Stochastic defense against ideal grid attacks
Daniel Bienstock
Columbia University

June 2018

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

“Cyber-physical” attacks
Fact or fiction?
1

An adversary carries out a physical alteration of a grid(example: disconnecting a power line)2

This is coordinated with a modification of sensor signals(“data replay”) – a hack3

The goal is to disguise, or keep completely hidden, the natureof the attack and its likely consequences

4Power industry: it will never happen (“we would know what
happened”)

5

Really?

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Control centers, RTUs, PMUs, state estimation
tie line= sensor

control
centerBienstock
Stochastic defense against ideal grid attacks

Columbia University

Control centers, RTUs, PMUs

Control center performs a regulatory and economic role
Sensors report to control center
Control center issues commands to (in particular) smaller
generators
Sensors: RTUs (old), PMUs (new – and expensive)
RTUs report once every four seconds
PMUs report
30 to 100 times a second
PMUs report (AC) voltage and current (plus more ...)

Anecdotal: PMUs overwhelming human operators

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

State estimation
A data-driven procedure to estimate relevant grid parameters
Even with PMUs, data is sketchy and noisy
Statistical procedure: “state estimation” (at control center)
DC power flow equations:Bθ = P g − P d
B = susceptance matrix, θ = phase angles, P g , P d generation and load vectors

Sensors provide information that fit some of theθ, P d , (P g ?) parameters
State estimation: least squares procedure to estimate the rest,
plus more
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Prior basic researchAll, or mostly, DC-basedIntelligent procedures for enriching state estimation so as todetect and reconstruct attacks
Unavoidable: a model for attacking behavior is essential
Liu, Ning Reiter (2009), Kim and Poor (2011),
Deka, Baldick, Vishwanath (2015)
Soltan, Yannakakis, Zussman (2015 - )Warning: watch out for those assumptions!

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Soltan, Yannakakis, Zussman 2017
Attacker disconnects lines plus alters sensor output in an(unknown) zone of the grid
As a result, the equationBθ = P g − P d
is wrong because B is incorrect and measurements θ are(sparsely) false
A statistical procedure to try to “fit” a correction to B and a
discovery of false data
Important: testing done using AC phase angles θSome assumptions
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Today: load change, signal hacking – all AC

An attacker causes physical changes in the network: inparticular load changes (no generator changes)
Attacker also hacks the signal flow: the output of some
sensors is altered
Goal of the attacker is twofold:
Hide the location of the attack and even the fact that an
attack happened
2 Cause line overloads that remain hidden
1

We assume full PMU deplyoment. Everything is AC based.

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

AGC, primary and secondary response
What happens when generation - loads spontaneously changes(i.e. a net imbalance)?
AC frequency changes proportionally (to first order)
near-instantaneously
Primary response. (very quick) Inertia in generators
contributes electrical energy to the system
Secondary response. (seconds) Suppose estimatedgeneration shortfall = ∆P. Then:
Generator g changes output by αg ∆P

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

AGC, primary and secondary response
What happens when generation - loads spontaneously changes(i.e. a net imbalance)?
AC frequency changes proportionally (to first order)
near-instantaneously
Primary response. (very quick) Inertia in generators
contributes electrical energy to the system
Secondary response. (seconds) Suppose estimatedgeneration shortfall = ∆P. Then:
Generator g changes output by αg ∆PPg αg = 1, α ≥ 0,

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

AGC, primary and secondary response
What happens when generation - loads spontaneously changes(i.e. a net imbalance)?
AC frequency changes proportionally (to first order)
near-instantaneously
Primary response. (very quick) Inertia in generators
contributes electrical energy to the system
Secondary response. (seconds) Suppose estimatedgeneration shortfall = ∆P. Then:
Generator g changes output by αg ∆PPg αg = 1, α ≥ 0, α > 0 for “participating” generators
Preset participation factors∆P sensed by control center, which issues commands
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Ideal attack: setup
For this talk, PMUs everywhere: at both ends of each line
Attacker has been in the system long enough to learn thesystemAttacker chooses, in advance, a non-generator, sparse set A
of buses to attack and in particular a line uv to overload
In near real-time, the attacker learns the current loads andtheir stochastics
In near real-time, the attacker solves computational problem
that diagrams the attack on A
This will specify the load changes and the signal distortion
Post-attack, attacker cannot recompute much and only relies
on adding “noise” to the computed distorted signals
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Undetectable attack: The attacker’s perspective

attacked set

participating generator

boundary
generator

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Undetectable attack: decisions for the attacker (abridged!)

