Topology Learning Aided False Data Injection Attack without Prior Topology Information
IIEEE POWER & ENERGY SOCIETY GENERAL MEETING 2021, SUBMITTED ON 06 NOVEMBER 2020 1
Topology Learning Aided False Data InjectionAttack without Prior Topology Information
Martin Higgins, Jiawei Zhang, Ning Zhang and Fei Teng
Abstract —False Data Injection (FDI) attacks against powersystem state estimation are a growing concern for operators.Previously, most works on FDI attacks have been performedunder the assumption of the attacker having full knowledge ofthe underlying system without clear justification. In this paper, wedevelop a topology-learning-aided FDI attack that allows stealthycyber-attacks against AC power system state estimation withoutprior knowledge of system information. The attack combinestopology learning technique, based only on branch and bus powerflows, and attacker-side pseudo-residual assessment to performstealthy FDI attacks with high confidence. This paper, for thefirst time, demonstrates how quickly the attacker can developfull-knowledge of the grid topology and parameters and validatesthe full knowledge assumptions in the previous work.
Index Terms —Cyber-security, false data injection attacks,static state estimation, topology estimation
I. I
NTRODUCTION C YBER-attacks against power systems have gained in-creased focus in recent years, with the events in Ukraine,Russia, Iran and Israel [1] highlighting the importance ofdefence against cyber threats. Recently, a specific kind ofattack against power system state estimation [2] has emerged,called the false data injection (FDI) attack [3]. It has beenshown that by altering these measurements in a very specificmanner, negative consequences such as line overloading [4],outage masking [5] or load shedding [6]. Research into stealthyFDI has focused on both the development of new forms ofattack and enhancing the detection of FDI. This work focuseson enhancing attacks under limited knowledge assumptions.Below, we outline a literature review of relevant FDI attacksand the topology discovery technique which featured in ourproposed attack. II. B
ACKGROUND
A. FDI Attacks
The principles behind FDI attacks were first outlined in [3].Liu et al . used knowledge of the system topology to structureattack vectors so that the the system operator was unaware ofthe attack for a linearised DC model. However, in practice,it is unlikely that an attacker will have full knowledge of theunderlying system topology. As a result, attacks that requireda lower knowledge assumption were introduced, such as the
Martin Higgins and Fei Teng are with the Department of Electrical andElectronic Engineering, Imperial College London, London, SW7 2AZ, U.K.(Email: [email protected]).Jiawei Zhang and Ning Zhang are with the State Key Laboratory of PowerSystems, Department of Electrical Engineering, Tsinghua University, Beijing,China incomplete knowledge attack in [7], which showed that an DCsystem could be attacked with only partial knowledge of thesystem topology, and the ’blind’ FDI attack, which showeda system could be attacked with no prior knowledge of thesystem topology. The original blind FDI attack required noprior system knowledge, provided the attacker had access toall meters within the attacked grid system [8] [9]. The ACmodel has also been explored in the context of blind FDIattacks. While the majority of these early works focused on alinear approximation of the FDI attack, it was shown in [10]that an AC model was indeed possible, provided the attackerhad knowledge of the system topology. In [11], a geometricapproach was applied for blind attacks against AC systems,but this attack still made some linearisation assumptions andlacked the significant flexibility in objective control grantedby the full-knowledge attack. While papers such as [12] offera partial blind model that builds branch information. Otherworks in this field include [13], where a method of FDIdetection using unknown input internal observer is proposed.While in [14], event-based triggers are used to enhance phasormeasurement unit (PMU) based detection. Event-based FDIdistributed detection is also explored in [15].
