Admittance Matrix Research Articles

Computing the Network’s Equilibrium Point at the Fault Clearing Instant in Transient Stability Studies

This paper proposes an approach for computing the network’s equilibrium point related to the fault clearing time in transient stability studies. The computation of this point is not a trivial task, particularly when the algebraic network’s equations are expressed in the power balance form. A natural attempt to solve this problem is using Newton’s method. However, convergence issues are found because of the lack of a general strategy for initializing nodal voltages at the clearing time. This problem has not been widely discussed in the existing literature and, therefore, is comprehensively analyzed in this paper. Furthermore, the paper proposes the use of a network’s model based on current injections and an extended admittance matrix to overcome the problem. This model is efficiently solved via the fixed-point iteration method, which involves factorization of the extended admittance matrix into the product of a lower triangular matrix [L] and an upper triangular matrix [U]. This solution executes a just once and only forward–backward substitution during the iterative solution process. Case studies clearly demonstrate the proposal’s effectiveness in computing the equilibrium point in operating conditions where Newton’s method fails to converge.

Graph-GIC: A smart and parallelized geomagnetically induced current modelling algorithm based on graph theory for space weather applications

Geomagnetically Induced Current (GIC) refers to the electromagnetic response of the Earth and its conductive modern infrastructures to space weather and would pose a significant threat to high-voltage power grids designed for the alternative current operation. To assess the impact of space weather on the power grid, one needs to calculate the GIC on a national or continental scale. In this study, we developed a smart and parallelized GIC modelling algorithm, Graph GIC. This algorithm deploys a graph representing a power grid in a single-line diagram, in which substations/transformers act as nodes and transmission lines as edges. With these denotations, a power grid and its electric parameters are mathematically represented with an adjacency matrix and an admittance matrix. We used sparse matrix and parallelisation techniques to expedite the intensive computation in cases of large-scale power grids. The Graph GIC was validated with a benchmark grid, applied to the GIC calculation of the 500 kV power grid of Guangdong, China, and conducted preliminary analysis on the grid’s susceptibility to geomagnetic storms. The Graph GIC algorithm has the advantage of an intuitive and highly scalable graph representation of a power grid at any scale. It achieves high-accuracy calculation and a speedup of about 18 times after parallelisation. This algorithm could be applied to assess the impact of space weather on a power grid up to continental scales and could be incorporated into global space weather modelling frameworks.

On the Solution to Optimal Topology Adjustment in Long-Term Power System Operation with Explicit Short-Circuit Current Limitation Constraints

To restrict the excessive short-circuit current (SCC), this letter proposes an SCC-constrained optimal topology adjustment model considering the N-1 security criterion. Topology adjustment, including transmission switching (TS), bus sectionalization (BS), lines operating out of breaker bay (LOB) and commitment status of units (CU), has nonlinear relationships with SCC and is difficult to express explicitly. In this letter, an explicit formulation of SCC considering topology adjustment is proposed based on the equation of admittance matrix and nodal self-impedance, which is further recast as a mixed-integer linear programming (MILP) model. In addition, the N-1 security criterion is included for avoiding jeopardizing system security by topology adjustment. Numerical case studies validate the effectiveness and advantages of the proposed model in SCC restriction.

Harmonic resonance evaluation and suppression of railway power conditioner-network-train coupling system

The coupling of railway power conditioner (RPC), network, and train will change the impedance characteristics of the existing traction power supply systems, which will lead to the unclear law of high-frequency harmonic resonance. This paper aims to study the resonance mechanism of the RPC-network train coupling system, and then solve the resonance problem of the existing traction power supply system from the perspective of reshaping the high-frequency impedance of the system. Firstly, the RPC-network-train coupling system’s dynamic node admittance matrix is established. After that, a comprehensive resonance evaluation method is proposed to obtain the resonance impact factors (RIFs) of multiple virtual impedances in the control strategy and the filtering parameters, which can realize the comparison and selection of five existing impedance reshaping strategies. To ensure the safe and stable operation of the RPC-network-train coupling system, a multi-objective sorting optimization strategy (MOSOS) considering resonance suppression, harmonics filtering, filter cost, and control system stability is proposed for the RPC based on the RIFs. Finally, the effectiveness of the proposed method is verified by the simulation result in MATLAB/Simulink and the experiment result in the StarSim hardware-in-the-loop (HIL) platform respectively.

