As the need for faster power system dynamic simulations increases, it is essential to develop new algorithms that exploit parallel computing to accelerate those simulations. This paper proposes a parallel algorithm based on a two-level, Schur-complement-based, domain decomposition method. The two-level partitioning provides high parallelization potential (coarse- and fine-grained). In addition, due to the Schur-complement approach used to update the sub-domain interface variables, the algorithm exhibits high global convergence rate. Finally, it provides significant numerical and computational acceleration. The algorithm is implemented using the shared-memory parallel programming model, targeting inexpensive multi-core machines. Its performance is reported on a real system as well as on a large test system combining transmission and distribution networks.

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Power System Dynamic Simulations Using a Parallel Two-Level Schur-Complement Decomposition

Dynamic simulation for transient stability assessment is one of the most important, but intensive, computational tasks for power system planning and operation. Several commercial software tools provide functionality for performing multiple dynamic simulations such as those in contingency analysis simultaneously on parallel computers. Nevertheless, a single dynamic simulation is still a time consuming process performed sequentially on one single computing core as the tools were originally designed. Modern high performance computing (HPC) holds the promise to accelerate a single dynamic simulation by parallelizing its kernel algorithms without compromising computational accuracy. Parallelizing a single dynamic simulation is a much more challenging problem than the contingency-type parallel computing. It requires a good match between simulation algorithms and computing hardware. This paper provides guidance for such a match so as to design and implement parallel dynamic simulation to maximize the utilization of computing hardware and the performance of the simulation. The guidance is derived through comparative implementation of four parallel dynamic simulation schemes in two state-of-the-art HPC environments: 1) message passing interface and 2) open multi-processing. The scalability and speedup performance of parallelized dynamic simulation are thoroughly studied to determine the impact of simulation algorithms and computing hardware configurations. Several testing cases are presented to illustrate the derived guidance.

Comparative Implementation of High Performance Computing for Power System Dynamic Simulations

This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, which is a mathematical tool able to obtain power series coefficients by transformation rules instead of calculating high order derivatives and has proved to be effective in solving state variables of nonlinear differential equations in our previous study. This paper further solves non-state variables, e.g., current injections and bus voltages, directly with a realistic DAE model of power grids. These non-state variables, nonlinearly coupled in network equations, are conventionally solved by numerical methods with time-consuming iterations, but their differential transformations are proved to satisfy formally linear equations in this paper. Thus, a non-iterative algorithm is designed to analytically solve all variables of a power system DAE model with ZIP loads. From test results on a Polish 2383-bus system, the proposed method demonstrates fast and reliable time performance compared to traditional numerical approaches including the implicit trapezoidal rule method and a partitioned scheme using the explicit modified Euler method and Newton Raphson method.

Solving Power System Differential Algebraic Equations Using Differential Transformation

In this paper the diakoptics-based branch-tearing method for solving large electric networks, known as the Multi-Area Thevenin Equivalents (MATE), is combined with the alternating method for parallelizing the transient stability simulations of bulk power systems. In the proposed framework, equations associated with dynamic and static devices and passive network are distributed among computing processes. The paper discusses an implementation of the parallel transient stability simulator along with results for two power systems with about 4,000 and 15,000 buses, both based on the Brazilian Interconnected Power System. Performance metrics for assessing the effectiveness of the proposed methodology are also presented and discussed. In order to validate the implementation, the results are also compared with those from an industrial-grade transient stability program, ANATEM developed by CEPEL.

Parallel Transient Stability Simulation Based on Multi-Area Thévenin Equivalents

This paper proposes a novel approach for power system dynamic simulation based on the differential transformation (DT). The DT is introduced to study power systems as high-dimensional nonlinear dynamical systems for the first time, and is able to avoid computations of high-order derivatives with nonlinear differential equations by its transform rules. This paper, first, proposes and proves several new transform rules for generic nonlinear functions that often appear in power system models, and then uses these rules to transform representative power system models such as the synchronous machine model with trigonometric functions and the exciter model with exponential and square root functions. This paper also designs a DT-based simulation scheme that allows significantly prolonged time steps to reduce simulation time compared to a traditional numerical approach. The numerical stability, accuracy, and time performance of the proposed new DT-based simulation approach are compared with widely used numerical methods on the IEEE 39-bus system and Polish 2383-bus system.

Power System Time Domain Simulation Using a Differential Transformation Method

This work presents a parallel transient stability simulation based on waveform relaxation for large-scale power systems. A power system described by large-scale differential-algebraic equations (DAE) is decomposed into several subsystems by a partitioning algorithm based on epsilon decomposition. The method adopts preconditioning and waveform prediction to accelerate convergence of the system. Moreover, a two-stage parallel strategy based on OpenMP further improves parallel efficiency. All subsystems are solved using a very dishonest Newton (VDHN) method combined with an iteration method based on Adomian decomposition independently after the state variables are discretized by implicit-trapezoidal rule. Finally, two large-scale test cases with detailed dynamic models verify the proposed algorithm. The computational results show that the proposed waveform relaxation method achieves high parallel efficiency.

Two-Stage Parallel Waveform Relaxation Method for Large-Scale Power System Transient Stability Simulation

Medical image segmentation is widely used in clinical medicine, and the accuracy of the segmentation algorithm will affect the diagnosis results and treatment plans. However, manual segmentation of medical images requires extensive experience and knowledge, and it is both time-consuming and labor-intensive. To overcome the problems above, we propose a novel interval iterative multi-thresholding segmentation algorithm based on hybrid spatial filter and region growing for medical brain MR images. First, a hybrid spatial filter is designed to perform on the original image, which can make full use of the spatial information while denoising. Second, the interval iterative Otsu method based on region growing is proposed to segment the original image and its filtering layer. The initial thresholds can be quickly obtained by region growing algorithm, which can reduce the time complexity. The interval iterative algorithm is used to optimize the thresholds. Finally, a weighted strategy is used to refine the segmentation results. The segmentation results of our proposed algorithm outperform other comparison algorithms in both subjective and objective evaluations. Subjectively, the obtained segmentation results have clear edges, complete and consistent regions. We use the uniformity measure (U) for objective evaluation, and the U value is significantly higher than other comparison algorithms. The proposed algorithm achieved an average U value of 0.9854 across all test images. The proposed algorithm can segment medical images well and expand the doctor’s ability to utilize medical images.

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Yunfei Liu

Papers

Two-Stage Parallel Waveform Relaxation Method for Large-Scale Power System Transient Stability Simulation

A Novel Interval Iterative Multi-Thresholding Algorithm Based on Hybrid Spatial Filter and Region Growing for Medical Brain MR Images