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Performance analysis of a robust and multi-approach model in retail electricity market achieving efficient contracts between retailer, end users and wholesalers

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Abstract

In this paper, a new bi-level model is presented in order to set the interaction between different players in electricity market contracts. The proposed model framework is multi-objective so that the aims of retailer and customers are met simultaneously. In this study, new parameters and indexes for interaction of players will be introduced. In the upper level of this model, the retailer’s profit will be maximized and in the lower level, the customer’s cost will be minimized. Based on the retailer’s interaction with customers in the proposed model, some customers will be selected from the customers group to contract with power retailer. In the proposed model, a robust optimization approach (ROA) is used to manage the retailer’s risk in different conditions due to the uncertainty of energy supply by the wholesaler. The analysis of multi-objective approach in this model is also carried out based on Torabi-Hassini (TH) method. Finally, after the required linearization, the proposed Mixed Integer linear programming (MILP) model in the presence of Karush–Kuhn–Tucker conditions will implement in GAMS software and solved via GUROBI solver.

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Abbreviations

\(S=\{\mathrm{1,2},\dots ,s\}\) :

Wholesalers' set

\(B=\{\mathrm{1,2},\dots ,b\}\) :

Customers' set

\(T=\{\mathrm{1,2},\dots ,24\}\) :

Set for specific hours or periods of the day

\(H=\{\mathrm{0,1}\dots ,h\}\) :

Set for determining the number of months of the contract with the customers

\({B}^{\mathrm{^{\prime}}}\subseteq B\) :

Customers' subset that retailer has a contract with them at all times and supplies their energy needs

\({D}_{\mathrm{b}} (\mathrm{kW})\) :

Customer's total daily energy consumption

\({r}_{\mathrm{bt}} (\%)\) :

Rate of consumption by customer “b” during period “t”

\({V}_{\mathrm{b}} (\mathrm{kW})\) :

Amount of storage available for the customer “b”

\({\gamma }_{\mathrm{bh}}(\%)\) :

The amount of discount desired by the customer “b” in each energy unit for a contract of length “h”

\({\theta }_{\mathrm{bh}}(\$)\) :

Income resulting from the renewal of the contract with the customer “b” and length “h”

\({p}_{\mathrm{b}}(\frac{\$}{\mathrm{kWh}})\) :

Energy storage system cost of customer “b”

\(\mu_{\text{t}} \left( {\frac{\$ }{{{\text{kWh}}}}} \right)\) :

Energy prices for time “t”

\(\rho_{{{\text{st}}}} \left( {\frac{\$ }{{{\text{kWh}}}}} \right)\) :

Costs of energy supplied by wholesalers “s” for “t”

\(\overleftrightarrow {{\text{cap}}_{{{\text{st}}}} }\) :

Parameter with uncertainty in the model (generation capacity of wholesalers)

\({x}_{1}\) (g/kWh):

Coal consumption

\({x}_{\mathrm{w}}\) (\({\mathrm{m}}^{3}/\mathrm{kWh}\)):

Water consumption

\({x}_{{\mathrm{Co}}_{2}} \)(g/kWh):

Carbon dioxide emissions amount

\(z\) (g/kWh):

Total quantity of pollutants

\({x}_{{\mathrm{No}}_{\mathrm{x}}}\) (g/kWh):

Nitrogen oxide emissions amount

\({x}_{{\mathrm{So}}_{2}}\) (g/kWh):

Sulfur dioxide emissions amount

\({x}_{\mathrm{APP}}\) (g/kWh):

The amount of particulate pollution

\({x}_{\mathrm{st}} (\mathrm{kWh})\) :

The volume of energy purchased from wholesaler “s” in time “t”

\({m}_{\mathrm{bt}} (\mathrm{kWh})\) :

The volume of energy sold by the retailer to customer “b” in time “t”

\({\alpha }_{\mathrm{bt}} (\%)\) :

Amount of discount for customer “b” in time “t”

\({y}_{\mathrm{bh}}\) :

A variable in binary form indicates the presence or absence of a contract between the customer and the retailer

\({I}_{\mathrm{bt}} (\mathrm{kWh})\) :

Volume of energy which stored by customer “b” in time “t”

\({a}_{\mathrm{bt}}\) :

A variable in binary form indicates the accept or reject of a discount from customer “b” by retailer in time “t”

\(J (\frac{\$}{\mathrm{kWh}})\) :

The cost of energy shortages

\({U}_{\mathrm{t}}(\mathrm{kWh})\) :

Volume of energy shortage in time “t

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Authors and Affiliations

  1. Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

    Kourosh Apornak, Soodabeh Soleymani, Faramarz Faghihi & Babak Mozafari

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  1. Kourosh Apornak
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  2. Soodabeh Soleymani
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  3. Faramarz Faghihi
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Correspondence to Soodabeh Soleymani.

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Apornak, K., Soleymani, S., Faghihi, F. et al. Performance analysis of a robust and multi-approach model in retail electricity market achieving efficient contracts between retailer, end users and wholesalers. Electr Eng 105, 1811–1823 (2023). https://doi.org/10.1007/s00202-023-01747-0

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