Distributed Solution Method Research Articles

Distributionally Robust Chance-Constrained Transmission Expansion Planning Using a Distributed Solution Method

Distributionally Robust Chance-Constrained Transmission Expansion Planning Using a Distributed Solution Method

Distributed low-carbon economic dispatch of integrated power and transportation system

Electric vehicles (EVs) are widely recognized as promising solutions to reduce carbon emissions from the transportation sector. The rapid proliferation of EVs intensifies the interdependency between the power distribution system (PDS) and transportation system (TS). This paper proposes a distributed low-carbon economic dispatch scheme for the integrated power and transportation system (IPTS). Carbon emissions from the TS are quantified by a carbon dioxide calculation model, and the emissions from the PDS are determined by the electricity generation of fossil-fueled generators and the carbon reduction of carbon capture and storage (CCS) devices. An integrated model reformulation method is employed to transform the original non-convex model into a tractable one. Then a distributed solution method based on the spectral penalty parameter based adaptive alternating direction method of multipliers (SPPA-ADMM) is developed to protect the privacy of the PDS and TS. The reformulated model is solved iteratively, and the penalty parameter of the SPPA-ADMM is adjusted adaptively to improve the convergence performance of the method. Numerical results on three test systems demonstrate the effectiveness of the proposed scheme in achieving low-carbon economic dispatch of IPTS. Moreover, case studies validate the superiority of the SPPA-ADMM based distributed solution method in computation performance.

A Cooperative Hierarchical Multi-Agent System for EV Charging Scheduling in Presence of Multiple Charging Stations

The increasing penetration of plug-in electric vehicles (EVs) to the electrical grid raises concerns over secure and economic operation of the system. A coordination mechanism between system operator and EV aggregators is necessary to ensure that the system is operated within the security limits, and to reduce the charging costs while satisfying EV users’ energy needs. In this work, we present a cooperative hierarchical multi-agent system and propose an EV charging scheduling strategy in order to minimize the demand and energy charges while meeting the EV users’ energy requirements and satisfying the system security constraints. Within the designed framework, the higher-level agents calculate a set of proposed control signals by solving the designated optimization problems, and send them to the lower-level agents to facilitate an optimal scheduling in line with the aforementioned objectives. Through this hierarchically distributed approach, it is possible to effectively coordinate multiple EV charging stations without the need of direct communication or any prior information related to EV arrivals. The computational complexity of the problem is reduced by distributing the work among agents, and the privacy of sensitive data, such as system topology, load profiles, and EV parameters, is preserved. Moreover, unlike the traditional distributed solution methods that converge iteratively, the proposed approach calculates the optimal charging schedule after a single round of communication. The efficacy of the proposed methodology is demonstrated by a series of case studies on 33-bus and 118-bus distribution test feeders.

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.

Incentivizing distributed energy trading among prosumers: A general Nash bargaining approach

In this paper, we study the energy interaction problem among the autonomous prosumers, and develop an incentive scheme to encourage proactive energy trading. Specifically, without the need for any coordinators, each prosumer makes optimal strategy to share idle resources (renewable energy or loads) and maximizes the social welfare of a multi prosumers system. To incentivize proactive energy trading among prosumers, an incentive scheme is designed to achieve the fair benefits allocation according to their contributions. According to the summation of daily net transaction power, we quantify prosumers’ contributions by leveraging the bargaining power combined with the rate of return. Based on various bargaining power, a distributed energy trading problem is formulated as a general Nash bargaining problem. We propose a distributed solution method with disclosing limited information to preserve prosumers’ privacy. Simulations on different cases are conducted based on the actual data in Shanghai, China. Through a practical case study, the effectiveness of the method is verified in terms of distributed energy trading and fair benefits allocation.

Optimal planning method of renewable distributed generation for multiple prosumers participating in distribution networks

In the situation that distribution system operator (DSO) and multiple prosumers jointly invest distributed generation (DG) in the distribution network, it is difficult to achieve the balance of multi-agents interests under the requirements of security operation and privacy protection. To solve this problem, an optimal planning method of DG for multiple prosumers participating in distribution networks is proposed. First, the DG planning model of DSO and prosumers are constructed separately, and the network tariff dynamic updating strategy is proposed for the optimal guidance of multi-agent collaborative planning. Then, based on the collaborative planning framework for distributed autonomous decision-making of prosumers and the global coordination of DSO, a distributed solution method is proposed. Finally, the effectiveness of the proposed method is proved through the simulation results, the experiment proves that the network tariff updating strategy can better guide the multi-agent DG collaborative planning, and has better effects in balancing the benefit of prosumers and DSO.

