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Talk in Multi-agent based Applications for Smart Grids and Sustainable Energy Systems Workshop (MASGES), in PAAMS '14 conference (SAlamanca, 2014)
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Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Consensus in Smart Grids for Decentralized EnergyManagement
M. Rebollo C. Carrascosa A. Palomares
Univ. Politècnica de València (Spain)
MASGES ’14Salamanca, June 2014
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Energy management problem
MotivationNew control mechanisms are needed for the near future powersystems
components connected in some network structurelarge scale → avoid information overloaddecentralized and distributed control mechanisms
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Our proposal
The challengeCreate a self-adaptive MAS that adapts itself to the electricaldemand using local information.
What is done. . .combination of gossip protocols to spread information todirect neighborsreal-time adaption to changes in the demandfailure tolerant
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Outline
1 Outline
2 Network characterization
3 Adaptive consensus-based distributed coordination mechanism
4 Adaption to demand
5 Adaption to failures
6 Conclusions
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Balearic Islands power grid
0 1 2 3 4 5−0.5
0
0.5
1
1.5
2
2.5Station Degree Distribution
log(nodes)
log(
degr
ee)
57 substations and 82lines (30kV to 220kV)average degree = 2.8diameter = 14average path length = 4.7clustering coef. = 0.33
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Centrality measures
degree: node with moreconnectionscloseness: distance to therest of the nodesbetweenness: number ofpaths that uses the nodeeigenvector: links withother important nodesk-core: connected withnodes with degree ≥ k
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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 network
consensus is used to adjust the total demand (follow theleader)
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Energy pattern
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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)
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
0 200 400 600 800 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA 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
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Conclusions
What we’ve doneTo apply a combination of gossip methods to create a failuretolerant, self-adaptive MAS that manages an electrical network
information exchanged with direct neighbors onlyno global repository of data nor central control neededpush-sum and consensus protocol combinedthe network adapts itself to changes in the electrical demandfailures are detected and assumed by the rest of activesubstations
M. Rebollo et al. (UPV) MASGES’14Consensus in Smart Grids for Decentralized Energy Management
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