For every bus in A, a “true” and “reported” complex voltage(magnitude and angle) VkT and VkR
True and reported voltages must agree on the boundary of A!
True and reported currents for lines within A
Voltages and currents on all other lines (true and reported are
identical)
Two power flow solutions; each must satisfy AC power flow line
A generation change consistent with secondary response

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Undetectable attack: formulation (abridged!)
T 2

T 2

Max (puv ) + (quv )

(1a)

s.t.
∀k ∈ A

C

T

R

T

R

∪ bd(A), |Vk | = |Vk |, θk = θk
X
d,R
d,R
R
R
∀k ∈ A, −(Pk+ jQk ) =(pkm + jqkm ),

(1b)
(1c)

km∈δ(k)
d,T

− (Pk

d,T

+ jQk

)=

X

T

T

(pkm + jqkm ),(1d)

km∈δ(k)gC∀k ∈ A \R :

g

d

g

X

P̂k − P̂k + j(Q̂k − Q̂k ) =TT(pkm + jqkm )(1e)km∈δ(k)g∀k ∈ R :gdg

Pk − P̂k + j(Qk − Q̂k ) =

X

T

T

(pkm + jqkm )(1f)

operational limits on all buses, generators and lines (other than uv)(1h)km∈δ(k)g

g

Pk − P̂k = αk ∆T

T

(AGC response)

T

T

(1g)

T

T

all pkm , qkm related to |Vk |, |Vm |, θk , θm through AC power flow laws

Bienstock
Stochastic defense against ideal grid attacks(1i)

Columbia University

Ideal attack: follow-up
Following the attack, for any bus ∈ A − bd(A) the attacker
reports (at each time t) a complex voltage valueRṼk = (|VkR | + νk (t))e j(θk +φk (t))
Here,E(νk (t)) = E(φk (t)) = 0,

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Ideal attack: follow-up
Following the attack, for any bus ∈ A − bd(A) the attacker
reports (at each time t) a complex voltage valueRṼk = (|VkR | + νk (t))e j(θk +φk (t))
Here,E(νk (t)) = E(φk (t)) = 0,
(consistent with zero expected load change)

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Ideal attack: follow-up
Following the attack, for any bus ∈ A − bd(A) the attacker
reports (at each time t) a complex voltage valueRṼk = (|VkR | + νk (t))e j(θk +φk (t))
Here,E(νk (t)) = E(φk (t)) = 0,
(consistent with zero expected load change)andvar(ν(t))
agrees with observed covariances
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Noise is not just noise
From real time series, voltage angle deviation histogram

Kolmogorov-Smirnoff gaussianity test strongly rejected, always
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Noise is not just noise
From real time series, voltage magnitude deviations

Strong and nontrivial correlation structure
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Learning noise

Theorem. (Co)variance of time series can be learned
In real time
In streaming fashion
Under evolving stochasticity
Bienstock, Shukla, Yun, Non-Stationary Streaming PCA, Proc.
2017 NIPS Time Series Workshop.

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

A large-scale example

From case2746wp (that has 2746 buses) from the Matpower caselibrary
attacked zone

1491
1137

1139

1361

1141
1138

1110

85

1625

1844

1287

1252

1295

104

1512

1651

1358

Undetectable attack with strong overloads on branches(1361, 1141) and (1138, 1141).

