a tutorial on blockchainfor microgrids: securing distributed...
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A Tutorial on Blockchain for Microgrids: Securing Distributed Optimization
Prof. Scott Moura
Energy, Controls, & Applications Laboratory (eCAL)University of California, Berkeley
EricMunsing
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Challenges: Intermittency, Variability, Quantity of DERsActors: Consumers, Aggregators, Utilities, System Operators
Motivation
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Example: Renewable Energy Credits Issues:
SinceRECsarenotphysical,howdoweknowSaraactuallyhas5RECstosell?
HowdoweverifytheRECsarelegitimate?
WhotracksandmanagesRECtransactions?
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Background Fields and Relevant Tools
Optimization & Control
Power Systems
Economics
• Mathematical Programming
• Optimization Theory
• Statistical Learning
• Optimal Power Flow
• Electricity Mkt Design• Game Theory
• Sequence and Planning
• Blockchains
• Strategic Bidding
• Distributed Optimization
• Regulation
• Economic Dispatch
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Distributed v. Decentralized
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Network Topologies
System Operator
Aggregator
Centralized
Distributed
Fully Decentralized
Centralized: Pros: Simple formulationCons: Limited privacy, slow computations
Distributed: Pros: Fast computation, protect privacyCons: High communication overhead
Pros: Low communication overhead, islanding Cons: Increased vulnerability to cyberattack
Fully-Decentral:
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Distributed v. Decentralized
Weaknesses of aggregator-based consensus:• Monopoly distortions and trust issues • Single point of failure/attack• Limited scalability
Alternative: Decentralized optimization
• Consensus with neighbors who share variables• Effective for sparsely connected problems
Mota et al: “D-ADMM: A Communication-efficient distributed algorithm for separable optimization” IEEE Transactions on Signal Processing (2012)
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Do you trust your neighbors?
Challenges:• Identify compromised nodes• Reach stable operation despite
compromised nodes
Assumptions: Compromised nodes…• Can affect problem data/constraints• Can send spurious messages
? ? ?
?
?
? ?
?
?
✓ ✓ ✓
☠
☠
✓ ✓
✓
☠
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Options for Securing Fully-Decentralized Optimization
✓ ☠ ✓
Create database of state variables• Securely timestamp variables • Requires trusted database manager
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Blockchain-Secured Decentralized Optimization
Blockchain as decentralized record-of-trust:• Record variable updates• Run feasibility checks• Compute update step• Anything a centralized aggregator can do!
…And more:• Transparent & auditable• Fully decentralized: robust to dropouts
✓ ☠ ✓
✓
✓ ☠ ✓
✓
Abstraction:
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New Technology: Blockchains
M1t
MNt
Block Bt Contents
M2t
Header
� Block No.
� Timestamp
� Validator ID
� Hash of Contents:
ϒ(B1 )
B1B0M1
0
Bt Bt+1ϒ(B0)
ϒ(B0)
ϒ(Bt−1)
ϒ(Bt+1)ϒ(Bt )
ϒ(Bt )
ϒ(Bt−1)
ϒ(Bt )
Decentralized, transparent database• Consensus mechanism for state updates• Trustless• Guarantees of security + execution• Robust, scalable, stable
Open Research Areas• Coordinating decentralized devices• Decentralized optimization• Trusted sensors and data networks
Appendix
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Why Blockchains?
Aggregators are great if:• One entity owns everything• No incentives to cheat• Communication is reliable• Aggregator isn’t attacked
Why Blockchains?• Benefits of decentralization• Strengths of central
auditors
Failure Mode Aggregator Fully-Decentralized
BlockchainADMM
Infeasible Constraints ✓ X ✓
Noise-injection attack ✓ ✓ ✓
Communication dropouts X ✓
✓
Monopoly distortions X ✓ ✓
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Outline
Background: What problem does blockchain solve?
Security: Cybersecurity in decentralized and fully-decentralized optimization
Coordination: Model trustless DER coordination respecting distribution constraints
0
1
2
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1 Decentralized DER Coordination
Q: How do we address trust issues in decentralized coordination networks?
