichshows large differences in the readings on the same day in successive years. In fact, without using moving averages, the standard der at io (T ) is 0.017 and 0.012
viation of the ratio samples σr at io of Q avд
for the Texas and Irish datasets respectively. Using a smoothening

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Figure 5: (a) AM (T ) unstable, (b) Q avд
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All HMt and AMt over the time window T are recorded, suchthat the corresponding daily averages are given by HMavд (T ) =


P
P
24
24
t =1 AM t /24 over this wint =1 HM t /24 and AM avд (T ) =Raw Power Usage Data (W)i=1 ptmoving average will further lower the standard deviation and produce a more stable invariant under normal conditions.
Additionally, higher the variance in the power consumption
dataset, the lesser is the mean of ratio sample distribution and vicer at io (T ) is a more robust
versa. Hence, we conclude that the Q avд
metric for anomaly detection than other typical measures suchas mean, mode, median due to its high invariance to legitimatechanges in data over successive days across years.

Ratio

Let ptmix = {pt1 , · · · ,ptN } denote the power consumption data series on an power transformed scale gathered from N smart metersat any time slot t (t is slotted hourly). The harmonic mean (HMt )and arithmetic mean (AMt ) of aggregate power consumption in atime slot is defined as:
PN i
pt
N
AMt = i=1
HMt = PN 1
N
i

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

40
20

300

0
0.89

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0.91

0.92

0.93

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Ratio

(a)
(b)
r
at
io
Figure 6: (a) Q avд (T ) of Irish Dataset, (b) Ratio Distribution(ii)
Special asymmetry property of Pythagorean Means:
Asymmetric growth (or decay) rates of harmonic mean comparedto the symmetric growth (or decay) of arithmetic mean undervarious attacks, is another reason which helps to infer the presence and type of falsification precisely, quickly, and with highsensitivity. With this attack context information, it is possible
to estimate the true consensus accurately. When a subset of p ivalues in pmix are increased/decreased (with a false bias δ ), theAM value grows or decays linearly. On the contrary, the behaviorof HM is inherently different and can be summarized as follows:
Property (1) : We observe that HM grows slower and decays fasterthan corresponding AM, when sub-portions of a data set generated from multiple sources experience additive and deductive
manipulation, respectively.
Property (2) : Growth and decay rates of HM under the same δis unequal when used for additive and deductive attacks, unlike
AM which show equal rates. In HM, decay rate is larger than its
growth rate induced by the same δ .
Property (3) : We observed that growth and decay rates of HM
compared to AM and the effects on the proposed ratio metric also
depend on (a) whether the datapoint being biased are on the lesser(left) or greater (right) than the actual arithmetic mean, and (b)the magnitude of δ .
The above properties can be mathematically illustrated by thefollowing: Consider a sorted series with two numbers U = (u 1 ,u 2 )such that its mean and standard deviation is (AM,σ ). In Fig. 7, thex-axis represents the variable u 1 . Let us fix the u 2 as constant suchthat u 2 = {2} is a singleton set, while u 1 is a set such that u 1 ∈ R+ .

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

2.52

u2 = 2
E

a+

y

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+

h
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1

y = AM (u1,u2)h−y = HM (u1,u2)

0.5
0
0

0.5

1

1.5

u1

2

2.5

3

Figure 7: Growth Decay Rates of HM and AM
Hence, the cartesian product of u 1 and u 2 is the set U = u 1 ×u 2 ,whose elements are a two tuple dataset. In Fig. 7, let the y-axis
represent the value of AM (u 1 ,u 2 ) or HM (u 1 ,u 2 ) for every possible element in the set U . Given any element say U = (1, 2), visualize increasing/decreasing value of u 1 as mimicking additive or
deductive biases to U = (1, 2), that changes both the AM (u 1 ,u 2 )or HM (u 1 ,u 2 ). In Fig. 7, AM function of (u 1 , 2) ∀ u1 ∈ (0, ∞](represented by the solid blue line) shows a linear growth with increasing u 1 , and is neither strictly concave or convex. On the other
hand, the HM function of (u 1 , 2) ∀ u 1 ∈ (0, ∞] (represented bya dashed red line) is a strictly Schur-Concave Function [32]. Thisdifference in concavity is the theoretical basis that trigger changes
in the proposed ratio metric under various attack types and is illustrated below using the same example.
Illustration of Properties: For dataset U = (1, 2), let the AM =1.5 and HM = 1.33 be represented by points A and H as marked in
M
Fig. 7. Hence, their ratio value say Q r at io = H
AM = 0.88.
Suppose in U = (1, 2), u 1 = 1 is biased with deduction of δ = 0.3,
such that U − = (0.7, 2). Points a − = 1.35 and h − = 1.037 correspond to the biased arithmetic and harmonic means respectively.
Thus, decay in HM and AM are ∆HM − = h − − H = −0.293
and ∆AM − = a − − A = −0.15. Ignoring the signs which signify decay, |∆HM − | > |∆AM − |, proving that HM decays fasterthan AM. Note that the biased ratio of HM to AM in this caseis Q − = 0.76 < Q r at io = 0.88. Suppose, the same δ = 0.3
is instead added to u 1 . However, with δ = 0.3, added to u 1 , theQ + = 0.95 > 0.88 = Q r at io . Since |0.76 − 0.88| > |0.95 − 0.88|, itproves Property 2. While, we may be temped to believe that additive attacks increase ratio while deductive attacks decrease them,this is not true. Consider an additive bias value of δ = 3.5 instead,that is added to data-point u 1 = 1. The resultant ratio in this case is
Q + = 0.82, which is a decrease from the original ratio 0.88. Therefore, the fact that magnitude of δ , plays a role in the observed riseor drop in the ratio is established. Finally, suppose the δ = 0.3 wereadded to u 2 instead of u 1 . Note that in U = (1, 2), the data-pointu 2 = 2, is on the greater than (right side) of the true mean of U(= 1.5). Now the Q + = 0.80 < Q r at io = 0.88. This proves that position of the data-point being biased by an δ , w.r.t to true AM also plays
a role in the ratio change. The above clearly explains property 1,2
and 3. The necessary and sufficient conditions of δ avд , for observing a drop or rise in ratio metric under each attack type and theeffect of biased datapoint’s position relative to the true mean is detailed in Appendix A. The basic conclusion from the illustration in
Appendix A, is that the ratio metric decreases only when the biased

