1. 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 ’14
Lucca, September 2014
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
2. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Energy management problem
Motivation
Smart cities depend on a smart grid to ensure resilient delivery of
energy to supply their functions
intelligent components connected in some network structure
large scale ! avoid information overload
decentralized and distributed control mechanisms
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
3. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Our proposal
The challenge
Create a self-adaptive system that adapts itself to the electrical
demand using local information.
What is done. . .
combination of gossip protocols to spread information to
direct neighbors
supportive
real-time adaption to changes in the demand
failure tolerant
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
4. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
The city
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
5. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Districts
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
6. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Population density
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
7. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Power supply network
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
8. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
The model
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
9. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus
what is it?
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
10.
11.
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14. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus
what is it used for?
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
15.
16.
17.
18.
19.
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21.
22. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
1.
each node has an initial value
x1 = 0.4 x2 = 0.2
1 2
3 4
x1 = 0.4
x3 = 0.3 x4 = 0.9
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
23. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
2.
the value is passed to the
neighbors
x1 = 0.4 x2 = 0.2
x1 = 0.4
1 2
3 4
x3 = 0.3 x4 = 0.9
x1 = 0.4
x1 = 0.4
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
24. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
3.
the values from the neighbors
are received
x1 = 0.4 x2 = 0.2
x2 = 0.2
1 2
x4 = 0.9
3 4
x3 = 0.3
x3 = 0.3 x4 = 0.9
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
25. 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)+"
X
j2Ni
[xj (t) − xi (t)]
where " < mini
1
di
x1 = 0.45 x2 = 0.425
1 2
3 4
x3 = 0.325 x4 = 0.6
x1 = 0.4
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
26. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Consensus process
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
x = 0.45
0 5 10 15 20 25 30
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
27. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Data aggregation protocols
consensus can not calculate aggregate values
consensus belongs to a broader family of protocols
network topology: unstructured
routing scheme: gossip
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
28. 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 − 1
2 si (t)
P
r ^sr
3 wi (t)
P
r ^wr
4 a target fi tis chosen randomly
() 5
12
si (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’14
Supportive Consensus for Smart Grid Management
29. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Push-Sum formulation
si (t+1) =
si (t)
di + 1+
X
j2Ni
sj (t)
dj + 1, wi (t+1) =
wi (t)
di + 1+
X
j2Ni
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!1
si (t)
wi (t)
=
X
i
si (0)
when wi (0) = 1 8i.
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
30.
31. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
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
3 update the total demand
consensus is used to adjust the total demand (follow the
leader)
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
32. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Follow the leader behaviour
If one node does not follow the process, all the network converges
to its value
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
33. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
How it can be corrected?
Key: sum conservation
s =
X
i
xi (0) =
X
i
xi (t) 8t
If a node reaches its bound xi (t) − maxi units are lost from total
sum P
i xi (t)
this excess will be assumed by the rest of the network
Compensation
it is equivalent to a new initial value for i
zi (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’14
Supportive Consensus for Smart Grid Management
34. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Supportive Consensus evolution
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
35. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Energy pattern
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
36. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to the demand
700
600
500
400
300
200
100
0
Adaption to the Demand
0 50 100 150
#epoch
demand (MWh)
cummulated demand
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
37. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to the demand
700
600
500
400
300
200
100
0
Adaption to the Demand
0 50 100 150
#epoch
demand (MWh)
cummulated demand
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
38. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to the demand
700
600
500
400
300
200
100
0
Adaption to the Demand
0 50 100 150
#epoch
demand (MWh)
cummulated demand
660
650
640
630
620
610
600
590
580
Adaption to the Demand (zoom)
50 55 60 65 70
#epoch
demand (MWh)
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
39. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to the demand
700
600
500
400
300
200
100
0
Adaption to the Demand
0 50 100 150
#epoch
demand (MWh)
cummulated demand
660
650
640
630
620
610
600
590
580
Adaption to the Demand (zoom)
50 55 60 65 70
#epoch
demand (MWh)
700
600
500
400
Adaption to the Demand (2 weeks)
0 200 400 600 800 1000 1200 1400 1600 1800 2000
#epoch
demand (MWh)
cummulated demand
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
40. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Evolution of the relative error
0.04
0.02
0
−0.02
Evolution of the relative error
0 200 400 600 800 1000 1200 1400 1600 1800 2000 −0.04
%error
#epoch
300
250
200
150
100
50
0
Distribution of the relative error
−0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04
error rate
freq.
0.04
0.02
0
−0.02
Evolution of the relative error adapting to a random demand
0 200 400 600 800 1000 1200 1400 1600 1800 2000 −0.04
#epoch
%error
180
160
140
120
100
80
60
40
20
0
−0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.02 0.03 0.04
error rate
freq.
Distribution of the relative error for a random demand
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
41. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to failures
7000
6800
6600
6400
6200
6000
5800
350 375 400 425 450
#epochs
error rate
Evolution after a change in the demand
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
42. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Adaption to failures
7000
6800
6600
6400
6200
6000
5800
350 375 400 425 450
#epochs
error rate
Evolution after a change in the demand
1.5
1.48
1.46
1.44
1.42
1.4
1.38
4
x 10
350 400 450 500 550
#epochs
error rate
Evolution after the failure of one substation
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
43. 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
error rate
Comparitions of the evolution of the error rate (Llucmajor substation failure)
no failures
substat fail
difference
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management
44. Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions
Conclusions
What we’ve done
To apply a combination of gossip methods to create a supportive,
failure tolerant, self-adaptive system for smart-grids
information exchanged with direct neighbors only
no global repository of data nor central control needed
push-sum and consensus protocol combined
supportive for nodes out of their bounds
the network adapts itself to changes in the electrical demand
failures are detected and assumed by the rest of active
substations
M. Rebollo et al. (UPV) CITINET’14
Supportive Consensus for Smart Grid Management