Research On Distributed Optimal Dispatch Methods For Multi-area Power Systems With Continuous/discrete Controls

Due to the rapid development of the national economy,and the reverse distribution of electricity generation resources and electricity demands,large-sacle multi-area interconnected power grids,such as China Southern Power Grid and East China power grid,have become an inevitable pattern.As the scale of power grids continues to expand,the traditional centralized optimized dispatching for the whole grid will face the following challenges: the storing of massive amounts of data,large-scale data exchange,real-time information transfer,and super large-scale computing requirements,etc.Additionally,the centralized optimized dispatching cannot satisfy the requirements of independent operation for different areas and the confidentiality of data.According to the existing scheduling management mode,the optimal dispatch problems(e.g.,economic dispatch,optimal power flow,and reactive power optimization)for multi-area interconnected power systems are essentially a joint optimal scheduling problem for multiple control centers,which can be solved effectively in a decomposition and coordination mode(i.e.,distributed manner).Thus,it is of great significance to study the mathematical theory and effective algorithm on distributed optimal dispatching of multi-area interconnected power systems for multiple control centers.This paper focuses on distributed optimal dispatch methods for multi-area power systems with continuous/discrete control.The main research contents and results can be summarized as follows:First of all,a synchronous coordination power dispatch model between the regional and provincial grids for the AC-DC interconnected power system is eatablished,which contains the global equality and inequality constrains,and considers the active power losses of transmission lines.According to the characteristic of layering and zoning in dispatch of the AC-DC interconnected power system,a hierarchical coordination optimization framework is formed.To achieve the daily coordination between AC-DC tie-line schedules and provincial generation schedules,this paper proposes a distributed interior point method(DIPM)with the coordinator.In each iteration of the interior point method,the linear correction equations are converted into a quadratic programming problem,which is then solved in a decentralized manner using a two-stage optimization method.The DIPM is proved to be equivalent with the centralized interior point method(CIPM),and the convergence property of DIPM is analyzed.The modified 2-area IEEE 39-bus and real 4-area 6056-bus AC-DC interconnected systems are tested to verify that the proposed method can obtain the synchronously coordinated tie-line and generation scheduling.Next,in the absence of the upper control center,a decentralized optimal power flow model for multi-area interconnected power systems is established.To achieve the fully decentralized solutions of the multi-area optimal power flow problem,based on a unidirectional ring communication network,this paper attempts to cast DIPM and further proposes a fully distributed interior point method(F-DIPM)without the coordinator.In each iteration of the interior point method,solving the regional correction equation is converted into solving a quadratic programming problem,and then each area transmits the quadratic function of boundary variables' increments to the communication network for information sharing among areas.The F-DIPM and the CIPM are demonstrated to be equivalent.Results on 3-bus test system,4 IEEE test systems,and real 4-area 6056-bus interconnected system show that the proposed algorithm not only inherits the quadratic convergence of the CIPM in solving the nonconvex optimization problem,but also has robustness to network partitions.Then,considering a point to point communication mode,a decentralized reactive power optimization(RPO)model for multi-area interconnected power systems is established.Since a decentralized algorithm based on point to point communication—alternating direction method of multipliers(ADMM)usually can guarantee its convergence and the optimality of the convergent solution only when solving convex optimization.Therefore,this paper attempts to embed ADMM into the CIPM as a solver of the correction equation,and proposes a fully distributed interior point method(denoted as IPM-ADMM).The exchange of information among adjacent regions is required.During Newton-Raphson iterations,ADMM is employed to solve the quadratic programming problem,which is equivalent to the correction equation.The convexity of the quadratic programming problem can guarantee the convergence of the ADMM algorithm.In the case of the existence of discrete variables,the ADMM can still be used to solve the correction equation of the CIPM incorporating quadratic penalty functions during each iteration.Five modified IEEE systems and real 739-bus system are tested to verify the correctness and effectiveness of the proposed method.Finally,based on the Ward equivalence,a multi-area RPO model with Ward equivalent parameters is established,in which the load tap changing transformer branch is modeled as an equivalent power injection circuit in order to avoid repetitive updates of the equivalent admittance matrix.In order to ensure the accurate updating of the Ward equivalent parameters during iterations,it is necessary to introduce the boundary voltage coupling consensus constraints in the model,which are favor to remain the equivalence between the decentralized RPO model and the original centralized RPO model.Inspired by the idea of fully decentralized ADMM algorithm,a decentralized algorithm(denoted as ADMM-Ward)for multi-area RPO model with the Ward equivalent parameters is proposed.Due to the introduction of the Ward equivalent parameters,for each area,its inner network and its equivalent external network are essentially the simplified network of the entire power system.The integrity of the network in physics is in favor of improving the solvability of the sub-RPO problem of each area,therefore,our proposed ADMM-Ward is expected to offer better convergence compared to previous ADMM approaches.Numerical results for 5 IEEE test systems and a real 739-bus system verify the correctness and effectiveness of the proposed method.