datapoints move original datapoints away from the true arithmetic
mean in a way that flattens the shape of the distribution (increasing the sample standard deviation), while, rise in ratio occurs if thebiased datapoints move original datapoints closer to the true mean
(increasing the sample standard deviation).
(iii) Effect of Attacks on the Ratio Metric : Since we know that
datapoints regardless of meter ids are more frequently on the lesser
than of the mean (as shown in Section 3.2), it is a natural consequence that the more attacked data-points, will also be lesser than
the true mean, regardless the attack type. Given this, a deductive
attack, will cause more datapoints to move further away from thetrue mean. Therefore, we can conclude that the ratio is going to decrease for deductive attacks, regardless the δ avд . For camouflage
attacks, also since the HM has a higher decay rate than growth rateof AM for the same δ bias, the ratio is bound to decrease regardless the δ avд . In contrast, the additive attacks with lower margins
of false data will cause the final biased datapoints to be proximate
to the true mean, thus reducing the sample standard deviation, andtherefore increasing the ratio metric. However, for higher margins
of δ avд , the biased datapoints will end up being greater than truemean, and the ratio will show a decrease.
Above conclusions on increase and decrease of ratios have been
experimentally verified in Fig 8, where ρmal = 40% was used for
different attacks with varying δ avд . The deductive and camouflage
attacks correspond to a δ avд = 600W . The additive small and additive large denote the ratio lines under an attack of δ avд = 200W
and δ avд = 800 respectively. The exceptions to the above observations may happen, if the attacker possess complete knowledge ofsystem, defense mechanism and insider leaks; the details of which
is discussed in Sec. 5.2.4.
0.94
0.92
0.9 Attack Started

Ratio

3

Bhattacharjee et al.

0.88
0.86
0.84
0.82

No Attack
Additive Smallδ avg

Additive Largeδ avg

Deductive
Camouflage

20

Attack Stopped

40

60

80

T (days)r at io (F ) under various attacks
Figure 8: Q avд

5.1.2 Inferring presence of Organized Falsification: We
know that asymmetric growth and decay rates of the HMavд (T )r at io (T ),and AMavд (T ) trigger a decrease or an increase in the Q avд
as false data is injected from a subset of numbers generating thesemeans. Leveraging this knowledge, we propose the unsupervisedand semi-supervised versions of the detection criterion that indicates the presence of an organized falsification, and thereby theneed to invoke a suitable type of consensus correction.
A sustained drop or rise in ratio indicates malicious activity.
Therefore, we need a collective anomaly detection (monitoring a
subsequence of states) instead of point anomalies (monitoring eachstate independently). To capture collective anomalies, we define ar at io (T )sliding frame that contains the cumulative average of Q avд

Semi-supervised Identification of Smart Meters Launching Data Falsification
samples over the last F days. If the cumulative average in the current frame F has deviated from the cumulative average in the previous frame F − 1 by a threshold ϵ, then this forms a premise fora sustained change in the ratio metric. Formally, the unsupervised
detection criterion is:
r at io (F − 1) ± ϵ∈ Q avдr at ior at io<Q
Q avд
(F ) : avд (F − 1) − ϵ > Q r at io (F − 1) + ϵavд
No Anomaly;
Orchestrated Attack;Low Additive Attack;(4)

where ϵ is a threshold parameter such that ϵ ∈ (0, 3σr at io ]. The
choice of ϵ controls whether the consensus correction step will be
invoked or not. The appropriate ϵ can be learned by studying thetrade-off between ϵ and classification error rate, over various δ avд
and ρmal combinations as shown later in Figs. 11(a) and 11(b). Note
that, the required sensitivity of ϵ to attacks need not to be very
precise, since the purpose of Eqn. 4 is to only catch evidence oforchestrated attacks, that disturb the consensus significantly andtherefore need the consensus correction. In contrast, isolated or
smaller scale attacks (with low δ avд /ρmal ) do not drastically deviate the ratio metric and thus may not get detected under the given
ϵ. However, at the same time such small scale attacks will also notaffect the consensus in a way that causes large classification errors.
r at io (F ) over time is enough to conclude
Therefore, observing Q avд
r at io (F )whether an orchestrated falsification is happening. If Q avд
has decreased (or increased) more than ϵ, than the previous framer at io (F − 1), it is an evidence of the start of an orchestrated falQ avд
sification. Let this frame be marked as Ft r iд , such that Ft r iд − 1 isthe last frame with a normal ratio value.
Now, after a period of sustained drop (or rise) in the ratio metricr at io (F ) may indicate
outside the ϵ, an increasing (or decreasing) Q avд
that attacks are now ceasing. As seen in Fig. 8, the ratio increases(decreases) back to the normal range Q r at io (Ft r iд − 1) ±ϵ value on
the 72nd day, when our implemented attack was stopped on the
68-th day. Note that, isolated attacks from individual customers,
may not have a drastic effect on the ratio margin (±ϵ), and these
attacks are countered by the trust model discussed later. This is avery simple but very powerful technique to differentiate between
legitimate changes due to environment and false data injections.
Semi-Supervised Version of Detection Criterion: One disadvantageof the unsupervised detection criterion (Eqn. 4), is that it may missincremental attacks where δ avд slowly increases over time, suchthat the drop of ratio compared to the previous time window will
be within the ϵ. However, if enough historical (attack free) data
is available (e.g. the Texas Dataset), the historical normal range
r at io (F hist ) ± ϵ of the ratio can be learned easily given its stable
Q avд
nature. In such as case, even with incremental attacks, the ratio
metric will eventually cross the learned stable historical range.
5.1.3 Inferring Type of Data Falsification: Once falsification is inferred at Ft r iд , observing the direction of HMavд (T ) andAMavд (T ) growth or decay, indicates the type of data falsification:
additive, deductive, camouflage. For notational simplicity, henceforth we will refer to HMavд (T ) and AMavд (T ) as HM and AM
respectively. The resilient mean ( µ M R (T ) ) and standard deviation( σ M R (T ) ) for window T , is referred as µ M R and σ M R respectively.
If both HM and AM values have increased compared to Ft r iд ,then it is an additive attack. In deductive attack, both HM and AM