Identification of generator coherency in power systems with wind farm

In the context of the "dual carbon" goal, the penetration rate of new energy represented by wind power is gradually increasing. The large-scale grid connection of wind power makes the power system more complex and uncertain. The output of wind farms changes the system flow, indirectly affecting the power angle characteristics of synchronous generators, and thereby changing the coherence between generators. Affects synchronous generator homology identification. This paper proposes a generator homology identification method for power systems containing wind farms, in response to the problem that the existing methods for identifying unit homology have not taken into account the adverse effects of wind farms on identification results. Translate the influence of wind farms on the homology of synchronous generators into the contraction admittance matrix as a static electrical distance indicator; Select dynamic data reflecting the homology of synchronous generators after disturbance, and form four dynamic indicators to measure the power angle increment curve between each generator: Euclidean distance, Chebyshev distance, grey correlation, and correlation coefficient; By using the combination weighting method to determine the weights of each indicator, a comprehensive similarity matrix is formed, and the optimal clustering results are determined using fuzzy system clustering and F-statistical values. Finally, the effectiveness of the proposed method was verified using EPRI-9 node system, EPRI-36 node system, and IEEE68 node system as examples.© 2017 Elsevier Inc. All rights reserved.

A novel design method for wideband bandpass filters with fewer inductors

Inductors that are widely used in wideband filter designs could result in large filter size and high insertion loss. A novel design method using admittance matrix based on direct circuit implementation is introduced for wideband bandpass filters. Firstly, a frequency transformation is performed on cross-couplings to realize the conversion between inductor and capacitor, thereby reducing usage of inductors. Moreover, by virtue of an enhanced resonator (type I), an approach of adding extra transmission zero is proposed to improve the out-of-band rejection without any additional usage of inductors. Thirdly, based on the frequency transformation, another enhanced resonator (type II) is introduced to further improve the frequency characteristics without compromising usage of inductors. Finally, by cascading the enhanced resonators of type I and type II, a novel filter can be constructed. This novel filter is designed and fabricated using a glass-based integrated passive device (IPD) technology. The measurement results are highly consistent with the simulation results. It is shown that the proposed design method can reduce the filter size and thus improve the chip integration. It enriches the freedoms during the filter design.

Admittance stability model and equivalent circuit analysis of three‐phase AC systems in different coordinate systems

AbstractIn recent years, with a large number of distributed energy sources connected to the grid, the distribution network has shown a clear trend towards the use of power electronics. As a power conversion interface, the stability of the converter's interaction with the grid has received considerable attention. Adequate admittance (impedance) modeling of the three‐phase grid‐connected converter is a prerequisite for analyzing the stability and resonance characteristics of the grid‐connected system. Understanding the internal mechanisms and proposing effective solutions are crucial to enable power systems to effectively cope with the impact of power electronics. Therefore, by studying the admittance equivalence relationship and equivalent circuit of three‐phase AC systems in various coordinate systems, this paper focuses on solving the non‐uniqueness problem of impedance admittance modeling of three‐phase converter system. It is proposed that the input admittance of the three‐phase asymmetrical system in the dq and fb rotating coordinate systems is a 2‐order matrix and equivalent. The input admittance of the three‐phase unbalanced system in the αβ and “12” static coordinate systems is a 4‐order matrix and equivalent. From both theoretical analysis and simulation verification, it is shown that the number of eigenvalues of the three‐phase asymmetrical system in the stationary coordinate system is twice that in the rotating coordinate system, and the overall damping of the system is improved. The control strategy based on the stationary coordinate system will make the system more stable. The second contribution of this paper is to establish the equivalent circuit of the three‐phase symmetric converter system by the node admittance matrix and extend it to the multi‐machine system to explain the system instability mechanism by the circuit resonance mechanism. Finally, the frequency coupling phenomenon is studied for the three‐phase asymmetrical converter system, and it is explained that it cannot establish an equivalent circuit similar to the three‐phase symmetrical converter system.

