Backward Substitution Research Articles

Power Flow Calculation for Distribution System Including PV Type Distributed Generation

After distribution network with PV type distributed generation, it emerged PV nodes. Advanced forward and backward substitution method is proposed based on ant colony optimization method to improve power flow solution, which is a method based on ant colony optimization calculation algorithm of reactive power correction, improved the model of PV type distributed generation in the power flow calculation.Use PSSSINCAL power system simulation software to set up the model of distribution System including PV type distributed generation. Through the results of simulation calculation show that the algorithm can cope with power flow solution for distribution system including PV type distributed generation effectively, and the convergence property is very good.

Research on the Voltage Influence of Active Distribution Network with Distributed Generation Access

Distributed generation (DG) has an important influence on the voltage of active distribution networks. A unidirectional power distribution network will be transformed into a bidirectional, multiple power supply distribution network after DGs access to the distribution network and the direction of power flow is also changed. Considering the traditional forward and backward substitution algorithm can only deal with the equilibrium node and PQ nodes, so the other types of DGs should be transformed into PQ nodes, then its impact on active distribution network can be analyzed via the forward and backward substitution algorithm. In this paper, the characteristics of active distribution networks are analyzed firstly and a novel approach is proposed to convert PI nodes into PQ nodes. Finally, a novel forward and backward substitution algorithm is adopted to calculate the power flow of the active distribution network with DGs. Extensive validation of IEEE 18 and 33 nodes distribution system indicates that this method is feasible. Numerical results show that when DG is accessed to the appropriate location with proper capacity, it has a significant capability to support the voltages level of distribution system.

A Sequential Numbering Power Flow Calculation Method for Distribution Network

As distribution network is of radial pattern, the forward and backward substitution algorithm and its variations are widely used for radial distribution network power flow calculation, which needs to form associated admittance matrix and matrix operations. This paper proposes a sequential numbering power flow calculation algorithm for distribution network. Based on the graph theory of nodes, the proposed method can handles multiple branches radiation network.. In the simulation test, our proposed algorithm is applied to a typical radial distribution network in order to verify the efficacy on power flow calculation. The results show that the sequential numbering power flow algorithm has good performance in terms of convergence rate and reliability.

Power Flow Calculation of Distribution Network with DG Based on Advanced Forward and Backward Substitution Algorithm

Compared with the traditional power system, there are some differences in the aspect of distribution network structure, line parameters and load parameters in the power system with distributed generations. Therefore, the conventional power flow algorithm can not be applied to this kind of networks. Considering that the distributed generations have special influence on the operation of distributed network, a novel power flow calculation method for this kind of distribution network is studied in this paper. Several equivalent circuit models of distributed generations and the corresponding approaches have been researched. The feasibility of this proposed power flow algorithms can be verified through the program designed in Matlab software.

An Advanced Algorithm of Power Flow Calculation for Radial Distribution Networks

Through the analysis of traditional forward and backward substitution method, put forward an advanced algorithm of power flow calculation applied for the radial distribution network. This method optimizes the numbered embranchments, nodes, branches, uses directly the branch impedance parameter and the given power of the end node to calculate the voltage and power distribution, And use MATLAB to compile power flow calculation program, which is proved to be feasible by an example.

Systolic parallel architecture for brute-force autoregressive signal modeling

The paper describes a parallel architecture in the form of a systolic automaton consisting of three distinct stages for the computation of the model parameters of an autoregressive (AR) signal. The three stages perform auto-correlation, matrix triangularization, and backward substitution; they are designed such that their combination computes the brute-force Wiener-Hopf solution to this minimum-mean-square problem in a completely parallel fashion. The signal values are fed serially into the array of the first stage, and the AR parameters emerge from the array cells of the last stage, one parameter from each. Although the systolic architecture under consideration aims at computing the AR parameters that minimize the mean square error (MSE) rather than the least squares sum, thereby limiting its use to time-invariant environments, it has the potential for improved throughput and reduced latency compared to existing methods.

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Predictive anthropometric measurements for humeral head curvature

Estimation of size, shape, and curvature of the humeral head is important for shoulder replacement procedures and allograft transplantation, especially as we try to recreate normal anatomy. The purpose of this study was to investigate the value of various anthropometric measurements for predicting humeral head curvature. Cadaveric humeri were scanned with a 3-dimensional laser scanner. Length of the humerus, epicondylar breadth, and humeral head curvature were determined using data from the scans. A linear regression was performed for the length of the humerus, epicondylar breadth, gender, age, height, and weight. A stepwise linear regression with forward and backward substitution (α = 0.15) was performed for the most predictive variables from the initial linear regression. An equation for the prediction of humeral head radius of curvature was generated using this data. The most predictive factors (R(2) > 0.5) were epicondylar breadth, height, sex, and humeral length. These 4 factors were included in a forward and backward stepwise regression. The resulting equation had an R(2) value of 0.812. Of the predicted measurements evaluated, patient height, maximum humeral length, epicondylar breadth, and gender were most correlated with humeral head curvature. Including these 4 factors in a linear regression model increased the R(2) value to 0.812. If only a single measurement can be used to size the humeral head curvature, patient height will give the same accuracy as epicondylar breadth and can more easily be obtained. A patient's height can help accurately predict the patient's humeral head anatomy.

