Transient stability simulation of a large-scale and interconnected electric power system involves solving a large set of differential algebraic equations (DAEs) at every simulation time-step. With the ever-growing size and complexity of power grids, dynamic simulation becomes more time-consuming and computationally difficult using conventional sequential simulation techniques. To cope with this challenge, this paper aims to develop a fully distributed approach intended for implementation on High Performance Computer (HPC) clusters. A novel, relaxation-based domain decomposition algorithm known as Parallel-General-Norton with Multiple-port Equivalent (PGNME) is proposed as the core technique of a two-stage decomposition approach to divide the overall dynamic simulation problem into a set of subproblems that can be solved concurrently to exploit parallelism and scalability. While the convergence property has traditionally been a concern for relaxation-based decomposition, an estimation mechanism based on multiple-port network equivalent is adopted as the preconditioner to enhance the convergence of the proposed algorithm. The proposed algorithm is illustrated using rigorous mathematics and validated both in terms of speed-up and capability. Moreover, a complexity analysis is performed to support the observation that PGNME scales well when the size of the subproblems are sufficiently large.
YNAMIC simulation has always been an essential tool to study and evaluate power systems [1], [2]. As design, planning, analysis and operation of a large and complex interconnected power system would inevitably involve the evaluation, understanding and prediction of the dynamic behaviors of the system under a wide range of scenarios, computational simulation provides an effective and essential tool to facilitate this requirement throughout the whole design process.
One of the major challenges for power system dynamic simulation is on the scale and complexity of the current and future power grid. As the backbone of the power system, electric grids all over the world are undergoing fundamental revolutions. Take the US power grid for example, according to the U.S. Department of Energy, a national electricity backbone will be built to link the east and west coasts, as well as Canada and Mexico by year 2030 to give customers “continental” access to energy supplies [3], [4]. As part of this envisioned national grid, according to Oak Ridge National Lab’s estimation, the Eastern Interconnection model (EI) at year 2030 will be expanded to include over 70,000 buses and 8,000 generators, compared with the current EI model which only contains 16,000 buses and 3,000 generators. It is evident that the power system of the future will be a much larger interconnected system on a scale that has never been encountered before. This, combined with the wide deployment of smart-grid technologies, such as mini-and micro-grids and distributed energy technologies, has added significant complexity to the already sophisticated structure of the interconnected power grid. There is a growing realization that contribution from the computer industry will directly affect and influence the shape of the next-generation power grid.
However, as pointed out in [3][4][5], the application of advanced computing techniques in power and energy industry has significantly lagged behind other industries. Legacy codes and algorithms written back in the 80’s based on single-process and serial operation are still dominating in the current power system analysis tools. To fully cope with the scale and complexity of the problem and adequately capture the sophisticated dynamic interactions and interdependencies, new power system simulation techniques need to be developed to accommodate the accelerated growth of the size, complexity and heterogeneity of the problem and provide improved computational efficiency, accuracy, capacity, and scalability. Meeting this challenge requires both the introduction of parallelism in algorithm design and the advanced computing platforms such as High Performance Computing (HPC) cluster [5][6][7].
While the multi-core, parallel computing hardware provide the necessary computational capabilities, parallel processing adds the dimension of concurrency and brings benefits such as speed-up, capability and scalability. To D achieve parallelism, a natural approach to undertake is through Domain Decomposition Methods (DDM) [8]. In the context of power system dynamic simulation, DDM generally refers to a class of techniques that decompose the original problem defined over a domain into smaller “subproblems” on overlapping or non-overlapping subdomains and coordinate the solution among subproblems to yield the equivalent solution of the original problem.
This manuscript proposes a novel relaxation-based decomposition technique named Parallel-General-Norton with Multiple-port Equivalent (PGNME) to facilitate the distributed dynamic simulation and analysis for largescale and very large-scale power systems on HPC platforms. The design algorithm of PGNME can be seen as a combination of two techniques: a Jacobi-like Parallel Updating Relaxation (PUR) process and a novel ME based Spectral Radius Reduction (SRR) technique. While the PUR algorithm is introduced to reconcile the solutions of subproblems until reaching a global convergence, in this paper, we particularly focus on demonstrating that through the analytical modeling of the convergence properties of PUR, an effective and scalable SRR method can be derived as the preconditioning mechanism to tune the configurations of PUR in order to achieve significantly enhanced global convergence. We will start by illustrating the formulation of PGNME method for a general multiplesubgraph, multiple-port system, followed by demonstrating PGNME on an intuitive single-port system containing two-subgraphs and a more complicated example system with 3 subgraphs and a total of 6 ports.
The main contribution of this paper can be summarized as the following aspects:
• System size and degree of parallelism: While previous work [6][7], [9], [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] (please refer to Section 2.1 for a comprehensive literature review) have been successful in achieving parallelism for power system dynamic simulation, they are designed for and validated based on small
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