Impedance Matrix Research Articles

Expansion planning of joint medium- and low-voltage three-phase distribution networks considering the optimal integration of distributed energy resources

This article proposes a novel hybrid approach based on the three-phase bus impedance matrix to solve the medium and low voltage planning problem of three-phase distribution systems considering the optimal integration of battery energy storage systems (BESSs) and different renewable energy sources (RESs). The mathematical formulation to describe the problem involves a mixed-integer non-linear model that considers the allocation and selection problem of distribution substations and transformers, medium and low voltage branches, RESs, and BESSs. Furthermore, the optimal operation of BESSs, the load balancing among low voltage system phases, the upgrading of existing elements, and the uncertainty of RESs, demands, and energy prices are considered. To solve the investment problem, an Iterated Local Search algorithm with neighborhood structures is applied, which uses the electrical information from the three-phase bus impedance matrix to generate new solutions. In addition, a two-step decomposition stochastic optimal power flow is proposed to solve the operational problem considering the stochastic scenarios. The performance of the new methodology is tested on a real distribution system. The numerical results show that integrating RESs and BESSs in the planning problem minimizes the cost of energy losses by 14.16% and the energy purchased from substations by 18.78%.

Inertial imitation method of MMC with hybrid topology for VSC-HVDC.

A new virtual synchronous generator (VSG) control strategy was researched and proposed for a VSC-HVDC (High Voltage Direct Current Based on Voltage Source Converter) transmission system. It can be applied to half-bridge or full-half-bridge hybrid topology modular multi-level converter (MMC) to improve the stability and reliability of the system. First, it is proposed that the energy stored in the equivalent capacitor of MMC power module was used to imitate the rotor inertial of synchronous generator. It can buffer transient power fluctuations and synchronize autonomously with the grid. Then the impedance characteristics of the proposed control method have been deduced and analyzed. The results show that the VSG control loop mainly improves the low frequency characteristics of the converter. Secondly, the ability to suppress transient fault current is weak. So, a method, that the given values of inner current loop are calculated by grid impedance matrix, was used. A double closed loop control structure composed by a power outer loop based on VSG control and a current inner loop is obtained. The simulation results show that it can effectively improve the current control capability during the transient process for systems with a 1:2 ratio of converter capacity to grid capacity (The grid short-circuit capacity is 60MW and the MMC is 30 MW). Finally, a hybrid MMC simulation model was built based on PSCAD and the steady-state and transient fault ride-through simulations were performed. The power adjustment time of MMC under the proposed VSG control is about 1s, while the adjustment time under the conventional control strategy is greater than 4s.

An Efficient Method of Moments for Thick-Wire Antennas

Detailed formulation of a simple Galerkin method of moments (MoM) is presented. It is based on compact closed-form expressions of mutual impedance among filamentary sinusoidal monopoles. Using piecewise sinusoidal basis functions, the mutual impedance of thick-wire sections can be computed through an azimuthal integration of the mutual impedance between filamentary dipoles. Each element of impedance matrix is calculated through a rapidly convergent single integral only. This is unlike other MoM techniques, where double or triple integrals are needed to evaluate impedance matrix. In our formulation, it has been assumed that the wire current is uniform in azimuth, and changes along the axial direction only. No approximation on the segment length or radius of the thick-wire is made, and hence our formulation remains efficient for arbitrarily long/thick antennas.

Unified Theory of Characteristic Modes—Part I: Fundamentals

A unification of characteristic mode decomposition for all method-of-moment (MoM) formulations of the field integral equations describing free-space scattering is derived. The work is based on an algebraic link between the impedance and transition matrices, the latter of which was used in early definitions of characteristic modes and is uniquely defined for all the scattering scenarios. This also makes it possible to extend the known application domain of characteristic mode decomposition to any other frequency-domain solver capable of generating the transition matrices, such as finite difference or finite element methods. The formulation of characteristic modes using a transition matrix allows for the decomposition of induced currents and scattered fields from arbitrarily shaped objects, providing high numerical dynamics and increased stability, removing the issue of spurious modes, and offering good control of convergence. This first part of a two-part article introduces the entire theory, extensively discusses its properties, and offers its basic numerical validation.

