Statistical Security Incident Forensics against Data
Falsification in Smart Grid Advanced Metering
Infrastructure
Shameek Bhattacharjee1 , Aditya Thakur2 , Simone Silvestri1 , and Sajal K. Das1
{shameek, astvd3, silvestris, sdas}@mst.edu
1

Department of Computer Science, 2 Department of Electrical Engineering
Missouri University of Science and Technology, Rolla, MO, USA

ABSTRACT

1.

Compromised smart meters reporting false power consumption data in Advanced Metering Infrastructure (AMI) may
have drastic consequences on a smart grid’s operations. Most
existing works only deal with electricity theft from customers.
However, several other types of data falsification attacks are
possible, when meters are compromised by organized rivals.
In this paper, we first propose a taxonomy of possible data
falsification strategies such as additive, deductive, camouflage and conflict, in AMI micro-grids. Then, we devise astatistical anomaly detection technique to identify the incidence of proposed attack types, by studying their impact
on the observed data. Subsequently, a trust model basedon Kullback-Leibler divergence is proposed to identify compromised smart meters for additive and deductive attacks.
The resultant detection rates and false alarms are minimized
through a robust aggregate measure that is calculated basedon the detected attack type and successfully discriminating
legitimate changes from malicious ones. For conflict andcamouflage attacks, a generalized linear model and Weibull
function based kernel trick is used over the trust score tofacilitate more accurate classification. Using real data setscollected from AMI, we investigate several trade-offs that
occur between attacker’s revenue and costs, as well as themargin of false data and fraction of compromised nodes. Experimental results show that our model has a high true positive detection rate, while the average false alarm rate is just
8%, for most practical attack strategies, without dependingon the expensive hardware based monitoring.

Advanced Metering Infrastructure (AMI) is one of the elementary units of the smart grid technology, which collects
data on loads and consumer’s power consumption [10], from
Smart Meters installed on the customer site (see Fig. 1).
Such data play a pivotal role in several critical tasks suchas automated billing, demand response, load forecast andmanagement [10].

Keywords
Statistical Anomaly Detection; Security Incident Forensics;
Trust Models; Data Falsification; Information Theory; Supervised Learning; Smart Grid; Advanced Metering Infrastructure; Relative Entropy
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CODASPY’17, March 22-24, 2017, Scottsdale, AZ, USA
c 2017 ACM. ISBN 978-1-4503-4523-1/17/03. . . $15.00
DOI: http://dx.doi.org/10.1145/3029806.3029833

INTRODUCTION

Figure 1: Architecture of AMI
Apart from automated billing, (already in use), strategic
decisions are expected to be taken by future smart grids,
based on the power consumption data. For example, thesedata will have implications on tasks such as daily and critical peak shifts [22]. When the consumption increases beyond a certain critical limit, emergency ‘peaker plants’ arecurrently used by most utilities for additional power generation to meet the demand. However, such peaker plants are
extremely carbon as well as cost intensive. In the modern
grid, the utility will also have the option for automated demand response where utilities pay customers to shut certain
appliances temporarily (peak shifting) to obviate the needfor additional generation [21]. In general, an accurate shortor long term data on loads and consumption will aid in accurate demand response, load forecast and planned generationin the future smart grid. Hence, the integrity of the data
generated from the AMI is of utmost importance.
Defense against falsification of power consumption datafrom AMIs, has largely focused on electricity theft [3, 7, 9,17], where individual customers are primary adversaries whoreport lower than actual usage for lesser bills. Since isolated

smart meters belonging to rogue customers reduce the valueof power consumption, we term such adversarial strategy asa Deductive mode of data falsification.
However, it has been widely acknowledged that given the
cyber and interconnected nature of AMI, it could potentially be the target of powerful and organized adversaries
such as rival nation states, utility insiders [20], organized cyber criminals and business competitors [4]. Such adversaries
can compromise several smart meters and then spoof false
power consumption data [7] from smart meters. Powerful
and organized adversaries are more equipped to crack/leakcryptographic secrets, have a higher attack budget, and possess the ability to simultaneously attack other elements ofthe grid (e.g., audit logs, transformers meters) in order toavoid easy consistency checks on false data. Existing research does not focus on defense against such adversaries
and is only restricted to attacks from isolated adversaries.
Additionally, the goals of these organized adversaries are
not just restricted to monetary benefits on the customer sidethat result from electricity theft. As a recent real example,
in Puerto Rico [20] a manufacturer and a utility insider colluded to install a large number of tampered smart metersthat reported higher than actual power consumption. We
term such an attack as Additive mode of data falsification.
Conversely, an additive attack launched by a rival utility on
its competing company’s meters may induce loss of business
confidence by the customers of the victim company, due tohigher bills as reported in [19]. A class action lawsuit filed
against a victim utility was reported in this case. If theutility participates in demand response, then utility may
lose revenue from additive attacks for undue compensation
payed to customers for induced peak shifts. Indirectly, additive attacks can be triggered when a load altering attack(LAA) [11] occurs on the individual appliances of a Home
Area Network (HAN), thus increasing the net consumption
sensed by the smart meter. It may also be noted that rival
nations, businesses, or organized cyber criminals may orchestrate large scale deductive attacks to cripple the utility
companies through revenue losses. Additive and deductive
attacks are termed as ‘simple’ attack types.
Furthermore, we argue the possibility of mixed attack
types on the smart meter data. For example, a balancing additive and deductive attack with the same margin offalsification of either type, could evade mean aggregate demand check/forecast models. We term such a strategy asa Camouflage attack, which may be motivated for generating lesser bills to one set of customers at the expense of
the other set. Such attacks may stay undetected, without
raising any suspicion because the total inflow and outflow ofpower measured at the transformer meters, and the total demand and reported usage remain unchanged. The attacker
in such a case need not attack other elements in the grid(for e.g. transformer meters) to prevent easy consistency
checks. In general, random additive and deductive attacks
may simultaneously coexist in the same AMI network, when
launched by different adversaries with conflicting goals. We
term such a scenario as a Conflict attack, which is a mixed
attack type with unequal margins of falsification for eachunderlying simple attack type. Existing literature cannot
handle all of the above data falsification strategies.
In this paper, we first introduce a taxonomy of possible
data falsification attacks launched by organized adversaries.
Then we study the statistical properties of the distributionof power consumption data and analyze the effects of various data falsification attacks types on the parameters of thepower consumption data. With the help of the observed
statistical effects, a security incident forensics criterion is
proposed that indicates the presence and the type of attack while discriminating effect of attacks from legitimatechanges. Subsequently, we propose a light weight KullbackLeibler divergence based trust model that identifies compromised meters with a high detection rate, by exploitingknowledge of the statistical impact caused by each attack
type, cyclostationarity of overall power consumption patterns, and factoring in for any legitimate change in the consumption patterns.
We use a generalized linear model (GLM) and Weibull
function based kernel trick to extend our trust model, for robust classification of compromised nodes based on the computed trust values with least missed detections and false
alarms, even for stealthy camouflage and conflict attacks.
We also perform a cost benefit and sensitivity analysis forboth of our attack and defense models. Specifically, we computationally study tradeoffs, such as breakeven time (i.e., thetime required for attacker’s revenue to equal its cost of attack) and breakdown point (i.e., the attack strategy for which
the defense mechanism is no longer able to distinguish thecompromised meters from honest ones). Experimental results show that our detection technique is able to identify
compromised meters with higher detection rates while incurring lower false positives, than most existing works, underrational attack strategies that may be employed by adversaries. We perform extensive sensitivity analysis to show thelimits of our model.
To the best of our knowledge, our proposed work is thefirst effort to establish trustworthiness in AMI against multiple attacks types and organized rivals. Secondly, ours is thefirst work that focus on data falsification strategies otherthan electricity theft, which can be devised by organizedadversaries rather than rogue customers. Unlike most existing works, our approach works without meter specific storage and maintenance of fine grained consumption data fromeach meter to obviate important privacy concerns [26]. Our
proposed method is also light weight compared to the classical bad data detection mechanisms. Since our method does
not require installation of additional hardware as in the statebased monitoring, it is more cost effective.