B. Topology Discovery
Attacks that can learn the underlying system topology offersmore flexibility in how targets are chosen. There have beenattempts to develop topology-discovery-style attacks, but theyhave been largely done under the assumptions of the linearmodel, such as in [12]. In [16], voltage correlations are usedto identify bus incidence, however, branch values are notcalculated. This leaves a large portion of the required topologymatrix unknown and, in practice, insufficient information forFDI attack. In other papers, such as, [17] a test is developedfor estimating the dynamic Jacobin in the presence of topologychanges, but this method requires PMU measurements, whichare not always available for the attacker. Similarly, in [18] and[19], models for network parameter estimation are suggested,but they also require PMU data in order to build an accuratemodel of the power system. As shown in [20], it is possibleto evaluate network branch parameters without PMU data.An initial approximation can be made using regression viamatrix operations; this gives a quick approximation of the per-unit network topology. This is then used as a starting pointover which a fine identification is run. The fine identificationuses a modified Newton-Raphson to get high-quality per-unitestimations of network topology. a r X i v : . [ ee ss . S Y ] F e b EEE POWER & ENERGY SOCIETY GENERAL MEETING 2021, SUBMITTED ON 06 NOVEMBER 2020 2
C. Novel Contributions
The topology learning technique is combined with attacker-side pseudo-residual assessment to create a topology-learning-aided FDI attack (TL-FDIA) that has the capabilities of a fullknowledge attack with no prior system knowledge require-ments. Our contributions are outlined as below: • A topology-learning-aided FDI attack capable of attack-ing power systems under a blind assumption model (nobranch or network incidence information available). Theattack is committed against the AC power system anduses the latest state-of-the-art topology discovery tech-niques to build a model for the network. • We introduce an attacker-side criteria assessment via apseudo-residual calculation to allow probabilistic assess-ment of attack success before any attack committed,allowing the attacker to ensure stealthiness. We also showregional pseudo-residuals can be used to verify localattacks even in the presence of global topology errors. • We demonstrate how quickly the attacker can developfull knowledge of the system topology and parametersand effectively invalidate the full-system-knowledge as-sumptions in previous studies.The rest of this paper is organized as follows; the problemformulation is outlined in Section 3; Section 4 details thedesign of the FDI attack vectors; Section 5 introduces thebasis of the topology learning algorithm; Section 6 containsthe results of the TL-FDIA and Section 7 concludes the paper.III. AC S
TATE E STIMATION
We consider a standard AC power system with real powerflow measurements under the non-linear expression defined by P ij = V i g ij − V i V j g ij cos ∆ θ ij − V i V j b ij sin ∆ θ ij . (1)and reactive power flows by (2) Q ij = − V i ( b ij + b shij ) + V i V j g ij cos ∆ θ ij − V i V j b ij sin ∆ θ ij .V and θ are the system states, while P and Q are the powermeasurements. This system is measured by estimating a set of n state variables x ∈ R n × estimated by analysing a set of m meter measurements z ∈ R m × and corresponding error vector e ∈ R m × . The non-linear vector function h ( . ) relating metermeasurements z to states h ( x ) = ( h ( x ) , h ( x ) , ..., h m ( x )) T isshown by z = h(x) + e . (3)The state estimation problem is to find the best fit estimateof ˆ x corresponding to the measured power flow values of z . Under the most widely used estimation approach, thestate variables are determined by minimization of a WLSoptimization problem as min x J ( x ) = ( z − h(x) ) T W ( z − h(x) ) . (4)This is done using iterative processes, usually the Newton-Raphson [2] utilising the Jacobin J of partial derivatives J = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) δh δx ... δh δx n ... ... ... δh δx m ... δh m δx n (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) . The aim with these iterative processes is to minimise thedifference between the individual estimated values of powerflows and the measured ones where the error (or line residual) r p for real powers is defined by e p = − P mij + V i g ij − V i V j g ij cos ∆ θ ij − V i V j b ij sin ∆ θ ij . (5)with a similar equation for reactive power. At the systemlevel, the error check for final decision making is based onthe absolute value of the sum of errors known as the 2-norm difference between measured and estimated power flowsdefined by r = || z − h ˆ x || . (6)We have an alarm value τ , which is defined using engineer-ing judgement, usually based on chi-squared testing criteriabased on a 99% confidence interval derived via regression ofprevious residual values, such that an alarm is raised if r > τ .IV. T OPOLOGY -L EARNING -A IDED
FDI A
TTACKS
A. Full-Knowledge AC FDI Attack
If an attacker has knowledge of how the non-linear functionis formed h ( . ) they can define a set of x values to achieve theirstated aims in terms of P and Q such that z a = h (ˆ x + c ) . (7)Where c is an n × matrix denoting the desired biasinjected into the system states (usually voltage angles) by theattacker and z a denotes the desired attack vector profile ofmeasurements. The residual under such attack will thereforebe defined by r = || z a − h (ˆ x + c ) || . (8)The attacker can ensure this value is close to 0 as theinjected (measured) value has been designed specifically toequal the one estimated using these flows. In practice, however,it is unlikely that an attacker will have the required knowledgean FDI attack, as this information will rarely be availablepublicly and maybe intentionally hidden. B. Attack Assumption and Overview of TL-FDIA
For TL-FIDA, we operate from the assumptions usuallypresent in the blind attack models [21], as below: • The attacker has reading access to all measurements andcan alter all or some real and reactive power measure-ments in the system. • The attacker has no knowledge of system interconnectionor branch admittance/resistance values.Keeping these assumptions in mind, the attacker will needto create a model of the power system only from the available
EEE POWER & ENERGY SOCIETY GENERAL MEETING 2021, SUBMITTED ON 06 NOVEMBER 2020 3
Figure 1. Overview of the Topology Learning FDI Attack algorithm imple-mentation. power flow measurements. Once the attacker has gained accessto the system, the algorithm enters a period of data collection.When sufficient data has been received, the attacker attemptsto perform the topology learning step of the attack based onthe received data. This allows the attacker to subsequentlyperform an attack-side state estimation to verify the accuracyof the model using the derived topology. If the proposed vectorpasses the pseudo-state estimation residual check, the attackercan then proceed to attack phase. If not, the attacker waits foradditional data and reruns the topology learning step of theattack. This proposed flow is outlined in Figure 1.
