Dynamic simulation of large-scale power systems using a parallel schur-complement-based decomposition method

Power system dynamic simulations are crucial for the operation of electric power systems as they provide important information on the dynamic evolution of the system after an occurring disturbance. This paper proposes a robust, accurate and efficient parallel algorithm based on the Schur complement domain decomposition method. The algorithm provides numerical and computational acceleration of the procedure. Based on the shared-memory parallel programming model, a parallel implementation of the proposed algorithm is presented. The implementation is general, portable and scalable on inexpensive, shared-memory, multi-core machines. Two realistic test systems, a medium-scale and a large-scale, are used for performance evaluation of the proposed method

An efficient null space inexact Newton method for hydraulic simulation of water distribution networks

Null space Newton algorithms are efficient in solving the nonlinear equations arising in hydraulic analysis of water distribution networks. In this article, we propose and evaluate an inexact Newton method that relies on partial updates of the network pipes' frictional headloss computations to solve the linear systems more efficiently and with numerical reliability. The update set parameters are studied to propose appropriate values. Different null space basis generation schemes are analysed to choose methods for sparse and well-conditioned null space bases resulting in a smaller update set. The Newton steps are computed in the null space by solving sparse, symmetric positive definite systems with sparse Cholesky factorizations. By using the constant structure of the null space system matrices, a single symbolic factorization in the Cholesky decomposition is used multiple times, reducing the computational cost of linear solves. The algorithms and analyses are validated using medium to large-scale water network models.Comment: 15 pages, 9 figures, Preprint extension of Abraham and Stoianov, 2015 (https://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001089), September 2015. Includes extended exposition, additional case studies and new simulations and analysi

Accelerating the computation of critical eigenvalues with parallel computing techniques

Eigenanalysis of power systems is frequently used to study the effect and tune the response of existing controllers, or to guide the design of new controllers. However, recent developments in the area lead to the necessity of studying larger power system models, resulting from the interconnection of transmission networks or the joint consideration of transmission and distribution networks. Moreover, these models include new types of controls, mainly based on power electronic interfaces, which are expected to provide significant support in the future. The consequence is that the size and complexity of these models challenge the computational efficiency of existing eigenanalysis methods. In this paper, a procedure is proposed that uses domain decomposition and parallel computing methods, to accelerate the computation of eigenvalues in a selected region of the complex plane with iterative eigenanalysis methods. The proposed algorithm is validated on a small transmission system and its performance is assessed on a large-scale, combined transmission and distribution system

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

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

Parallel scalability study of three dimensional additive Schwarz preconditioners in non-overlapping domain decomposition

In this paper we study the parallel scalability of variants of additive Schwarz preconditioners for three dimensional non-overlapping domain decomposition methods. To alleviate the computational cost, both in terms of memory and floating-point complexity, we investigate variants based on a sparse approximation or on mixed 32- and 64-bit calculation. The robustness of the preconditioners is illustrated on a set of linear systems arising from the finite element discretization of elliptic PDEs through extensive parallel experiments on up to 1000 processors. Their efficiency from a numerical and parallel performance view point are studied

Partitioning, Ordering, and Load Balancing in a Hierarchically Parallel Hybrid Linear Solver

Institut National Polytechnique de Toulouse, RT-APO-12-2PDSLin is a general-purpose algebraic parallel hybrid (direct/iterative) linear solver based on the Schur complement method. The most challenging step of the solver is the computation of a preconditioner based on an approximate global Schur complement. We investigate two combinatorial problems to enhance PDSLin's performance at this step. The first is a multi-constraint partitioning problem to balance the workload while computing the preconditioner in parallel. For this, we describe and evaluate a number of graph and hypergraph partitioning algorithms to satisfy our particular objective and constraints. The second problem is to reorder the sparse right-hand side vectors to improve the data access locality during the parallel solution of a sparse triangular system with multiple right-hand sides. This is to speed up the process of eliminating the unknowns associated with the interface. We study two reordering techniques: one based on a postordering of the elimination tree and the other based on a hypergraph partitioning. To demonstrate the effect of these techniques on the performance of PDSLin, we present the numerical results of solving large-scale linear systems arising from two applications of our interest: numerical simulations of modeling accelerator cavities and of modeling fusion devices