Consensus-Based Distributed Control for Economic Dispatch Problem with Comprehensive Constraints in a Smart Grid

Over the past few decades, the smart grid technology has been developed rapidly due to its main features of more involvement of customers and abilities to accommodate all renewable energy and distributed storages. More importantly, it offers an improved reliability, power quality and self-healing capability. However, there are many problems and challenges associated the development of smart grid. For example, the economic dispatch problem (EDP) in a smart grid has become more complex and challenging due to special characteristics of smart grid. For example, one of the major characteristics of smart grids is plug-and-play due to its accommodation of distributed energy. Economic dispatch is the short-term determination of the optimal output of a number of electricity generation facilities, to meet the system load, at the lowest possible cost, subject to transmission line loss and generation constraints. In short, EDP is an optimization problem and its aim is to reduce the total operation cost. Various mathematical and optimization methods have been developed to solve EDP in power systems. Most of the conventional methods collect global information and process commands in a centralized controller. In a smart grid, it's expensive and unreliable for these conventional centralized methods to achieve a minimum cost when generating a certain amount of power within certain power constraints. There are several reasons why it's not suitable to use centralized methods for EDP in a smart grid. First of all, the centralized controller requires a high level of connectivity to collect all the information among power generators. A failure or error may impair the effectiveness of the centralized controller. Secondly, the topologies of the smart grid and the communication network are likely to be variable in a smart grid. Therefore, a small change in the smart grid may lead to reconfiguration of the centralized algorithm. Thirdly, the centralized controller is not able to accommodate the plug-and-play characteristic of smart grid. In this work, we propose a distributed controller based on consensus algorithm to solve the EDP in a smart grid. The consensus algorithm is based on graph theory in the area of communication. Compared with the centralized method, the distributed algorithm features advantages of less information requirement, robustness, and scalability. In order to present a more practical scenario of EDP, a quadratic cost function and comprehensive constraints are assumed in the problem definition. It's assumed that the valve point effect of the generation unit is negligible. Different from the centralized approach, the proposed algorithm enables each generator to collect the mismatch between power demand and power generations in a distributed manner. The mismatch power is used as a feedback for each generator to adjust its power generation. In order to implement the consensus algorithm, the incremental cost of each generator is selected as the consensus quantity and will converge to a common value eventually. Simulation results of different case studies are provided to show the effectiveness of the proposed algorithm. Effect of power constraints, communication topology and generator dynamic on the convergence and iteration speed of proposed algorithm is also examined. These case studies are simulated and analyzed in Matlab/Simulink. The convergence speed and total generation cost of proposed algorithm are also compared with the conventional algorithms such as lambda iteration method and particle swarm optimization. The consensus algorithm has a better combined performance of convergence and total generation cost compared to lambda iteration method and particle swarm optimization. In order to validate the consensus algorithm, an IEEE 14 bus system with the proposed algorithm is established in PSCAD/EMTDC and verified by comparing with the analytical results.