Objectives Hydrogen energy, as a clean energy source with high energy density and zero carbon emissions, is an important component of future energy systems. For park-level hydrogen-electric coupling systems (HECS), a two-stage robust optimization scheduling model that considers demand response and tiered carbon trading is proposed. Methods First, a park-level HECS is established, consisting of wind and solar power generation units, backup generation units, energy storage systems, and hydrogen-electric conversion devices. Then, demand response and tiered carbon trading are integrated into the model, aiming to minimize the total costs of system energy procurement, operation and maintenance, and carbon emissions, thereby establishing a deterministic optimization model for the system. Finally, a source-load uncertainty set is incorporated into the deterministic optimization model to mitigate the effect of source-load uncertainty on scheduling results, forming a two-stage robust optimization model. This model is re-established using a master-slave framework and solved using the column-and-constraint generation method. Results With source-load uncertainty coefficients of 12 and 6, demand response loads with an adjustable ratio below 0.5 can reduce the system's operating costs by 1.6%. The introduction of tiered carbon trading can reduce carbon emissions by 604.9 kg. Conclusions The proposed model can improve the risk resilience of park-level HECS, and the integration of demand response and tiered carbon trading can ensure the economic and low-carbon operation of HECS.

Under the goal of “Dual Carbon” strategy，how to realize the flexible interaction between virtual power plants and promote the low-carbon operation of virtual power plants through carbon price is a problem worthy of study. Therefore，the peer to peer （P2P） trading model of virtual power plants is studied based on the carbon flow theory. Firstly，based on the carbon emission flow theory，the distribution characteristics of carbon flow in the network are analyzed，and natural gas is introduced to form a multi-energy network，and a low-carbon economic scheduling model is established. Secondly，considering the privacy of each virtual power plant participating in the trading，a quantitative index method including the trading information of the bid volume and quotation is proposed，and a P2P trading model based on comprehensive priority is established. At the same time，combined with the carbon emission responsibility of virtual power plants in the network，carbon pricing method is introduced into the P2P trading mechanism，and a comprehensive price model of “energy-carbon” based on carbon tax is established. Finally，an example is given to verify that the proposed method can not only reduce the operating cost of the virtual power plant，but also effectively reduce the carbon emission.

To optimize the operation of shared energy storage，this study investigates the non-cooperative game problem in transactions between shared energy storage and multi-prosumer. First，a bi-level optimization model is established to characterize the non-cooperative game relationship among the participants，aiming to optimize the trading strategies of the shared energy storage operator and the prosumers. The upper-level model maximizes the operator’s profit by optimizing its operational schedule and pricing strategy to provide charging and discharging services. The lower-level model responds to these prices by minimizing each prosumer’s operational cost through optimizing their electricity trading and storage schedules. This approach helps the operator optimize trading strategies and enhance both market competitiveness and profitability. Next，the Karush-Kuhn-Tucker（KKT）conditions are applied to transform the bi-level problem into a single-level model. The reformulated model is linearized using the big-M method and then solved numerically. Finally，simulation results demonstrate that the proposed method effectively balances the interests of both the shared energy storage operator and the prosumers，achieving a mutually beneficial outcome.

The access to substantial distributed photovoltaic and energy storage resources on the low-voltage user side is conducive to the local consumption of renewable energy power generation. However, low-voltage users and medium-voltage distribution networks are different stakeholders, and their operation optimization indicators often conflict with each other. Therefore, a multi-objective distributed coordinated optimization operation strategy for medium- and low-voltage distribution networks with high-permeability distributed photovoltaic and energy storage resource access is proposed. Considering the power flow constraints of the medium- and low-voltage distribution networks, an optimization model of the medium- and low-voltage distribution networks is established with the objectives of minimizing the total cost of the distribution network, load rate difference among multiple stations, and energy storage operation cost of the low-voltage distribution network and maximizing the photovoltaic absorption rate. The optimization objectives of the medium- and low-voltage distribution networks are weighted by the entropy weight method. Based on the alternating direction method of multipliers (ADMM), the objective function form of iterative optimization for medium- and low-voltage distribution networks is derived to solve the coordinated optimization model, and a coordinated optimization strategy for medium- and low-voltage distribution networks is designed. The medium-voltage distribution network continuously guides the users of low-voltage distribution networks to adjust the output of distributed power sources through shadow price iterations and realizes the multi-objective coordinated optimization operation of medium- and low-voltage distribution networks through a minimal exchange of boundary information. Finally, the effectiveness and feasibility of the proposed multi-objective distributed optimization operation strategy for medium- and low-voltage distribution networks is verified using the IEEE 33-7 node standard example system.