Distributed Optimization Model Research Articles

Consensus alternating direction multiplier method based fully distributed peer-to-peer energy transactions considering the network transmission distance

The zero-carbon concept for combating climate change boosts the development of distributed renewable energies in distribution grids. However, the lack of appropriate incentives limits their gains. The virtual power plant aggregates distributed energy resources on the demand side for cost-effective renewable energy consumption via flexible transactions. When compared to trading directly with retailers, virtual power plants can improve their efficiency through peer-to-peer energy trading, thus promoting the development of distributed renewable energies in the distribution network. This paper proposes a peer-to-peer energy transaction mechanism between multiple virtual power plants. First, a multi-VPP model based on peer-to-peer energy trading is constructed. It includes modeling of electric vehicles, gas turbines, renewable energy, and flexible loads. Second, because prosumers are owned by different stakeholders, a distributed optimization model is developed. The model is then solved based on a fully decentralized consensus alternating direction multiplier method. In addition to the energy transaction, the benefit distribution of peer-to-peer energy trading is then investigated using the Shapley value method. The simulation results confirm the proposed peer-to-peer energy transactions can not only effectively improve the overall benefits of virtual power plant alliance, but also improves the income of renewable energies. Finally, the conclusion section summarizes the contributions and analyzes the limitations.

Distributed transaction optimization model of multi-integrated energy systems based on nash negotiation

Integrated energy system (IES) can achieve multi energy complementarity, but it still faces the problem of energy surplus or shortage. Therefore, there are demands for energy sharing among different IESs, but how to determine the trading quantity and trading price? To address this confusion, a distributed optimization model for multi-IES participating in peer-to-peer (P2P) transactions based on asymmetric Nash negotiation is innovatively proposed. First, to facilitate the energy sharing of several IESs with different structures, a P2P trading framework is designed. Second, to meet the needs of individual rationality and alliance cooperation at the same time, a distributed transaction optimization model based on Nash negotiation is proposed. Considering the discourse power determined by contribution, an asymmetric bargaining mechanism is designed. Third, to protect the privacy and improve solution performance, the improved adaptive step-size alternating direction multiplier algorithm (ADMM) is used for the distributed sequential solution. Finally, the effectiveness of the proposed trading framework, bargaining mechanism, optimization model, and solution algorithm are verified by the implementation of simulation. The simulation results show that: 1) The proposed model and algorithm can assist managers in determining the quantity and price of P2P electricity transactions. 2) Compared with the independent operation mode, the cooperative operation mode has significantly improved the overall interests and individual interests. 3) In distributed transactions, managers only need to submit limited information, which protects the privacy and security of each agent. 4) The asymmetric Nash negotiation mechanism can measure discourse power based on contribution. 5) The improved ADMM has the advantages of stronger convergence performance and faster solution speed.

Exploring Symmetry-Induced Divergence in Decentralized Electric Vehicle Scheduling

Due to the low computational efficiency and high communication pressure caused by centralized control, decentralized coordination of electric vehicles (EVs) has become a research hotspot in recent years. However, the integration of numerous EVs with homogeneous parameters brings unprecedented challenges for the optimal scheduling of the power system. To explore symmetry-induced divergence in decentralized electric vehicle scheduling, the established centralized optimization scheduling model of electric vehicles is decomposed into a distributed optimization model by Lagrange relaxation, achieving parallel control of each EV aggregator (EVA). To solving the oscillation caused by parameter symmetry in the process of optimization, we propose a convergence acceleration algorithm based on a perturbation function, which is a random distribution function used to break parameter symmetry within an acceptable calculation error range. On the premise of sensitivity analysis, a closed form of the perturbation limit is theoretically derived. Case studies based on different scales of users validate the effectiveness and computational efficiency of the proposed method.

Optimization study of computational methods in coordinated integrated carrying capacity assessment of multi-voltage hierarchies

Abstract In this paper, we take a two-level distribution grid as the infrastructure of a multilevel distribution grid and study the comprehensive carrying capacity assessment model in depth. The minimum value of the maximum access capacity under each scenario is used to assess the maximum carrying capacity of the distribution network, and the maximum access volume of the multilevel distribution network is taken as the objective function, and the particle swarm algorithm is improved to establish the maximum carrying capacity assessment model. Using the alternating direction multiplier method, a two-level distribution grid carrying capacity distributed optimization model is established, and the multilevel distribution grid access volume problem is transformed into the maximum access volume subproblem at all levels of the distribution grid. Comparing the whale algorithm and particle swarm algorithm, the model in this paper converges at 7465 kW access capacity and about 12 iterations, respectively, and the weak degree is below 0.4 at different distribution network states, which is a good performance in terms of optimization accuracy and weak degree. We conduct simulation experiments with the modified IEEE33 nodes and find that using this paper’s model to participate in optimal scheduling reduces the total operating cost of the distribution network system by more than 6.24% compared to not using it. Finally, we use the model in this paper to evaluate the comprehensive carrying capacity of the distribution network in Ningxia, China.

