Aggregate Load Research Articles

Optimal Scheduling and Compensation Pricing Method for Load Aggregators Based on Limited Peak Shaving Budget and Time Segment Value

Load-side peak shaving is an effective measure to alleviate power supply–demand imbalance. As a key link between a vast array of small- and medium-sized adjustable resources and the bulk power system, load aggregators (LAs) typically allocate peak shaving budgets using fixed pricing methods based on peak shaving demand forecasts. However, due to the randomness of supply and demand, fluctuations in peak shaving demand occur, making it a significant technical challenge to meet peak shaving needs under limited budget allocations. To address this issue, this paper first conducts a clustering analysis of various adjustable load characteristics to derive typical electricity consumption curves, and then proposes a differentiated calculation method for the value of multi-time-segment peak shaving. Subsequently, an optimization model for LA scheduling and compensation pricing is established based on the limited peak shaving budget and time-segment peak shaving value. While ensuring the economic benefits of LAs, the model also analyzes the impact of different peak shaving budget allocations on the scale of peak shaving that can be achieved. Finally, case studies demonstrate that, compared to traditional fixed compensation pricing, the proposed pricing method reduces scheduling costs by an average of 16.5%, while significantly improving the overall satisfaction of adjustable users.

Master–Slave Game Optimization Scheduling of Multi-Microgrid Integrated Energy System Considering Comprehensive Demand Response and Wind and Storage Combination

This paper addresses the critical challenge of scheduling optimization in regional integrated energy systems, characterized by the coupling of multiple physical energy streams (electricity, heat, and cooling) and the participation of various stakeholders. To tackle this, a novel multi-load and multi-type integrated demand response model is proposed, which fully accounts for the heterogeneous characteristics of energy demands in different campus environments. A leader–follower two-layer game equilibrium model is introduced, where the system operator acts as the leader, and campus load aggregators, energy storage plants, and wind farm operators serve as followers. The layer employs an enhanced particle swarm optimization (PSO) algorithm to iteratively adjust energy sales prices and response compensation unit prices, influencing the user response plan through the demand response model. In the lower layer, the charging and discharging schedules of energy storage plants, wind farm energy supply, and outputs of energy conversion devices are optimized to guide system operation. The novelty of this approach lies in the integration of a game-theoretic framework with advanced optimization techniques to balance the interests of all participants and enhance system coordination. A case study is conducted to evaluate the effectiveness of the proposed strategy, demonstrating significant economic benefits. The results show that the model encourages stakeholders to invest in energy infrastructure and actively participate in coordinated dispatch, leading to improved overall system efficiency and comprehensive revenue enhancement for the multi-agent energy system.

Optimization Strategy for Integrated Energy Microgrids Based on Shared Energy Storage and Stackelberg Game Theory

The implementation of community power generation technology not only increases the flexibility of electricity use but also improves the power system’s load distribution, increases the overall system efficiency, and optimizes energy allocation. This article first outlines the operational context of the system and analyzes the roles and missions of the various participants. Subsequently, optimization models are developed for microgrid operators, community power storage facility service providers and load aggregators. Next, the paper explores the game relationship between microgrid operators and load aggregators, proposing a model based on the Stackelberg game theory and proving the presence and singularity of the Stackelberg equilibrium solution. Finally, simulations are conducted using Yalmip tools and the CPLEX solution on the MATLAB R2023a software platform. A combination of heuristic algorithms and solver methods is employed to optimize the strategies of microgrid operators and load aggregators. The research findings show that the proposed framework is not only able to achieve an effective balance of interests between microgrid operators and load aggregators but also creates a win–win situation between load aggregators and shared energy storage operators. Additionally, the solution algorithms used ensure the protection of data privacy.

Low-Carbon Optimization Scheduling of Integrated Energy Systems Based on Bilateral Demand Response and Two-Level Stackelberg Game

In the context of low-carbon energy transformation, fully utilizing the integrated demand response (IDR) resources on the load side can improve the operational flexibility and economy of the integrated energy system (IES). However, establishing a reasonable trading mechanism to enhance users’ participation in IDR has become a key issue that IES urgently needs to solve. To this end, this paper first establishes an IES model that includes electricity, heat, and gas. To reduce carbon emissions, a ladder-type carbon trading mechanism is introduced while adding low-carbon technologies such as carbon capture devices and power-to-gas conversion. Secondly, a bilateral IDR mechanism centered on the load aggregator (LA) is proposed, and a multi-agent operation model including IES, LA, and users is established. The IDR subsidy price is dynamically determined through a two-level Stackelberg game model involving IES, LA, and users. Then, through KKT conditions and the Big M method, the two-level game model is turned into an IES-LA game model, which is solved using a combination of the White Shark Optimization method and the Gurobi solver. The final simulation results show that the scheduling model can fully reflect the time value of IDR resources, and the IES cost is decreased by USD 152.22, while LA and user benefits are increased by USD 54.61 and USD 31.85. Meanwhile, the ladder-type carbon trading mechanism and low-carbon technology have effectively achieved low-carbon operation of the system.

