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 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


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



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



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

2.5Station 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



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



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 = 0.4x1 = 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 = 0.9x3 = 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 < mini1di

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 valuesconsensus belongs to a broader family of protocols

network topology: unstructuredrouting scheme: gossip



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



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 .



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)



Energy pattern



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




0 50 100 1500

100

200

300

400

500

600


#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)




0 50 100 1500

100

200

300

400

500

600


#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



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



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




350 375 400 425 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




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



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


￼consensus in smart grids for decentralized energy management

Technology

consensus in smart grids for decentralized energy management