Distributed Adaptive Primal Algorithm for P2PETS over Unreliable Communication Links
Abstract
:1. Introduction
 We propose a DAP routing algorithm to efficiently route energy request information in a network of proactive prosumers until a consensus is reached. The robustness of the proposed DAP routing algorithm is tested against unreliability and other link constraints that have impacts on the optimal communication amongst the trading prosumers, compared to the existing literature that assumes perfect communication links exists among the energy trading entities [12,17,18,19];
 The algorithm tends to reduce communication delay resulting from long queuing of messages. This is achieved by setting a limiting indicator on the communication link using the gradient update of the link states to adaptively route the messages via less congested paths, compared to [25] that calculate the shortest path based on link state marginal cost. With the limiting indicator and gradient update, the delay cost function associated with maximum capacity utilization is maximally reduced;
 As a result of the adaptive nature of the proposed routing algorithm, future grids will benefit through reduced delay and lower bandwidth requirement. This can be observed from the result which shows a 20% reduction in delay compared to hopbyhop adaptive link state routing algorithm [25]. Further, in contrast to [8,15] that examined delay and packet loss, we tested the robustness of the proposed DAP routing algorithm to more stringent communication network constraints including delay, packet loss, congestion and different network topologies. The result shows that these constraints if not checked, would impact negatively the communication and transactions of the energy trading entities.
2. Literature Review
3. Problem Formulation
3.1. Communication Network
3.2. MultiCommodity Network Flow Model
4. DAPAdaptive Routing Algorithm
4.1. The Proposed DAP Iterative Algorithm
4.2. Implication of Model Solution to P2PETS
Algorithm 1 Proposed DAP Routing Algorithm. 

5. Simulation and Result Analysis
5.1. Performance Analysis of the DAP Routing Algorithm
5.2. Cases of Unreliable Communication Link and Varying Step Sizes
5.3. Evaluating Congestion on the Communication Link
5.4. Scalability Check to Increasing Number of Prosumers
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
DAP  Distributed Adaptive Primal algorithm 
MCF  Multicommodity flow network 
ETS  Energy trading and sharing 
$\mathcal{G}\left(t\right)$  The timevarying network graph 
$\mathcal{V}$  Interconnected nodes representing the prosumers 
$\mathcal{E}$  Set of network links $(i,j)$ connecting the prosumers 
${d}_{i}$  Energy demand messages transmitted by each prosumer in the network 
$\mathcal{D}$  Total energy demand messages in the network 
${x}_{i,j}^{d}$  The flow on link $(i,j)$ corresponding to commodity d 
${x}_{i,j}$  Total traffic flow on link $(i,j)$ 
${k}_{i,j}$  Signal loss probability on link $(i,j)$ 
${n}_{i}$  Source prosumer transmitting ${d}_{i}$ 
${n}_{j}$  Destination prosumer receiving ${d}_{i}$ 
${c}_{i,j}$  Bandwidth capacity on link $(i,j)$ 
${\Phi}_{i,j}$  Network delay function of link $(i,j)$ 
${l}_{i,j}$  Link utilization indicator for each link in the network 
${v}^{d}$  Peer capacity utilization indicator 
${\mathcal{U}}_{n}$  Egress link from a source or intermediary peer ${n}_{i}$ 
${\mathcal{I}}_{n}$  Ingress link to an intermediary or destination peer ${n}_{j}$ 
$\mathcal{O}\left(n\right)$  Order of n 
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Ref.  Energy Netw.  No of Peers  Method  Network Constraints  

Delay  Loss  Netw. Util.  Conges.  
[8]  Yes  5  Gradient Pushsum  No  Yes  No  No 
[15]  Yes  Up to 14  Gradient Pushsum  Yes  No  No  No 
[13]  Yes  4  Subgradient  No  No  No  No 
[14]  Yes  3  Subgradient  No  No  No  No 
[12]  Yes  Up to 64  ADMM  No  No  No  No 
[25]  No  Up to 50  MC  Yes  No  Yes  Yes 
DAP  Yes  Up to 30  MC Subgradient  Yes  Yes  Yes  Yes 
Simulation Parameter  Value 

Demand/message request $d\in \mathcal{D}$  45, 35, 35, 40 (kb) 
$\alpha $  0.01, 1 
Signal loss probability  0.1 
Total link capacity  $\mathcal{C}$ = 400 kb 
Asynchronous message update  0–5 time steps 
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Jogunola, O.; Adebisi, B.; Anoh, K.; Ikpehai, A.; Hammoudeh, M.; Harris, G.; Gacanin, H. Distributed Adaptive Primal Algorithm for P2PETS over Unreliable Communication Links. Energies 2018, 11, 2331. https://doi.org/10.3390/en11092331
Jogunola O, Adebisi B, Anoh K, Ikpehai A, Hammoudeh M, Harris G, Gacanin H. Distributed Adaptive Primal Algorithm for P2PETS over Unreliable Communication Links. Energies. 2018; 11(9):2331. https://doi.org/10.3390/en11092331
Chicago/Turabian StyleJogunola, Olamide, Bamidele Adebisi, Kelvin Anoh, Augustine Ikpehai, Mohammad Hammoudeh, Georgina Harris, and Haris Gacanin. 2018. "Distributed Adaptive Primal Algorithm for P2PETS over Unreliable Communication Links" Energies 11, no. 9: 2331. https://doi.org/10.3390/en11092331