A market framework to exploit the multi-energy operating reserve of smart energy hubs in the integrated electricity-gas systems

Faced with increasing uncertainties in the integrated electricity and gas system (IEGS), the multi-energy operating reserve(MOR), i.e., extra electric and gas reserve capacity, is becoming vitally important to guarantee the reliable operation of the system. Smart energy hubs(SEHs) located at the demand side of the IEGS can adjust their electricity and gas consumption through energy substitution, which has great potential to provide the MOR. Current studies mainly concentrate on the energy trading mechanism among different SEHs in the energy-only market, which may not effectively incentivize SEHs to provide MOR for system operation. Besides, due to the limited energy capacity, SEHs cannot directly participate in the wholesale reserve market along with other large-capacity resources, e.g., power plants and gas wells. To address these, a two-stage market framework is proposed for exploiting the multi-energy operating reserve of SEHs. In the first stage, the wholesale market is cleared considering the participation of large-capacity resources to determine the clearing results of MOR. Based on the results, an energy-loss-cost calculation model is developed to measure the value of the specific MOR level. By altering the reserve requirements, the values of different MOR levels can be accordingly calculated to formulate the multi-energy operating reserve demand surface(MOR-DS), which can quantify varying MOR values with different levels of the reserve. With the MOR-DS describing the price elasticity of the MOR, a distributed MOR clearing mechanism is developed in the second stage to determine the quantity and price of the reserve from SEHs. The clearing mechanism is constructed as a distributed optimization model considering optimal collaboration among different SEHs. Case studies verify that the proposed market framework can effectively stimulate SEHs to provide MOP through economic incentives, which can realize the reliability improvement of IEGS and the revenue increase of SEHs.

Inverse-free distributed neurodynamic optimization algorithms for sparse reconstruction

This article proposes three novel inverse-free distributed neurodynamic optimization algorithms to reconstruct sparse signal and image by addressing the L1-minimization problems. Based on multi-agent consensus theory, we successfully transform the original L1-minimization problem into a distributed optimization model. To tackle such model, a three-layer inverse-free distributed algorithm is proposed by using projection operator and derivative feedback, which enjoys global convergence. To simplify the structure of this three-layer distributed algorithm, a time-varying parameter-based two-layer inverse-free distributed algorithm is designed, which has global convergence. Moreover, to accelerate convergence and further simplify the structure of this two-layer distributed algorithm, we develop a Tikhonov-like regularization-based single-layer inverse-free distributed algorithm, which achieves consensus within finite time for any given initial point and possesses an O(1/ξ(t)) convergence rate of the linear-equality constraint function. Finally, experimental results on signal and image reconstruction are presented to illustrate the efficiency of our inverse-free distributed algorithms.

Distributed economic optimisation of multi‐energy park operation based on cloud platform architecture considering network delivery capacity

AbstractTo address the issues of node interaction power overrun and high carbon emissions that may arise during distributed optimization in multi‐energy parks (MEPs), this paper proposes a distributed low‐carbon and economic operation method for multi‐energy parks based on a cloud platform that considers network transmission capacity.The proposed method achieves maximun profit by designing a two layer collaborative architecture for distributed optimization operations. At the top level, cloud platform services are utilized to build a model for checking network transport capacity and carbon emission quotas, optimizing network node over‐limit inspection . The bottom layer constructs a distributed optimization model for multi‐energy complementation in each park, taking into account the information privacy and individual interests of each multi‐energy park. An improved alternating direction multiplier method (ADMM) is proposed to effectively solve the two‐layer framework. The case studies show that the distributed optimization method under cloud platform services proposed in this paper can achieve maximum revenue for integrated energy service provider while ensuring the safe operation of multi‐energy parks, and reasonably allocate the benefits of collaborative operation among various parks while promoting carbon emission reduction.

