A Stackelberg Game Model for the Energy–Carbon Co-Optimization of Multiple Virtual Power Plants

As energy and carbon markets evolve, it has emerged as a prevalent trend for multiple virtual power plants (VPPs) to engage in market trading through coordinated operation. Given that these VPPs belong to diverse stakeholders, a competitive dynamic is shaping up. To strike a balance between the inte...

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Asıl Yazarlar: Dayong Xu, Mengjie Li
Materyal Türü: Makale
Dil:English
Baskı/Yayın Bilgisi: MDPI AG 2025-02-01
Seri Bilgileri:Inventions
Konular:
Online Erişim:https://www.mdpi.com/2411-5134/10/1/16
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author Dayong Xu
Mengjie Li
author_facet Dayong Xu
Mengjie Li
author_sort Dayong Xu
collection DOAJ
description As energy and carbon markets evolve, it has emerged as a prevalent trend for multiple virtual power plants (VPPs) to engage in market trading through coordinated operation. Given that these VPPs belong to diverse stakeholders, a competitive dynamic is shaping up. To strike a balance between the interests of the distribution system operator (DSO) and VPPs, this paper introduces a bi-level energy–carbon coordination model based on the Stackelberg game framework, which consists of an upper-level optimal pricing model for the DSO and a lower-level optimal energy scheduling model for each VPP. Subsequently, the Karush-Kuhn-Tucker (KKT) conditions and the duality theorem of linear programming are applied to transform the bi-level Stackelberg game model into a mixed-integer linear program, allowing for the computation of the model’s global optimal solution using commercial solvers. Finally, a case study is conducted to demonstrate the effectiveness of the proposed model. The simulation results show that the proposed game model effectively optimizes energy and carbon pricing, encourages the active participation of VPPs in electricity and carbon allowance sharing, increases the profitability of DSOs, and reduces the operational costs of VPPs.
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spelling doaj.art-dbdb1e47a98c4b6c9f006bfd9dc6fe6e2025-02-25T13:32:33ZengMDPI AGInventions2411-51342025-02-011011610.3390/inventions10010016A Stackelberg Game Model for the Energy–Carbon Co-Optimization of Multiple Virtual Power PlantsDayong Xu0Mengjie Li1Huizhou Electric Power Supply Bureau of Guangdong Power Grid Corporation, Huizhou 516003, ChinaHuizhou Electric Power Supply Bureau of Guangdong Power Grid Corporation, Huizhou 516003, ChinaAs energy and carbon markets evolve, it has emerged as a prevalent trend for multiple virtual power plants (VPPs) to engage in market trading through coordinated operation. Given that these VPPs belong to diverse stakeholders, a competitive dynamic is shaping up. To strike a balance between the interests of the distribution system operator (DSO) and VPPs, this paper introduces a bi-level energy–carbon coordination model based on the Stackelberg game framework, which consists of an upper-level optimal pricing model for the DSO and a lower-level optimal energy scheduling model for each VPP. Subsequently, the Karush-Kuhn-Tucker (KKT) conditions and the duality theorem of linear programming are applied to transform the bi-level Stackelberg game model into a mixed-integer linear program, allowing for the computation of the model’s global optimal solution using commercial solvers. Finally, a case study is conducted to demonstrate the effectiveness of the proposed model. The simulation results show that the proposed game model effectively optimizes energy and carbon pricing, encourages the active participation of VPPs in electricity and carbon allowance sharing, increases the profitability of DSOs, and reduces the operational costs of VPPs.https://www.mdpi.com/2411-5134/10/1/16virtual power plantsStackelberg gamepricingenergy-carbon coordinationKarush-Kuhn-Tucker conditions
spellingShingle Dayong Xu
Mengjie Li
A Stackelberg Game Model for the Energy–Carbon Co-Optimization of Multiple Virtual Power Plants
Inventions
virtual power plants
Stackelberg game
pricing
energy-carbon coordination
Karush-Kuhn-Tucker conditions
title A Stackelberg Game Model for the Energy–Carbon Co-Optimization of Multiple Virtual Power Plants
title_full A Stackelberg Game Model for the Energy–Carbon Co-Optimization of Multiple Virtual Power Plants
title_fullStr A Stackelberg Game Model for the Energy–Carbon Co-Optimization of Multiple Virtual Power Plants
title_full_unstemmed A Stackelberg Game Model for the Energy–Carbon Co-Optimization of Multiple Virtual Power Plants
title_short A Stackelberg Game Model for the Energy–Carbon Co-Optimization of Multiple Virtual Power Plants
title_sort stackelberg game model for the energy carbon co optimization of multiple virtual power plants
topic virtual power plants
Stackelberg game
pricing
energy-carbon coordination
Karush-Kuhn-Tucker conditions
url https://www.mdpi.com/2411-5134/10/1/16
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