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

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

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

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

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

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

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

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

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

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

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

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

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)

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

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

Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions

Supportive Consensus evolution

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

Introduction The environment ACDC Support Adaption to demand Adaption to failures Conclusions

Energy pattern

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

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

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)

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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

M. Rebollo et al. (UPV) CITINET’14Supportive Consensus for Smart Grid Management

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