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Modeling multiple-criteria decision making of the electrical grid considering optimal demand management

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This study presents the day-ahead operation of a smart residential distribution electrical grid as a multiple-criteria decision-making modeling. The multiple-criteria decision-making modeling is implemented from view point of the grid's operator for optimization of the energy consumption costs, power losses and demand side comfort. The operation of the residential distribution electrical grid is modeled based on the enhancing penetration of the renewable energies with implementation of the demand management strategies. Modeling the penetration of the renewable energies is presented based on the adaptation of deferrable loads with renewable energies output using load shifting approach. In addition, load interruption approach is proposed for demand clipping considering electricity pricing in peak hours. The multiple-criteria decision-making process by improved epsilon-constraint and TOPSIS approach are handled for confirmation of the optimization approach. The day-ahead energy scheduling is applied on the 33-bus distribution network to investigate the effectiveness of the system considering obtained results from mathematical modeling and demand management strategies.

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Data availability

The data are available from the corresponding author upon reasonable request.


  1. Power generation of the PVs and WTs in Fig. 5, is shown by PPW.


\(t,T\) :

Time (Hour)

\(b,B\) :


\({\text{wt,WT}}\) :

Wind turbine

\({\text{pv,PV}}\) :


\({\text{dl,DL}}\) :

Deferrable loads

\({\text{CL}}\) :

Clippable loads

\(a,k,\Lambda\) :


\(v\) :

Wind speed

\(V_{{\text{R}}} ,V_{{{\text{Ci}}}} ,V_{{{\text{Co}}}}\) :

Rated wind speed, cut-in wind speed, cut-off wind speed

\(P_{{{\text{WT}}}}^{N}\) :

Wind turbine power rated

\({\text{SI}},{\text{SI}}_{{{\text{ref}}}}\) :

Solar radiation and reference solar radiation

\(P_{{{\text{PV}}}}^{{{\text{STC}}}}\) :

Photovoltaic power rate

\(\eta_{{{\text{PV}}}}\) :

Photovoltaic efficiency

\(P_{B}\) :

Battery power rate

\(\eta_{{{\text{dis}}}} ,\eta_{{{\text{ch}}}}\) :

Battery efficiency in discharging and charging status

\(D_{{{\text{TE}}}}\) :

Total active demand

\(Q_{{{\text{TE}}}}\) :

Total reactive demand

\(D_{{{\text{LS}}}}\) :

Demand based on the load shifting

\(D_{{{\text{IL}}}}\) :

Demand based on the load interruption

\(D_{{{\text{WP}}}}\) :

Demand without participation in load optimization

\(\lambda_{{{\text{PV}}}} ,\lambda_{{{\text{WT}}}} ,\lambda_{b}\) :

Cost factors of Photovoltaic, wind turbine and battery

\(\lambda_{{{\text{EG}}}}\) :

Electricity price in electrical grid (EG)

\(\Pi_{{{\text{LS}}}} ,\Pi_{{{\text{IL}}}}\) :

Participation rates in load shifting and load interruption

\(r_{a}\) :

Resistance of the lines between buses

\(f_{1} ,f_{2} ,f_{3}\) :

Multiple-criteria such as generation side costs, power loss and consumers comfort

\(P_{{{\text{WT}}}} ,P_{{{\text{PV}}}}\) :

Power output of Wind turbine and Photovoltaic units

\(P_{{{\text{EG}}}} ,Q_{{{\text{EG}}}}\) :

Active and reactive power of EG

\(D_{{{\text{DL}}}} ,D_{{{\text{CL}}}}\) :

Demand of deferrable loads and clippable loads

\(P_{B}^{{{\text{dis}}}} ,P_{B}^{{{\text{ch}}}}\) :

Discharge and charge power of battery

\(D_{{{\text{NS}}}} ,QD_{{{\text{NS}}}}\) :

Nonsupplying of the active and reactive demand

\(P_{{{\text{loss}}}} ,Q_{{{\text{loss}}}}\) :

Active and reactive power losses

\(V_{a}\) :

Voltage's buses

\(\mu_{{{\text{NS}}}}\) :

Binary variable for determining state of the nonsupplying demand

\(\mu_{B}\) :

Binary variable of battery in charge and discharge status


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All authors have equal contribution in Writing, Original draft preparation, Conceptualization, Supervision, Project administration.

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Correspondence to Rahul Pradhan.

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Elfizon, Pradhan, R., Asaad, R.R. et al. Modeling multiple-criteria decision making of the electrical grid considering optimal demand management. Multiscale and Multidiscip. Model. Exp. and Des. (2024).

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