2.

RELATED WORK

Existing work on AMI data falsification can be broadly
categorized into classical bad data detection, and state based
detection. Both categories focus only on the electricity theft.
Classical bad data detection uses techniques such as Support
Vector Machine (SVM), Neural Networks and Auto Regressive Moving Average (ARMA) models. In contrast, statebased detection includes sensor based monitoring, mean aggregate outlier inspections and transformer state estimation.
Classical bad data detection schemes such as Multi-class
SVM and Neural Networks are used in [3, 15] for offline andretrospective identification of rogue customers stealing electricity by reporting lower usage. Such techniques containa series of seven steps for identifying abnormal customers.
The obvious disadvantage of these approaches are that they
are highly computation expensive, deal with long term retrospective identification, and do not consider organized adversaries or their attack strategies, and require full and fine3.

SYSTEM MODEL

Probability of Power Value

We consider a collection of N smart meters reporting
power consumption data to a Data Collector (DC) periodically and independently. The i-th smart meter, si , records
an actual power consumption data Pti (act) at the end ofeach time slot t. The reported power consumption Pti (rep)is equal to Pti (act) if si is not compromised. However,Pti (rep) 6= Pti (act), if si is compromised by an adversary.
We model Pti (act) as the realizations of a random variable
P i . The Data Collector piggybacks data from each smart
meter and sends it to the billing utility. The total power
reported at a time by all N meters is sent to a transformer
meter.
To characterize the distribution of P i from the i-th smart
meter, we conducted preliminary investigations on real power
consumption data sets [25], of 200 houses from 16 different
microgrids. Each home consists of one smart meter. We observed that for each house or meter, the power consumption
can be approximated as a log normal distribution. We also
observed that all such log normal distributions are clusteredclose to each other; that is, the variance between them is
not arbitrarily large. Fig. 2(a) summarizes the results.
We approximate the aggregate of the individual log normals using a mixture distribution, which is also lognormal
as evident from Fig. 2(a). We denote Pmix as the randomvariable (r.v.) of such aggregate approximate mixture distribution.
For mathematical tractability and visual intuitiveness, wetransform Pmix on a natural logarithm scale to obtain an
approximate normally distributed r.v. denoted as pmix . Results of this approximate normal mixture pmix , for different
months in the recent past is depicted in Fig. 2(b). Notethat both Pmix and pmix , do not reveal any consumption
pattern for each specific meter, but only a general trend on
the consumption.
We also denote pit (act) = ln(Pti (act)), as the effective
power consumption report recorded at each meter si on alog scale at any time slot t. Note that, for certain other data
sets (like a wider area monitoring), with more than one consumption clusters, as in [15], our approach can be applied toeach such cluster independently. The proposed trust model
calculates and updates trust of each smart meter at the endof each month. We assume a window size of T slots permonth based on how t is slotted. To prove the generality,
we repeated the experiments for a different AMI data set [3],and reported similar observations like Figs. 2(a) and 2(b)as shown in Appendix B.
500

Frequency of Power Value

grained profiling of each smart meter. A comparative analysis of classical bad data detection schemes is provided in [2]which concludes that while these schemes require full profiling of each customers’ energy consumption (thus cannot
protect their privacy), the detection rate of most of theseschemes is approximately 60%-70%. Moreover, only two
schemes provide a quantitative false positive rate.
Finally, ARMA based models [9] profile each customer’stime series data separately to increase accuracy, using ARMAGLR detector. However, in most practical cases, the consumption cannot be accurately modeled as an ARMA process [3], resulting in the detection rate of only about 62%.
Additionally, several privacy threats [10, 26] are associatedwith such approaches since they require customer specificmonitoring and maintainance of fine or coarse grained consumption data.
State based detection techniques like sensor based monitoring [5, 8], transformer state monitors [1] require additional hardware deployed at various points across the AMI
and distribution network for identifying anomalies. However, most of them do not identify the compromised meters.
Additional hardware requirement makes such approaches
costly [2]. Some works (e.g., [8]) combines the audit logs forphysical and cyber events in the meter to check for consistency in the data reported. But these approaches are nullified when the meters are compromised by external adversary
who are intelligent enough to change the audit logs. Furthermore, cyber connected sensors/monitors are also similarly
vulnerable to cyber attacks.
Mean aggregate based outlier approaches used in statebased detection [15, 17] have the advantage that they doneed not store and maintain fine grained meter specific trends
on power consumption. In [17], an arithmetic mean aggregate approach is proposed; but the number of rogue meters
is small compared to the population, hence the aggregatemean values are not affected enough. They also do not discriminate between legitimate and malicious changes in themean consumption, thus incurring a high false positive rateof around 30%, and consider only electricity theft. Legitimate changes in consumption may occur due to weather
and other contextual factors. Approaches focusing on only
arithmetic mean aggregates and median have difficulty todiscriminate malicious changes from legitimate ones whenthe margin of false data or the fraction of compromised
nodes is higher. Thus, such approaches suffer from highfalse positive rates or lower detection rates. Additionally,such methods will also fail to identify camouflage and conflict attacks as discussed earlier. In [3], a false positive rateof 28% is reported although the detection rate is high.
Finally, cryptographic approaches [6, 16] may fail to provide any help as organized adversaries may be able to crack
the cryptographic secrets. Moreover, given the latency critical nature of functions like demand response and management [23], advanced cryptographic defense is impractical due
to additional overhead [14]. This further exacerbates thevulnerability of the AMI data falsification.
Given the above limitations, we believe there is a dire needfor trustworthy computing approaches based on the anomaly
detection in the data reported by each meter. This motivates
us to propose a novel scheme that provides security forensics
to identify various falsification attacks and a trust model
based on aggregate data monitoring to identify compromised
meters. Hence, our work significantly advances this field of
research.

