supportive consensus for smart grid management
DESCRIPTION
Slides for the 3rd International Workshop on Citizen Networks (CitiNet'14), at ECCS. Lucca, September 2014TRANSCRIPT
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Supportive Consensus for Smart Grid Management
Miguel Rebollo C. Carrascosa A. Palomares
Univ. Politècnica de València (Spain)
CITINET ’14Lucca, September 2014
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Energy management problem
MotivationSmart cities depend on a smart grid to ensure resilient delivery ofenergy to supply their functions
intelligent components connected in some network structurelarge scale → avoid information overloaddecentralized and distributed control mechanisms
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Our proposal
The challengeCreate a self-adaptive system that adapts itself to the electricaldemand using local information.
What is done. . .combination of gossip protocols to spread information todirect neighborssupportivereal-time adaption to changes in the demandfailure tolerant
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
The city
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Districts
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Population density
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Power supply network
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
The model
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus
what is it?
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus
what is it used for?
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
1.each node has an initial value
1 2
3 4
x1 = 0.4 x2 = 0.2
x3 = 0.3 x4 = 0.9
x1 = 0.4
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
2.the value is passed to the
neighbors
1 2
3 4
x1 = 0.4 x2 = 0.2
x3 = 0.3 x4 = 0.9
x1 = 0.4
x1 = 0.4x1 = 0.4
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
3.the values from the neighbors
are received
1 2
3 4
x1 = 0.4 x2 = 0.2
x3 = 0.3 x4 = 0.9
x2 = 0.2
x4 = 0.9x3 = 0.3
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
4.the new value is calculated by
x(t+1) = x(t)+ε∑j∈Ni
[xj(t)− xi(t)]
where ε < mini1di
1 2
3 4
x1 = 0.45 x2 = 0.425
x3 = 0.325 x4 = 0.6
x1 = 0.4
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
0 5 10 15 20 25 300
0.1
0.2
0.3
0.4
0.5
0.6
0.7
x = 0.45
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Data aggregation protocols
consensus can not calculate aggregate valuesconsensus belongs to a broader family of protocols
network topology: unstructuredrouting scheme: gossip
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Push-Sum algorithm
1 {(sr , wr )} the pairs received by i at step t − 12 si(t)←
∑r sr
3 wi(t)←∑
r wr
4 a target fi(t) is chosen randomly5(
12si(t), 1
2wi(t))
is sent to fi(t) and to i (itself)
6 si (t)wi (t) is the value calculated for step t
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Push-Sum formulation
si(t+1) = si(t)di + 1+
∑j∈Ni
sj(t)dj + 1 , wi(t+1) = wi(t)
di + 1+∑j∈Ni
wj(t)dj + 1
where di is the number of neighbors of agent i (degree of i).si(t)/wi(t) converges to
limt→∞
si(t)wi(t)
=∑
isi(0)
when wi(0) = 1 ∀i .
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Combination of Push-Sum and consensus
gossip is used to1 determine the number of active substations2 calculate the total capacity of the network3 update the total demand
consensus is used to adjust the total demand (follow theleader)
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Follow the leader behaviourIf one node does not follow the process, all the network convergesto its value
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
How it can be corrected?
Key: sum conservation
s =∑
ixi(0) =
∑i
xi(t) ∀t
If a node reaches its bound xi(t)−maxi units are lost from totalsum
∑i xi(t)
this excess will be assumed by the rest of the network
Compensationit is equivalent to a new initial value for izi(0) = xi(0) + xi(t)−maxi
we just have to add zi(0)− xi(0 = xi(t)−maxi to xi(t)
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Supportive Consensus evolution
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Energy pattern
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to the demand
0 50 100 1500
100
200
300
400
500
600
700Adaption to the Demand
#epoch
dem
and
(MW
h)
cummulated demand
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to the demand
0 50 100 1500
100
200
300
400
500
600
700Adaption to the Demand
#epoch
dem
and
(MW
h)
cummulated demand
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to the demand
0 50 100 1500
100
200
300
400
500
600
700Adaption to the Demand
#epoch
dem
and
(MW
h)
cummulated demand
50 55 60 65 70580
590
600
610
620
630
640
650
660Adaption to the Demand (zoom)
#epochde
man
d (M
Wh)
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to the demand
0 50 100 1500
100
200
300
400
500
600
700Adaption to the Demand
#epoch
dem
and
(MW
h)
cummulated demand
50 55 60 65 70580
590
600
610
620
630
640
650
660Adaption to the Demand (zoom)
#epoch
dem
and
(MW
h)
0 200 400 600 800 1000 1200 1400 1600 1800 2000
400
500
600
700
Adaption to the Demand (2 weeks)
#epoch
dem
and
(MW
h)
cummulated demand
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Evolution of the relative error
0 200 400 600 800 1000 1200 1400 1600 1800 2000−0.04
−0.02
0
0.02
0.04
%er
ror
#epoch
Evolution of the relative error
−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.040
50
100
150
200
250
300Distribution of the relative error
error rate
freq.
0 200 400 600 800 1000 1200 1400 1600 1800 2000−0.04
−0.02
0
0.02
0.04Evolution of the relative error adapting to a random demand
#epoch
%er
ror
−0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.040
20
40
60
80
100
120
140
160
180
error rate
freq.
Distribution of the relative error for a random demand
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to failures
350 375 400 425 4505800
6000
6200
6400
6600
6800
7000
#epochs
erro
r rat
e
Evolution after a change in the demand
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to failures
350 375 400 425 4505800
6000
6200
6400
6600
6800
7000
#epochs
erro
r rat
e
Evolution after a change in the demand
350 400 450 500 5501.38
1.4
1.42
1.44
1.46
1.48
1.5 x 104
#epochs
erro
r rat
e
Evolution after the failure of one substation
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to failures
200 400 600 800 1000 1200 1400 1600 1800 2000−20
−10
0
10
20
#epochs
erro
r rat
e
Comparitions of the evolution of the error rate (Llucmajor substation failure)
no failuressubstat faildifference
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Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Conclusions
What we’ve doneTo apply a combination of gossip methods to create a supportive,failure tolerant, self-adaptive system for smart-grids
information exchanged with direct neighbors onlyno global repository of data nor central control neededpush-sum and consensus protocol combinedsupportive for nodes out of their boundsthe network adapts itself to changes in the electrical demandfailures are detected and assumed by the rest of activesubstations
M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management