C. Attack Side Verification
Compared with the full knowledge attack, an important con-sideration for TL-FDIA is to know when they have collectedenough data and are ready to attack. This can be difficult, asthe attacker has zero prior information and no access to thesystem operator residual data, so any indication as to whetherthe proposed attack vector may pass BDD is based only onnew inbound measurements. Consequently, we propose anattacker-side pseudo-residual calculation as an assessment onwhether the attack can proceed based on r p = || z a − ˆ h (ˆ x + c ) || . (9)Where ˆ h is the estimated non-linear transformation functionbased on the estimated topology values and state measure-ments themselves. D. Sub-graph Residual
In fact, even in the presence of global residual errors, theattacker may be able to identify subgraphs within the networkwhere they can attack without altering other regions with poorresidual performance.In practice, this will be similar to the incomplete-information-type attacks in [7]. Areas of high regional residual will be assumed to have incomplete knowledge, and other,lower-error regions can be attacked. Therefore, the attackercan use the regional meter error given by an alarm triggered,defined by r mp = z m − z mest > τ m . (10)With respect to the FDI attack, the sub-graphs are givenby the number of non-zero terms in the column vector ofthe topology matrix H for a given node n or the Jacobian J in the non-linear model. The attacker can then identifythe corresponding sub-graphs related to this branch using thenetwork incidence matrix I . For meter number m, col n ( I m ) = (cid:40) meter m is part of bus n subgroup meter m is not part of the subgroup . (11)The attacker then can structure the state adjustment vector c such that I n,m = 0 .V. B LIND T OPOLOGY I DENTIFICATION
For the initial topology identification, we employ themethod outlined in [20]. The aim of topology identification isto identify the network incidence as well as the branch valuesfor the conductance and susceptance matrices [ G ij ] & [ B ij ] .The technique we have employed here was originally used tomap distribution networks for system operators. However, weturn this method against the system operator for the purposesof an FDI attack where the attacker has limited systeminformation. The method outlined by Zhang et al . utilisesa two-step identification process to identify per-unit branchtopology information. The initial step introduces a regressionto calculate approximations of conductance and susceptance.Initially, the regression uses a linearised approximation ofthe relationship between branch parameters, voltages, real andreactive powers to create a basis initial approximation.We can consider the matrix formulation for this in terms [ P/V ] = G ij [ V ] , (12) [ Q/V ] = − B ij [ V ] . (13) B ij & G ij are approximations of the real and imaginarybranch elements. These are based on assumption of small stateangle differences under the standard equations for real andreactive power injection. Given this approximation, the branchcomponents can be extracted using matrix operations fromwhich a solution for the approximate G ij = [ P/V ][ V ] T ([ V ][ V ] T ) − , (14) B ij = [ Q/V ][ V ] T ([ V ][ V ] T ) − . (15)These initial steps are basic matrix operations. This meansthey can be performed quickly and with limited computationalpower. Under a DC approximation, these can on their own EEE POWER & ENERGY SOCIETY GENERAL MEETING 2021, SUBMITTED ON 06 NOVEMBER 2020 4 give reasonable approximations of the network branches in-cidences. Under the method proposed by Zhang et al . theyprovide an initial approximation for the network topologywhich is used as the starting point for the fine identificationstage. This is then followed by a modified Newton-Raphson,which incorporates the branch topology values to refine theapproximation. Given the power system bus injections underpolar coordinates as (cid:20) ∆ p ∆ q (cid:21) × n = (cid:34) δpδg δpδg δpδgδpδg δpδg δpδg (cid:35) · ∆ g ∆ b ∆ θ × (2 m + n − . (16)where g & b are conductance and susceptance of m branches. A pseudo-power flow calculation is performed andthe generalised inverse is then applied to solve for the differ-ence in both topology and state angle such that ∆ g ∆ b ∆ θ = (cid:20) δPδG δPδG δPδGδPδG δPδG δPδG (cid:21) + · (cid:20) ∆ P ∆ Q (cid:21) . (17)This is used in the usual additive process to derive anestimation for the topology. gbθ ( k +1) = gbθ k · ∆ g ∆ b ∆ θ . (18)A full outline of the applied algorithm for the topologydiscovery component can be found in [20].VI. R ESULTS & A
NALYSIS
This section assesses the performance of the proposed attackon IEEE-14 bus system. To replicate the real-time operationof a power system as closely as possible, system loads havebeen simulated using mock load profiles and the MATPOWERtoolset [22].
