Co-optimization and benefit allocation mechanism of DSO-VPP under the secondary flexibility market based on SPP

• Introducing dual-attribute SPP to quantify flexibility responsibility. • Proposing an SPP-based trading framework for SecFlex market. • Constructing a DSO-VPP hybrid game optimization model. • Introduce the VCG mechanism to determine the marginal contribution. • Construct an entropy weight modified Shapley value-based benefit allocation strategy. In modern power systems with large-scale renewable energy (RE) integration, regulating capacity is increasingly scarce. Its cost rises significantly, creating an urgent need for all market participants to share RE consumption responsibilities. This paper proposes a Secondary Flexibility (SecFlex) market co-optimization and benefit distribution mechanism based on substitutable power products (SPP) to avoid the negative externalities arising when RE generation focuses solely on power output and shifts regulation responsibilities to other power sources. First, the SPP-based Secondary Flex market trading framework is constructed. By introducing dual-attribute commodities shape and electricity, the market trading process is standardized, and the regulation responsibilities and contributions of each SecFlex market participant (SFMP) are clearly defined. Secondly, a Stackelberg-Cooperative hybrid game model is proposed to be led by the distribution network operator (DSO). In the upper level, the DSO minimizes system regulation costs by optimizing incentive signals and the target power curve; in the lower level, substitutable power product (VPP) coalition aggregates adjustable (ADR) and non-adjustable resources (NADR) to generate SPP response curves that meet flexibility requirements. Based on this, a two-stage revenue allocation mechanism is designed: first, the Vickrey-Clarke-Groves (VCG) mechanism identifies marginal contributions; second, the entropy-weight modified Shapley value (E-S) addresses contribution disparities and information asymmetries among SFMPs, ensuring reasonable benefits and fair distribution for flexibility resources. Simulation results demonstrate that, compared to traditional schemes, this mechanism reduces system regulation costs by 12.7 %, increases market matching to 98.64 %, and boosts ADR members’ revenues by 384.8 %, thus verifying its effectiveness in quantifying regulation contributions and distributing revenue equitably.