Giant cell tumor of the temporal bone—An unusual presentation

Estimation of size, shape, and curvature of the humeral head is important for shoulder replacement procedures and allograft transplantation, especially as we try to recreate normal anatomy. The purpose of this study was to investigate the value of various anthropometric measurements for predicting humeral head curvature.Cadaveric humeri were scanned with a 3-dimensional laser scanner. Length of the humerus, epicondylar breadth, and humeral head curvature were determined using data from the scans. A linear regression was performed for the length of the humerus, epicondylar breadth, gender, age, height, and weight. A stepwise linear regression with forward and backward substitution (α = 0.15) was performed for the most predictive variables from the initial linear regression. An equation for the prediction of humeral head radius of curvature was generated using this data.The most predictive factors (R2 > 0.5) were epicondylar breadth, height, sex, and humeral length. These 4 factors were included in a forward and backward stepwise regression. The resulting equation had an R2 value of 0.812.Of the predicted measurements evaluated, patient height, maximum humeral length, epicondylar breadth, and gender were most correlated with humeral head curvature. Including these 4 factors in a linear regression model increased the R2 value to 0.812. If only a single measurement can be used to size the humeral head curvature, patient height will give the same accuracy as epicondylar breadth and can more easily be obtained. A patient's height can help accurately predict the patient's humeral head anatomy.

Multi-GPU Implementation of LU Factorization

LU factorization is the most computationally intensive step in solving systems of linear equations. By obtaining first the LU factorization of the coefficient matrix, we then may readily solve the system using backward substitution. The computational cost of LU factorization in terms fioating point operations is cubic. There are various efforts to improve the performance of LU factorization. We propose a multi-core multi-GPU hybrid LU factorization algorithm that leverages the strengths of both multiple CPUs and multiple GPUs. Our algorithm uses some of the CPU cores for panel factorization, and the rest of the CPU cores together with all the available GPUs for trailing submatrix updates. Our algorithm employs both dynamic scheduling and static scheduling. Experiments show that our approach reaches 1134 Gflop/s with 4 Fermi GPU boards when combined with the total of 48 CPU cores from AMD. This is the first time such level of performance have been reported in a shared memory environment. Execution trace shows that our code also achieves good load balance and high system utilization.

Graph Grammar-Based Multi-Frontal Parallel Direct Solver for Two-Dimensional Isogeometric Analysis

This paper introduces the graph grammar based model for developing multi-thread multi-frontal parallel direct solver for two dimensional isogeometric finite element method. Execution of the solver algorithm has been expressed as the sequence of graph grammar productions. At the beginning productions construct the elimination tree with leaves corresponding to finite elements. Following sequence of graph grammar productions generates element frontal matri-ces at leaf nodes, merges matrices at parent nodes and eliminates rows corresponding to fully assembled degrees of freedom. Finally, there are graph grammar productions responsible for root problem solution and recursive backward substitutions. Expressing the solver algorithm by graph grammar productions allows us to explore the concurrency of the algorithm. The graph grammar productions are grouped into sets of independent tasks that can be executed concurrently. The resulting concurrent multi-frontal solver algorithm is implemented and tested on NVIDIA GPU, providing O(NlogN) execution time complexity where N is the number of degrees of freedom. We have confirmed this complexity by solving up to 1 million of degrees of freedom with 448 cores GPU.

Estimation of dynamic panel data models with sample selection

SUMMARYWe propose a new method for estimating dynamic panel data models with selection. The method uses backward substitution for the lagged dependent variable, which leads to an estimating equation that requires correcting for contemporaneous selection only. The estimator is valid under relatively weak assumptions about errors and permits avoiding the weak instruments problem associated with differencing. We also propose a simple test for selection bias that is based on the addition of a selection term to the first‐difference equation and subsequent testing for significance of this term. The methods are applied to estimating dynamic earnings equations for women. Copyright © 2011 John Wiley & Sons, Ltd.

Partial factorization of a dense symmetric indefinite matrix

At the heart of a frontal or multifrontal solver for the solution of sparse symmetric sets of linear equations, there is the need to partially factorize dense matrices (the frontal matrices) and to be able to use their factorizations in subsequent forward and backward substitutions. For a large problem, packing (holding only the lower or upper triangular part) is important to save memory. It has long been recognized that blocking is the key to efficiency and this has become particularly relevant on modern hardware. For stability in the indefinite case, the use of interchanges and 2 × 2 pivots as well as 1 × 1 pivots is equally well established. In this article, the challenge of using these three ideas (packing, blocking, and pivoting) together is addressed to achieve stable factorizations of large real-world symmetric indefinite problems with good execution speed. The ideas are not restricted to frontal and multifrontal solvers and are applicable whenever partial or complete factorizations of dense symmetric indefinite matrices are needed.

