Distributed Economic Dispatch Research Articles

Real‐time distributed economic dispatch scheme of grid‐connected microgrid considering cyberattacks

Cyber security of microgrids attracts increasing attention since the relatively open communication network of the microgrids is vulnerable to hacker attacks. This study proposes a real-time distributed economic dispatch scheme for the grid-connected microgrid against the cyberattacks. Firstly, a virtual leader agent is placed at the point of common coupling to measure the real-time power tracking error for achieving the power supply–demand balance, and then the optimal solution of the economic dispatch model is solved by the consensus algorithm of the multi-agent system theory. Subsequently, a set of detection algorithms is designed for each generator to determine whether its neighbouring generators suffer from the cyberattacks. The attacked generator is gradually marginalised from the communication network through updating the weight in the communication adjacency matrix based on its reputation value, thereby the impact of the attacked generator on the whole system is reduced greatly. Finally, the numerical simulations are carried out to verify the effectiveness of the proposed cyberattack-resilient distributed economic dispatch scheme.

Distributed Economic Dispatch Scheme for Droop-Based Autonomous DC Microgrid

In this paper, a distributed economic dispatch scheme considering power limit is proposed to minimize the total active power generation cost in a droop-based autonomous direct current (DC) microgrid. The economical dispatch of the microgrid is realized through a fully distributed hierarchical control. In the tertiary level, an incremental cost consensus-based algorithm embedded into the economical regulator is utilized to search for the optimal solution. In the secondary level, the voltage regulator estimating the average voltage of the DC microgrid is used to generate the voltage correction item and eliminate the power and voltage oscillation caused by the deviation between different items. Then, the droop controller in the primary level receives the reference values from the upper level to ensure the output power converging to the optimum while recovering the average voltage of the system. Further, the dynamic model is established and the optimal communication network topology minimizing the impact of time delay on the voltage estimation is given in this paper. Finally, a low-voltage DC microgrid simulation platform containing different types of distributed generators is built, and the effectiveness of the proposed scheme and the performance of the optimal topology are verified.

Distributed Economic Dispatch for Islanded DC Microgrids Based on Finite-Time Consensus Protocol

This paper presents a fully distributed finite-time control strategy to optimize the load power dispatch of islanded DC microgrids (MGs) in a finite-time manner. In which, based on the finite-time consensus protocol, a power optimizer is developed to realize MG's optimal operation by matching the incremental costs (ICs) of all the distributed generators (DGs) within a finite settling time. Moreover, the finite-time voltage regulator restores the average voltage across the MG to preserve the power balance among generation and demand. The developed controller achieves an improved performance with an accelerated convergence rate, which is important for MGs with a high penetration level of renewable distributed generators (RDGs), over the conventional distributed secondary controllers. The convergence of the proposed controller is confirmed by a thorough analysis. The performance of the developed controller is validated through simulation and experimental results under different case studies.

A Dual Splitting Method for Distributed Economic Dispatch in Multi-energy Systems

Multi-energy systems which bring together different forms of energy, such as electricity, gas and heat, to coordinate in the process of supply, transmission and consumption provide much higher flexibility over traditional energy systems in energy utilization. This paper deals with the economic dispatch problem in multi-energy systems in a distributed manner. Each agent optimizes its local objective function with regard to local coupled limits and a global constraint via local communications only. A distributed algorithm is proposed based on duality analysis and splitting methods.This algorithm adopts a non-linear mapping method to linearize the nonlinearity arisen from coupling relationship among energy carriers. We show that the proposed algorithm converges at a nonergodic rate of O(1/k). Simulations are demonstrated to show the effectiveness of the algorithm.

Multi-Agent Based Fully Distributed Economic Dispatch in Microgrid Using Exact Diffusion Strategy

To solve the economic dispatch (ED) problem of multiple distributed generations in the microgrid, this paper proposes a fully distributed method by using the exact diffusion strategy which can achieve exact convergence under sparse communication network. Firstly, a multi-agent hierarchical control architecture for the microgrid is designed. The microgrid central controller (MGCC) agent does not act as centralized control but instead participates in the distributed optimization between the bottom layer agents. Furthermore, an economic dispatch optimization model is established which aims at minimizing the operation cost, optimizing the active power of all dispatchable agents including distributed generators and flexible loads on demand side, and realizing the economic utilization of resources. A modified diffusion algorithm supporting full distributed optimization is proposed to solve it, which does not depend on the “leader unit” and is applicable to the actual problem. The modified algorithm has faster convergence speed, higher stability and stronger expansibility than consensus algorithm. Six scenarios are adopted to verify the proposed method. The result shows that the agent framework and the algorithm can cope with changing of communication topology and realize the “plug and play”. The output will converge to the optimal dispatch solution even if communication fails.