Chance-constrained bi-level optimal scheduling model for distribution network with thermal controllable load aggregators

An increasing amount of distributed renewable energy is being integrated into distribution networks to achieve decarbonization. It is essential to exploit demand-side flexible resources further to enhance system flexibility in response to the intermittency and unpredictability of renewable energy sources. This paper introduces a polytope-based aggregation method for thermostatically controlled loads (TCLs), aggregating numerous individual TCLs into a unified virtual battery via the aggregator (AGG). This approach avoids the dimensionality curse faced by the distribution system operator when directly controlling each TCL, while efficiently utilizing TCL flexibility. Subsequently, a bi-level optimization model is established, where AGGs are treated as independent stakeholders participating in the distribution network scheduling optimization through the local energy market. This model incorporates chance constraints to address the uncertainty of renewable energy sources. Finally, the distributionally robust chance constraint (DRCC) method is used to convert chance constraints into a linear form, and strong duality theory and Karush–Kuhn–Tucker conditions are applied to transform the bi-level model into a single-level model with equilibrium solutions. Case studies on the IEEE 33-bus network demonstrate that the proposed polytope-based aggregation method substantially improves computational efficiency with minimal optimality loss. Additionally, the DRCC method offers superior economic performance compared to robust and deterministic optimization approaches, while maintaining robustness.

Two-Stage Optimal Scheduling Strategy of Microgrid Distribution Network Considering Multi-Source Agricultural Load Aggregation

With the proposed “double carbon” target for the power system, large-scale distributed energy access poses a major challenge to the way the distribution grid operates. The rural distribution network (DN) will transform into a new local power system primarily driven by distributed renewable energy sources and energy storage, while also being interconnected with the larger power grid. The development of the rural DN will heavily rely on the construction and efficient planning of the microgrid (MG) within the agricultural park. Based on this, this paper proposes a two-stage optimal scheduling model and solution strategy for the microgrid distribution network with multi-source agricultural load aggregation. First, in the first stage, considering the flexible agricultural load and the market time-of-use electricity price, the economic optimization is realized by optimizing the operation of the schedulable resources of the park. The linear model in this stage is solved by the Lingo algorithm with fast solution speed and high accuracy. In the second stage, the power interaction between the MG and the DN in the agricultural park is considered. By optimising the output of the reactive power compensation device, the operating state of the DN is optimised. At this stage, the non-linear and convex optimization problems are solved by the particle swarm optimization algorithm. Finally, the example analysis shows that the proposed method can effectively improve the feasible region of safe operation of the distribution network in rural areas and improve the operating income of a multi-source agricultural load aggregation agricultural park.

Collaborative optimization for energy hub and load aggregator considering the carbon intensity-driven and uncertainty-aware

To achieve optimization operation between the energy hub operator and the load aggregators, this paper proposes a collaborative model for the energy hub and load aggregator considering the carbon intensity-driven and uncertainty. Firstly, a time-coupled carbon emission flow model for energy storage is proposed to cope with the change in carbon intensity at the injection node. Meanwhile, a carbon intensity-based incentive price is developed for interruptible loads with diverse carbon intensity. Secondly, the Wasserstein metric-based distributionally robust optimization method is leveraged to height against the energy hub uncertainty, in which the infinite-dimensional distributionally robust optimization model is reformulated into a tractable linear programming. Thirdly, considering the multi-entity characteristics of energy hub and load aggregators, a collaborative optimization method based on the alternating direction method of multipliers algorithm is constructed. Finally, to meet the convergence requirements of the alternating direction method of multipliers algorithm, the iterative convexification algorithm is applied to transform the nonconvex bi-level energy hub-users model into an iterative convex model by avoiding binary variables and big-M parameters. Consequently, the energy hub and load aggregator can operate cooperatively and protect privacy in uncertain conditions. Simulation results verify the effectiveness of the proposed model and method. Simulation results demonstrate the effectiveness of the proposed model and method. Specifically, the iterative convexification algorithm achieved a profit of ¥1653.82 for the load aggregator, which is 24.4 % higher than the profit obtained by CONOPT (¥1329.73) and 20.3 % higher than that obtained by IPOPT (¥1374.69), thus providing substantial advantages over traditional nonlinear solvers.

