Distributed resource allocation algorithm design and its application to economic dispatch in smart grids - Bai, Lu (Nanyang Technological University, 2020)
In nowadays, there is an increasing number of networked systems and the scale of which is becoming larger and larger. To improve the efficacy and safety of the large-scale networked system, distributed methods come to the fore as the time requires. The resource allocation (RA) problem is one of the most important problems in networked systems. It addresses how to economically assign the available resources to a set of users such that the overall objective is optimized. The RA problem has various applications, such as portfolio selection, production planning, queuing control, and economic dispatch (ED) in power systems. As a typical example of RA, ED produces optimal generation references for the distributed energy resources, such that the total generation cost is minimized under the power balance and generation capacity constraints. In this thesis, a basic RA problem with separable convex objective function and equality resource constraint is investigated. We focus on developing initialization-free distributed algorithms to solve the basic RA problem through a multi-agent framework. The algorithms developed mainly have their basis on consensus algorithms in multi-agent systems and gradient descent methods in optimization theory. This thesis starts with the static RA problem where the optimal solution is fixed. Distributed approaches based on consensus protocols and the saddle point dynamics (SPD) are proposed to solve the RA problem under quadratic objective functions. By utilizing Lyapunov stability analysis and singular perturbation analysis, the stability of the proposed algorithms is proven. No global information is needed in the proposed method and the requirement on initial conditions of the variables is mild. The algorithms are then extended to solve a more general RA problem where the objective functions are strictly convex instead of quadratic. Then, the ED problem in smart grids is explored. In addition to solving the basic ED problem, the algorithms are further extended to solve the ED problem with line flow limits. Simulations on the IEEE 9-bus system and the IEEE 118-bus system are conducted to verify the algorithms, demonstration platform based on Matlab GUI is developed to demonstrate the algorithms. Noting that the resources in many problems exhibit time-varying nature, the RA problem with continuously time-varying resources (TVR) is then investigated. Since the resources are time-varying, the optimal solution changes over time. Thus, the algorithm should not only find the optimal solution but also have the ability to track the time-varying optimal solution trajectory. When the local allocation feasibility constraint is not considered and the objective function is quadratic, a distributed algorithm based on sign function and consensus algorithms is proposed. The tracking error is proven to converge to zero in finite time. With the local allocation feasibility constraint, a distributed algorithm based on singular perturbation theory and penalty function is proposed. The tracking error is proven to be uniformly ultimately bounded. The algorithms are applied to the ED problem with continuously time-varying loads. Simulation on the 24-bus system is conducted to illustrate the algorithms. Considering the valve-point effect and multiple fuel options of the generators, the last part of this thesis proposes a distributed algorithm to solve the practical ED problem. The cost functions of the practical ED problem is non-convex and non-smooth. The Gaussian smoothing is used to approximate the non-smooth cost functions. Based on the approximated smoothed cost functions, randomized gradient and consensus algorithms are utilized to develop a distributed algorithm to solve the practical ED problem. To summary, this thesis solves the RA problem in a distributed manner through a multi-agent framework. Two cases where the resources are static and time-varying are investigated, respectively. To demonstrate the practical relevance of our proposed algorithms, the ED problem in smart grids is investigated. Various simulation case studies are conducted to verify the algorithms. In addition, a randomized gradient and consensus based distributed algorithm is developed to solve the practical non-convex ED problem.