Large Power Grid Networks Research Articles

Modal Decomposition of the Linear Swing Equation in Networks With Symmetries

Symmetries are widespread in physical, technological, biological, and social systems and networks, including power grids. The swing equation is a classic model for the dynamics of powergrid networks. The main goal of this paper is to explain how network symmetries affect the swing equation transient and steady state dynamics. We introduce a modal decomposition that allows us to study transient effects, such as the presence of overshoots in the system response. This modal decomposition provides insight into the peak flows within the network lines and allows a rigorous characterization of the effects of symmetries in the network topology on the dynamics. Our work applies to both cases of homogeneous and heterogeneous parameters. Further, the model is used to show how small perturbations propagate in networks with symmetries. Finally, we present an application of our approach to a large power grid network that displays symmetries.

Power grid simulation applications developed using the GridPACK™ high performance computing framework

The need for accelerating power grid simulation through high performance computing (HPC) has long been recognized, and prior efforts have been devoted to developing one-off parallel computing applications for particular power grid functions. Non-transferable software codes and duplicated implementations in these prior efforts are a major barrier to more widespread HPC adoption in power grid applications. Modern HPC hardware and architecture require significant computing expertise for application development. The GridPACK™ software framework described in this paper provides an HPC-compatible software structure to access modern parallel solvers and HPC-ready modules for common components in power grid simulation applications. GridPACK hides the HPC details and enables power system developers to focus on applications instead of computational details. Several example applications of GridPACK are presented to demonstrate the capabilities of GridPACK and the performance of HPC simulations with large power grid networks. Examples discussed include: a dynamic simulation application capable of running a 17,156-bus Western Electricity Coordinating Council (WECC) system in a computational speed faster than real time (e.g., under 30s for a 30-s simulation), a static contingency analysis application using a task manager, and a dynamic contingency analysis application utilizing two levels of parallelism. These example applications illustrate GridPACK's capabilities to support different types of simulations within a unified framework and to support reuse of transferable software codes across power grid applications. The computational results indicate strong performance improvements for power grid simulations with GridPACK.

Parallel GMRES solver for fast analysis of large linear dynamic systems on GPU platforms

In this paper, we propose an efficient parallel dynamic linear solver, called GPU-GMRES, for transient analysis of large linear dynamic systems such as large power grid networks. The new method is based on the preconditioned generalized minimum residual (GMRES) iterative method implemented on heterogeneous CPU–GPU platforms. The new solver is very robust and can be applied to power grids with different structures as well as for general analysis problems for large linear dynamic systems with asymmetric matrices. The proposed GPU-GMRES solver adopts the very general and robust incomplete LU based preconditioner. We show that by properly selecting the right amount of fill-ins in the incomplete LU factors, a good trade-off between GPU efficiency and convergence rate can be achieved for the best overall performance. Such tunable feature can make this algorithm very adaptive to different problems. GPU-GMRES solver properly partitions the major computing tasks in GMRES solver to minimize the data traffic between CPU and GPUs to enhance performance of the proposed method. Furthermore, we propose a new fast parallel sparse matrix–vector (SpMV) multiplication algorithm to further accelerate the GPU-GMRES solver. The new algorithm, called segSpMV, can enjoy full coalesced memory access compared to existing approaches. To further improve the scalability and efficiency, segSpMV method is further extended to multi-GPU platforms, which leads to more scalable and faster multi-GPU GMRES solver. Experimental results on the set of the published IBM benchmark circuits and mesh-structured power grid networks show that the GPU-GMRES solver can deliver order of magnitudes speedup over the direct LU solver, UMFPACK. The resulting multi-GPU-GMRES can also deliver 3–12×speedup over the CPU implementation of the same GMRES method on transient analysis.

Statistical analysis of large on-chip power grid networks by variational reduction scheme

One of the most critical challenges in today's CMOS VLSI design is the lack of predictability in chip performance at design stage. One of the process variabilities comes from the voltage drop variations in on-chip power distribution networks. In this paper, we present a novel analysis approach for computing voltage drops of large power grid networks under process variations. The new algorithm is very efficient and scalable for huge networks with a large number of variational variables. This approach, called variational extended truncated balanced realization ( varETBR), is based on model order reduction techniques to reduce the circuit matrices before the variational simulation. It performs the parameterized reduction on the original system using variation-bearing subspaces. After the reduction, Monte Carlo based statistical simulation is performed on the reduced system and the statistical responses of the original system are obtained thereafter. varETBR calculates variational response Grammians by Monte Carlo based numerical integration considering both system and input source variations in generating the projection subspace. varETBR is very scalable for the number of variables and flexible for different variational distributions and ranges as demonstrated in experimental results. Experimental results, on a number of IBM benchmark circuits up to 1.6 million nodes, show that the varETBR can be 1900 X faster than the Monte Carlo method and is much more scalable than one of the recently proposed approaches.