Distributed Learning Algorithms and Lossless Convex Relaxation for Economic Dispatch with Transmission Losses and Capacity Limits

This paper considers problems of economic dispatch in power networks that contain independent power generation units and loads. For efficient distributed economic dispatch, we present a mechanism of multiagent learning in which each agent corresponding to a generation unit updates the power generation based on the received information from the neighborhood. The convergence of the proposed distributed learning algorithm to the global optimal solution is analyzed. Another method of distributed economic dispatch we propose is a decentralized iterative linear projection method in which the necessary optimality conditions are solved without considering the generation capacities and the obtained solutions are iteratively projected onto the convex set corresponding to the generation capacities. A centralized method based on semidefinite programming for economic dispatch with a loss coefficient matrix is also presented for comparisons. For demonstration, the proposed methods of distributed economic dispatch are applied to a 6-generator test case and the three different methods of economic dispatch give the same solutions. We also analyze parametric dependence of the optimal power generation profiles on varying power demands in economic dispatch.

Distributed Economic Dispatch Control via Saddle Point Dynamics and Consensus Algorithms

In this brief, a distributed control algorithm is proposed to solve the economic dispatch problem. Without a central control unit, the generators work collaboratively to minimize the generation cost while balancing the supply and demand. The proposed method is based on consensus protocols and the saddle point dynamics. The consensus protocols are employed to estimate the global information in a distributed fashion, and the saddle point dynamics are leveraged to search for the optimal solution of the economic dispatch problem. By utilizing Lyapunov stability analysis, exponential stability of the optimal solution is derived if the capacity limits of the generators are not considered; with the capacity limits, practical stability of the optimal solution is obtained. No global information is needed in the proposed method, and the requirement on initial conditions of the state variables is mild. Several case studies on the IEEE 9-bus and IEEE 118-bus systems are presented to demonstrate the effectiveness of the proposed algorithms.

Consensus-Based Distributed Economic Dispatch Control Method in Power Systems

This paper introduces a new consensus-based control scheme for distributed power systems to solve the distributed economic dispatch (DED) problem. With the development of renewable energy, smart grid, and microgrid, more and more distributed generators will be connected to power systems. Thus the distributed control schemes become more and more important for power systems to control and manage the distributed equipment. Therefore, some consensus-based methods are published previously to solve the DED problem. But the challenge to apply the consensus-based method is to meet the power balance constraint without the centralized facility, since the value of power mismatch is hard to be obtained for a distributed control system. To solve the problem, this paper proposes the method to combine the frequency control methods with the consensus protocol from graph theory to develop the DED control method, so that the real power between the load and the generation can be balanced during the economic dispatch. With this method, a totally distributed optimal control scheme is obtained. The PI frequency controller and neural network frequency controller are employed to develop the DED control method. Then the communication failure problem is considered in this paper. The robust DED control method is proposed to improve the robustness of this distributed control method, allowing the system to stay at the optimal dispatching even if the communication is failed. In addition, the model of transmission line losses is incorporated in the DED problem to reduce the line losses. Finally, several case studies are given in this paper to verify the proposed method.

Distributed Piecewise Approximation Economic Dispatch for Regional Power Systems Under Non-Ideal Communication

Appropriate distributed economic dispatch (DED) strategies are of great importance to manage wide-area controllable generators in wide-area regional power systems. Compared with existing works related to ED, where dispatch algorithms are carried out by a centralized controller, a practical DED scheme is proposed in this paper to achieve the optimal dispatch by appropriately allocating the load to generation units while guaranteeing consensus among incremental costs. The ED problem is decoupled into several parallel sub-problems by the primal-dual principle to address the computational issue of satisfying power balance between the demand and the supply from the distributed regional power system. The feasibility test and an innovative mechanism for unit commitment are then designed to handle extreme operation situations, such as low load level and surplus generation. In the designed mechanism, the on/off status of units is determined in a fully distributed framework, which is solved using the piecewise approximation method and the discrete consensus algorithm. In the algorithm, the push-sum protocol is proposed to increase the system adaptation on the time-varying communication topology. Moreover, consensus gain functions are designed to ensure the performance of the proposed DED under communication noise. Case studies on a standard IEEE 30-bus system demonstrate the effectiveness of our proposed methodology.

Stealthy attack detection and solution strategy for consensus-based distributed economic dispatch problem

Distributed system is efficient and scalable in modern power grid. However, a distributed system is so susceptible to attack. In this paper, we formulate consensus-based distributed economic problem under attacks, and the convergence of the algorithm under a realizable and general stealthy attack is proved. Then the expression of the convergence point is also provided. Furthermore, a strategy based on a defined observation network is proposed to detect whether the system is attacked by the false data injection to broadcast information. Consequently, the misbehaving agents are detected and removed, and the other agents can reach the optimal point under new optimal objective, the incremental cost and total generation cost can be decreased. The simulation studies not only validate the theoretical results but also show the effectiveness of proposed strategy.