A. Effectiveness of TL-FDIA
In Figure 2, we show the system residual as we apply theTL-FDIA using a voltage angle bias of around 15% to bus1. This results in power flow changes across buses 1-2 and1-5. In blue we see the occasional residual spike past that ofthe acceptable alarm limit. In green we show the attackerspseudo-residual calculation, which, as expected, mimics theSO residual. As discussed, this pseudo-residual is used by theattacker as an attack-side assessment criterion. Without thepseudo residual we see around 80% success in attack with20 % of values exceeding the SO residual. This is comparedwith an expected type-2 error of around 1%. However, byapplying the residual check we decrease this error significantly.In Figure 3, we implement the pseudo-residual as a decisionstatistic, with the attacker choosing not to attack if they believethe residual will be violated. We note that the residual staysbelow the acceptable level and avoids detection. On timing,fine identification is achievable in around 5 seconds for a 33-bus system and 20 seconds for the 123-bus case. Increasingsize is not a significant challenge for the algorithm as attacking
Figure 2. Residual value measured by system operator and attacker inpresence of TD-FDI attack against 1% equivalent alarm.Figure 3. Residual value measured by system operator TD-FDI attack withpseudo-residual decision statistic considered against 1% equivalent alarm. region can always be divided into smaller regions to obtainquicker identifications.
B. Data Requirement for TL-FDIA
The previous successful attacks were performed with theassumption that 720 pieces of measurement data are available.However, the attacker may want to be ready to attack assoon as possible in order to avoid accidental exposure so itis critical to understand the minimum of measurement datathat allows such an attack. In Figure 4, we show how pseudo-residual decreases with additional available data points. It isclear that with increasing amounts of measurement data, thesystem residual declines quickly. In the case of 1% noise alarmand a 14-bus system, the attacker will likely wish to wait untilat least 200 points are available before attempting to build amap of the system.We simulate a time-domain attack scenario starting fromthe moment the attacker gains access to the full meter mea-surement to the moment the attack is ready to launch. Thetiming of attacks is a crucial consideration as the attackerseeks to minimise their time in the system. In Figure 5, asindividual measurements come in, we show how the systemresiduals from both operator and attacker change over timeas additional measurements become available to the attacker.We assume the attacker has access to measurements in similarfrequency to the central system operator, with state estimationand measurement set received once every minute. First, it
EEE POWER & ENERGY SOCIETY GENERAL MEETING 2021, SUBMITTED ON 06 NOVEMBER 2020 5
Figure 4. Residual value measured by system operator in presence of TD-FDIattack with increasing number of available data points.Figure 5. Residual value measured by system operator in presence of TD-FDIattack. X-axis shows number of minutes since intrusion. is important to note again that, once the attacker’s pseudo-residual converges to an acceptable level, the operator resid-ual also approaches the level that will pass BDD, whichdemonstrates the effectiveness of attacker-side pseudo-residualassessment. In addition, the figure suggests that the attackerwill need about 3-4 hours of data collection before theycan initiate the attack without detection. Compared with thelengthy process of reconnaissance and penetrating the system,such a duration is almost negligible, which validates the full-knowledge assumptions in the previous works.VII. C
ONCLUSIONS AND F UTURE W ORK
In this paper, we propose a topology-learning-aided FDI at-tack that combines topology learning techniques and attacker-side pseudo-residual assessment. We show via simulations ona 14-bus system that such an attack allows the performanceof a full-knowledge AC FDI attack under blind assumptions.In the next stage, we intend to apply the algorithm in a largerand time-varying network to investigate its effectiveness.R
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