October 2015
December 2015
October 2014

0.03

0.025

400

300

0.02

0.015

200

0

0.01

0.005

100

X: 925
Y: 49

0

2000

4000

Power (Watts)

6000

0

2

3

4

5

6

7

8

ln (Pmix)(a)(b)
Figure 2: Power Consumption Behavior: (a) Actual(b) Normal Mixture

3.1 Threat Model
We consider the following assumptions in our threat model.

3.1.1

Types of Adversary

We assume that the organized adversary belongs to either
rival nation states, business competitors, utility insiders or
cyber criminals, possessing the ability to compromise several
smart meters by bypassing cryptography.
False power consumption data from a meter can be achievedin the following ways: (a) manipulation of inputs to the meter, (b) in rest at the meter, and (c) in-flight from the meter.
The adversary then launches data falsification from multiple such compromised smart meters concurrently.A compromised meter in this context means either the input, content,or output coming from one specific meter is compromised.
We assume rational attackers who may have a long or
short term damage objective. Long term damage requires
evading detection for the maximum possible time, while still
benefiting from attacks. The adversary may accept to facesome initial loss in the hope of evading detection and accruing incremental benefits over time. Examples of long term
adversarial objectives include monetary gains in terms ofelectricity pricing and belief manipulation of learning demand forecast models. A short term damage, on the other
hand, requires inflicting the maximum damage in a shorttime, before getting detected. Examples of short term objectives include an attacker aiming to, gain quick revenue
or masquerade a false high demand response. Due to thecontrasting requirements on these two objectives, adversarial decisions such as fraction of compromised nodes ρmal andthe margin of false data are dependent on the nature of time
deadlines associated with such objectives.
Unlike existing works [3], we assume organized adversaries
to be intelligent enough to also tamper with transformer
meters and other portions of the grid, to escape easy consistency checks on false data. We also assume that the smart
meters report the consumed power to a data concentrator on
every time slot (hourly). Compromised Meters spoof false
data on all time slots, however, the attack margin ∆ (explained below) may be more in peak periods than non-peakperiods, to exploit the time dependent pricing of electricity.

3.1.2

Taxonomy of AMI Data Falsification

We define the manner in which the actual power consumption data Pti (act) of each meter si is modified as the modeof data falsification. We identify the following modes:
Additive: The adversary reports Pti (rep) = Pti (act) + ∆t ,where δmin ≤ ∆t ≤ δmax . This mode can lead to loss ofbusiness confidence from customers due to higher bills andmasquerade a critical peak leading to remote disconnect ofcustomer appliances, thereby causing utilities to pay undue
incentives.
Deductive: The adversary reports Pti (rep) = Pti (act) − ∆t ,where δmin ≤ ∆t ≤ δmax . This mode can lead to loss ofrevenue for power utility companies.
Camouflage: The adversary divides the compromised meters
into two teams equal in number, which simultaneously adopt
an additive and deductive mode, respectively. This modecan favor smart meter of one power utility at the expenseof others, and has less impact on the strategic decisions in
the grid. It cannot be detected by simple mean comparison
approaches, because no suspicion is raised due to negligible
change in the total reported power consumption.

Conflict: It is a scenario where additive and deductive attacks coexist simultaneously, but are not necessarily balanced. Such a scenario represents random attacks possible
if there are more than one uncoordinated adversarial teams.

3.1.3

Margin of Falsified Data

The value ∆t is generated randomly within an interval[δmin , δmax ], for δmin , δmax > 0, and accordingly added toor deducted from the actual power consumption. Note that,
arbitrarily high δmax may facilitate intuitively easy detection, while very low δmax hardly accrues any revenue. The
average value of ∆t is represented as ∆avg .
Apart from the type of attack, the attacker chooses a valueof ∆avg in the interval [δmin , δmax ] as part of its attack strategy. ∆avg may be high or low depending on the amount ofdamage it wants to inflict, and the short or long time horizonof the attack. All units of ∆avg values discussed throughout
the paper is in Watts.
Since the distribution of power consumption is unimodal,
the attacker refrains from any strategy that would makethe resultant distribution, multi modal. In that sense, auniformly distributed random noise injected into the actual
smart meter data does not change the overall shape of the
distribution but only effects its parameters. Such variantsof uniform distribution over time is adopted from [3].
From the defender’s perspective, we define the breakdown
point BDP = (∆avg , ρmal ), as a combination of ∆avg andρmal values for which the proposed defense model is nolonger able to identify between compromised and honest
nodes.

3.1.4

Attacker Budget

We assume that organized adversaries compromise a certain number Mmax of the N smart meters based on theattack budget. The fraction of compromised nodes is ρmal =Mmax. Hence, ρmal can be high when N is small.
N
We assume a fixed cost Cattack is required to compromisea smart meter. We refer to the budget as the total cost T Cof the attack, such that T C = Cattack × Mmax . We term theattacker’s revenue as RR over an attack period of D days interms monetary gain in the electricity bills.
We define TBE as the breakeven time, that is the timerequired for the revenue accrued from attacks to match thetotal cost T C. The tradeoffs that impact TBE and BDP isstudied in Section 6.
In certain implementations, a transformer meter checks
the total inflow of power versus total outflow. If δavg is high,then a smart adversary can may compromise the corresponding transformer meter, to avoid easy suspicion. Only simple
attack types like additive and deductive would require theadversary compromising the transformer meter, given thatin camouflage and conflict attacks, the total reported power
consumption is not affected significantly.