A novel model order reduction technique for solving horizontal refraction equations in the modeling of three-dimensional underwater acoustic propagation

Modeling three-dimensional (3D) underwater acoustic propagation is vital for underwater detection, localization, and navigation. This article introduces a novel model order reduction (MOR) technique to solve horizontal refraction equations (HREs) in the modeling of 3D underwater acoustic propagation. This approach relies on an adiabatic approximation of the 3D sound field, representing the field as a combination of local vertical modes with their modal coefficients governed by a system of two-dimensional (2D) HREs. Inspired by normal mode theory, the coefficients in the expansion over vertical modes are determined by projecting them onto a lower-dimensional, orthogonal space defined by their transverse eigenfunctions. By artificially truncating the horizontal domain in the transverse directions using two perfectly matched layers (PMLs), the eigenproblem associated with the transverse eigenfunctions of the modal coefficients is closed and thus can be solved through a modal projection method. The modal projection method enables fast computation of modal coefficients in a longitudinally invariant environment within seconds, offering a naturally wide-angle solution covering ±90°. The MOR method is extended to encompass fully 3D cases by introducing an admittance matrix, a memory-saving strategy that prevents numerical overflow when the longitudinal range is large. Moreover, the fact that the outer boundaries of the PMLs are range-independent allows the proposed MOR technique to perform well on a coarse grid when employing the Magnus scheme, significantly saving the numerical cost for the fully 3D simulation. Numerical simulations are provided for both longitudinally invariant and fully 3D scenarios, demonstrating the high accuracy and efficiency of the proposed MOR technique in solving HREs.

Research on Multi-type and Multi-level Real-time Simulation and Optimization of New Power System

Abstract Aiming at the problem that the current real-time simulation algorithm is difficult to improve the performance and accuracy of multi-type and multi-level real-time simulation when dealing with new power systems, we propose a new multi-type and multi-level real-time simulation and optimization algorithm for power systems. Firstly, the efficiency and accuracy of the solution are improved by directly updating the conductance nodes (Gnodes) and current nodes (Inodes) on power system components, and the updating of Gnodes and Inodes is replaced by the prior calculation based on the inverse matrix (Ginv) of admittance matrix, thus further optimizing the simulation solution process and reducing the computational complexity. Then, the efficient numerical method, data structure optimization, and parallel computing technology are used to optimize the construction process of the inverse matrix (Ginv) of the admittance matrix to reduce the computational complexity and memory consumption of electromagnetic transient simulation. Finally, the idea of the sparse matrix is introduced to optimize the operation process of Gstruct and improve the calculation speed of the simulation solution. The research proves that the multi-type and multi-level real-time simulation solution and its optimization method of new power systems can be studied more systematically through the above technical route, which can improve the efficiency and accuracy of power system simulation solutions and provide strong support for practical application.

Stability Analysis of Multi-Bus Power Electronics Defined Power Systems Using Phase Information of Nodal Admittance Matrix

Stability Analysis of Multi-Bus Power Electronics Defined Power Systems Using Phase Information of Nodal Admittance Matrix

Enhancing computation performance of rational approximation for frequency-dependent network equivalents with parallelism and complex vector fitting

This work examines two strategies for enhancing the rational approximation of Frequency-Dependent Network Equivalents (FDNE) using an 8-port FDNE featuring a frequency response marked by numerous peaks and valleys. Firstly, we employ Complex Vector Fitting (CVF), an alternative to the Vector Fitting (VF). CVF eliminates the constraint of complex conjugate pairs and was originally conceived for modeling baseband equivalents through scattering parameters. The implications of CVF for admittance (or impedance) matrix synthesis have not yet been previously reported in specialized literature. To enhance code performance and remove dependence on commercial software such as MATLAB®, VF and CVF were implemented in the C-language, utilizing a low-level linear algebra package and exploiting parallelism. We evaluated performance by varying the model order, number of ports, and frequency samples. The results confirm the feasibility of our approach, prompting a more in-depth exploration of the potential benefits regarding FDNE realization.