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

decreases from the Ft r iд . In camouflage, the AM does not changemuch and HM decreases. The various possibilities are depicted inTable 1. A pictorial view of this is shown later in Fig. 12 and Fig. 13.
5.1.4 Consensus Correction: We calculate the resilientmean at each window T (µ M R ), as an estimation of the actual mean,
given the information on presence and the type of attack. We exploit the robustness of HM and AM, under different attack types
for estimation of the actual mean.
Table 1: Inferring Attack Types
Ratio
Down
Down
Down
Similar
Similar

HM,AM
Up,Up
Down,Down
Down,Similar
Up,Up
Down,Down

Inference
Additive
Deductive
Camouflage
Legit Up
Legit DownµM R
HM-(AM-HM)
AM+(AM-HM)
HM
AM
AM

Mean Correction: The choice of µ M R is guided by how the detected attack type biases the actual values of HM and AM. For additive attacks, the growth in HM is less than AM due to slower
growth rate although both increases from actual AM. Hence, we
deduct corrective factor (AM − HM ) from the observed HM to estimate the µ M R . For deductive attacks, HM has a faster decay rate
than AM. Since, HM ≤ AM, for deductive attacks, HM is evenlesser than the reduced AM. Hence, we add to the observed AM,
the corrective factor (AM − HM ), to estimate the µ M R such thatµ M R = AM + (AM − HM ) is closer to the actual mean and far fromdeductive outliers at the same time. We choose to add (AM − HM )to the AM because of larger HM drop for deductive attacks cancause (AM − HM ) value to be very high (when ρmal and/or δ avд
is high). Adding it to HM may be far less than the true mean. Hence,adding it to AM makes µ M R closer to the actual AM.
For camouflage attacks, HM works as a good measure of µ M R
due to its stability to partial presence of false additive data. In fact,using the HM for camouflage helps distinguish meters launching
additive falsification from meters launching deductive falsification,
because HM is not symmetrically distant from the additive and deductive outliers, unlike AM. The deductive meters will have trust
values lesser than honest meters but higher trust than additive meters. This is because HM will be closest to the data generated fromhonest meters followed by deductive and furthest from data generated from additive meters. Alternatively, if the separate identification of additive and deductive outlier meters are not desired
AM may be used for µ M R . In general, AM is more robust mean for
camouflage attacks, when ρmal for camouflage attack is ≥ 50%.
r at io (T ) is an indication of ρ
The extent of drop in the Q avд
mal andr at io (T ) larger is the ρδ avд . The larger the drop in Q avд
mal and δ avд
and larger the bias in the observed mean. In case, no organized attack is detected from anomaly detection phase, µ M R is equal to theobserved AM. Table 1, summarizes the calculation of µ M R .
Standard Deviation Correction: The σ M R will increase regardlessthe type of data falsification attack (except for low additive attacks).
Therefore, a directional correction is not possible like µ M R basedon the attack types. Using the measured σ M R of the last time window, before detection of orchestrated attack, may not be wise since

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

5.2 Consensus Aware Trust Scoring Model
The trust scoring model has three parts: discrete rating criterion,
Folded Gaussian distribution based weights, inverse power law kernel based trust metric.
The discrete rating criterion assigns a rating level to each meter i, by comparing proximity of its reported data pti with the resilient mean consensus µ M R , over a time window of lengthT . Then,
weights are assinged to these discrete rating levels according toboth prior frequency of occurrence, density of each rating level ina Folded Gaussian distribution, and their proximity to µ M R . This
step finally yields an aggregate weight R i for each i. Then, an inverse power law kernel is used to map the R i weights into a trust
value T R i between 0 and 1, for linearly separable classification ofcompromised meters from honest meters.
5.2.1 Discrete Rating Levels: . We propose a criterion to assign
a discrete rating level to the reported pti based on its proximity toµ M R . The σ M R is the corrected standard deviation of all pti fromthe calculated µ M R in the window T . We define ∆abs = σ M R . The
absolute difference between the pti for any meter i and the µ M R isidenoted by Θdif
= |pti − µ M R |. Given this, the discretized ratingflevels denoted by l is given by Table 2, using the 68 − 95 − 99.7 rulefor Gaussian distributions to assign pti as belonging to one of the
4 possible rating levels (bins) according to proximity to the µ M R .
The highest rating 4 is closest in terms of proximity to µ M R , andsimilarly lower ratings are obtained if the meter’s data is further
from the µ M R . Over a time window of say T hours, the ratingson each time slot t for meter i is collected to form a rating vectorisequence r i , which is sorted as r sor
t = r 0 ≤ r 1 ≤ · · · ≤ rT −1 .
Table 2: µ M R based Discrete Rating Levels