Wind Power Accommodation Method for Regional Integrated Heat-Power System Considering Generation and Load Uncertainties

Due to the anti-peak shaving characteristics of wind power under the operation mode of “power determined by heat”, a large number of wind power is abandoned at night. In order to solve the problem, this paper proposes a method of coordinated operation of ground source heat pump (GSHP) and combined heat and power (CHP) units. Through indirectly reducing the generation power of CHP units, the accommodation space of wind power in power grid is improved. A two-stage robust optimal scheduling model of regional integrated heat-power system (RIHPS) considering the uncertainty of wind power generation and power load is established. And a distributed solution method based on Alternating Direction Method of Multipliers (ADMM) method and column-and-constraint generation (C&CG) algorithm is designed. Then, the Locational marginal pricing strategy with the goal of guiding users to participate in wind power accommodation is analyzed. The numerical simulation results show that the wind power accommodation capacity of the integrated system under the operation mode of “power determined by heat” can be improved through installing GSHP at CHP units and using price signal guidance.

Distributed Big-Data Optimization via Blockwise Gradient Tracking

We study distributed big-data nonconvex optimization in multiagent networks. We consider the (constrained) minimization of the sum of a smooth (possibly) nonconvex function, i.e., the agents' sum-utility, plus a convex (possibly) nonsmooth regularizer. Our interest is on big-data problems in which there is a large number of variables to optimize. If treated by means of standard distributed optimization algorithms, these large-scale problems may be intractable due to the prohibitive local computation and communication burden at each node. We propose a novel distributed solution method where, at each iteration, agents update in an uncoordinated fashion only one block of the entire decision vector. To deal with the nonconvexity of the cost function, the novel scheme hinges on successive convex approximation techniques combined with a novel blockwise perturbed push-sum consensus protocol, which is instrumental to perform local block-averaging operations and tracking of gradient averages. Asymptotic convergence to stationary solutions of the nonconvex problem is established. Finally, numerical results show the effectiveness of the proposed algorithm and highlight how the block dimension impacts on the communication overhead and practical convergence speed.

Distributed Voltage Control in Active Distribution Network Considering Renewable Energy: A Novel Network Partitioning Method

With the increasing integration of distribution generations (DGs), active distribution networks (ADNs) need to address the new challenges in voltage control. Meanwhile, the traditional centralized method in reactive power optimization usually leads to a heavy computational burden for large-scale distribution networks. A distributed voltage control model with a novel network partitioning method is proposed in this study, where the capacity curve of DGs and the regulation of electrical storage systems (ESS) are specially addressed. According to the number of decision variables and the number of constraints in the optimization model, the computational complexity can be utilized in the network partitioning method with the power balance and the electrical distance to automatically partition a distribution network in an optimal manner. Taking the coordination between two boundary sub-areas into consideration, a distributed voltage control strategy is developed and solved by a distributed solution method based on Lagrangian dual relaxation. Finally, numerical studies based on two IEEE test systems and a practical 152-bus system are performed to verify the effectiveness of the proposed method.

Distributed State Estimation of Multi-region Power System based on Consensus Theory

Effective state estimation is critical to the security operation of power systems. With the rapid expansion of interconnected power grids, there are limitations of conventional centralized state estimation methods in terms of heavy and unbalanced communication and computation burdens for the control center. To address these limitations, this paper presents a multi-area state estimation model and afterwards proposes a consensus theory based distributed state estimation solution method. Firstly, considering the nonlinearity of state estimation, the original power system is divided into several non-overlapped subsystems. Correspondingly, the Lagrange multiplier method is adopted to decouple the state estimation equations into a multi-area state estimation model. Secondly, a fully distributed state estimation method based on the consensus algorithm is designed to solve the proposed model. The solution method does not need a centralized coordination system operator, but only requires a simple communication network for exchanging the limited data of boundary state variables and consensus variables among adjacent regions, thus it is quite flexible in terms of communication and computation for state estimation. In the end, the proposed method is tested by the IEEE 14-bus system and the IEEE 118-bus system, and the simulation results verify that the proposed multi-area state estimation model and the distributed solution method are effective for the state estimation of multi-area interconnected power systems.

An Information Analysis of Iterative Algorithms for Network Utility Maximization and Strategic Games

A variety of resource allocation problems on networked systems, for example, those in cyber-physical systems or Internet-of-things applications, require distributed solution methods. Modern distributed algorithms usually require bandwidth-limited digital communication between the system and its users, who are often modeled as independent decision makers with individual preferences. This paper presents a quantitative information flow and knowledge gain analysis of decentralized iterative algorithms with bounded trajectories in the context of convex network utility maximization problems and strategic games with a unique Nash equilibrium solution. First, a novel generic framework is introduced to quantify knowledge gain in network resource allocation problems using entropy by taking into account priors in the solution space. Second, a general result is presented on the interplay between quantization of information and distributed algorithm performance both for linear and sublinear convergence. Third, information flow in distributed algorithms is studied and a lower bound is derived on the total amount of information exchanged for convergence under uniform quantization. The well-known primal-dual decomposition algorithm is used as an example to illustrate the results. Finally, convergence guarantees for distributed algorithms with estimation are investigated. This paper establishes specific links between information concepts and iterative algorithms in addition to building a foundation for integrating learning schemes into distributed optimization.