3.1.5

A Concrete Example

Suppose in an AMI facility of N = 100 smart meters,
Mmax = 20 implying ρmal = 0.2. The actual aggregate
power consumption distribution has a mean and a standard
deviation of µA = 2000 units and σA = 100 units, respectively. If the amount of additive error to be introduced in
the final mean is Λ = 500 units, the ∆avg for each malicious node is given by ∆avg = MΛ∗N
= 2500. Since false
maxnoise values are generated uniformly at random in the rangemax(δmin , δmax ), ∆avg = δmin +δ
. Therefore in this example,2

In this section, we study how different data falsification
strategies affect the attacked mixture distribution from theactual (authentic) mixture distribution from real data gathered from 215 smart meters from a solar Village [25]. In
particular, we show effects of various attack types, on theArithmetic Mean (AM), Geometric Mean(GM) and Harmonic Mean (HM). The mathematical definitions of the difPN
i
Q
1
i N
i=1 xt, GMt = ( N
ferent means are AMt =i=1 xt ) ,N
HMt = PNN 1 .
i=1 xitBased on the simultaneous changes between the various
means, a security forensics criterion is provided to unravel
the type of data falsification attack. This criterion that isbased on the absolute difference (denoted by AD) between
AM and HM of the observed mixture distribution, can also
help to distinguish between a legitimate change and malicious change. Subsequently, a robust mean µR is derived
exploiting the contrasting robustness of AM, GM, HM measures to various types of attacks.
All trends on power consumption use pi values on an ln
scale. For comparison between legitimate and attacked data,
the reference authentic distribution is called historical distribution denoted by phismix . The attacked distribution is called
the observed distribution denoted by pobsmix .

4.1 Investigative Comparison under Various
Attacks
4.1.1

Authentic Data on Different Years

Fig. 3(a) shows the actual mixture distribution for two
different years (2014 and 2015) for the month of September.
We can observe, that the difference between the distributions is not large. In fact, the mean, and higher moments
are very similar. This is attributed to similar coarse grained
usage patterns given the weather in a particular month at
the same location. Hence, power consumption at a microgrid is cyclostationary in the wide sense. The AM for 2014
and 2015 are 7.053 and 7.07 respectively. The HM for thesame are 6.680 and 6.675 respectively.
However, sometimes it may happen that the same monthin two different years experience varying weather conditions
at certain locations. For example, winter 2015 was much

0.014

0.025

0.01

Probability

Probability

Nov 2014
Nov 2015

0.03

Sept 2014
Sept 2015

0.012

0.008
0.006
0.004

0.02
0.015
0.01
0.005

0.002
0
3

4

5

6

7

8

0

9

3

4

5

6

7

8

9

ln(Pmix)ln(Pmix)(a)(b)

Figure 3: Legitimate Data Comparison: (a) September (b) November
0.03

HonestAdditive

0.02

HonestDeductive Attack

0.025

Observed HM

0.015
Observed HM

0.01

Original AM

0.02
0.015
Observed AM

0.01

Original AM

Observed AM

0.005

0

Probability

4. STATISTICAL EFFECTS OF VARIOUS
ATTACKS ON AMI DATA

warmer than winter 2014 in certain geographical locations
in USA. For example in this data set, AM is 6.88 and 6.58,
while the HM are 6.52 and 6.23 respectively. Such a difference is shown in Fig. 3(b). Hence, we conclude that comparison of a meter’s data with the parameters of observed(current) mixture distribution (pobsmix ) is equally important,
as is the comparison with the historical values of power consumption.

Probability

if δmin = 128, as the minimum false value to be considered asattack, then δmax = 4782. Here δmax and ∆avg are a rather
high value, which may easily be detected, given the nature of
power consumption. However, if ρmal = 0.4, then to achieve
the same Λ = 500, it is sufficient to have δmax = 2372 and∆avg = 1250, which are more believable values.
The above proves that with higher ρmal , the adversary canafford to decrease the margin of false data to avoid getting
intuitively and easily detected. Although the cost increases
with higher ρmal , the adversary may reduce the chance of detection, and look to recover the initial cost in the long term.
This is however not an option for adversaries with shortterm objectives. In this case, the attack revenue/payoff andthe cost have to breakeven within a short time deadline.
This implies very high ρmal and low ∆avg do not lead to apractical attack strategy, since low ∆avg accrues slow attack
revenue per unit time. In the experimental results, we study
the trade-offs between ∆avg and ρmal .

0.005

3

4

5

6

ln(Pmix)

7

8

9

0

3

4

5

6

7

8

9

ln(Pmix)(a)(b)
Figure 4: Comparison: (a) Honest vs. Additive (b)Honest vs. Deductive

4.1.2

Authentic Data vs. Additive Attack

Fig. 4(a) shows the comparison between honest data set
phis
mix and the same data set polluted with additive falsification, with ∆avg = 800 and ρmal = 0.40 for the month ofOctober. Due to higher than actual power consumption reported, the observed AM is highly shifted from the original
AM. Hence, when using the observed mixture distribution
for anomaly detection, the observed AM is biased towards
the additive false data. We observe instead that the harmonic mean (HM) of the observed mixture, although shifted,
is closer to the original AM. Hence false readings will be located farther away from the observed HM. Hence HM is amore robust aggregate in unraveling positive outliers. Another key observation is that the absolute difference between
HM and AM, given by AD = |AM − HM | is higher in theattacked data set than the legitimate data set. Geometricmean (GM) is an intermediate value, but slightly closer tothe AM value as compared to HM.

4.1.3

Authentic Data vs. Deductive Attack

Figure 4(b) shows the results for the case of deductive
attacks where ∆avg = 500 and ρmal = 0.40 for October.
Intuitively, the observed mixture distribution, shifts to theleft, due to reporting of lower than actual consumption. As
a result, the observed AM is lower than the actual AM.
Nonetheless, the observed HM is even lesser than observed
AM since HM ≤ AM is always true. Hence for deductive
attacks, the observed AM is more robust than HM. However,AD still increases.

0.02

0.02

Camouflage
HonestHonestConflict Attacked

0.018
0.016
0.014

Observed HM

0.01

Observed AM
Original AM

Probability

Probability

0.015
0.012
Observed HM

0.01
0.008

Original AM

0.006

0.005

Observed AM

0.004
0.002

0

3

4

5

6

ln(Pmix)

7

8

9

0

3

4

(a)

5

6

ln(P

7

8

9

)

mix

(b)

Figure 5: Comparison: (a) Honest vs. Camouflage(b) Honest vs. Conflict

4.1.4

Authentic Data vs. Camouflage Attack

Fig. 5(a) shows the effect of camouflage attacks where∆avg = 960 and ρmal = 0.40. There is a negligible change
in the AM. However, we observe that there is a shift in the
HM of the observed mixture, thereby causing the resultant
AD to increase.

4.1.5

Authentic Data vs. Conflict Attack

Fig. 5(b) shows the effect of conflict attacks where ∆avg is
700 and 500 for additive and deductive attacks, respectively,
with ρmal = 0.40. There is a little change in the AM. However, we observe a shift in the HM of the observed mixture.
Hence, AD increases.

4.2 Security Incident Forensics
Based on the observations from comparison between authentic versus attacked data distributions, we identified asecurity incident forensics criteria, based on AD and the simultaneous change/bias in the observed AM, HM, and GM
that indicate presence and type of data falsification (security
incident). Based on this knowledge, we calculate a robust
aggregate µR , which is less biased than the otherwise observed arithmetic mean values.