ScenarioiΘdif≤ ∆absfi∆abs < Θdif f ≤ 2∆abs
i
2∆abs < Θdif≤ 3∆absfotherwise

Discrete Rating Level(l)432
15.2.2 Folded Gaussian based Weights: . Now we find the correi
sponding (normalized) weights of each rating in the r sort whichi
is denoted as W = w 0 , · · · ,wT −1 . Figs. 9(a) and 9(b), signify theapproximate Gaussian nature of the rating distributions, under no60

Percentage Rating (%)

70

Percentage Ratings (%)

there may be a longer delay between the launch and the actual detection of the falsification (such as in incremental attacks). Alternatively, one may be tempted to use the historical value of SD avд (T )on the corresponding T -th day in the previous years. However, thiswould add to the storage complexity. Moreover standard deviationon the same days on successive years are not necessarily same. We
studied the distribution of SD avд (T ) over the years and found thata distinct mode of SD avд (T ) distribution occurs at 425 − 475W
range in the non-transformed scale. The probability of SD avд (T )being around 425 − 475W is very high over 50% while all otherranges are less than 10%. As an approximation, we choose σ M R asln(450), whenever orchestrated attacks have been confirmed for using it in the subsequent trust model. The distribution of SD avд (T )is shown in Appendix B.

Bhattacharjee et al.

60
50
40
30
20
10
0

1

2

3

4

3

2

50
40
30
20
10
0

1

Discrete Rating Levels

1

2

3

4

3

2

1

Discrete Rating Levels

(a)

(b)

Figure 9: Real Rating Distribution (a) Meter 1 (b) Meter 2
attacks for two real meters from Texas dataset. It is clear that themost common and highest rating level is 4 followed by all others. This gaussian nature is known as Folded Gaussian where variables around the mean do not have different signs, since only themagnitude of the level is important. Intuitively, meters with more
observed lower ratings should have lesser weights. The sorting
makes it easier to give lower weights to smaller ratings throughEqn. (5) by dividing the rating space over the considered time window. Then via Eqn. 6, the distance between this weight x t from thehighest rating level (which is 4 known from no attacks) is determined. If the distance is larger, it assigns a non-linearly decreasing
density value based on the shape of Gaussian distribution.
Additionally, higher percentage of lower ratings in a window,
will give even lesser weights to those smaller ratings, than a scenario with lower percentage of low level ratings and vice versa
achieved through Eqn. (6). We denote µ BR = 4 as the best or highi denote the standard deviation of disest possible rating level, σdrcrete ratings of each meter from µ BR = 4 in a window length T .
i for each meter will be different based on different obserThe σdrvations compared to common mixture data, which captures certain
individual differences in consumption. First, a weight parameter x t
distributed between 1 to 4 is calculated as:(K − 1)t∀ t = 0, · · · ,T − 1(5)xt = 1 +(T − 1)
where K = 4, is the total number of discrete rating levels in thesystem, T is the window size. Therefore, the corresponding raw
weight cw t of the rating at time index t is:
cw ti =

1
√
i

σdr

2π

e

−

(x t −µ BR ) 22(σ i ) 2
dr

(6)

The weights yielded from Eqn. (6), are normalized by w ti =cw i
PT −1 t i . Let I (l,t )t =0 cw t

be an indicator function which indicates

whether a particular rating level l occurs in that time slot. All
weights corresponding to each unique rating level l, such l =P −1{1, · · · , 4} within T is added up, such that W D (l ) = Tt =0
w t I (l,t ).
(1,
If l occurred in time slot t
where, I (l,t ) =(7)0,
Otherwise
For example, sum of weights inW i corresponding to each occurrence of rating level 2 is denoted by W D (2). The aggregate weightrating R i of the i-th meter is a continuous value between 1 and 4
and is given by:
Ri =

K
X
l =1

l × W D (l ),R i ∈ {1, 4}(8)

Semi-supervised Identification of Smart Meters Launching Data Falsification

1

Trust Value

Probability

0.4

0.2

0

η=7
η=6
η=5
η=4
η=3
η=2

0.8

Meter #1
Meter #2
Meter #3

0.6

0.6
0.4
0.2

1

2

Ratings

(a)

3

4

0

0

1

2

Ri

3

4

(b)

Figure 10: (a) Folded Gaussian (b) Inverse Power Law Kernel
5.2.4 Under Advanced Persistent Threats: . For advanced persistent adversaries, possessing full knowledge of our defense mechanism is ‘not’ enough to escape detection completely. The adversary has to ensure that deviation in the ratio metric never exceeds ϵon every time window. To completely escape detection, it is mandatory for adversary to possess four additional knowledge: (i) Closed
Form Expressions of Harmonic Means (ii) Exact (non-attacked)
harmonic and arithmetic mean on each time slot (iii) ϵ value (iv)skewness of data distribution. The skewness knowledge is public(right skewed) and has no attack cost. Different microgrids will
have completely different ϵ values, hence the attacker needs toknow ϵ of each micro-grid. The ϵ value may be leaked by compromising an utility insider for each micro-grid, or the databasestoring all the ϵ values. Both possibilities increase the attack cost.
Assuming, that attacker knows the ϵ, it further needs the exact
knowledge of HM and AM in each time slot. This is rather implausible for adversary to know at runtime, unless it compromises 100%of the meters. This is because the means do not have any stablehistorical trend or time series, so attacker cannot reliably predict
them. Unless actual HM and AM is known, one cannot ensure thatr at io (F ) from the attack will have a ratio deviation
the resultant Q avд
that is lesser than the ϵ. Most importantly, the exact closed form expressions of harmonic means do not exist, and is an open problem
in real analysis. Several approximations exist [18], but note that

