The power generation and consumption of distributed energy resources (DERs) offer significant flexibility potential, which can be utilized to provide services such as peak and frequency regulation. DERs introduce a vast number of variables and constraints, making it complicated to directly integrate them into upper-level dispatch. To address this challenge, virtual power plants (VPPs) emerge, which treat diverse DERs as a collective entity and use aggregated flexibility envelopes to reduce the variable and constraint scale, facilitating upper-level optimization. In VPPs, unified DER modeling and efficient DER aggregation play a crucial role but are challenging. This paper first introduces a novel unified polytope model to represent heterogenous DERs' flexibility region. A coordination transformation is utilized to eliminate redundant variable dimensions and maintain DERs' interface characteristics. A sample-based projection method is then developed, further removing all state variables, resulting in a unified flexibility region. This method is then utilized to calculate the Minkowski sums of individual flexibility polytopes for aggregation. The results of numerical tests demonstrate a considerable reduction in computation time and maintain satisfactory accuracy when the proposed modeling and aggregation approach is adopted.

With the proliferation of distributed energy resources (DERs), electricity consumers in virtual power plants (VPPs) are transitioning into prosumers and are encouraged to share surplus energy with peers. Nevertheless, large-scale energy sharing among thousands of prosumers may encounter communication-related challenges. Communication network congestion may result in a significant increase in the negotiation waiting time to reach a sharing agreement, and potentially risks exceeding the deadline of negotiation before the market gate closes, rendering energy sharing ineffective. This paper proposes an online partial-update algorithm for the alternating direction method of multipliers (ADMM)-based energy sharing. By restricting the update connection between the VPP and the prosumers, the algorithm selects a subset of the prosumers participating in ADMM updates each round, hence eliminating the excessively long waiting time caused by communication congestion. Considering the delay induced by massive prosumer communication access requests, a method for determining the optimal number of prosumers participating in updates is provided. To fully utilize the limited update opportunities, a fair and efficient prosumer update scheduling policy is designed. The VPP schedules the participation of prosumers in updates such that the convergence-critical prosumers receive higher priority, yet every prosumer is granted sufficient update opportunities. Additionally, the extra computation and communication overheads brought by the prosumer scheduling are minimized, allowing the whole algorithm to be executed in real time. Numerical studies are conducted to validate the effectiveness of the algorithm and its performance in reducing the overall convergence time.

Equilibrium analysis has been widely studied as an effective tool to model gaming interactions and predict market results. However, as competition modes are fundamentally changed by the decarbonization and decentralization of power systems, analysis techniques must evolve. This article comprehensively reviews recent developments in modelling methods, practical settings and solution techniques in equilibrium analysis. Firstly, we review equilibrium in the evolving wholesale power markets which feature new entrants, novel trading products and multi-stage clearing. Secondly, the competition modes in the emerging distribution market and distributed resource aggregation are reviewed, and we compare peer-to-peer clearing, cooperative games and Stackelberg games. Furthermore, we summarize the methods to treat various information acquisition degrees, risk preferences and rationalities of market participants. To deal with increasingly complex market settings, this review also covers refined analytical techniques and agent-based models used to compute the equilibrium. Finally, based on this review, this paper summarizes key issues in the gaming and equilibrium analysis in power markets under decarbonization and decentralization.