AD obs :∈ AD norm> AD norm

No Falsification ;Falsification Occurred;(1)

Table 1: Effects of Different Attacks on AD
ParameterAM
GMHM
AD = |AM-HM|

Actual
7.053
6.860
6.680
0.373

Add
7.68
7.35
6.92
0.76

Deduct
6.67
6.29
5.88
0.79

Camo
7.04
6.65
6.02
1.02

Conf
7.26
6.79
6.11
1.15

From the above, we conclude that an authentic change
in the observed distribution may cause the mean consumption to increase or decrease but ADobs remains the same
as compared to the historical range of values ADnorm =[ADmin , ADmax ]. An additive attack causes the mean consumption to increase but also causes ADobs to increase compared to historical values. This way a legitimate versus amalicious change can be distinguished. A deductive attack
causes the mean consumption to decrease and causes ADobs
to increase from the historical range. Similarly, camouflage
and conflict attacks do not have much change in the mean
consumption but causes a large increase in the ADobs fromthe normal. In this way, it is possible to detect which typeof data falsification has been launched.
Table 2: Concluding the Security Incident TypeAD
Increased
Increased
Increased
Increased
Same

AM
Increased
Decreased
Same
AnyDon’t CareHM
Increased
Decreased
Decreased
AnyDon’t Care

GM
Increased
Decreased
Decreased
AnyDon’t Care

Conclusion
Additive
Deductive
Camouflage
Conflict
No Attack

1.2
1

AD = | HM-AM |Note that, the maximum possible bias introduced in theobserved AM under deductive attacks is less than that ofadditive attacks, because the feasible margin of deductive
false data is bounded by zero, because Pti (rep) ≥ 0.

Previous Year 2014
Next Year2015

0.8
0.6
0.4
0.2

4.2.1

Detecting the Anomaly from Legitimate Change

We study how each attack type impacts various statisticalparameters and identify a criterion (see Eqn. 1)that reveals
the presence and the type of attack launched. From ourstatistical study, we found that AD = |AM − HM | could bean effective indicator for anomalies.
Fig. 6 shows the comparison of instantaneous values ofAD between historical (2014) and current non-attacked distribution (2015) for different years. It can be verified that
under no attacks, the average value of AD is about 0.45
for both years, although contextual factors may have caused
AM, GM and HM to readily change over time. The lowest ADmin and highest ADmax values of AD for two years
are between 0.35 and 0.55 Hence, AD is almost stable for
legitimate data sets, and we call this range ADnorm
In contrast, from Fig. 7, it is easy to conclude that for all
attacks scenarios, the ADobs is larger than ADnorm range.
This figure clearly shows that when additive, deductive,
camouflage, and conflict attack samples were introduced in
the current data set, starting from the 250th day of 2015,
AD has increased for each attack type.

50

100

150

200

250

300

350

Time (days)
Figure 6: AD under No Attacks

4.2.2

A Robust Mean for Different Attacks

The manner and extent to which different observed mean
aggregates like HM, GM and AM get biased by different
attacks is unique. We exploit this property for the calculation of robust mean. Additionally, the magnitude of thebias depends on ∆avg and/or ρmal . Hence, an adjusted robust mean helps to get an approximate value closer to theoriginal mean. Note that, the highest possible ∆avg is lesser
in deductive attacks than additive ones, because the feasible
margin of deductive false data is bounded by zero. As themargins of false data or compromised fraction increases, theobserved means get biased from the actual mean.
From the statistical observations, we conclude that HM ismore robust than AM to the effect of additive attacks, due
to slower increase in HM as opposed to AM. However, this is1.2
HonestDeductive
Additive
Camouflage
Conflict

1

AD= | AM-HM |more the indication of anomalous behavior. The trust of ameter is calculated at the end of the window (in days). The
total number of observations (T ) over the window depends
on how time is slotted.

0.8

5.1
Statistical
Anomaly

0.6
0.4
0.2

Attack Started

50

100

150

200

250

300

350

Time (days)
Figure 7: AD in Observed Data: Various Attacks
not the case for deductive attacks because of HM ≤ GM ≤AM , causing HM to be even lesser than the already biased
AM. But, GM + AD is more robust than AM for deductive
attacks, and results show that it is a good approximation
to the actual mean. From the example in Table 2, it canbe verified that for deductive attack, the robust mean µR =6.29 + 0.79 = 7.08 is closer to the actual mean 7.05. For
camouflage attacks, AM is the most robust and hence µR is
set as the AM. For conflict attacks, GM is an intermediaterobust choice as it shows a relative stability to both partially
positive and negative outliers.

True and Current Proximity Distributions

We introduce a binary random variable Xi = {0, 1} foreach meter si , for i = 1, . . . , N , which acts as a historicalreference distribution. If the historical data reported pit (rep)at time t from meter si falls within one standard deviationof µt , then Xi = 1, else 0. Formally,
1 if pit (rep) ∈ {µt ± σt };(2)
Xi (t) =0 otherwise
where Xi (t) follows a Bernoulli distribution with parameterr, that is the probability of Xi = 1 is r, and the probabilityof Xi = 0 is 1 − r.
Suppose, S(X) be the variable that denotes the numberPof successes, that is S(Xi ) = Tt=1 Xi (t). Let S(X) = k be
the observed value of the variable.
Similarly, we have a binary random variable Yi for the current distribution of each smart meter, such that the probability of Y = 1 is q and the probability of Y = 0 is 1 − q. In
this case,Pthe number of successes is denoted by a variable
R(Yi ) = Tt=1 Yi (t). Let l be the observed value of R(Y ). If
an anomaly has been detected through monitoring the HM,
AM and AD, then µRt is assigned accordingly, and the corresponding standard deviation σRt is calculated. In absenceof attacks, µRt = µt . Thus,

Table 3: Robust Aggregate guided by Incident Type
Security Incident
Additive
Deductive
Camouflage
Conflict
No Attack

Choice of Aggregate µR
HM
GM+AD
AM
GM
AM

5. AN ENTROPY BASED TRUST MODEL
We pursue a light weight supervised learning approachfor defending against data falsification from compromised
smart meters. A prior historical data set is considered as
the authentic distribution of power consumption. From thehistorical data set, a true proximity distribution denoted as
X i for each smart meter is generated based on its reported
consumption’s proximity to the arithmetic mean of the authentic data set. Since the authentic historical data set isattack-free, the measure of mean is arithmetic mean (AM),denoted by µ.
Then an observed data set is considered with data fromspurious meters. We define µR as the robust mean of theobserved distribution calculated as discussed in Section 4
based on the occurred security incident. The current proximity distribution Y i of each smart meter si is calculated
based on the proximity of its reported consumptions to µR .
In contrast, to the historical distribution, when an attack ispresent, we set µR according to Table 3.
If the true distribution is very different from the current
distribution, it is an indication that this meter is unusually far from the aggregate. This difference is measured as
Kullback-Leibler divergence (also called KL Distance) whichmeasures the relative entropy between the two distributions.
The higher the divergence between the two distributions, theYi (t) =

10

if pit (rep) ∈ {µRt ± σRt };otherwise(3)

Intuitively, in absence of attacks the distribution of Y
should be very close to X. On the contrary, the two distributions should show a difference when an attack is present.