A market-based load regulation method for heterogeneous residential air-conditioning loads under cloud-edge collaboration

Residential air-conditioning load on the power demand side has gradually increased. The air-conditioning loads have thermal storage characteristics, and adjusting their temperature settings will not cause significant negative impacts to users, making them well-suited for demand response. In existing studies, load aggregators usually serve as demand response implementors, and reducing the energy consumption levels of air conditioning loads directly. However, this method often lacks a clear definition of the flexibility of individual air-conditioning units and fails to account for their variations. The absence of well-defined commodity characteristics for the flexible regulation potential complicates pricing, making it difficult to safeguard the interests of the load aggregator and each air-conditioning user. Furthermore, the diversity among residential air-conditioning loads introduces high-dimensional variables into demand response optimization, making it challenging to balance data security with computational efficiency. To address these challenges, this paper proposes a market-based load reduction method for heterogeneous residential air-conditioning loads using cloud-edge collaboration. First, the flexible adjustment capability of air-conditioning loads is defined as a tradable commodity. Then, a cloud-edge collaborative trading scheme is proposed to guarantee the benefits of the load aggregator and each air-conditioning user in a data-neutrality manner. Finally, a hybrid method based on encrypted clustering is developed to compute the optimal trading strategy, ensuring data security and computational efficiency. Simulation results based on data from the Austin area show that Pareto improvement is achieved compared to other load reduction schemes, and the proposed encrypted clustering method reduces computational complexity and data security risks compared to traditional analytical and iterative approaches.

Optimising load control of multi-type air conditioning in demand-side management

ABSTRACT With the continuous expansion of renewable energy capacity and the increasing demand for thermostatically controlled loads in China, new challenges have arisen for maintaining power supply stability. This paper establishes a control model for the aggregation of different types of air conditioning loads. To improve unsatisfactory demand response outcomes, a novel incentive mechanism based on tracking the target load curve is proposed. Additionally, a cost model for air conditioning load aggregators and the regional grid operator, along with an implementation scheme for trading mechanisms, is also developed. Case simulations validate the effectiveness and rationality of the proposed incentive mechanism.

Modeling and detection of false data injection attacks in cyber-physical distribution system with load aggregator interaction

With the increasing number of users and multi-type loads accessing the cyber–physical distribution system (CPDS), the bidirectional interaction between the system becomes more and more frequent. The Load aggregator (LA) also plays an increasingly important role in the interaction process. However, the LA’s high dependence on information and lack of security measures make it vulnerable to attacks, so this paper analyzes the interactive security of the LAs from two points. Considering the game process between the LAs and users from the attacker’s point of view, this paper puts forward an attack strategy aiming cost function of the LAs, establishes a bi-level multi-objective programming attack model of false data injection attacks(FDIAs), and proposes an attack detection method based on the multi-state matching method and improved similar daily data preprocessing generative adversarial network (P-GAN) from the defender’s point of view to defend against the above attack strategy. Furthermore, a hybrid detection mechanism combining event triggering and periodic detection is proposed to ensure response speed and adaptability of detection. The effectiveness of the proposed attack model and the detection method is verified by simulation analysis.

Effect of size and loading of waste single-used plastic (SUP) aggregates on a bio-based high density polyurethane composite

Abstract The utilization of waste single-use plastic (SUP) as fillers by containment in a polyurethane matrix was investigated as an alternative solution to the detrimental disposal of these waste materials. High-density bio-based rigid polyurethane composites were prepared by adding polyol, isocyanate, and additives, along with densified SUP, which served as aggregate fillers to enhance the bulk density and flexural strength of rigid polyurethane while increasing the thermal conductivity. The aggregated SUPs were prepared using agglomeration-densification machine and exhibited size variations of 12.44 mm (A), 14.12 mm (B), and 15.56 mm (C). The resulting aggregates were added to the rigid polyurethane matrix at varied loadings of 40%, 50%, and 60% v/v. The green composites were cured in heated hydraulic press at constant temperature and pressure. Based on the obtained results, it was found that the formulation with a SUP size of C and a loading of 60% produced the composite of highest bulk density due to relatively high density of agglomerated SUP as the size enlarges. Additionally, the SUP size of A and a loading of 50% (50A) exhibited the highest flexural strength value. This behaviour was attributed to the increased filler-matrix interfacial area achieved with the smallest size aggregates. However, a further increase in aggregate loading resulted in a decrease in this property as common attribute for composite materials. On the other hand, it was revealed that increasing the loading of SUP aggregates provided a lesser insulating effect due to the increase in thermal conductivity resulting from the presence of filled pores within the polyurethane foam. The findings of this study contributed to understanding the effects of aggregate size and loading on the mechanical and thermal properties of the composite material, providing valuable insights for the development of energy-efficient and environmentally-friendly polyurethane structures.

