## Nomenclature  
Acronyms  
AEL  
Aggregated electrical load  
ATL  
Aggregated thermal load \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Method** & **Number of Run** & **Minimum Profit** & **Maximum Profit** & **Averege Profit** & **Standard Deviation** \\ \hline
**DE** & 100 & 6.03 & 8.50 & 7.85 & 0.77 \\ \hline
**BAT** & 100 & 5.40 & 7.80 & 7.71 & 0.33 \\ \hline
**PSO** & 100 & 6.03 & 7.18 & 6.54 & 0.43 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of deviation, average and minimum cost between applied optimization methods. \begin{tabular}{l l} CHP & Combine heat and power \\ DE & Differential evolution algorithm \\ DR & Demand respond \\ DR+, DR- & Amount of responsive load demand that goes/comes to/from other time period \\ DP & Dynamic Pricing \\ DW & Dish washer \\ DT & Duration Time \\ DRP & Demand response based on price \\ DRE & Demand response based on emission \\ DRPE & Demand response based on price and emission \\ ES & Energy storage \\ ESP & Electrical solar panel \\ EMS & Energy management system \\ EMS-DR & Energy management system based on Demand respond \\ EMS-DRP & The EMS Algorithm Including DR based on Price \\ EMS-DRPE & The EMS Algorithm Including DR based on Price and Emission \\ EN & Energy \\ EV & Electric vehicle \\ GB & Gas boiler \\ HHW & Heat and hot water \\ H-MG & Home Microgrid \\ MCP & Market clearing price \\ PSO & Particle swarm optimization \\ REF & Refrigerator \\ RET & Retailer \\ SBP & System buy price \\ SSP & System sell price \\ SOC & State of charge \\ TD & Thermal dump \\ TES & Thermal energy storage \\ TSP & Thermal solar panel \\ TOAT & Taguchi Orthogonal Array Testing \\ Tot & Total \\
**Indices** & \\ \(e\)/\(nt\)/\(th\)/\(n\)/\(E\)/ & electricity/heat/time interval [1,2,...,24]/H-MG number, n\(\in\{1,2,\cdots,g\}\) \\  & /Emission/Fuel \\ \(i\)\(\in\)\(\{\)CHP, GB, TSP\(\}\) & thermal distributed energy resources \\ \(j\)\(\in\)\(\{\)ESP, CHP\(\}\) & electrical distributed energy resources \\ \(c\)\(\in\)\(\{\)DW, EV, REF, AEL\(\}\) & electrical consumers \\ \(k\)\(\in\)\(\{\)HHW, ATL, TD\(\}\) & thermal consumers \\ \(\Omega\)\(\in\)\(\{\)CHP, GB, Retailer\(\}\) & Producers that emit pollution \\
**Constant Values** & \\ \(SOC^{m},SOC^{m},\)\(\hat{p}^{m},\hat{p}^{m}\) & minimum/maximum values of SOC/power during m charging and \\  & discharging mode, \(\ m\in\{ES_{d},ES^{ch},EV_{d},EV^{ch},TES_{d},TES^{ch}\}\) \\  & total value of m energy capacity \\  & maximum/minimum of f temperature, \(\ \  
\(\tilde{P}_{e/ht,i},\tilde{P}_{e/ht,i}\)  
\(\tilde{\xi}_{e/ht,i}\)  
\(tU_{h}^{CHP},\sigma_{e}^{CHP}\), and \(\tilde{\varsigma}_{h}^{CHP}\)  
\(T^{HHW}\), \(T^{HHW}\)  
\(\tilde{E}^{m},\tilde{E}^{m}\)  
\(\pi^{pb},\pi^{pb}\)  
\(pb\)\(\in\) {i,j,c,l}  
\(ngp_{h}\)  
\(\mathbf{Decision Variables}\)  
\(m_{h}^{RET},m_{h}^{ES},m_{h}^{TES},m_{h}^{DR}\)  
\(P_{h,e,e},P_{h,ht,k}\)  
\(B_{ht,e,i},P_{ht,e,j}\)  
+++ ==WARNING: Truncated because of repetitions==
(CO\)  
\(u\)  
\(\pi^{pb}_{ht,e},\pi^{pb}_{ht,ht}\)  
\(p_{h,e,n}^{RET*},P_{h,e,n}^{RET*}\)  
\(\lambda_{h,W}^{-MCP}\)  
\(\lambda_{h,W}^{MCP}\)  
\(\lambda_{h,W}^{MCP}\)  
\(\lambda_{h,W}^{MCP}\)  
\(\rho_{e/ht,i},\tilde{P}_{e/ht,i}\)  
++  
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Framework for smart transactive energy in home-microgrids considering coalition formation and demand side management. _Sustain. Cities Soc._**2018**, _40_, 136-154. [CrossRef]
* [PERSON] et al. (2018) [PERSON]; [PERSON]; [PERSON]; [PERSON] An advanced retail electricity market for active distribution systems and home microgrid interoperability based on game theory. _Electr. Power Syst. Res._**2018**, _157_, 187-199. [CrossRef]
* [PERSON] and [PERSON] (2017) [PERSON]; [PERSON] A survey of game theory approach in smart grid with emphasis on cooperative games. In Proceedings of the 2017 IEEE International Conference on Smart Grid and Smart Cities (ICSGSC), Singapore, 23-26 July 2017; pp. 237-242. [CrossRef]
* [PERSON] et al.