5.2

Estimating Parameters of True and Current Proximity Distributions

Next we need to estimate the parameters r and q for corresponding distributions Xi and Yi . An obvious estimate
is the minimum variance unbiased estimate (frequentist),
which is the sum of all successes divided by the total number of observations T . However, this approach may cause
r = 0, q = 0, or r = 1, q = 1, for which the relative entropy(see Eqn. 9) is undefined. Moreover, frequentist probability
unbiased estimator makes sense only if there is a large set ofobservations [13]. However, since our trust model works on ashorter horizon of time (typically on a few days or monthly
basis), such approaches are improper. Hence, we need toaccommodate a Bayesian approach for estimation of r andq, so it is theoretically sound and mathematically tractable.
Since the following is true for all meter’s si , we drop thesuffix i from the notational simplicity.
First, we estimate the parameter r. We prove that theestimated probability r = Tk+1
, where k is the realization+2of the total number of successes observed. Thus S(X) = kfollows a binomial distribution with parameter r.
Hence, the probability of observing exactly k successes out
T times, given the probability of success of each trial was r,
is given by,

P (S(X) = k|r) =!

T kr (1 − r)T −kk(4)

The Bayesian posterior estimate of r, based on prior T observations by Bayes theorem, is given as:
P (X(T + 1)), S(X) = k)
P (S(X) = k)
(5)
The denominator is the marginal probability of P (S(X) =k) marginalized over all possible outcomes of r. Hence,
P (X(T + 1) = 1|S(X) = k) =P (S(X)) =

Z1
0

!

T k
r (1 − r)T −k f (r)drk(6)

Assuming conditional independence between S(X), r andXi (t + 1) of the prior and likelihood can be solved as:
P (Xi (T + 1)), S(X) = k) ⇒=Z1

P (X(T + 1) = 1|r)P (S(X) = k|r)dr(7)0

Since there is no prior information on r, we assume a noninformative prior such that f (r) = 1, for the above Eqn (6)and Eqn. (7). Plugging in Eqn. (6) and Eqn. (7) to Eqn. (5),it can shown that:
P (Xi (T + 1) = 1|S(X) = k) =

k+1
=r
T +2

(8)

. Similarly, q = Tl+1.
Hence, r = Tk+1
+2
+2
It can be verified that r, q 6= 0, 1. Hence, the logarithms of
distributions X and Y in terms of r and q are always definedand exist as evident from Eqn (9).

5.3 Kullback-Leibler Divergence based TrustModel
We adopt the Kullback Leibler divergence to measure thedifference between the historical distribution Xi and the observed distribution Yi for a smart meter. It may be notedthat Xi and Yi are not consumption patterns but a trend on
proximity to the aggregate. Subsequently, the KL distanceis transformed into a trust value between zero and one. The
trust values are fed to a generalized linear model based logit
link function for linearly separable trust values that facilitate classification between compromised and honest meters
through a single threshold.
The KL distance between two distributions X and Y fora smart meter si , is given by:r
1 − r+ p × ln(9)
Di (Xi ||Yi ) = (1 − r) × ln
1−qq

The Di (X||Y ) is a positive real value. The final trust valueof a smart meter si , is given by:
Qi =

1+

p

1
Di (X||Y )0 ≤ Qi ≤ 1(10)

Any classification problem such as identifying compromised meters from honest ones, require a threshold for separation. In order to ensure the efficiency of our method, ourgoal is to ensure that the compromised and honest meters
form two clearly linearly separable clusters in terms of theirtrust values. However, for certain attacks, especially camouflage and conflict attacks, the distributions may not be
sufficiently far from each other to ensure linear separation
through a threshold.
To address this problem, we introduce a kernelized trust
metric that maps the trust values into a higher dimension.
We use a light weight two step kernel mapping function.
The first step is the use of a generalized linear model (GLM)
predictor (logit link function) where Qi is mapped into W i ∈
IR as follows.
Qii
W = log2

1 − Qi(11)

The second step is a Weibull scaling function convertingW i into the final kernelized trust metric KT i ∈ [−1, +1]:i
 1 − e−|W |if W i > 0;
i
i
KT =
(12)
−(1 − e−|W | ) if W i < 0;i0if W = 0

Eqn. (11), is a logit link function used in logistic regression for binary classification problems. Since, our problem
is to classify malicious from honest, the corresponding linkfunction for such response variables is a logit function.
Remark on privacy concerns: Note that, our defense
model does not require the storage and maintainance of actual power consumption trends of each individual house.
Rather, we only store the information of Xi , thus less privacy intrusive. So, by policy the individual Pti (rep) need not
be used and may be discarded. In particular, the data collector only knows the historical mixture distribution pmix andthe historical private parameter r of each house. The q parameter is the current private parameter of each house. The
challenge is resolved by depending on phismix rather than theindividual pi distribution. Since r and q are compared for
KL divergence, both comparison to history and comparison
with current mixture distribution is achieved in a privacy
preserved manner.

6.

PERFORMANCE EVALUATION

The data set from three residential micro-grids of N = 215
houses, was obtained from PeCan Street Project [25], containing hourly power consumption data from a solar village
near Austin, Texas. We studied some results of anomaly
detection and trust model for various attacks. To display
the performance of the defense models, a 30 day data from2014 was used as a training data set. The training data set
is used to derive a threshold (through K-means clustering)that linearly separates between honest and compromised labels based on their trust score. A data set for a 30 day
period in 2015 is used a testing data set.
The malicious data sets were generated from the real data
samples that were fed into a simulated AMI micro-grid, andρmal and ∆avg were carefully chosen to avoid overfittingor underfitting. In the compromised testing data set, theresulting distributions of each smart meter is modeled as
the distribution Y . The KL distance is calculated for eachsmart meter, and subsequently their trust values are plotted.
Then, the threshold obtained from training is applied

6.1

Training Set

We use a training data set from 36 houses and use power
consumption reported in 2014 for a month. We label some

1

0.6

Malicious:

0.8

HonestThreshold (0.515)

0.5
0.4

0.4
0.3

20

30

Meter ID

10

20

1

Kernelized Trust Values

Kernelized Trust Value

Malicious: ρmal ~ 33%

HonestThreshold (0.155)
Classification Threshold

0.2
0

-0.2

20
Meter ID

(a)