Coupling model for time-domain analysis of nonparallel overhead wires and buried conductors in the presence of lossy ground

Buried conductors crossing paths with overhead transmission lines is a common occurrence. Interference caused by overhead lines has been found capable of affecting the safe, sustainable operation of the buried conductors. Such occurrences introduce an electromagnetic problem of a nonparallel structure with conductors present in both air and ground half-spaces. Electromagnetic transient (EMT) simulations of such structures are vital in predicting the behaviour of modern power networks. This paper develops a novel EMT compatible time-domain model for nonparallel overhead wires and conductors that are buried in a frequency-dependent lossy (finitely-conducting) ground. Analytical expressions are derived for the per-unit-length (PUL) impedance and admittance matrices based on thin-wire electromagnetic scattering theory. The closed-form formulations derived in this work can be easily incorporated in an EMT simulator to calculate the coupling effect between nonparallel overhead lines and buried conductors. The validity of the proposed approach is examined for various values of the ground conductivity, the radius of the buried conductor, the crossing angle, and burial depth of the conductor by comparing with results with those obtained using a full-wave approach. A case study on the induced voltage in buried conductors due to typical lightning transients in overhead lines has also been performed. • A novel closed-form formulation has been obtained for the mutual coupling of a nonparallel overhead and buried conductors. • Results obtained using the proposed model has been compared with those calculated using a commercial full-wave solver. • Case studies on the induced voltage in buried conductors due to typical lightning and switching transients in overhead lines have also been performed. • Results indicate that hazardous voltages might be induced in buried conductors at such occurrences.

Fault Location Method for the Double-circuit Transmission Line Based on Electromagnetic Time Reversal

The current fault location ways for the double-circuit transmission lines on the same tower do not consider the coupling relationship of transmission lines. The fault location accuracy is low in practical application. Therefore, a fault location method for the double-circuit transmission lines on the same tower basing on electromagnetic time reversal is proposed in this paper. The six-sequence component method is used to transform the transmission line’s impedance matrix to eliminate the coupling between the lines of the double-circuit transmission line on the same pole. The positive and negative phase characteristics of the transmission line are analyzed by using the fault section identification function to decide the transmission lines’ fault section. The mirror line is constructed by applying the electromagnetic time reversal to measure the distance of the fault point. The experimental results indicate that the maximum error of fault location is only 0. 01 km for a double-circuit transmission line on the same tower, which has high measurement accuracy and good practicability.

An Efficient Volume Integral Equation Method for Analysis of Boresight Error of a Radome with Minor Ablation

In this paper, an efficient method based on volume integral equation is developed to analyze the effects of ablation of a radome on the boresight error. To avoid recalculating the whole impedance matrix when the permittivity of the radome or the shape of the top portion is slightly changed due to ablation, the radome is divided into unaffected and affected parts and the volume equivalent current instead of the displacement current is used as the unknown. This permits us to reassemble rather than recalculate the impedance matrix when the ablation condition is altered. Moreover, a viable preconditioning technique is introduced and integrated with the multilevel fast multipole algorithm (MLFMA) to cope with the electrically large antenna-radome system (ARS). Simulation results are provided for the boresight error (BSE) and boresight error slope (BSES) of the ARS at some different ablation states. The present approach is considerably faster than using the conventional methods.