Delay Effects on Consensus-Based Distributed Economic Dispatch Algorithm in Microgrid

For microgrids with connected but sparse communication networks, consensus-based approach can provide a distributed solution to the economic dispatch problem. However, as time delays in communication networks are nonnegligible, performances of consensus-based distributed economic dispatch algorithms are not well disclosed and investigated. Considering the effects of time delays, we first provide a novel consensus-based economic dispatch algorithm. The algorithm is fully distributed such that the optimal dispatch of energy resources in microgrid can be implemented in a distributed manner. The influence of time delays on distributed economic dispatch is strictly analyzed. The maximum allowable delay bounds are derived by applying the generalized Nyquist criterion. Several simulations are presented to verify the effectiveness of the algorithm and the correctness of the theoretical results.

A Distributed Economic Dispatch Algorithm Based on Multi-Agent Consensus Control and Incremental Power Supplying

Abstract In this paper, the economic dispatch problem (EDP) is studied for an energy internet, which is composed of energy routers (ERs) and intelligent microgrids interconnected with the main grid. The intelligent microgrid consists of several distributed generators (DGs), energy storage units, loads and intelligent control units. A distributed economic dispatch algorithm is proposed based on the leader-follower consensus and the average-consensus protocols. The average power mismatch of all buses of the whole microgrid is iteratively estimated by the average-consensus algorithm. After each iteration, the increment of power is adjusted by the energy router. By algebraic graph theory and limit theory, it is proved that if the network topology of the energy internet contains a spanning tree with the energy router as the root node, then the algorithm ensures that the incremental costs (ICs) of all distributed generators tend to the electricity price obtained by the energy router, the balance of energy supply and demand is asymptotically achieved for the whole microgrid system, and the economic dispatch is asymptotically optimal. The simulation results demonstrate the effectiveness of the proposed algorithm.

Hybrid Consensus-based Algorithm for Distributed Economic Dispatch Problem

Economic dispatch is one of the fundamental problems in the power system research. The existing algorithms are either discrete iterative algorithms or continuous-time dynamical algorithms. By virtue of the hybrid techniques, a hybrid consensus-based algorithm is proposed in this paper, which consists of a finite-time continuous-time algorithm and a discrete-time interacted scheme. Moreover, inspired by the cluster synchronization and the benefit of the projection operator, a supervised strategy is carried out to ensure that each generator unit will work within its power generation constraint. For a better understanding of the supervised hybrid distributed algorithm, the detailed pseudo-code is presented. Finally, a numerical example is given to illustrate the effectiveness of the algorithm.

Analysis of Consensus-Based Distributed Economic Dispatch Under Stealthy Attacks

In a smart grid, distributed energy management (DEM) is a promising approach to realize reliable and efficient operation. Since cyberattack is one of the crucial threats faced by smart grid, the investigation of the effect of cyberattacks on DEM is both a theoretical merit and a practical value. This paper considers the typical DEM problem, i.e., distributed economic dispatch (ED) problem, under attacks. Under a well-developed consensus-based ED protocol, we first define the stealthy attack through false data injection for offline and online cases, respectively. The necessary and sufficient conditions are provided to guarantee convergence of the algorithm when the attacker only injects false data into the broadcast information. And the offline stealthy attack can be realized under this kind of attack. Then, we prove that there exists no stealthy attack injecting false data into the broadcast information for the online case. Further, we provide the stealthy attack by merely injecting constant false data into generation cost parameters for the online case. We also prove that for every node, there exists false data injection into generation cost parameters, which reduces the generation efficiency. Simulation studies validate the theoretical results.

Distributed Optimal Active Power Control of Multiple Generation Systems

A novel coordinated power controller design framework is proposed to optimize the active power output of multiple generators in a distributed network. Each bus in the distributed generation systems includes two function modules: a distributed economic dispatch (DED) module and a cooperative control (CC) module. By virtue of the distributed consensus theory, a DED algorithm is proposed and utilized to calculate the optimal active power generation references for each generator. The CC module receives and tracks the active power generation references such that the generation–demand balance is guaranteed at minimum operating cost while satisfying all generation constraints. The distributed control and management strategies enhance the redundancy and the plug-and-play capability in microgrids. Optimal properties and convergence rates of the proposed distributed algorithms are strictly proved. Simulation studies further demonstrate the effectiveness of the proposed approach.