6

EXPERIMENTAL RESULTS

Data sets from 200, 700, and 5000 houses, were obtained
from PeCanStreet Project [25] and Irish Social Science Data
Archives [26], containing hourly power consumption data from
Texas, Austin and Dublin, Ireland respectively. The different microgrid sizes mimic decentralized and centralized deployments of defense frameworks. We studied results of anomaly detection andtrust model for all types of data falsification. Additionally, we studied the performance scalability of Irish data for 5000 houses. For
anomaly detection results, a period of no attacks is followed by aperiod of attacks. Deductive attack results have lesser δ avд thanthe others, since realistic values of power consumption are lower
bounded by zero. For clarity of representation, we show anomaly detection results using cumulative moving averages over timeframe (F ) of length 7 days. Additionally, for easy depiction of meter classification results, all the compromised meters are assigned
lower meter id than the honest ones. Finally, we show performanceover all values of ρmal and δ avд and compare with existing work.
0.3
0.25

0.25

0.2

Error Rate

0.8

it does guarentee success everytime and the defender needs success only once to raise an alarm. Even if the attacker knew everything somehow, we show that the signatures are visually evident
for δ avд values as low as 50W (see Appendix C).
The sensitivity to successful identification of compromised meters is different from sensitivity to successful detection of presenceof orchestrated attacks. Given our model, we report that if that
attacker’s δ avд < 300W , the missed detection rate drastically increases to 52%, since such δ avд is much less than standard deviation which ends of with higher rating levels. For the attacker tokeep atleast 50% of its compromised meters undetected, the highest possible δ avд = 300W when ρmal = 40%. However, at suchlow δ avд , the impact per unit time is less (see Appendix D).

Error rate

5.2.3 Inverse Power Law based Trust Value: . We know that theiΘdifis an unsigned value which can be visualized as a foldedfGaussian distribution, where ratings 3,2,1 regardless of whether
they are on the right or left of the rating level 4 are treated as
the same random variable. Therefore, the aggregate weight (R i ),when interpreted as a trust score must also follow a folded gaussian shape, meaning R i = 4 represents the greatest trustworthinessfollowed by a exponential ‘discounting’ of trust, as R i decreases.
For this, we propose the inverse power law inspired kernel trick totransform the R i into a final trust value, T R i , between 0 and 1, by:1
T Ri =(R i ) η , T R i ∈ {0, 1}(9)(K ) η
where η is a scaling factor controlling the rate of discounting. The
Eqn. (9), gives exponentially less trust to R i as it decreases from the
maximum value of 4, in adherence to the Folded Gaussian shapeof the rating distribution of legitimate meters (shown in Figs. 10(a)and 10(b)). The scaling factor η depends on the skewness of folded
gaussian in the benign data set. The Eqn. (9) produces trust values such that compromised and non-compromised meters have linearly separable, which enables to calculate an unsupervised threshold for classification. The trust maintenance over time uses a forgetting average [4] for periodic attacks.

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

0.15
0.1
0.05
0
400

3
800

2
1200

∆ avg

1

ǫ ( x σ ratio )

(a)

0.2
0.15
0.1
0.05
3
0
400

2.5
600

2
800

1000

1.5
1200

∆ avg

1400

1

ǫ (x σ ratio )(b)

Figure 11: Error Rates: (a) ρmal = 40% (b) ρmal = 10%

6.1 Choice of ϵ for consensus correction
The choice of ϵ decides, whether the anomaly detection raises analarm or not, which in turns decides whether or not the consensus
correction is invoked that subsequently affects classification error
rates. In the real-world, the drop/change in the ratio depends on
the attacker’s ρmal and δ avд values which is always unavailable
to the defense framework at run-time. To provide a suitable recommendation on the desired ϵ, we performed some experiments foran appropriate recommended value of ϵ.
It is important to understand that, smaller ρmal and δ avд pairs
will cause smaller drop/change in the ratios and therefore, ϵ willneed to be small to capture them. However, this aspect is offset by

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

Bhattacharjee et al.
is larger than the chosen ϵ (i.e. Q r at io (F ) is decreased for ρmal <85% values compared to the ratio when ρmal is 0%). This is the reason for successful anomaly detection to higher fractions of compromised meters. We also observe, that the minimum ratio is achieved
when ρmal ∼ 50%, for additive and deductive attacks. However,for camouflage attacks, the ratio always decreases with increasingρmal , since the deductive portion of the camouflage attack only affects the Harmonic Mean while keeping the AM same. Hence, theresultant ratio decreases regardless the ρmal .
1
0.8

0.2

7
Ratio Drop

6.5

6

T trig20

4060Time (days)

80

HM
AM

40

60

80

(b)

Figure 12: Ratio Change: (a) Additive (b) Deductive
0.94
HM
AM

0.92

Camouflage
Additive
Subtractive

0.9

7

Ratio

Power Consumption (ln(P))

7.5

0.88

6.5

0.86
0.84

6

0.82
5.5

40 Time (days)
60

(a)

80

0.8
0

0

50

100

150

200

Meter ID(b)

1

Trust Value

Trust Value

0.6

Additive Nodes
Honest Nodes
Classifier (0.56)

0.8Additive Nodes
Deductive Nodes
Honest Nodes
Classifier (0.81)

0.6
0.4

0.4

0.2

0.2
0

50

100
Meter ID

150

0

200

200

(a)

400
Meter ID

600(b)

Figure 15: Texas Dataset (a) Camouflage (b) 700 houses
Attacked Node
Honest Node

0.9

Trust Value

Attacked Node
Honest Node

0.9
0.8

0.8
0.7
0.6
0.5
0.4

0.7
0.6
0.5
0.4
0.3
0.2
0.1

0

200

400

600

800

0

200

400

600

Meter ID

Meter ID

(a)