Research on same-phase parallel connection technology of submarine cable

Offshore wind power generation has been developed rapidly. In order to improve the efficiency of offshore wind power generation, this paper studies the parallel connection of two same-phase cables of two-circuit of submarine cables. Firstly, the mathematical model of same-phase parallel connection of submarine cables is established, and the cable impedance matrix and the expression of cable current unbalance are obtained. Then, two parallel cable parallel schemes are selected for comparative analysis. The results show that the triangle parallel scheme is more suitable for same-phase parallel connection of submarine cables. In addition, this paper is optimized for the triangle parallel scheme. On this basis, the operation strategy of the cable combined with cable temperature is studied in this paper. Enables cables to carry higher currents and to operate longer overloads. This study is beneficial to provide recommendations for the laying of practical submarine cables.

Equivalent Circuit to Analyze the Transmitting Characteristics of a Cymbal Array.

A cymbal transducer has a simple structure consisting of a piezoceramic disk and metallic caps and has broadband characteristics when built as an array. The finite element method (FEM) is generally used to analyze the characteristics of acoustic transducers. However, the FEM requires a longer analysis time as the model becomes larger, which makes it limited and less efficient for analyzing the cymbal array. In this study, a new equivalent circuit with higher efficiency and accuracy, comparable to that of the FEM, was proposed to analyze the performance of cymbal arrays. The equivalent circuit for the array was constructed by connecting the equivalent circuits of individual cymbal transducers in parallel with a radiation impedance matrix that included both the self- and mutual radiation characteristics of the array. The validity of the new equivalent circuit was verified by measuring the transmitting voltage response of a cymbal array specimen and comparing it with that calculated using the circuit. The comparison confirmed the efficiency of the equivalent circuit in analyzing the characteristics of the cymbal array. The proposed equivalent circuit can facilitate the design of a large array of cymbal transducers.

Comparison of different power flow techniques for power grid vulnerability assessment against symmetrical faults using bus impedance matrix

Due to the widespread proliferation of distributed generation resources and the current market situation, ensuring the security and reliability of power grids against fault events has become a more challenging task. The aim of this paper is to compare different power flow techniques for power grid vulnerability assessment against symmetrical fault incidents using bus impedance matrix. In this study, first, the relationship of the post-fault voltage phasor at each bus with the pre-fault voltage phasors at that bus and the faulted bus, impedance matrix elements, and fault impedance is investigated through power system analysis under pre-fault and post-fault circumstances. Subsequently, the accuracy of different iterative and non-iterative power flow algorithms, i.e. Newton Raphson (NR), Fast Decoupled (FD), and Direct Current (DC) methods, for the power grid vulnerability assessment is compared. To achieve this, the fault analysis at each bus is performed commencing with a very large fault impedance and ending with the fault impedance at which one of the buses reaches the low voltage violation limit. Finally, to appraise the proposed strategy, several simulations have been undertaken on IEEE 14 bus system using MATLAB software. The simulation results indicate that the power grid vulnerability against symmetrical faults is highly influenced by the type of applied power flow technique.

The Applications of the Symmetric Layered Medium Green’s Function in Magnetic Field Integral Equation

A symmetry relation of the integral operators in a layered medium proved by the reciprocal theory can be applied to improve the accuracy of the magnetic-field integral equation (MFIE). Based on the symmetric layered medium Green’s function, the normal vector can be transferred into the inner integral to keep the field integral as the inner integral of the elements in the impedance matrix. When discretized by the divergence-conforming function, this field-extracted scheme shows better performance than the classic expression in accuracy. Meanwhile, this form of expression can be applied in the combined-field integral equation (CFIE). Several numerical results are provided to validate the formulation of the symmetry relations from the layered medium Green’s function to the impedance matrices and to reveal its advantages in enhancing the accuracy of the field-extracted form of MFIE.