Generalized fraction-free LU factorization for singular systems with kernel extraction

Linear systems are usually solved with Gaussian elimination. Especially when multiple right hand sides are involved, an efficient procedure is to provide a factorization of the left hand side. When exact computations are required in an integral domain, complete fraction-free factorization and forward–backward substitutions are useful. This article deals with the case where the left hand side may be singular. In such a case, kernels are required to test a solvability condition and to derive the general form of the solutions. The complete fraction-free algorithms are therefore extended to deal with singular systems and to provide the kernels with exact computations on the same integral domain where the initial data take their entries.

Power Flow Calculation of Distribution Network Considering Distributed Generation Switch-In

Firstly, the present paper makes a brief introduction to types of the distributed power and the processing mode of PV node in the electricity grid; secondly, the forward and backward substitution method to calculate the power flow has been improved and used to analyze some examples; thirdly and most importantly, taking the multi-node distribution network which incorporates distributed generation (DG) as an example, the author analyzes the influences of DG on load flow distribution and network loss in different positions, capacities and power factors.

An integer-arithmetic algorithm for observability analysis of systems with SCADA and PMU measurements

This paper presents an efficient numerical method for observability analysis of systems including both conventional (SCADA) measurements and synchronized phasor (PMU) measurements, using integer preserving Gaussian elimination of integer coefficient matrices. The observable islands are identified in a noniterative manner, by performing backward substitutions on the integer triangular factors of the integer gain matrix. Multiple placement of conventional and phasor measurements for a system that is found to be unobservable is done by a direct method, using the integer triangular factors of a Gram matrix associated with a reduced size Jacobian matrix. Since all computations performed are exact, no round-off error, numerical instability, or zero identification problems occur. The IEEE 14-bus system is used to illustrate the steps of the proposed method. Test results for the IEEE 300-bus and the FRCC 3949-bus systems are provided to demonstrate the features of the proposed algorithms.

A Low-Cost MMSE-SIC Detector for the MIMO System: Algorithm and Hardware Implementation

We consider the minimum mean-squared error with successive interference cancellation (MMSE-SIC) detection of a frame of data in the spatially multiplexed multiple-input–multiple-output (MIMO) system. A complete MMSE-SIC detector needs to compute at both the preprocessing and SIC-detection stages. Since the SIC detection, which can be regarded as a backward substitution, is inevitable, we develop a computationally efficient preprocessing algorithm that relies on the backward substitution. We then propose a low-cost hardware architecture with a commonly shared backward-substitution module to work at both the preprocessing and detection stages. The very-large-scale-integration implementation results of our architecture for the four-by-four MIMO system using the 0.18- <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\mu\hbox{m}$</tex></formula> complementary metal–oxide–semiconductor technology reveal that our architecture requires the fewest 79-K gates, provides the high throughput rate of 416 Mb/s, and works with the smallest preprocessing latency of 64 clock cycles. Our MMSE-SIC detector is a cheap solution for MIMO detection.

Out-of-core multi-frontal solver for multi-physics hp adaptive problems

In this paper we present the out-of-core solver algorithm for three dimensional (3D) multi-physics problems solved by the Finite Element Method (FEM). The solver is able to solve problems where 3D meshes contain finite elements of different kind (tetrahedral, prism and pyramid elements) with the number of equations and polynomial orders of approximation varying locally on finite element edges, faces, and interiors. The solver works at the level of nodes, representing blocks of the global matrix associated with different vertices, edges, faces, and interiors of different elements. The solver minimizes the memory usage by dumping out all local systems from all nodes of the entire elimination tree during the elimination phase. The systems are going to be reutilized later during the backward substitution stage. The solver is tested on a challenging computational problem: acoustics of the human head. The memory usage of the solver is compared against that of the MUMPS solver.

Some results for the fast MMSE-SIC detection in spatially multiplexed MIMO systems

We study the implementation algorithm for the MMSE-SIC detection with optimal detection order in a VBLAST system. We develop the LDLH decomposition based algorithm with backward substitution (LDBABS), which is shown to require as many multiplications as two other most efficient algorithms. We then propose a modified LDBABS algorithm that utilizes the scheme of incomplete LDLH decomposition together with the initial ordering information. The modified LDBABS algorithm is shown to require averagely fewer multiplications than any other implementation algorithm under the independent identically distributed Rayleigh fading channel. It is known that the real-valued MMSE-SIC detector with optimal detection order outperforms its complex-valued counterpart by approximately 1 dB. We finally propose a fast algorithm for the real-valued MMSE-SIC detector with optimal detection order. The number of real-valued multiplications required by this fast algorithm is approximately 1.57 times that required by the complex-valued LDBABS algorithm.

A parallel direct solver for the self-adaptive hp Finite Element Method

In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p -FEM, with finite elements of various sizes and polynomial orders of approximation varying from p = 1 to p = 9 . From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf.