Convergent Double Auction Mechanism for a Prosumers’ Decentralized Smart Grid
Abstract
:1. Introduction
1.1. Prosumers’ Decentralized Smart Grid
1.2. MarketBased DemandSide Management (DSM)
1.3. Convergent Double Auction Mechanism
Characteristics  RTPDDSG  LFSDA  CLFSDA 

Fully decentralized    √  √ 
Balance of demand and supply    √  √ 
Convergence  √    √ 
2. Model and Conventional RealTime Pricing (RTP)
2.1. Basic Assumptions of iRene
2.2. Primal Problem
2.3. Dual Decomposition (DD)
2.3.1. Dual Problem
2.3.2. SubProblems
2.3.3. Master Problem
2.3.4. RealTime Pricing based on a Dual Decomposition with a SubGradient Method (RTPDDSG)
3. Convergent Linear Function SubmissionBased DoubleAuction (CLFSDA)
3.1. Overview
3.2. Transactions with the Convergent Linear Function SubmissionBased DoubleAuction (CLFSDA)
Algorithm 1 Iterative update in the CLFSDA. 
$k\leftarrow 1$ 
Initialize the price profile ${p}^{\left(k\right)}={\left({p}_{t}^{\left(k\right)}\right)}_{t\in \mathcal{T}}$ and the state vectors ${\left({x}_{i}^{\left(k\right)}\right)}_{i\in \mathcal{N}}$. 
Each agent submits ${\upsilon}_{i}={\left({\upsilon}_{i}^{t}\right)}_{t\in \mathcal{T}}$ to the market. 
repeat

until a predefined stopping criterion is satisfied. 
return Transact ${\left({x}_{i}^{\left(k\right)}\right)}_{i\in \mathcal{N}}$ with ${p}^{\left(k\right)}$ as a price profile. 
3.3. Iterative Process of the Convergent Linear Function SubmissionBased DoubleAuction (CLFSDA)
3.4. Convergence Proof of the Convergent Linear Function SubmissionBased DoubleAuction (CLFSDA)
3.5. Simple Convergent Linear Function SubmissionBased DoubleAuction (CLFSDA)
4. Experiment
4.1. Experimental Conditions
4.2. Results
5. Conclusions
Acknowledgments
Author Contributions
Nomenclature
☐ Variables controlled by each agent (output)  
${l}_{i}^{t+}\in [{l}_{i}^{t+,min},\infty )$  Electric energy consumption profile 
${l}_{i}^{t}\in [0,{l}_{i}^{t,max})$  Electric energy generation profile 
${b}_{i}^{t+}\in [0,{b}_{i}^{t+,max}]$  Battery charge profile 
${b}_{i}^{t}\in [0,{b}_{i}^{t,max}]$  Battery discharge profile 
${m}_{i}^{t+}\in [0,{m}_{i}^{t+,max}]$  Profile of electric energy sold to the local electricity market 
${m}_{i}^{t}\in [0,{m}_{i}^{t,max}]$  Profile of electric energy bought from the local electricity market 
${g}_{i}^{t+}\in [0,\infty )$  Profile of electric energy sold to the outside grid 
${g}_{i}^{t}\in [0,{g}_{i}^{,max}]$  Profile of electric energy bought from the outside grid 
${x}_{i}^{t}$  Profile of state vector 
${s}_{i}^{t}\in [0,{s}_{i}^{max}]$  Profile of the state of charge (SOC) of the battery 
${\alpha}_{i}^{t}$  Constant term of parameters of the bidding function 
${\upsilon}_{i}^{t}>0$  Initial slope of the bidding function, i.e., ${\beta}^{\left(1\right)}={\upsilon}_{i}^{t}$ 
☐ Variables determined by the market (output)  
${\beta}_{i}^{t}>0$  Primary coefficient term of parameters of the bidding function 
${p}_{t}$  Price profile 
☐ Fixed parameters and functions for each agent (input)  
${\eta}_{i}\in [0,1]$  Storage efficiency 
${C}_{i}^{t}$  Cost function for generating electric energy 
${D}_{i}^{t}$  Utility function for consuming electric energy 
${\varphi}_{i}^{t}$  Individual utility function 
${W}_{i}^{t}$  Individual welfare function 
☐ Fixed parameters for the electricity network (input)  
$\gamma \in [0,1]$  Electricity transmission efficiency 
${p}_{t}^{G+}$  Price of electricity sold to the outside grid 
${p}_{t}^{G}$  Price of electricity bought from the outside grid 
Appendix
A. Convergence Proof of the RTPDDSG
Conflicts of Interest
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Taniguchi, T.; Takata, T.; Fukui, Y.; Kawasaki, K. Convergent Double Auction Mechanism for a Prosumers’ Decentralized Smart Grid. Energies 2015, 8, 1234212361. https://doi.org/10.3390/en81112315
Taniguchi T, Takata T, Fukui Y, Kawasaki K. Convergent Double Auction Mechanism for a Prosumers’ Decentralized Smart Grid. Energies. 2015; 8(11):1234212361. https://doi.org/10.3390/en81112315
Chicago/Turabian StyleTaniguchi, Tadahiro, Tomohiro Takata, Yoshiro Fukui, and Koki Kawasaki. 2015. "Convergent Double Auction Mechanism for a Prosumers’ Decentralized Smart Grid" Energies 8, no. 11: 1234212361. https://doi.org/10.3390/en81112315