(b)

800

Figure 16: Irish Dataset (a) δ avд = 500 (b) δ avд = 600
Time (days)

(a)

200

Figure 14: Texas Dataset: (a) Additive (b) Deductive

0.1

6

5

Meter ID

150

0.2

6.5

5.5

100

Trust Value

Power Consumption (ln (P))

Power Consumption

7.5

50

0.3

Deductive
AttackStarts

7

0.4

(a)

0.8

Additive
AttackStarts0.6

0.2
0Figure 12(a), shows the directional changes in HM and AM andratio drop to distinguish between legitimate changes and malicious attacks. In the first 57 days, HM and AM changed but
their growth/decay had a symmetry, indicating legitimate changes
r at io (F ) ∼ 0.92 value. Howin consumption through same Q avд
ever, when additive attack phase was launched at 58th day, ther at io (F ) started to decrease from within 2 days of attack, due to
Q avд
slower increase of HM compared to AM. The directional changeof both HM and AM values from Ft r iд (arrow upwards) indicate
the additive nature of attack. The inference of attack and its typeis quick. The Fig. 12(b) and Fig. 13(a), show real time anomaly detection for deductive and camouflage attacks respectively.
7.5

Trust Value

0.4

6.2 Inferring Presence and Type of Falsification

HM
AM

Malicious
HonestClassifier (0.70)

0.8

Malicious
HonestClassifier (0.45)

0.6

1

8

1

Trust Value

the fact that they also do not affect the consensus in a drastic way.
In that case, an unwarranted consensus correction will cause theclassification errors to increase. As a proof, it can be observed from
Fig. 11(a) and 11(b), error rates are higher for very low values ofϵ. On the flip side, if the ϵ is too large, it will fail to raise alarmfor many possible ρmal and δ avд pairs. Therefore, the consensus
correction will not be invoked, the trust scoring model will be executed with a biased consensus increasing the classification error
rates. Again this could be verified from Fig. 11(a) and 11(b), where
we see the error rates are very high when ϵ ∼ 3σr at io . Naturally,
there will be an intermediate optimal region of ϵ, where the error
rates will be minimized. From computational study, we observedthat regardless the wide variation of δ avд (from 350W to 1400W),
the error rate minima is achieved at ϵ = [1.5σr at io , 2σr at io ] of theratio sample distribution, at ρmal = 10%,ρmal = 40% respectively.
Therefore, although ρmal and δ avд may not be known apriori, therecommended ϵ value could be learned a priori, by the above manner. Following this, we have used ϵ = 2σr at io , for all performance
results, even for results parameterizing different ρmal .

20
40
60
80
100
Percentage of Compromised Meters(b)

Figure 13: Ratio Change: (a) Camouflage (b) Over all ρmal

6.3 Robustness of Anomaly Detection over ρmalr at io (F ) based detection is robust across larger fractions of comQ avд
promised meters. Fig. 13(b), show that the drop in the Q r at io (F )6.4 Compromised Meter Classification
Fig. 14(a) and Fig. 14(b), show the performance in terms of steadystate trust values, under additive and deductive falsification when
50% meters are compromised for δ avд = 900 and δ avд = 760 for asmall subset of 200 houses from Texas dataset. It is clear that compromised meter’s trust values, marked in red (asterisk) are significantly less than non-compromised smart meters marked in blue
(circles), such that they are linearly separable through a threshold. The threshold is obtained through a standard K-means unsupervised learning classifier. Similarly, Fig. 15(a) shows the steadystate trust distribution under camouflage attacks with ρmal = 50%,
where additive and deductive meters are marked in green and red
while non-compromised are marked in blue. Fig. 15(b) confirms
the scalability results for 700 houses in Texas dataset under an additive attack. Note that, the false alarm (FA) rate scale well with 3%
and 2.8% for 200 and 700 houses given same δ avд as evident fromFig 14(a) and Fig. 15(b).

Semi-supervised Identification of Smart Meters Launching Data Falsification

Attacked Meters
Honest Meters

0.6
0.5

0.7

0.4
0.3

Isolated Malicious
Meters Detected

0.8

Threshold

20

40

60

Days

(a)

80

100

120

Trust Value

0.6
0.4

0.6

0.4

0.2

0.2
0

Malicious
HonestThreshold

0.8

0

50

Meter
100ID

0

150

200

0

50

100

150

200

Meter ID(a)(b)

Figure 18: (a) Omission (b) Incremental

0

5

10

15

20

Meter ID(b)

Figure 17: (a) Fast Time to Classification (b) Isolated Attacks

6.5 Time to Detection of Compromised Meters
One key advantage of our work is that it allows for quick identification of compromised meters compared to most accurate classification based methods [8, 9]. Fig. 17(a), shows that difference in theevolution of trust values after the attack is launched. Since, it is notlegible to show every single meter in one plot, we plot the averagetrust of the compromised set and the average trust of the honest
set over time. Fig. 17(a) shows that the average trust of compromised set of meters falls below the threshold within 10 days fromthe start of attack. Therefore steady state as described in Figs. 14(a)and 14(b) is achieved within 10 days on average. Hence, rogue meters are identified before drastic damages have been inflicted.