Strategic joint bidding and pricing of load aggregators in day-ahead demand response market

Load aggregators (LAs) purchase demand response (DR) capacity from users by incentive compensation and then resell them by bidding in the day-ahead DR market to gain profits. Existing related research fails to adequately integrate bidding and pricing decision-makings and lacks sufficient consideration of uncertain user response behaviors, resulting in unstable trading returns. To this end, we propose a novel joint optimization method for bidding and pricing of the LA. First, a two-stage joint optimization framework is constructed to coordinate the temporally coupled bidding and pricing decisions, where these two strategies are simultaneously optimized to form the DA bidding strategy at first, and the pricing adjustment is then introduced after market-clearing to develop the formal user incentive scheme. Second, to account for the risks from uncertain response behaviors, the first stage incorporates DR settlement rules and the hedging effect of the aggregated response uncertainty to develop a relatively aggressive bidding strategy. After that, a user selection mechanism is then introduced to filter out users with both low response costs and reliable responses for participation. Numerical studies are presented to validate the proposed methodology in formulating optimal trading strategies that effectively tradeoff transaction revenue and risks.

A decision-making model for joint energy and reserve scheduling of wind power producers with local intraday demand response exchange market

In this paper, a three-stage stochastic bi-level optimization framework is presented for optimal participation of wind power producers (WPPs) in day-ahead (DA), intraday, and balancing markets. In this framework, to leverage demand response (DR) services, a peer-to-peer (P2P) energy trading platform is implemented that allows local load aggregators (LAs) to contribute to the intraday markets improving both LAs’ and WPP’s benefits. Participating in the intraday DR exchange (IDRX) market enables WPP to purchase DR services from LAs, to reduce the penalty cost on the deviation between the day-head bidding and the real-time dispatch. A Stackelberg game for the bi-level decision-making model captures the conflict of interests between the WPP and LAs, in which, the upper level seeks to maximize WPP profit, while the lower level aims to maximize LAs’ economic surplus. The bi-level model is converted into its equivalent single-level mixed-integer quadratic problem (MIQP) employing the Karush-Kuhn-Tucker (KKT) conditions and strong duality theorem. Simulation results show that participation of the WPP in the IDRX market and employing spinning reserve and DR services for compensating the uncertainties are greatly dependent on its risk preferences and increase its expected profit in all conditions, significantly.

Enhancing Aggregate Load Forecasting Accuracy with Adversarial Graph Convolutional Imputation Network and Learnable Adjacency Matrix

Enhancing Aggregate Load Forecasting Accuracy with Adversarial Graph Convolutional Imputation Network and Learnable Adjacency Matrix

Research on time-of-use compensation pricing strategies for load aggregators based on user demand response

As the electric power market reform deepens, the strategic role of load aggregators in demand-side response becomes increasingly important. The inherent variability of distributed renewable energy generation and user demand response often leads to a mismatch between the purchased electricity and the market bid volume, resulting in punitive costs for companies. To address this issue, this study treats demand-side controllable loads as dispatchable resources and proposes a tiered pricing strategy to adjust power distribution. By establishing a Stackelberg leader-follower game model, the study promotes a mutually beneficial relationship between load aggregators and controllable load users. Through case studies, this paper examines the operational profits of load aggregators and the power adjustment behaviors of controllable load users under tiered and fixed compensation pricing schemes. The results indicate that tiered compensation pricing significantly reduces punitive costs and enhances user participation in demand response.

Continuous-Time Aggregation of Massive Flexible HVAC Loads Considering Uncertainty for Reserve Provision in Power System Dispatch

Continuous-Time Aggregation of Massive Flexible HVAC Loads Considering Uncertainty for Reserve Provision in Power System Dispatch

Optimal scheduling of multiple entities in virtual power plant based on the master-slave game

