Graph-Based Power Flow Solution Methods for Electric Power Systems

Abstract

For over half a century, Power Flow (PF) and its optimized version, Optimal Power Flow (OPF), has become one of the most important and widely used tools in power system planning, operational planning, and operation/control. The solution to the PF problem is carried out extensively for various power system activities and is essential for both offline applications, such as planning and stability studies and online applications, including security monitoring and contingency analysis, optimal power flow, to name a few. In comparison, OPF seeks to optimize the operation and planning of electric power generation, transmission, and distribution networks subject to various system constraints and control limits. Different PF/OPF techniques have been proposed, each with its own unique formulation, solution methodology, advantages, and drawbacks. Motivated by the growing inclusion of distributed energy resources, such as highly variable renewable generating resources; and further, by the speed and convergence limitations of existing tools, this research focuses on developing simple, accurate, fast; yet, computationally efficient tools for operation and planning of electric power systems. This thesis introduces a radically new generalized direction in power system problem formulations and proposes a novel Graph Theory-based optimization algorithm for solving the PF/OPF problem, that is also suitable for transmission, distribution, and hybrid AC/DC power systems.

To start, a novel algorithm is developed for a power flow solution based on maximumflow formulation, titled “Flow-Augmentation PF.” Modeling of power system components for the proposed network-flow formulation is presented, followed by s-t flow modeling. The proposed method formulates a power flow problem as a network-flow problem and solves it by using a maximum-flow algorithm, inspired by the push-relabel max-flow technique. In contrast to previously established methods in the literature, the proposed methodology relies on transforming the power system configuration and topology into an efficient analytical form (matrices and arrays). The solution methodology of the proposed PF algorithm is discussed in detail. The methodology includes a discussion on the algorithm correctness, termination, and computational complexity. The developed Flow-Augmentation method solves the power flow problem using matrix-vector multiplication in its most abstract form, and further, the developed method is independent of system parameters and network configuration. The proposed algorithm captures the full system model and handles any system configuration without resorting to special treatment. The presented algorithm is computationally efficient and compares favorably with current methods, in terms of execution time and accuracy.

Second, a new generalized PF/OPF framework based on the minimum-cost flow network model is introduced. The proposed formulation seeks to find the network-flow distribution that optimizes a stated objective function, such as generator costs or gas emissions, system losses, or any other indices. The solution of the PF problem is obtained by using a proposed modified version of the minimum-cost flow model, termed MinLoss-Flow PF algorithm. This algorithm builds upon the models developed in the above-mentioned maximum-flow-based method, in terms of system component modeling and graph formulation. The developed MinLoss-Flow PF focuses on finding the minimum system losses that satisfy both the technical and engineering constraints. As such, the generalized mathematical formulation, based on cost flow calculation and its properties, is developed. The MinLoss-Flow PF method is fully discussed and validated against well-known methods used for transmission and distribution systems.

Third, this thesis presents a sequential network-flow graph-based method for a steadystate power flow solution in hybrid AC/DC multi-terminal power systems. The proposed method is a unique and novel one, which differs from other established methods that involve the use of modified versions of classical power flow methods. The proposed method formulates the hybrid AC/DC power flow problem as a maximum network-flow problem and solves it, using a max-flow-based algorithm. The proposed flow-augmentation power flow algorithm solves the AC and DC sides sequentially while employing the detailed converter model, including the converter transformer, filter, and the converter loss parameters for converter power loss calculations. The proposed method is validated using standard hybrid 5-bus and CIGR´E-B4-DC systems.

The performance of the novel graph-based PF/OPF tools is validated using several benchmark networks of different sizes, topologies, and parameters. Many case studies v were conducted and compared with the most commonly used techniques for transmission, distribution, and hybrid AC/DC systems. The proposed algorithm is also validated and compared with the results obtained from two commercial software packages, PSS/E and PSCAD. The proposed formulation is computationally efficient, as it is based on matrixvector multiplication, and is also scalable, considering the formulation works as a graphbased method, which, inherently, allows for parallel computation for added computational speed. This proves to be a strong advantage for the proposed method, as a significant reduction in computational time is observed, as a result. Test results show significant computational gains of about 70% when compared with the Newton-Raphson on the IEEE 118-bus system, and a value less than 50% reduction compared with the Newton-Raphson method applied to hybrid AC/DC system. The results also show that the proposed algorithm takes less than 1.4% of the execution time required by the Backward-Forward-Sweep method on the 69-bus. The developed graph-based PF/OPF algorithms are coded in GNU OCTAVE environment and the simulation results are presented to validate the effectiveness of the proposed techniques.