One benefit of our work is the robustness to higher fractions ofcompromised meters compared to most consensus based methods
that fail when ρmal and/or the δ avд is high. Fig. 19(a) and Fig. 19(b),shows the average trust values of all compromised meters versus
honest ones. Our technique completely fails at 75% percentage
of compromised meters for a 200 house Texas dataset, which isresilient. Similarly, Fig. 20(a), shows the average trust difference
among compromised and honest sets of meters over various δ avд
under additive attacks, when ρmal = 50%. Fig. 20(b), shows theperformance of our model, when compromised meters alternate
true and false behavior periods based on pricing. We can observe,that although the difference between trusts are lesser than earlier
case, we can still classify the compromised ones.
1

1
Avg. Trust:Malicious
Avg Trust: Honest

Average Trust Value

0.9

Attack Started

0.8

Average Trust Value

1

0.8
0.7

Malicious
HonestThreshold

6.8 Avg. Performance over ρmal and δ avд

Trust Value

Average Trust Value

0.9

1

1

Trust Value

To prove that our work is valid, scalable and robust across different data sets, we show the performance of steady state trust
values using a bigger subset of the Irish dataset with 1000 houses
for deductive attacks with lower margins of false data. Figs. 16(a)and 16(b), shows trust value distribution and classification performance for δ avд = 500 and δ avд = 600. We see that even for a large
and different region, with lower δ avд than Texas data, the false
alarm and missed detection rates are 9% and 8%. A performanceaccuracy for 5000 houses over all δ avд and ρmal values and ourcomparison with existing works is shown later in Sec. 6.9.

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

0.8
X: 75
Y: 0.7248

Blinding Point
ρ
~ 75%

0.6

mal

0.4
20
40
60
80
Percentage of Compromised Meters

6.7 Classification against Omission andIncremental Attacks
Fig. 18(a), shows the evidence that the proposed model can detect omission attacks, where 30% of the meters dropped the data.
Fig. 18(b), is the performance against incremental attacks after 45days of the initial attack was launched. The amount of false data
was incremented by 2W per meter every 4 hours.

ρ mal

X: 82.5
Y: 0.4568

=
82%

0.4
0.2

(a)

100

(b)

Figure 19: Robustness over ρmal (a) Additive (b) Deductive
1

0.8
0.6

Avg. Trust Value

Avg. Trust Value

6.6 Classification against Isolated Attacks

Blinding Point

0.6

0
0
50
Percentage
of Compromised
Meters1

Although, our work is focussed on defending against orchestrated
attacks, with large number of compromised meters, our work is
still valid in identifying isolated malicious meters that may act
alone. In such isolated attacks, the ratio drop may not be observably significant unless δ avд is abnormally high. However, this is
not necessary as such isolated attacks in such cases would not drastically affect the means and get revealed through the discrete rating
criterion and the proposed trust model. As an evidence, the trust of
two isolated meters launching additive and deductive attacks withδ avд = 600, (shown in Fig. 17(b)), is far less than other honest meters. Hence, this is a proof of validity for isolated attacks. Hence
our defense model is sensitive to small scale low ρmal attacks.

Avg. Malicious
Avg. Honest

0.8

Avg. Compromised Meters
Avg. Honest Meters

0.4
0.2
0

500
1000
1500
Margin of False Data (W)

(a)

2000

0.8
Honest Node
Additive NodeClassifier (0.88)

0.6

0.4

0.2

0

50

100
Meter ID

150

200

(b)

Figure 20: (a) Avg. Trust vs. δ avд (b) Periodic Attacks

6.9 Performance Accuracy & Comparison with
Existing Works
Fig. 21(a), shows our classification error rate over different δ avд forall 5000 houses in Irish dataset with ρmal = 40%. To understandhow it compares with existing works, Table 3 describes performance of other works in terms of various parameters such as False
alarms(FA), Missed Detection(MD), learning type (S=supervised,
SU=semi-supervised), and time to detection. Apart from this, we
also qualitatively compare the level of privacy intrusion and complexity compared to other schemes.
Fig. 21(a) shows that the worst case false alarm (FA) and missed
detection (MD) rate for δ avд = 350W is 18% and 9%. At δ avд = 400

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

16

20

False Alarms
Missed Detection

14

Missed Detections
False Alarms

15% Error% Errorwill discuss the theoretical details of the Pythagorean means forvery low δ avд < 350 in the future work.

25

18

12
10

ACKNOWLEDGMENTS

10

8

5

6
4
350

Bhattacharjee et al.

400

450

500

550

δavg

600

650

700

0

0
20
40
60
Percentage of Compromised Meters

(a)

80

(b)

Figure 21: Classification Performance with Scalability (a) All
5000 houses over δ avд (b) 200 houses over ρmal(used in [9] over the same dataset,did not report ρmal ), our workwith FA = 13.8% and MD = 9.3% outperforms [9] at a high ρmalvalue. At δ avд = 600W, we have FA = 6% and MD = 5% outperforming [1] that reported FA=9% and MD=8% but over a muchsmaller set of 200 houses without scalability evidence and higherδ avд of 700W-800W that favors good performance. False alarms
increase with decreasing δ avд and below 400 it increases more, because the standard deviation of the dataset usually range around
400W . To our best knowledge, only [19] using a synthetic data reported lesser error rates than us. But this happens only if numberof users are less than, 25 making this comparison unfair and therefore not scalable. Apart from this, [11] reports detection of around90%, but for δ avд as high as 1200W to 1800W , which will facilitate
easy detection in our case anyway.
Fig. 21(b), shows our classification error rate over different ρmalvalues for a smaller dataset of 200 houses in Texas. It can be seenthat missed detection and false alarm rates are less than 2% and 5%,
upto ρmal = 0.60. Above ρmal > 65%, the performance degrades,but missed detection rates are still lower at 13% and 25%, whereother works fail completely. A smaller population is chosen sincerealistic attack budgets may become a significant ρmal percentage
for the smaller micro-grids sizes, making such a study practical.
Table 3: Comparison with Existing Work
ParameterFAMDδ av д
ρmal