Admittance matrix estimation of radial distribution grids using power and voltage magnitude measurements

Accurate knowledge of the admittance matrix of distribution grids is essential for grid operation and control as more renewable energy sources and electric vehicles are integrated into distribution grids. Due to limited observability, measurement noise, topology assumptions, and partial data availability, the exact calculation of the admittance matrix of distribution grids is challenging. In this paper, we present a method for estimating the admittance matrix of radial distribution grids. The proposed method uses low-cost measurement devices that record ten-minute-based measurements of voltage magnitudes, active power, and reactive power at a single end of the lines or transformers instead of second-based phasor measurements. The impedance of lines or transformers is then estimated using a statistical optimization subject to the distribution flow (DistFlow) model. The effectiveness of proposed method is demonstrated by simulation, laboratory testing, and field measurements taken from a distribution grid in Switzerland.

A new method for synthesis and designing transmissive linear-to-circular polarization converters based on branch line circuit model

This paper proposes a new design method of a linear-to-circular polarization converter based on the branch line circuit model. The series branches are implemented by dielectric spacers and the shunt branches are implemented by anisotropic admittance sheets. The admittance matrix of the anisotropic admittance sheets is derived by even and odd mode analysis. A unit cell consisting of two metal layers and a dielectric spacer is then designed using an iterative algorithm for operation from 15.5 to 23 GHz. Results indicate that the axial ratio and insertion loss of the designed polarizer are better than 3 and 1.5 dB respectively, for incident angles between ±45°. To validate the simulation results, a waveguide-based test setup is designed and fabricated, with measurement results indicating good agreement with simulations. The proposed method can be potentially applied to design other anisotropic structures such as half-plate polarizers and polarization rotators.

Voltage differences as functions of a matrix eigensystem

We firstly consider an electrical network that consists of multiple subnetworks. We refer to some basic definitions which relate net current flows and voltages, the edges and nodes respectively of each subnetwork, and define matrix G, as the direct sum of the admittance matrices that correspond to each subnetwork. Then, we prove that any voltage difference at two arbitrary nodes can be explicitly written as a function only of the eigensystem of G, namely its eigenvalues and their corresponding eigenvectors. Next, we consider a DC/AC circuit network and by using duality properties of a matrix pencil related to the network, we obtain expressions for voltage differences as functions of the pencil’s eigenvalues and their corresponding eigenvectors. To validate our findings, we present illustrative numerical examples.

SPICE-Compatible Circuit Models of Multiports Described by Scattering Parameters with Arbitrary Reference Impedances

New SPICE-compatible circuit models of a multiport are presented here that are suitable for the frequency-domain and time-domain analyses of hybrid systems containing linear distributed elements and possibly non-linear lumped elements. Distributed elements models are based on scattering parameters with potentially complex reference impedances, which are not necessarily equal for all ports. Both exact and approximated (lumped) models are proposed. The scattering parameters are directly taken as the model element values in the former case. In the latter case, the model element values are equal to the real and imaginary parts of the poles and residues of the rational approximation. The models comprise a multiport (with an admittance matrix numerically equal to the modeled scattering matrix or approximating it) equipped with a pair of coupled impedances at each port. A few examples validate the proposed approach and prove its efficiency in terms of matrix size and analysis time compared to some selected commercial counterparts.