Novelty• Use blockchains to secure distributed optimization
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Blockchains and Decentralized Optimization
Appendix
Local Computation
Verification Step
Updated Blockchain
State
Local Computation, … ,
Auditable Consensus
Blockchains:
Examples: Bitcoin, Ethereum, …
Decentralized Optimization:
Local Optimization
Update Step
Solution
Local Optimization,…,
Consensus
Examples: ADMM, Dual Splitting, …
Local Problem
Verifiable Update Step
Solution Stored on Blockchain
Local Problem, … ,
Auditable Consensus
Combined Paradigm:
Novel Paradigm
Munsing, Mather, Moura: “Blockchains for Decentralized Optimization of Energy Resources in Microgrid Networks” CCTA 2017
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Application: Coordinating Distributed Energy Resources
Local Problem
Verifiable Update Step
Solution Stored on Blockchain
Local Problem, … ,
Auditable Consensus…
…
ADMM Update (on Blockchain)
Consensus: Day-ahead Schedule
Local ProblemLocal Problem
…
Munsing, Mather, Moura: “Blockchains for Decentralized Optimization of Energy Resources in Microgrid Networks” CCTA 2017
• Private problem: Minimize private costs
• Global variables: Voltage & power estimates
• Update step (blockchain): ADMM average
• Converge when agree on network state
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Distribution Networks and Convex Relaxations of OPF
Single-phase AC distribution flow equations:
li �P 2i +Q2
i
vi()
������
2Pi
2Qi
li � vi
������2
li + vi
SOCP Relaxation:
pi = Pi �X
k2�(i)
Pk + rili, i = 0, . . . , n
qi = Qi �X
k2�(i)
Qk + xili, i = 0, . . . , n
vi = v⇡(i) + 2(riPi + xiQi)� (r
2i + x
2i )li
li =P 2i +Q2
i
vi, i = 1, . . . , n
Evs & Shapeable Loads1:Psi,min
ss(t) Psi,max
TX
t=1
ss(t) = Esi,demand
ssi (t) = 0 8t = 1, . . . , ti,startby
ssi (t) = 0 8t = ti,endby, . . . ,T
Batteries1:sbi (t) = dbi (t)� cbi (t)
Pbi,dis dbi (t) 0 cbi (t) Pb
i,charge
Eb,min
Eb(t) Eb,max
Ebi (t) = Eb
i (t� 1) + cbi (t)�thi,in
� dbi (k)�t/hi,out
(1 + ")Ebi (1) Eb
i (T) (1� ")Ebi (1)
Deferrable Loads2:sd = �d
8t = 1 . . .T :
0 di(t� 1) di(t)
di(t) ai(t)
ai(t� ⇣) d(t)
di(t) 2 (0, 1)
2Le Floch et al: “Plug-and-Play Model Predictive Control for Load Shaping and Voltage Control in Smart Grids,” IEEE Transactions on Smart Grid, to appear3Chang, Alizadeh, Scaglione: “Coordinated Home Energy Management for Real-Time Power Balancing,” IEEE PES General Meeting, 2012
1M.E. Baran and F.F. Wul: “Optimal Capacitor Placements on Radial Distribution Systems”, IEEE Transactions on Power Delivery, 1989
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Formulation
Decompose using ADMM:• Local variables: Local line flows and injections• Global variables: Network line flows and injections
Appendix
min
TX
t=1
nX
i=1
Ci,t(sgi (t))
s.t. power flow equations t = 1, . . . ,T
and DER constraints, i = 1, . . . , n
over sgi (t) 2 [s
gi , s
gi ], i = 0, . . . , n, t = 1, . . . ,T
(Pi, Qi, li, vi)(t), i = 1, . . . , n, t = 1, . . . ,T
Objective: Minimize Energy Cost
Y. Wang, L. Wu, and S. Wang, “A Fully-Decentralized Consensus-Based ADMM Approach for DC-OPF With Demand Response,” IEEE TSGI, 2016.Q. Peng and S. H. Low, “Distributed Algorithm for Optimal Power Flow on an Unbalanced Radial Network,” 53rd CDC, 2015.P. Sulc, S. Backhaus, and M. Chertkov, “Optimal Distributed Control of Reactive Power Via the Alternating Direction Method of Multipliers,” IEEE TEC, 2014.
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Decentralize with ADMM and deploy on blockchain
repeatPi: Private Optimization, compute locally
Gather private constraints
Compute x̃i and send to smart contract S1
S1: ADMM Aggregator, on blockchainUpdate z
if krkk2 ✏pri, kskk2 ✏dual thenCompute final schedule and clearing prices
Send schedule to S2
enduntil krkk2 ✏pri, kskk2 ✏dual
Mi: Each Smart MeterRecord energy consumption
Send time-stamped & signed consumption to S2
...time progresses
S2: Billing contract, on blockchainCompare schedule from S1 with meter readings
Compute penalties, payments, and charges
Transfer payments between accounts
…
P1M1
P1M1
S1S2
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Initial Formulation and Results
Approach:• Goal: Minimize day-ahead energy costs
• Constraint: Voltage at all buses on grid
• Common knowledge: Topology & line resistance
Bus Voltage Across Microgrid
0 4 8 12 16 20 24Time (h)
10
20
30
40
50
Bus
Num
ber
1.0465
1.047
1.0475
1.048
1.0485
1.049
1.0495
Vol
tage
0 5 10 15 20 25Time (h)
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Rea
l Pow
er C
onsu
mpt
ion
(Gen
erat
ion)
, p.u
.