Multiagent System With Periodic and Event-Triggered Communications for Solving Distributed Resource Allocation Problem

This article mainly investigates how to reduce the communication cost in multiagent system (MAS) for distributed optimization. First, a continuous-time distributed optimization model based on MAS is proposed for resource allocation (RA) with periodic communication. All agents in the system do not need to be in constant contact with their neighbors, but contact at set intervals. This will greatly reduce the communication consumption of the system. Second, to further reduce the communication cost, MAS with event-triggered communication is proposed based on periodic communication. It is proved that the system is convergent to an optimal solution of the investigated problem subject to bound and equality constraints. Finally, two examples with simulations are given to verify the performance of the proposed system.

Partitional Collaborative Mitigation Strategy of Distribution Network Harmonics Based on Distributed Model Predictive Control

Dispersed harmonic control makes a critical guarantee for safe and stable operation of distribution networks. However, conventional point-to-point local control method has limitations. In addition, harmonic current injection has volatility and time-variability, and the residual capacity (RC) of multi-functional grid-connected inverter (MFGCI) employed for auxiliary harmonic compensation is uncertain, which challenges mitigation decision-making. In this study, a grid-side distributed mitigation strategy based on distributed model predictive control (DMPC) is proposed. Firstly, the voltage distortion observation node is selected based on node clustering, and sensitivity analysis of harmonic mitigation for observation nodes is conducted to divide the whole network into multiple control areas. Secondly, for global optimal of voltage distortion, the long time scale distributed optimization model for mitigation parameters orienting partitional coordination is established. Finally, a rolling optimization model based on DMPC for correction of conductance parameters is developed from regional autonomy perspective. The results show that: (1) Distributed mitigation scheme can improve the total harmonic distortion of voltage (THDV) of the whole network node; (2) Compared with control references, the corrected parameters can reduce the decision deviation and further lower the THDV by about 2%; (3) In multi-uncertain scenarios, multi-time-scale optimization can alleviate the uncertainty in harmonic control.

Research on second-order cone relaxation algorithm for multi-time linearization of distribution networks with distributed power sources

Distributed power supply connected to distribution network brings impact on system voltage distribution as well as tidal current analysis, which causes degradation of system power quality. For this reason, a system optimization model is needed to analyze and optimize system voltage and tidal current. The linearized second-order cone relaxation optimization algorithm for distribution networks with distributed power sources is proposed. First, the distribution network branch tide model is introduced to analyze the tide of the distribution network with distributed power supply access; based on this, the distributed distribution network tide optimization model is established. Secondly, the distributed distribution network tidal optimization model is simplified, and the multi-time second-order cone relaxation optimization algorithm is proposed for the non-convex nonlinearity in tidal analysis, and the segmental linearization is performed for the non-convex nonlinearity of capacitor bank and on-load regulator transformer. Finally, a modified IEEE33 node test system is used on the MATLAB simulation platform to verify the tidal optimization of this distributed distribution network tidal optimization system. The simulation results show that the tidal optimization algorithm can reasonably dispatch the output of on-load regulating transformers, capacitor banks and distributed power sources, effectively reduce the network loss and the voltage deviation of the grid.

Optimal operation for integrated electricity and natural gas systems considering demand response uncertainties

The volatility of wind power and the uncertainty of demand response have brought greater challenges to the operation of integrated electricity and natural gas systems. Therefore, an optimal operation model considering comprehensive demand response uncertainty is proposed. First, chance-constrained is used to deal with the uncertainty of wind power. The uncertainty of three demand response loads that can be transferred, reduced, and replaced are modeled respectively. Secondly, considering that the two systems are different stakeholders, a distributed optimization model is established, the mixed-integer nonlinear model established by incremental linearization and second-order cone relaxation processing is further used, and the distributed optimization model is realized through target cascade (ATC). Finally, a case study of the integrated electricity and natural gas system composed of an IEEE 33-bus power system and 24-node natural gas system verifies that: 1) considering the demand response will reduce the system cost by 3.57%; 2) the necessity of considering the uncertainty of demand response; 3) the convergence of this method is better than ADMM method.

