Virtual bidding provides a mechanism for financial players to participate in wholesale day-ahead (DA) electricity markets. The price difference between DA and real-time (RT) markets creates financial arbitrage opportunities for financial players. Physical market participants (MP), referred to as participants with physical assets, can also take advantage of virtual bidding but in a different way, which is to further amplify the value of their physical assets. Therefore, this work proposes a model for such physical MPs to maximize the profits. This model employs a bi-level optimization approach, where the upper-level subproblem maximizes the total profit from both physical generations and virtual transactions while the lower-level model mimics the multi-period network-constrained DA market clearing process. In this model, uncertainties associated with other MPs as well as RT market prices are considered. Moreover, conditional value-at-risk (CVaR) metric is utilized to measure the risk of diverse strategies. The optimal strategy of the strategic physical MP is derived by solving this bi-level optimization model. The proposed bi-level model is transformed to a single level mixed integer linear programming (MILP) model using Karush–Kuhn–Tucker (KKT) optimality conditions and the duality theory. Case studies show the effectiveness of the proposed method and reveal physical MP tends to deploy virtual transactions in a very different way than pure financial MPs.


Electrical and Computer Engineering

Research Center/Lab(s)

Intelligent Systems Center


This work was supported by the Defense Advanced Research Projects Agency (DARPA) under Grant D18AP00054.

Keywords and Phrases

Bi-Level Optimization; Bidding Strategy; Electricity Supply Industry; Financial Products; Games; Indexes; Optimization; Physical Market Participants; Profit Maximization; Real-Time Systems; Stochastic Processes; Uncertainty; Virtual Bidding

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version

Final Version

File Type





© 2021 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Creative Commons Licensing

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

Publication Date

01 Jan 2021