0.4

30

40

0.6
0.4
0.2
0
-0.2
0

Trust Values

0.3
0

200

10

20

30

Meter ID

6.2 Performance with Testing Set
We use the data set from 2015 as testing set. We set
ρmal = 0.4 and ∆avg = 768W . More results with differentρmal = {0.2, 0.3} are presented in Appendix A to prove thescalability. The results for additive and deductive attacks
are shown in Figs. 10(a) and 10(b). They exhibit a clear
separation between honest and compromised nodes with afalse alarm rate of 8.3% in the additive case, and 9.3% in the
deductive case. The missed detection rate is 0% for all attack
modes, and no compromised meter remains undetected.
Figure 11(a) shows the results for the testing set for δavg =880W , demonstrating a clear difference between honest andcompromised nodes. The false alarm rate in this case is
11.6%.
For conflict attacks, about 48% of the total meters arecompromised, with additive attack of δavg = 1300W , while
the deductive attacks with δavg = 900W . This is a casewhich considers random attacks from unorganized rivals.

100

150

200

(b)

Classification Threshold

0
-0.2
-0.4
-0.6

0

-0.5

-1
0

50

100

150

200

Malicious
HonestThreshold (0.15)

0.5

0

50

100

150

Smart Meter ID

Smart Meter ID

(a)

(b)

Figure 11: Testing Sets: (a) Camouflage; (b) Conflict

Trust Values over Time

Figs. 12(a) and 12(b) show the trust value comparison
between an honest meter and a compromised meter overtime. Fig. 12(a), shows trust values calculated every 30 days
while Fig. 12(b) shows them for every 10 days. The first
90 days are attack free, and hence trust values are above
the threshold. After the 90th day, the attack starts, and adecrease in the trust of compromised meter is clear while
the honest meter’s trust is unaffected.

(b)

Figure 9: Training Data: (a) Camouflage; (b) Conflict

50

Smart Meter ID

0.2

6.3

Malicious
HonestThreshold (0.15)

0.8

-0.4
10

0.6

-0.8

30

Figure 8: Training Data: (a) Additive; (b) Deductive
1

150

1
Malicious
HonestThreshold (0.15)

(b)

0.8

100

From Fig. 11(b), we show that our approach works with ahigh detection rate of 98% and the false alarm rate is about
7%. All the testing results, show improvement from mostexisting works in [2].

Meter ID

(a)

0

50

Figure 10: Testing Data: (a) Additive; (b) Deductive

Trust Values

10

0.5

(a)

0.8

0.6

Classification Threshold = 0.515

0.6Smart Meter ID

ρ mal =45%

0.7

0.7

0.4

0

1

0.9

0.5

-0.4

0.4

Kernelized Trust Values

Classification Threshold =0.534

Classification Threshold

0.5

0.3

Malicious
HonestThreshold (0.515)

0.8

0.6

Kernelized Trust Value

Trust Value

Trust Value

0.7

0.4

0.7

1
Malicious
HonestThreshold (0.534)

0.8

0.6

0.8

0.9

1

0.8

0.8

0.7

Trust Values

1
0.9

1
Malicious
HonestThreshold (0.534)

0.9

Trust Value

meters as compromised and alter their reported values andplot the corresponding trust values. We use these experiments to calculate a threshold that can linearly separate
between compromised and non-compromised nodes. We use
a logistic regression classifier to find the optimal linearly separable classifier. We choose ρmal = 0.4, and ∆avg = 1024W
which are intermediate values to prevent overfitting or underfitting. The results of training for various attack strategies are shown in Figs. 8(a) and 8(b).
Figure 9(a) shows the training sets for camouflage attacks
with kernelized trust metrics bounded between [−1, +1], forδavg = 960W and ρmal = 0.45. The kernel mapping function
yield a clear separation between honest and compromisedlabels even for stealthy camouflage attacks. We derive thethreshold as 0.155. Fig. 9(b) shows the training results forconflict attacks where ∆avg is 900 and 600 for additive anddeductive attacking meters respectively and ρmal = 0.45.

0.6

Honest Meter
Compromised MeterThreshold (0.53)

0.4

0.2

1

2

3

4

5

Time (Months)(a)6

Malicious
HonestThreshold (0.53)

0.6
ATTACK

0.5

0.4

NO ATTACK

50100Time (days)

150

(b)

Figure 12: Trust Propagation Over Time: (a) Every
30 days; (b) Every 10 days

6.4

Breakdown and Breakeven Point Analysis

We model the attacker revenue RR over an attack periodof D days in terms monetary gain in the electricity bills as:
RR =∆avg × Mmax × η × D × E
1000

(13)

where ∆avg is the average attack margin, η is the numberof reports a day, and E is the per unit (KW-Hour) cost ofelectricity in dollars.

ρ mal = 10%

1

Trust Value

Trust Value

Avg Malicious
Avg Honest

0.8
0.7
0.6
0.5

Breakdown Point

0.4
0.3

0

500

1000

1500

2000

2500

3000

0.7

0.5

Trust Value

0.6

2000

1500

2000

2500

3000

3500

2500

3000

ρ mal =10%

0

500

1000

1500

2000

2500

3000

Trust Value

Trust Value

0.6
Avg Malicious
Avg Honest

400

600

800

1000

0.8

0

200

600

800

1000

1200

1000

1200

ρ mal =60%

0.9

Trust Value

Trust Value

400

Average Noise Margin(W)Breakdown Point

0.7
0.6

0.4

7.

Avg Malicious
Avg Honest

0.5

1

0.9

Avg Malicious
Avg Honest

0.5

0

200

400

600

800

Average Noise Margin(W)

1000

3000

3500

0

500

1000

Trust Value

0.6
Breakdown Point

0.5

1500

2000

2500

3000

3500

3000

3500

Avg Malicious
Avg Honest

0.7
0.6
0.5

0.3
1000

2500

0.8

0.4
500

2000

0.9

0.7

0

1500

Average Noise margin (W)ρ mal =55.55%

1

Breakdown Point

0

500

1000

1500

2000

2500

3000

3500

Average Noise margin (W)

1200

ρmal
0.5
0.69
0.80
0.86
0.72
0.61
0.58
0.53
0.50
0.47
0.44
0.42
0.42

TC
9000
12500
14500
15500
13000
11000
10500
9500
9000
8500
8000
7500
7500

RR
398.131105.91924.32742.62875.32919.63251.43361.93583.13760.13892.83981.6
4313.0

TBE
22
11
7.53
5.6
4.52
3.76
3.22
2.82
2.5
2.26
2.05
1.88
1.73

Breakdown Point

0.6

0.4

1200

ρ mal =40%

0.8

2500

0.7

Average Noise Margin(W)1

Trust Value

Trust Value3500

ρ mal =25%

1

0.7

200

2000

Avg Malicious
Avg Honest

∆avg
256
512
768
1024
1280
1536
1792
2048
2304
2560
2816
3072
3328

Avg Malicious
Avg Honest

0.5

0.9

0

1500

Table 4: Breakdown and Breakeven analysis

Average False Margin (W)