A Distributed Optimization Model for Mitigating Three-phase Power Imbalance with Electric Vehicles and Grid Battery

Three-phase power imbalances may occur in the distribution network due to high electric vehicle (EV) charging demand. The imbalances become severe with the increasing number of EVs in the future and may be addressed with coordinated charging strategies. In this paper, we propose a phase-balancing and peak-shaving scheme for a community in the three-phase power distribution system by managing the charging and discharging strategies for EVs and grid battery energy storage systems (BESS). The proposed scheme includes energy transactions and distributed optimization models. In the transaction model, vehicle-to-vehicle (V2V) energy trading is considered. In the optimization model, the distribution system operator (DSO) optimizes the energy management strategy of the grid BESS while the EV owners optimize their charging strategies. Financial incentives are introduced to encourage the EV owners to assist the distribution system operator in reducing the phase imbalance. Simulation results show that the proposed scheme could mitigate the phase imbalance and reduce the difference between peak and valley load of the load curves in the three-phase distribution system. Both EV owners and the distribution system benefit financially. Moreover, the power quality and system reliability of the distribution network can also be improved.

Reinforcement Learning for Distributed Energy Efficiency Optimization in Underwater Acoustic Communication Networks

To solve the problems of poor quality of service and low energy efficiency of nodes in underwater multinode communication networks, a distributed power allocation algorithm based on reinforcement learning is proposed. The transmitter with reinforcement learning capability can select the power level autonomously to achieve the goal of getting higher user experience quality with lower power consumption. Firstly, we propose a distributed power optimization model based on the Markov decision process. Secondly, we further give a reward function suitable for multiobjective optimization. Finally, we present a distributed power allocation algorithm based on Q-learning and use it as an adaptive mechanism to enable each transmitter in the network to adjust the transmit power according to its own environment. The simulation results show that the proposed algorithm not only increases the total channel capacity of the system but also improves the energy efficiency of each transmitter.

Blockchain-based Distributed Power Market Trading Mechanism

Distributed power market trading has the characteristics of large number of participants, scattered locations, small single trading scale, and point-to-point trading. The traditional centralized power trading model has the problems of large load, low efficiency, high cost, reliance on third parties and unreliable data. With the characteristics of decentralization and non-tampering, blockchain can establish a point-to-point trusted trading environment and provide effective solutions to the above problems. Therefore, this paper proposed a distributed power market trading framework based on blockchain. In this framework, the distributed power supply characteristics and trading needs of each participant are analyzed, a complete distributed trading process based on blockchain is designed. In addition, we have studied the key technologies of distributed power market trading. With the goal of power service reputation and maximum revenue of distributed power providers, we have established a matching degree model, a distributed power market trading optimization model, and designed a smart contract-based power market trading optimization strategy and power trading settlement strategy. Finally, we designed experiments to verify the performance of the proposed framework.

Laparoscopic image enhancement based on distributed retinex optimization with refined information fusion

With intrinsic non-uniform illumination variations in laparoscopic images, such images often suffer from insufficient lighting and low visibility. This in turn may cause incorrect targeting, surgical risk, and extended operating time during laparoscopic surgery. Although various methods for nature image enhancement have been proposed in past decades, surgical laparoscopic image enhancement still needs improving due to issues including naturalness, blurred texture, color cast, and extensive computational time. To address these problems, this paper proposes a laparoscopic image enhancement method, based on distributed retinex optimization with refined information fusion. The proposed method minimizes a distributed optimization model with l2-norm regularization terms, resulting in a low computational complexity. By integrating the refined image information into the optimization process, our method significantly enhances dark regions while preserving naturalness and texture structures. Experimental results show that our optimization algorithm is more effective than conventional enhancement algorithms in terms of vision augmentation, performance index, and computation time.

Flexible Dispatch for Integrated Power and Gas Systems Considering Power-to-Gas and Demand Response

Aiming at the problem of insufficient flexibility of the power system caused by large-scale wind power grid integration, a flexible economic dispatch model of the electricity-gas integrated system that considers power-to-gas and demand responses is proposed. First, it elaborates on the scheduling flexibility and demand response model. Secondly, the power system and the natural gas system are regarded as different stakeholders; with the goal of minimizing their respective operating costs, a two-tier distributed coordination optimization model of electricity and gas system is established. In order to achieve the coordination and optimization of the upper and lower systems, slack variables are introduced to describe the infeasible part of the power system scheduling results in the natural gas system and are used for interactive iterative solution of the model. The numerical results of the revised IEEE 30-node power system and 10-node natural gas system illustrate the effectiveness and necessity of the proposed model, as well as the superiority of comprehensively considering power-to-gas and demand response in improving the flexibility and economy of the power system.

