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![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](https://image.slidesharecdn.com/mrebolloconsensuscitinet14slides-140925050041-phpapp02/85/Supportive-consensus-for-smart-grid-management-25-320.jpg)
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Supportive consensus for smart grid management
The document discusses a self-adaptive system for smart grid management that utilizes gossip protocols for real-time adaptation to electrical demand and failure tolerance. It details the consensus processes, data aggregation methods, and combines push-sum protocols to monitor and adjust the network's capacity and demand without central control. The results indicate that the system is effective in adapting to changes in demand and detecting failures within the grid.
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Supportive consensus for smart grid management
- 1. Introduction The environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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
- 14. Introduction The environmentACDC 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
- 22. Introduction The environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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
- 31. Introduction The environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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 environmentACDC 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