0.8

0.3

1000

Average Noise margin (W)ρ mal =44.44%

higher ρmal ≥ 0.42 and a simultaneous higher margin ∆avg
of false data. However, our model ensures the breakdown
happens only at very high levels of ∆avg . This is intuitively
detectable, since the power consumption has a thinner tail,and most of the power consumptions are below 2500W .
In Table 4 we also observe that when ∆avg = 3328W
and ∆avg = 3072W , the breakdown point is achieved atlower cost of ρmal = 0.42, and breakeven duration is alsosignificantly smaller. The problem for the adversary is thevery high margin and fraction of compromised meters, whichmakes it easily detectable and cost inefficient. This observation shows that although our defense model has breakdown points, most of these correspond to strategies which
are hardly convenient for the adversary.

0.6

3500

0.9

0.4

0.7

Figure 15: Sensitivity Analysis over ∆avg : Camouflage

Figure 13: Sensitivity Analysis over ∆avg : Additive
The breakdown points for deductive and camouflage attacks for different ρmal values are shown in Figs. 14 and 15.

0.5

500

Average Noise margin (W)0.7

Average False Margin (W)

1

0.8

0.6
0

0.8

0.4

0.8

0.3
1500

1000

Average False Margin (W)ρ mal = 60%

0.6

0.9

0.4

Breakdown Point

1000

500

0.7

1

Breakdown Point

0.7

500

0

Avg Malicious
Avg Honest

0.9
Avg Malicious
Avg Honest

0.8

0.5

ρ mal =28.88%

1

0.9

Avg Malicious
Avg Honest

0

Avg Malicious
Avg Honest

0.4

1

0.8

0.5

Breakdown Point

0.6

3500

Average False Margin (W)ρ mal = 40%

0.9

Trust Value

0.8

0.3

1

0.4

ρ mal = 25%

1
0.9

0.9

ρ mal =16.66%

1
0.9

Trust Value

Recall that the breakdown point occurs for some ∆avg andρmal such that the proposed model is no longer able to distinguish between compromised and honest nodes because
the average trust values of compromised meters are higher
than honest ones. We study the existence of such breakdown points, the feasibility of the adversary achieving the
breakdown point and associated cost benefit analysis. This
analysis can be used by the insider attackers to accordingly
design their attack strategy to evade detection.
The breakdown point could be achieved with very highor low margin ∆avg given ρmal . Very low margins makeshort term attacks impossible and very large margins makeattacks very obvious. Therefore, low margins make sense forlong term attacks, but require either a large ρmal or a longtime duration to be effective.
Figure 13 shows different breakdown points for ρmal values
0.10, 0.25, 0.4 and 0.6 for additive attacks over various ∆avg
values. Two break down points exist only for ρmal = 0.6,
which suggest that to evade detection with lower margin offalse data, the adversary has to compromise a large numberof nodes, thus increasing its cost. For lower ρmal , the attacker cannot evade detection, unless ∆ is very small, which
in turn rules out short term attacks and increases breakeventime (TBE ) significantly.

0.8
Breakdown Point

0.7
Avg Malicious
Avg Honest

0.6
0.5

0

200

400

600

800

Average Noise Margin(W)Figure 14: Sensitivity Analysis over ∆avg : Deductive
Table 4 numerically shows that for a very low margin∆avg = 256W and ρmal = 0.5, the adversary needs 22months to recover its initial investment and start to gain
profit. This acts as deterrent to implement such a strategy
although it may evade detection.
Another aspect shown in the plots and Table 4 is that the
breakdown point and attack evasion could be achieved with

CONCLUSION

In this paper we presented a taxonomy of various data falsification strategies in AMI micro-grids, as may be devisedby powerful and organized adversaries such as rival nation
states, business competitors, etc. rather than individual selfish customers only. We proposed statistical anomaly detection and forensics technique to identify presence of various
attacks and a trust model based on Kullback-Leibler divergence to identify the compromised smart meters. Our analysis on real data sets shows that both the margin of false data
and the fraction of compromised nodes play a key role in understanding the limits of a distributed detection scheme. We
also studied some strategies that could be employed by attackers to escape detection and the cost benefit analysis ofsuch strategies.
Acknowledgment: The work is partially supported by
the NSF grants under award numbers CNS-1545037, CNS1545050 and DGE-1433659.

Figs. 16(a) and 16(b) prove that our approach works fortesting sets with ρmal values that very different from thetraining sets.
1
1

0.9

Compromised
HonestThreshold (0.534)

Trust Values

0.9

Trust Values

0.8

0.7

Compromised
HonestThreshold (0.534)

0.8

0.7

0.6

0.6

0.5

0.5

0.4
0

50

100

0.4
0

150

50

100

150

Smart Meter ID

Smart Meter ID

(a)

(b)

Figure 16: Testing Set for Additive: (a) ρmal = 20%(b) ρmal = 30%

B.

POWER CONSUMPTION DATA: DIFFERENT REGION

To prove that the nature of power consumption studied isgeneric, we show in Figs. 17(a) and 17(b) that the nature of
power consumption is also similar for a different AMI data
set as used in [3].
7000

250

6000

5000

4000

3000

2000

1000

0

0

1000

2000

3000

4000

Power (Watts)

5000

6000

Average Frequency of Power Value[1] S.-C. Huang, Y.-L. Lo, and C.-N. Lu, “Non-technical loss
detection using state estimation and analysis of variance”,
IEEE Trans. on Power Systems, 28(3):2959-2966, Aug. 2013.
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infrastructure in smart grids”, Tsinghua Science andTechnology, 19(2):105-120, April 2014.
[3] P. Jokar, N. Arianpoo, and V. Leung, “Electricity theft
detection in AMI using customers’ consumption patterns”,
IEEE Trans. on Smart Grid, 7(1):216-226, Jan. 2016.
[4] T. Koppel, “Lights Out: A Cyberattack, A Nation Unprepared,
Surviving the Aftermath”, Crown Publishers, New York, 2015.
[5] C.-H. Lo and N. Ansari, “CONSUMER: A novel hybrid
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APPENDIX
A. TESTING SETS: LOWER FRACTION OF
COMPROMISED NODES

Frequence of Power Value

8. REFERENCES

200

150

100

50

0

2

3

4

5

6

7

8

Power (Watts)(a)(b)
Figure 17: Power Consumption Behavior: Different
Data Set