Bi-level decentralized control of electric heating loads considering wind power accommodation in real-time electricity market

Flexible resources on demand-side, such as electric heating loads (EHLs), are perceived as an effective way of supporting the power balance of power grids with large scale renewable energy integration. However, it is difficult to quickly, effectively and evenly aggregate and schedule a large population of these loads because of their heterogeneity and geographic dispersion. The efficiency and effectiveness of optimal control are important for achieving the power balance between power source and load, especially in real-time scheduling. Moreover, the even load allocation between these heterogeneous loads also needs to motivate users participation in real-time power balance. To follow wind power in the real-time electricity market, this study presents a bi-level control method for EHLs based on distributed optimization computing, which considers the bi-level queuing method, different load control modes and multi-time scales between different control levels. First, each load group, which includes a large population of EHLs is controlled by a distributed server (DS); all the load groups are scheduled by the central management server (CMS), which deals with the wind farm or electricity retailer. Next, a distributed optimization model is built based on the bi-level control structure, in which the different power balance statuses and multi-time scales between the electricity market and EHLs are considered. Furthermore, considering the power balance on the multi-time scales, layer-by-layer load allocation optimization through the bi-level time-varying temperature queuing method, and the load-leveling optimization, serve as the sequential optimization problems. Finally, a simulation including 12,500 EHLs based on measured data in northern China is carried out. The results show that the proposed approach can effectively realize real-time power balance between wind power and EHLs, while maintaining uniform load allocation between the EHLs.

Active and Reactive Power Collaborative Optimization for Active Distribution Networks Considering Bi-Directional V2G Behavior

Due to their great potential for energy conservation and emission reduction, electric vehicles (EVs) have attracted the attention of governments around the world and become more popular. However, the high penetration rate of EVs has brought great challenges to the operation of the Active Distribution Network (ADN). On the other hand, EVs will be equipped with more intelligent chargers in the future, which supports the EVs’ high flexibility in both active and reactive power control. In this paper, a distributed optimization model of ADN is proposed by employing the collaborative active and reactive power control capability of EVs. Firstly, the preference of EV users is taken into account and the charging mode of EVs is divided into three categories: rated power charging, non-discharging, and flexible charging–discharging. Then, the reactive power compensation capacity of the plugged-in EV is deduced based on the circuit topology of the intelligent charger and the active–reactive power control model of the EV is established subsequently. Secondly, considering the operation constraints of ADN and the charging–discharging constraints of EVs over the operation planning horizon, the optimization objective of the model is proposed, which consists of two parts: “minimizing energy cost” and “improving voltage profile”. Finally, a distributed solution method is proposed based on the Alternating Direction Method of Multipliers (ADMM). The proposed model is implemented on a 33-bus ADN. The obtained results demonstrate that it is beneficial to achieve lower energy cost and increase the voltage profile of the ADN. In addition, the energy demand of EV batteries in their plugin intervals is met, and the demand preference of EV users is guaranteed.

Research on Active Coordination Control Method of Distribution Network Power Supply Based on Improved Firefly Algorithm

The location and capacity optimization configuration of distributed power supplies ensures that they. Make better technical and economic use. When the distributed power supply is connected to the distribution network, it will cause the trend size and direction of each branch to change, so that the system loss is not only related to the load size, but also related to the location and capacity of DG. Therefore, it is important to study the rational planning of DG in depth. In order to improve the system network loss effectively, a distributed power distribution power distribution network reactive optimization model with the minimum active loss of the system is established, and an improved multi-target firefly algorithm is proposed for the problem that the traditional firefly algorithm will oscillate repeatedly near the extreme point later in the iteration. In view of the shortcomings of the traditional firefly algorithm, which is easy to precocious and over-dependent on control parameters, the chaotic search strategy and global idea are integrated into the firefly algorithm, and an improved firefly algorithm is proposed, which is applied to solve the planning problem of distributed power supply. The example shows that the proposed algorithm has good practicability and adaptability, and also verifies the practical significance of the proposed model[1].

Resilient distributed economic dispatch of a cyber-power system under DoS attack

The economic dispatch problem of a smart grid under vicious denial of service (DoS) is the main focus of this paper. Taking the actual situation of power generation as a starting point, a new distributed optimization model is established which takes the environmental pollution penalty into account. For saving the limited bandwidth, a novel distributed event-triggered scheme is proposed to keep the resilience and economy of a class of cyber-power systems when the communication network is subject to malicious DoS attack. Then an improved multi-agent consensus protocol based on the gradient descent idea is designed to solve the minimization problem, and the prerequisites to minimize the system power generation cost are analyzed from the aspects of optimality and stability. Finally, the theoretical results are verified through a single-area 10-generator unit simulation.