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 0Defender is likely to know that “something” happened (andquickly). But sensor data is noisy and “something” may be
inconsequential
We want a defensive action that is easily implementable interms of today’s grid operation
Should not lead to false positives
Solution: change the power flows in a way that the attacker
cannot anticipate, and identify inconsistent signals. How?
A solution: use responding generators – “pseudo AGC”

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 0Defender is likely to know that “something” happened (andquickly). But sensor data is noisy and “something” may be
inconsequential
We want a defensive action that is easily implementable interms of today’s grid operation
Should not lead to false positives
Solution: change the power flows in a way that the attacker
cannot anticipate, and identify inconsistent signals. How?
A solution: use responding generators – “pseudo AGC”
Mathematical statement: choose a random set ofparticipating generators, change their output by randomamounts so as to obtain a random, but valid, power flow
solution
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 0’
Following attack, and in suspicion of an attack
Defender only has access to reported data, which is accurate
in the non-attacked zone. But the defender does not know
the attacked zone.
(repeatedly) Defender chooses a random subset of the
AGC-responding generators, andDefender computes a random power flow solution where thechosen generators are allowed to change (up or down) their
output, within limits. The power flow solution must satisfy
e.g. voltage constraints.
Defender seeks to make the changes in generation large
subject to above constraints. “AGC” ⇒ generation change
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 1

But attacker cannot anticipate this random action. Therefore:

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 1

But attacker cannot anticipate this random action. Therefore:
Reported currents, and implied power flows, will havenear-constant values within attacked zone
But outside of attacked zone, with high-probability (?) mostlines will see significant changes in current and power flows
Above example (case2746wp) has over 3500 lines, but in a few
iterations we reduce the number of suspicious lines to < 100.

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 1

But attacker cannot anticipate this random action. Therefore:
Reported currents, and implied power flows, will havenear-constant values within attacked zone
But outside of attacked zone, with high-probability (?) mostlines will see significant changes in current and power flows
Above example (case2746wp) has over 3500 lines, but in a few
iterations we reduce the number of suspicious lines to < 100.
Good, but not good enough

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 2
boundary of attacked zone
must report accurate voltage

within attackedzone
near constant (and false)
reported voltage

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 2
boundary of attacked zone
must report accurate voltage

within attackedzone
near constant (and false)
reported voltage

On a line going from boundary to interior of attacked zone

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 2
boundary of attacked zone
must report accurate voltage

within attackedzone
near constant (and false)
reported voltage

On a line going from boundary to interior of attacked zone
reported current will be wrong

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 2
boundary of attacked zone
must report accurate voltage

within attackedzone
near constant (and false)
reported voltage

On a line going from boundary to interior of attacked zone
reported current will be wrong
because voltage at boundary bus is changing with our “AGC”

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Defense, 2
boundary of attacked zone
must report accurate voltage

within attackedzone
near constant (and false)
reported voltage

On a line going from boundary to interior of attacked zone
reported current will be wrong
because voltage at boundary bus is changing with our “AGC”
but voltage at interior bus is changing by very small amounts
In above example, one iteration identifies boundary lines with nofalse positives
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Publication: D. Bienstock and M. Escobar, Computing
undetectable grid attacks, and stochastic defenses, 2018 SIAM
Network Science Workshop. Journal version forthcoming.

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

A dead zone
attacked zone

rest of grid(no "trusted"
nodes)

More difficult/impossible to alter voltages in attacked zone

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

A dead zone
attacked zone

rest of grid(no "trusted"
nodes)

More difficult/impossible to alter voltages in attacked zone
More drastic maneuver:

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

A dead zone
attacked zone

rest of grid(no "trusted"
nodes)

More difficult/impossible to alter voltages in attacked zone
More drastic maneuver: use “AGC” to alter frequency ?
Theorem: under DC model if network is 2-node connected
there are no dead zones
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

A dead zone
attacked zone

rest of grid(no "trusted"
nodes)

More difficult/impossible to alter voltages in attacked zone
More drastic maneuver: use “AGC” to alter frequency ?
Theorem: under DC model if network is 2-node connected
there are no dead zones but there could be symmetry
Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Can the attacker defend against our defense?

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Can the attacker defend against our defense?
Can we defend against the attacker’s defense against our
defense?

Bienstock
Stochastic defense against ideal grid attacks

Columbia University

Can the attacker defend against our defense?
Can we defend against the attacker’s defense against our
defense?
Moment learning
Advantage: defender. Attacker cannot unroll previously
generated signals

Thu.Jun.28.000601.2018@blacknwhite

Bienstock
Stochastic defense against ideal grid attacks

Columbia University