Average Nodal Power Consumption/Generation
BatteryUncontrolableSolarShapeableDeferable
Tools: • Shapeable loads (e.g. electric vehicles)• Deferrable Loads (e.g. smart appliances)• Batteries
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Implementation
Implementation:• Smart contracts (S1, S2):
• Ethereum private blockchain• Access with ethjsonrpc
• Convex Optimization (P1): Cvxpy• Hardware: WeMo wifi lightbulbs
• Control with pywemo
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Revisiting Open Questions
• ✓How can we respect distribution constraints when coordinating DERs?
• ✓How can we manage trust problems among DERs (and utilities)?
• X How can we guarantee security with large populations of DERs?
Appendix
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2 Security in Distributed Optimization
Q: How do we scale to large networks without exposing our system to cybersecurity threats?
Novelty• Derive security checks that can be built into the
optimization algorithm
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Do you trust your neighbors?
Challenges:• Identify compromised nodes• Reach stable operation despite
compromised nodes
Assumptions: Compromised nodes…• Can affect problem data/constraints• Can send spurious messages
? ? ?
?
?
? ?
?
?
✓ ✓ ✓
☠
☠
✓ ✓
✓
☠
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Security in Distributed & Decentralized Optimization
Nefarious nodes may:• Distort private problem• Send unreachable update signal• Stop convergence by injecting noise
Prior work on security in optimization:• Failure-resistant scheduling• Impact of compromised sensors• Communication security• Greenfield: Design security checks into algorithm!
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Background: Alternating Direction Method of Multipliersminx,z
f(x) + g(z)
s.t. Ax+Bz = c
x 2 Xz 2 Z
Convex Centralized problem:• Separable objective and constraints
x
k+1 := argminx2X f(x) +
⇢
2kAx+Bz
k � c+ u
kk22
z
k+1 := argminz2Z g(z) +
⇢
2kAx
k+1 +Bz � c+ u
kk22
u
k+1 := u
k +Ax
k+1 +Bz
k+1 � c
ADMM: Augmented local problem• Guaranteed convergence• Big hammer, popular tool
Boyd et al: “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers,” Foundations and Trends in M.L. (2010)
x
k+1 := argminx2X f(x) +
⇢
2kAx+Bz
k � c+ u
k
x
k22
z
k+1 := argminz2Z g(z) +
⇢
2kAxk+1 +Bz � c+ u
k
z
k22
u
k+1x
:= u
k
x
+Ax
k+1 +Bz
k+1 � c
u
k+1z
:= u
k
z
+Ax
k+1 +Bz
k+1 � c
Fully Decentralized ADMM: • Local copies of penalty term• Same guarantees as ADMM!
Mota et al: “D-ADMM: A Communication-efficient distributed algorithm for separable optimization” IEEE Transactions on Signal Processing (2012)
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Attack vector: Noise Injection
Stop convergence by injecting noise:•
• Defense neededx̃
k+1 = x
⇤k+1 + �(k)
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Algorithm for Noise Detection
Given public information,
x1
�1.0�0.50.0
0.51.0x2
�1.0�0.8�0.6�0.4�0.2 0.0
f(x
1,x
2)
02468
Collect Iterates
1. Collect Iterates
x1
�1.0�0.50.0
0.51.0x2
�1.0�0.8�0.6�0.4�0.2 0.0
f(x
1,x
2)
02468
Assess Gradients
2. Assess Gradient
x1
�1.0�0.50.0
0.51.0x2
�1.0�0.8�0.6�0.4�0.2 0.0
f(x
1,x
2)
�2.50.02.55.07.5
Construct Hessian and Assess Convexity
3. Construct Hessian & Evaluate Convexity
Hypothesis: The local objective function is convex.If not, we conclude there was an attack
Eric Munsing and Scott Moura “Cybersecurity in Distributed and Fully-Decentralized Optimization: Distortions, Noise Injection, and ADMM” arXiv:1805.11194 [math.OC], 2018.
