Consensus in Smart Grids for Decentralized Energy Management

Outline Network characterization ADCDA Adaption to demand Adaption to failures Conclusions
Consensus in Smart Grids for Decentralized Energy
Management
M. Rebollo C. Carrascosa A. Palomares
Univ. Politècnica de València (Spain)
MASGES ’14
Salamanca, June 2014
M. Rebollo et al. (UPV) MASGES’14
Consensus in Smart Grids for Decentralized Energy Management

Energy management problem
Motivation
New control mechanisms are needed for the near future power
systems
components connected in some network structure
large scale → avoid information overload
decentralized and distributed control mechanisms

Our proposal
The challenge
Create a self-adaptive MAS that adapts itself to the electrical
demand using local information.
What is done. . .
combination of gossip protocols to spread information to
direct neighbors
real-time adaption to changes in the demand
failure tolerant

Outline
1 Outline
2 Network characterization
3 Adaptive consensus-based distributed coordination mechanism
4 Adaption to demand
5 Adaption to failures
6 Conclusions

Balearic Islands power grid
0 1 2 3 4 5
−0.5
0
0.5
1
1.5
2
2.5
Station Degree Distribution
log(nodes)
log(degree)
57 substations and 82
lines (30kV to 220kV)
average degree = 2.8
diameter = 14
average path length = 4.7
clustering coef. = 0.33

Centrality measures
degree: node with more
connections
closeness: distance to the
rest of the nodes
betweenness: number of
paths that uses the node
eigenvector: links with
other important nodes
k-core: connected with
nodes with degree ≥ k

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

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 = 0.4
x1 = 0.4

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 = 0.9
x3 = 0.3

Consensus process
4.
the new value is calculated by
x(t+1) = x(t)+ε
j∈Ni
[xj(t) − xi (t)]
where ε < mini
1
di
1 2
3 4
x1 = 0.45 x2 = 0.425
x3 = 0.325 x4 = 0.6
x1 = 0.4

Data aggregation protocols
consensus can not calculate aggregate values
consensus belongs to a broader family of protocols
network topology: unstructured
routing scheme: gossip

Push-Sum algorithm
1 {(ˆsr , ˆwr )} the pairs received by i at step t − 1
2 si (t) ← r ˆsr
3 wi (t) ← r ˆwr
4 a target fi (t) is chosen randomly
5 1
2 si (t), 1
2 wi (t) is sent to fi (t) and to i (itself)
6
si (t)
wi (t) is the value calculated for step t

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
lim
t→∞
si (t)
wi (t)
=
i
si (0)
when wi (0) = 1 ∀i.

Combination of Push-Sum and consensus
gossip is used to
1 determine the number of active substations
2 calculate the total capacity of the network
consensus is used to adjust the total demand (follow the
leader)

Energy pattern

Adaption to the demand
0 50 100 150
0
100
200
300
400
500
600
700
Adaption to the Demand
#epoch
demand(MWh)
cummulated demand

0 50 100 150
0
100
200
300
400
500
600
700
#epoch
demand(MWh)
cummulated demand
50 55 60 65 70
580
590
600
610
620
630
640
650
660
Adaption to the Demand (zoom)
#epoch
demand(MWh)

0 50 100 150
0
100
200
300
400
500
600
700
#epoch
demand(MWh)
cummulated demand
50 55 60 65 70
580
590
600
610
620
630
640
650
660
Adaption to the Demand (zoom)
#epoch
demand(MWh)
0 200 400 600 800 1000 1200 1400 1600 1800 2000
400
500
600
700
Adaption to the Demand (2 weeks)
#epoch
demand(MWh)
cummulated demand

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
%error
#epoch
Evolution of the relative error
0 200 400 600 800 1000 1200 1400 1600 1800 2000
−0.04
−0.02
0
0.02
0.04
Evolution of the relative error adapting to a random demand
#epoch
%error

Adaption to failures
350 375 400 425 450
5800
6000
6200
6400
6600
6800
7000
#epochs
errorrate
Evolution after a change in the demand

350 375 400 425 450
5800
6000
6200
6400
6600
6800
7000
#epochs
errorrate
Evolution after a change in the demand
350 400 450 500 550
1.38
1.4
1.42
1.44
1.46
1.48
1.5
x 10
4
#epochs
errorrate
Evolution after the failure of one substation

200 400 600 800 1000 1200 1400 1600 1800 2000
−20
−10
0
10
20
#epochs
errorrate
Comparitions of the evolution of the error rate (Llucmajor substation failure)
no failures
substat fail
difference

Conclusions
What we’ve done
To apply a combination of gossip methods to create a failure
tolerant, self-adaptive MAS that manages an electrical network
information exchanged with direct neighbors only
no global repository of data nor central control needed
push-sum and consensus protocol combined
the network adapts itself to changes in the electrical demand
failures are detected and assumed by the rest of active
substations

Consensus in Smart Grids for Decentralized Energy Management

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