Autonomous Vehicle Logistic System: Joint Routing and Charging Strategy

The smart city embraces gradual adoption of autonomous vehicles (AVs) into the intelligent transportation system. Contributed by their full-fledged controllability, AVs can respond to instantaneous situations with high efficiency and flexibility. In this paper, we propose a novel AV logistic system (AVLS) to accommodate logistic demands for smart cities. We focus on determining the optimal routes for the governed AVs in consideration of various requirements imposed by the vehicles, logistic requests, renewable generations, and the underlying transportation system. By coordinating their routes and charging schedules, the system can effectively utilize the renewable energy generated by distributed generations. We formulate the joint routing and charging problem in the form of quadratic-constrained mixed integer linear program. To improve its scalability, we develop a distributed solution method via dual decomposition. We conduct extensive simulations to evaluate the performance of proposed system and solution methods. The results show that AVLS can effectively utilize excessive renewable energy while accomplishing all logistic requests. The distributed solution can develop near-optimal solutions with compelling improvement in computational speed.

Robust Tracking Commitment

Many engineering problems that involve hierarchical control applications, such as demand-side ancillary service provision to the power grid, can be posed as a robust tracking commitment problem. In this setting, the lower level controller commits a set of possible reference trajectories over a finite horizon to an external entity in exchange for a reward corresponding to the size of the reference set and the allowed margin of tracking error. If the commitment is accepted, the lower level system is required to track any reference trajectory that can be sampled from the committed set. This paper presents the framework of robust tracking commitment and a method to solve the optimal commitment problem for constrained linear systems subject to uncertain disturbance and reference signals. The proposed method allows tractable computations via convex optimization for conic representable uncertainty sets and lends itself to distributed solution methods. We demonstrate the proposed method in a simulation based case study with a commercial building that offers frequency regulation service to the power grid.

Distributed State Estimation of Hybrid AC/HVDC Grids by Network Decomposition

State estimation (SE) for bulk power systems is traditionally formulated and executed as one integrated problem in a control center energy management system. This simultaneous approach may present challenges when the concerned network consists of different types of systems operated by different entities (independent system operator, transmission system operator, or utility). A leading example is provided by hybrid ac/high voltage dc (HVDC) grids. We propose a distributed solution method where the system network is decomposed into several subsystems on which SE problems are executed separately and are iteratively coordinated through updated boundary information. Hybrid ac/HVDC grids naturally decompose into ac and HVDC subsystems. The proposed method uses a Lagrangian relaxation-based approach and block-wise Gauss–Seidel solution technique to arrive at a solution. The paper describes the method in the context of HVDC grids based on voltage source converter (VSC) technology. It presents a unified modeling framework for monopole/bipole converter configurations, parallel converters, converter-less dc buses, and wind farm connections. Illustrations and test cases are drawn using hybrid ac/HVDC grids formed by IEEE 39 and 300 bus ac grid networks along with monopole and bipole VSC HVDC grids.

Distributed Spectrum Leasing via Vertical Cooperation in Cognitive Radio Networks

In hierarchical cognitive radio networks, unlicensed secondary users can increase their achievable rates by assisting licensed primary user transmissions via cooperation. In this paper, a novel approach to maximizing the transmission rates in the secondary network by optimizing the relay selection, the secondary transmit powers, and the cooperative relaying power splitting parameters is proposed. The resulting optimization problem is mixed integer and nonconvex, which makes it NP hard to find the optimal solutions. Therefore, centralized and distributed solution methods to find near-to-optimal solutions of this challenging problem are proposed. The methods are based on iteratively solving the secondary relay selection by a greedy approach, and the optimal power allocation problem by a fixed-point approach together with alternating direction method of multipliers. It is established that both centralized and distributed solution methods always converge. The numerical results illustrate how the performance of the proposed solution methods depend on the primary performance margins, and show that they give a near-to-optimal solution in few iterations.

On the Convergence of Alternating Direction Lagrangian Methods for Nonconvex Structured Optimization Problems

Nonconvex and structured optimization problems arise in many engineering applications that demand scalable and distributed solution methods. The study of the convergence properties of these methods is, in general, difficult due to the nonconvexity of the problem. In this paper, two distributed solution methods that combine the fast convergence properties of augmented Lagrangian-based methods with the separability properties of alternating optimization are investigated. The first method is adapted from the classic quadratic penalty function method and is called the alternating direction penalty method (ADPM). Unlike the original quadratic penalty function method, where single-step optimizations are adopted, ADPM uses an alternating optimization which, in turn, makes it scalable. The second method is the well-known alternating direction method of multipliers (ADMM). It is shown that ADPM for nonconvex problems asymptotically converges to a primal feasible point under mild conditions and an additional condition ensuring that it asymptotically reaches the standard first-order necessary conditions for local optimality is introduced. In the case of the ADMM, novel sufficient conditions under which the algorithm asymptotically reaches the standard first-order necessary conditions are established. Based on this, complete convergence of the ADMM for a class of low-dimensional problems is characterized. Finally, the results are illustrated by applying ADPM and ADMM to a nonconvex localization problem in wireless-sensor networks.