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Assess Gradient
x
i = argminx2X f(x) +
⇢
2kAx+Bz
i�1 � c+ u
i�1k22
0 = @f(x)|i +A
T + ⇢A
T (Ax
i +Bz
i�1 � c)
@f(x)|i = �A
T (⇢ui � ⇢B(zi � z
i�1))
From ADMM convergence proof, assess gradient from public information:
x1
0.0 0.5 1.0 1.5 2.0x2
0.00.5
1.01.5
2.0012345
f(xi)
f(xj)
xi xj
�x1�x2
Changes in the gradient between two points is associated with the Hessian…… We can use this to assess convexity!
Eric Munsing and Scott Moura “Cybersecurity in Distributed and Fully-Decentralized Optimization: Distortions, Noise Injection, and ADMM” arXiv:1805.11194 [math.OC], 2018.
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x1
0.0 0.5 1.0 1.5 2.0x2
0.00.5
1.01.5
2.0012345
f(xi)
f(xj)
xi xj
�x1�x2
From Gradient to Hessian
Changes in the gradient between two points is associated with the Hessian…… We can use this to assess convexity!
@
@x1f(x)|x
j
=@
@x1f(x)|x
i
+@
@
2x1
f(x)|xi
(xj
1 � x
i
1) +@
@x1@x2f(x)|x
i
(xj
2 � x
i
2)
@
@x2f(x)|x
j
=@
@x2f(x)|x
i
+@
@
2x2
f(x)|xi
(xj
2 � x
i
2) +@
@x2@x1f(x)|x
i
(xj
1 � x
i
1)
1st-order Taylor approximation between points xi and xj , 2-d case:
ITERATES ITERATESGRADIENT GRADIENT HESSIAN HESSIAN
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31
2
666666664
@
@x1f(x)|kj
@
@x2f(x)|kj
@
@x1f(x)|ki
@
@x2f(x)|ki
3
777777775
=
2
664
(x1)|kj (x2)|kj 0 00 0 (x1)|kj (x2)|kj
(x1)|ki (x2)|ki 0 00 0 (x1)|ki (x2)|ki
3
775
2
666666664
@
@
2x1
f(x)
@
@x1@x2f(x)
@
@x2@x1f(x)
@
@
2x2
f(x)
3
777777775
For 2-d case:
D =
2
6664
In ⌦ (xk � x
a)T
In ⌦ (xk � x
b)T
...In ⌦ (xk � x
k�1)T
3
7775
For n-D:
Rearrange to�!G = D
�!H
From Gradient to Hessian
Eric Munsing and Scott Moura “Cybersecurity in Distributed and Fully-Decentralized Optimization: Distortions, Noise Injection, and ADMM” arXiv:1805.11194 [math.OC], 2018.
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Numerical Tests: 10,000 Randomly Generated Quadratic Programs
RandomlyGenerate• Dimensionsofxandz• Positivesemi-definiteP,Q• A,B,c,d
ConsiderConvexQP
ADMMalgorithmis…
Randomlyinjectnoiseintox-update• 𝑥"#$ = Δ ⋅ argmin ⋯• Δ ∼ Ber 0.5 , Δ ∈ {0.9, 1.1}
Eric Munsing and Scott Moura “Cybersecurity in Distributed and Fully-Decentralized Optimization: Distortions, Noise Injection, and ADMM” arXiv:1805.11194 [math.OC], 2018.
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33
Classification Results
Atta
ck
x1
�1.0�0.50.0
0.51.0x2
�1.0�0.8�0.6�0.4�0.2 0.0
f(x
1,x
2)
0
2
4
Convexity of Attacked Hessian
x1
�1.0�0.50.0
0.51.0x2
�1.0�0.8�0.6�0.4�0.2 0.0
f(x
1,x
2)
�2.50.02.55.07.5
Construct Hessian and Assess ConvexityNo Attack AttackNo
Atta
ck
x1
�1.0�0.50.0
0.51.0x2
�1.0�0.8�0.6�0.4�0.2 0.0
f(x
1,x
2)
�2.50.02.55.07.5
Convexity of Attacked Hessian
Repo
rted
Actual
x1
�1.0�0.50.0
0.51.0x2
�1.0�0.8�0.6�0.4�0.2 0.0
f(x
1,x
2)
0
5
10
15
Convexity of Attacked Hessian
4.2%
96%
0%
100%
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Recap
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Summary of Contributions
Optimization & Control
Power Systems
Economics
• Optimization Theory
• Statistical Learning
• Optimal Power Flow
• Electricity Mkt Design• Game Theory
• Sequence and Planning
• Blockchains
• Strategic Bidding
• Distributed Optimization
• Regulation
• Economic Dispatch
1
Coordination
Security
1
2
2