Size
Learning
Detection Time

Proposed
13%
9%
400W

≥ 40%+

5000
SU≤ 10 days

CPBETD [9]
29%
24%
400W
NA
5000
S
1 yr

ARMA [14]
33%
28%
NA
NA
200
S
1 mo

Entropy [1]
11%
8%
800W

≤ 40%
200
S
1 mo

7 CONCLUSION AND FUTURE WORK
We conclude that Harmonic to Arithmetic Mean ratios is an effective light weight indicator of organized falsification over different types of falsification attack and robust under higher fractionsof compromised meters while distinguishing legitimate changes
in the data to malicious ones and helps in consensus correction.
A semi-supervised folded gaussian trust model produces trust values, which identifies meters launching both organized or isolated
attacks within a few days of attack, while preserving lower missed
detections and false alarms rates, even when percentage of compromised meters are significantly higher. We showed that the method
is generic and applicable across different real smart meter datasets.
In future, we will extend our work to attacks where δ avд < 350
which may be realistic for advanced, persistent and long term adversaries who sacrifice immediate benefit for long term gains. We

This research is supported by the NSF grants CNS-1545037, CNS1545050. Sajal K. Das is also a distinguished visiting professor at
Zhejiang Gongshang University, Hangzhou, China.

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Semi-supervised Identification of Smart Meters Launching Data Falsification

AppendixC

In this section, we provide a detailed explanation of the necessary and sufficient conditions for δ avд in terms of ρmal = M/N ,the mean µ and standard deviation σ of the power consumption
dataset. Each occurrence of ratio rise or drop given an attack type,has an upper bound and lower bound on the value of δ that isdependent on the position of bias as well. For example, k − (rlow ),denotes the lower bound for a deductive attack on the datapoints
on the right side of the actual mean, and so on. The average case+approximate lower bounds are: k − (rlowr ) = k (llow ) =kl ow =

σ
σ
+ √
M
M

N −M
+σ
N −1

(10)

where + and − denote additive and deductive attacks and l and rdenote whether the position of biased data-points are on the left or
right side of the true mean. The average case approximate upperbounds are: k + (lhiдh) = k − (rhiдh) =khiдh = max (σ 2,

2σ
σ
+ √
M
M

r

N −M
+ 2σ )
N −1

0.95

(11)

The average conditions for deductive attacks on data-points theleft and additive attacks on datapoints on right side of the true
mean is:rk − (lhiдh) = k + (r hiдh) = σNN −1khiдh > |x i

− µ| + σ2

B DAILY STANDARD DEVIATION
DISTRIBUTION
The Fig. 22, shows the probability bar plot for SD avд (T ) for the
Texas dataset. We see that in most cases under no attacks, the probability of SD avд (T ), being between 425W-475W, centered around
450W is 0.52. Probabilities of all other ranges are much lesser.
Hence, the mode of the distribution is a reasonable approximationfor σ M R , under attacks being confirmed.
0.6

Probability

0.5
0.4
0.3
0.2
0.1
0
300

350

400

450

500

550

600

SD avg (T)

650

700

750

800

Figure 22: Historical SD avд (T ):σ M R approximation

0.9
Attack Starts

0.85

Honest Ratio

AttackIndication
Attacked Ratio

0.8
20

(12)

The worst case happens when additive attack changes only theminimum value (say x i ) of the dataseries, and deductive attackchanges only the maximum value of the dataseries. The worst case
expressions have little practical significance, but could be for purpose of verification. The worst case expressions for klow and khiдhare:qklow > {(|x i − µ | + σ NN−1 ) + µ)} − x i , and

STEALTHY PERSISTENT ATTACKS

Fig. 23, shows an example that our ratio metric may work even under ultra-stealthy margins of false data. Here ρmal = 40% and δ avд
is as low as 50W , where our attack was implemented from the 41stday. We estimated that this ρmal ,δ avд will cause deviation lessthan the ϵ with all the knowledge we possessed. Indeed, this works
well for most of the time, but is not guaranteed to escape detection
altogether, since all the meters whether compromised or not haveerratically changing data that is difficult to predict beforehand. In
future work, we will propose a mathematical detection criterion
for such stealthy attacks.
Targeted one sided attacks, may happen theoretically, where attack only attacks datapoints greater than the mean, then the observations will reversed. Deductive attacks may show an increase inratio, but in this case it will be restricted to only attacking 36% of
the total datapoints which restricts the attack significantly.

Ratio

A NECESSARY AND SUFFICIENT
CONDITIONS FOR RATIO DROP AND RISE

ASIA CCS ’18, June 4–8, 2018, Incheon, Republic of Korea

40

Days

60

80

Figure 23: Deductive Attack with Full Knowledge

D

COST BENEFIT UNDER MISSED
DETECTION

The revenue of an adversary per day who has M undetected meδ

×M ×η×E, where η is the number ofters is given by: RR = av д 1000
reports a day, and E = $0.12 is the average per unit (KW-Hour)
cost of electricity in USA. In [29, 30] mentioned that cost of compromising the smart meter is about $500, in the puerto rico attack.
Here, utility maintainance personnel asked for $300 − $700 fromdifferent customers and hacked their meters that reported lesser
power consumption, and promised benefit over time. The optimallaser probes used for those attacks vary around 400. Therefore,
for compromising 80 meters, the attack cost is about $40, 000. Atδ avд = 300, we have missed detection of 42 meters, hence therevenue for attacker is $36/day. At this rate, it would take about 3
years to recover the attack cost $40, 000. For δ avд = 350, only 7 meters remain undetected by our method, with an average revenue of$6/day. At this rate, it will take 18 years to recover the attack cost.
In future, we will explore how to identify meters reliably whichhave δ avд < 300W. That study will be useful if the attacker devises/offers novel cheaper ways of attack. Also, note that in termsof time to detection also our work is quicker (less than 10 days)
compared to existing works. Hence, an attacker who does not intend to remain undetected, is not able to gain much attack revenue.