Distributed Algorithms For Economic Dispatch Problem In Smart Grids

With the rapid increase in demand for electricity and the development of the innovations of technologies in other areas in recent decades,such as communica-tion network,information processing,power engineering and control technology,renewable energy generation technology,etc.,smart grid is considered to be the development model of the future power system.As the nerve center of the smart grid,energy management can ensure that the power system operates safely,reli-ably and economically,and it has always been an important research topic.The centralized optimization algorithms for energy management of smart grid are not only lacking in robustness,but also limited by computation and communication.As a result,the algorithms are difficult to apply to the smart grid integrated with microgrids and a large number of distributed units.The consensus-based distributed optimization algorithms are supported by consensus theory of multi-agent system,and they can also overcome the shortcomings of the centralized op-timization algorithms.Therefore,the research of the consensus-based distributed algorithms is one of the hot research issues.However,there are some questions that will be studied further:(1)Commu-nication network of the smart grid is assumed as a fixed time-invariant network.The assumption is perfect and is not suitable for the actual situation of the com-munication network of the smart grid.(2)Synchronous communication in all nodes is one of the core requirement of the existing algorithms,which is difficult to implement in the smart grid integrated with a large number of distributed units.(3)The models of the economic dispatch are too simple,and most of them do not include the transmission losses.Based on the recent existing results,the thesis mainly studies the economic dispatch problem in the smart grid,and some new distributed algorithms are provided under the assumption that the commu-nication network of the smart grid is a fixed time-invariant graph or a random time-varying graph.The mainly contributions of the thesis are as follows:1.We study the economic dispatch problem of smart grids under the assumption that the communication network is a fixed time-invariant network,and propose a consensus-based distributed algorithm with multiple time-varying feedbacks.The algorithm takes advantage of the fact that incremental costs need to be equal for all buses at optimal output power values.Thus,the algorithm is designed by selecting the incremental cost of each bus as a consensus variable and assigning the local mismatch between total demand and generation as a feedback consensus variable to meet the demand constraint.Using multi-parameter eigenvalue perturbation theory and graph theory,the convergence of the algorithm is proved.Furthermore,an upper bound of the feedback gains is given theoretically.The simulation results illustrate the effectiveness of the algorithm even though there is a demand change or some generator is damaged.Meanwhile,we analyze the factors that affect the convergence rate of the algorithm,and design a large number of experimental simulations to show that the second largest eigenvalue of the system matrix dominates the convergence rate of the algorithm.2.We study the economic dispatch problem of smart grids under the assump-tion that the communication network is a random time-varying network,and propose an asynchronous gossip-based distributed algorithm.Firstly,the com-munication network with random communication link failures is modeled as a Bernoulli network.Then,considering the facts that asynchronous gossip algo-rithms are well suited for the random time-varying network and do not require the global clock synchronous constraint,we provide the distributed economic dispatch algorithm.It is important to prove the convergence of the algorithm because the algorithm is described as a probabilistic system.Using eigenvalue perturbation theory and graph theory,the algorithm can achieve almost sure consensus.Thus it converges to the optimal solution of the economic dispatch problem with probability one.Finally,some simulation results illustrate the effectiveness and plug-and-play capability of the algorithm.We analyze the factors that affect the convergence rate of the algorithm,and obtain that the second largest eigenvalue of the mean of the system matrix dominates the convergence rate of the algorithm.Furthermore,we run the algorithm on the IEEE 118-Bus system,and it is conservatively estimated that the algorithm can converge within 1 minute.Therefore,the algorithm can meet the require-ment of the actual scheduling time.3.We study the economic dispatch problem of smart grids with transmission loss-es under time-varying communication network,and provide an asynchronous gossip-based distributed algorithm.Based on Kron loss equation,the trans-mission losses are modeled as a quadratic function of output powers of genera-tors.As a result,the model of the economic dispatch with transmission losses is a non-convex optimization.Considering the influence of the constraint of transmission losses on the model,we give a distributed economic dispatch al-gorithm.Some simulations show that the convergence and robustness of the algorithm.Compared with some centralized algorithms,the algorithm can converge to the optimal output of each power generation unit,and achieve the goal of minimizing total power generation cost.Furthermore,we run the al-gorithm on the IEEE 118-Bus system,and it is conservatively estimated that the algorithm can converge within 2 minutes.Therefore,the algorithm can meet the requirement of the actual scheduling time.