As the energy market evolves into a dynamic and interactive landscape, the distributed nature of virtual power plant (VPP) becomes increasingly significant. This shift highlights the limitations of traditional centralized optimization approaches in capturing the complex interplay among various stakeholders. In response, this article introduces a novel multi-entity distributed collaborative optimization strategy for an integrated energy system (IES) that incorporates a VPP, electric vehicles, and carbon capture technologies, under the Stackelberg master-slave game framework. Within this framework, the VPP operator (VPPO) assumes the role of the leader, while the energy supply aggregator (ESA), customer side residential load aggregator (CSRLA), electric vehicles aggregator (EVA), and carbon treatment system aggregator (CTSA) are positioned as the followers. The paper delves into the development of interaction strategies for each entity, aiming at achieving optimal objectives. The study undergoes by presenting the mathematical model of the VPP-integrated energy system, which is seamlessly integrated into the master-slave game structure. This integration facilitates the creation of a distributed multi-entity cooperative optimization model featuring a single leader and multiple followers, with the uniqueness of the Stackelberg equilibrium being rigorously established. Therefore, the research employs a hybrid nutcracker optimization algorithm and quadratic programming (NOA-QP) method to address the engineering challenge of optimizing operator energy pricing. The case study conducted demonstrates that the proposed scheduling methodology improves the VPP system profit by 10.80%, increases the aggregation profit by up to 1317.22%, optimizes the carbon emissions by 15.59%, and significantly improves the solution efficiency of the VPP by 99.29%.

Multi-objective robust dynamic pricing and operation strategy optimization for integrated energy system based on stackelberg game

The integrated energy system (IES) with hydrogen storage has become one of the most important developments in multi-energy coupling field, where the severe conflict of interests between different entities leads to great challenges to the economy and low-carbon operation. A multi-objective robust dynamic pricing and operation strategy optimization method based on the Stackelberg game is proposed for the hydrogen-containing energy storage (HES) IES. Firstly, the HES-IES trading framework is established based on the introduction of an integrated energy operator (IEO) and a load aggregator (LA). Secondly, a multi-objective robust Stackelberg game model is developed with the IEO as the leader and the LA as the follower, considering the minimization of operating costs and carbon emissions of the IEO and the minimization of integrated energy costs of the LA as the objectives. Finally, the compromise planning and the max-min fuzzy are addressed to solve the multi-objective model, which adopts the adaptive differential evolution (ADE) algorithm. In addition, the robust optimization (RO) with adjustable coefficients is employed to tackle uncertainties of source and load. The results show that this method can effectively balance the operating costs and carbon emissions of the system, improve the benefit of the IEO, reduce the costs of the LA, and avoid the uncertainty risk. Compared with traditional algorithms, the ADE algorithm has significant advantages in the number of iterations and solving time. In summary, the multi-objective robust dynamic pricing and operation strategy optimization proposed in this paper could effectively achieve the benefit balance between the IEO and the LA, also further improve the economy and robustness of the system and reduce carbon emissions.

Adaptive Charging Simulation Model for Different Electric Vehicles and Mobility Patterns

Electric mobility is a sustainable alternative for mitigating carbon emissions by replacing the conventional fleet. However, the low availability of data from charging stations makes planning energy systems for the integration of electric vehicles (EVs) difficult. Given this, this work focuses on developing an adaptive computational tool for charging simulation, considering many EVs and mobility patterns. Technical specifications data from many EVs are considered for charging simulation, such as battery capacity, driving range, charging time, charging standard for each EV, and mobility patterns. Different simulations of charging many EVs and analyses of weekly charging load profiles are carried out, portraying the characteristics of the different load profiles and the challenges that system planners expect. The research results denote the importance of considering different manufacturers and models of EVs in the composition of the aggregate charging load profile and mobility patterns of the region. The developed model can be adapted to any system, expanded with new EVs, and scaled to many EVs, supporting different research areas.

Cooperative operation for multiple virtual power plants considering energy-carbon trading: A Nash bargaining model

With the development of the energy and carbon markets, it has become a trend for multiple virtual power plants (MVPP) that aggregate distributed resources from different regions to participate in market trading through cooperative operation. In order to study the energy-carbon interactions between VPPs and the supply-demand interactions for MVPP and users, this paper introduces a load aggregator (LA) and establishes a cooperative alliance consisting of MVPP and LA. Firstly, a carbon emission allowance allocation and transaction mechanism for MVPP is proposed based on the modified Shapley value method, which considers the impact of energy interactions within the alliance on the carbon emissions. Then, a cooperation model for the MVPP-LA alliance is established based on Nash bargaining theory, and it is decomposed into two subproblems of the maximal alliance benefits and the optimal benefit distribution. In terms of benefit distribution, this paper modifies the bargaining mechanism based on the contribution of each VPP to the alliance benefit. A dynamic penalty factor-based alternating direction method of multipliers (DP-ADMM) is used to solve the two subproblems in a distributed manner. Finally, the validity of the proposed trading mechanism, allocation method and solution algorithm are verified through several cases.