Vibration Characteristic Research of 100 m New Polar Exploration Cruise Based on Finite Element Modeling

Luxury cruise ships are high-end passenger ships with facilities on board for the leisure and entertainment of passengers, so the comfort of luxury cruise ships is a matter of great concern. In this paper, a finite element model of a new polar exploration cruise ship is established, and the wet modes of the whole ship are calculated using the virtual mass method and compared with the principal frequencies of the excitation forces to initially verify the rationality of the design of the structural vibration characteristics of the whole ship. The admittance matrix of the vibration velocity to excitation force was calculated by a frequency response analysis, and the vibration velocities at the stern plate and main engine foundations were tested during sailing. Then, the obtained propeller and main engine excitation forces were loaded into the finite element model; the vibration velocities of each compartment were calculated and compared with the compartment vibration velocity test values. The errors were within the engineering allowable range, verifying the accuracy of the excitation forces. The propeller and main engine excitation forces were loaded separately on the finite element model to calculate the vibration velocity of each cabin, and the contribution of the two excitation sources to the vibration velocity of each cabin was analyzed. It was found that the contribution of the excitation source to the cabin response was related to the relative position between the cabin and the excitation source. When the cabin was located in the cabin adjacent to or directly above a certain excitation source, the contribution of the excitation source to the cabin response was greater. When the cabin was farther away from both excitation sources, the contribution of the propeller excitation was greater. This provides a targeted reference for the preliminary vibration assessment and later vibration control of the new polar expedition cruise ship.

Electro-mechanical admittance matrix for modeling axial polarized cylindrical piezo-electrics

Electro-mechanical admittance matrix for modeling axial polarized cylindrical piezo-electrics

Analysis of Rail Potential and Stray Current with an Unified Chain Model of Dual Traction Power Supply System

In dual traction power supply systems, the overhead catenary system operates in different power supply modes. It passes across the AC section, DC section, and a neutral part, which influences the features and properties of the feedback current and aggregates its effects on stray current and rail potential. This research paper presents an integrated model of an AC and DC traction power system (TPS), along with a unified chain equivalent circuit model, the ground wire through the AC section, and the insulation joints fixed in the AC–DC neutral section under different operating positions. To make a unified impedance and admittance matrix for traction network, a virtual conductor wire has been added in the DC section to make the balance order of the TPS. The influence of reflex system configuration on rail potential, stray current, and distribution of rail potential at AC and DC stations has also been calculated. The simulation results demonstrate that establishing the insulation joints in the AC–DC section and using ground wires in the AC part can significantly decrease the stray current and rail potential.

Lumped‐element equivalent circuit modelling of district heating pipe in electromagnetic transients program

AbstractElectromagnetic transients program (EMTP) is widely used to analyze transients in power systems. With the increased interest in integrated energy systems (IESs), it would be beneficial to extend the application of EMTP to multi‐physics transients in integrated electrical and heating networks. In this paper, an accurate and efficient lumped‐element circuit model of the heating district pipe is developed in EMTP. The pipe is split into segments using spatial discretization. The application of the numerical discretization to the energy conservation equation gives the discretized pipe equation which is expressed in the form of a companion model of EMTP. In order to reduce the computational effort, the time‐varying terms in the admittance matrix of the companion model of pipe are eliminated. The modification of the admittance matrix is avoided. Furthermore, the internal nodes resulting from spatial discretization are eliminated, resulting in a lumped‐element circuit model with only two external nodes. Case studies are carried out to validate the proposed model in terms of accuracy and efficiency. The 2‐norm error of the proposed model is 0.0153%. With a pipe length of 100 m, the computational speed of the proposed model is increased by a factor of 2.94 compared with the existing distributed‐element circuit model. The implementation of the proposed pipe model in the EMTP‐type simulator enables the analysis of multi‐physics transients in a multi‐carrier energy system.

Static model of DFIG wind farms considering control strategies

The static equivalent models of DFIG grid-connected currents vary under different control strategies. Traditional static equivalent algorithms fail to consider these differences, posing risks in static security analysis. In this study, based on the internal structure of DFIG, grid-connected current models for DFIG under different control strategies are established. The appropriate model is selected during the current calculation process based on the coupling relationship between active power (P) and reactive power (Q) of DFIG. Subsequently, generator nodes to be retained are selected according to the reactive power sensitivity of external network generators based on the internal network, and the node admittance matrix is modified to perform static equivalence. Results show that the proposed model in this study has higher accuracy compared to the traditional Ward equivalent model.