Physics-Based Greedy Algorithm for Reliable Fast Frequency Sweep in Electromagnetics via the Reduced-Basis Method

A reliable fast frequency sweep model order reduction (MOR) process is detailed. A reduced-basis approximation is taken into account to accurately and efficiently describe the electromagnetic field in a frequency band of analysis. The reduced-basis space is made up of snapshots of the electric field adaptively chosen on a physics-based greedy algorithm. Following a theoretical analysis starting from time-harmonic Maxwell’s equations, in- band eigenresonances are shown to significantly contribute to the electric field in the band of analysis. An impedance matrix transfer function description of the microwave circuit is used and a pole-residue expansion of this matrix-valued impedance transfer function is detailed. A fundamental physical property is identified, from which a straightforward a posteriori error estimator arises, namely, matrix residues in the pole-residue expansion of the impedance transfer function must be rank-1. This cheap computation is well-suited for fast greedy algorithm strategies in adaptive construction of the reduced-basis approximation. Contrary to what has been previously done, a straightforward physics-based greedy algorithm that does not need to scan the whole frequency band of interest to enrich the reduced-basis approximation is proposed. Finally, actual microwave applications illustrate the capabilities and efficiency of the new physics-based a posteriori error estimator in the proposed methodology.

Fast short-circuit current calculation of unbalanced distribution networks with inverter-interfaced distributed generators

This study proposes an approach for the fast calculation of short-circuit currents in unbalanced distribution networks with inverter-interfaced distributed generators (IIDG). It is capable of estimating the short-circuit current in unbalanced distribution networks with several IIDGs based on the symmetric component without calculating the system bus impedance matrix. Furthermore, the effect of the load on the short-circuit current was considered. Because the IIDG fault characteristic is determined by its fault ride-through control models, the short-circuit current calculation process is formulated as an iterative linear system calculation and can be solved using the simple generalized minimal residual (SGMRES) method. Finally, the analytical results were verified by comparisons with the time-domain simulation results of several test systems in PSCAD.

The vibroacoustic characteristics and regulation rules of Panel–Cavity–Panel System controlled by Piezoelectric Shunt Oscillators with negative capacitors

Piezoelectric Shunt Oscillators (PSOs) are widely used in the passive and semi-active control of the vibration and acoustic radiation of flexible structures, due to PSOs’ high electromechanical coupling coefficients, robustness, effectiveness and adjustability at low frequencies. Panel–Cavity–Panel System (PCPS) is a common type of flexible structures, such as interior panels and windows of automobiles. In this paper, a theoretical model of PCPS controlled by PSOs and its vibration equations are established. The vibroacoustic characteristics of PCPS, including sound absorption coefficient (SAC), energy loss coefficient (ELC) and transmission loss (TL), are calculated using a unified mathematical form based on the vibroacoustic radiation impedance matrix, damping matrix and displacement response of PCPS, while a lumped parameter model of PCPS is derived to simplify the comprehension and extension of PCPS. Then the finite element simulation is used to calculate the vibroacoustic characteristics of the PCPS, which achieves good agreement with theoretical results, while three basic regulation modes are also summarized and verified. The regulation mechanism of PCPS controlled by PSOs is further analyzed by the velocity response of each panel. Finally, experiments of PCPS controlled by PSOs with negative capacitors are conducted in a standing wave tube, at non-eigenfrequencies ranging from 70 Hz to 220 Hz. It is found in experiments that PSOs with negative capacitor can increase the TL of PCPS about 8 dB to 25 dB, which depends on the target frequency. SAC and ELC can also be increased, which means less acoustic energy is reflected and more acoustic energy is dissipated in the shunt circuits.

Risk-Aware Travel Path Planning Algorithm Based on Reinforcement Learning during COVID-19

The outbreak of COVID-19 brought great inconvenience to people’s daily travel. In order to provide people with a path planning scheme that takes into account both safety and travel distance, a risk aversion path planning model in urban traffic scenarios was established through reinforcement learning. We have designed a state and action space of agents in a “point-to-point” way. Moreover, we have extracted the road network model and impedance matrix through SUMO simulation, and have designed a Restricted Reinforcement Learning-Artificial Potential Field (RRL-APF) algorithm, which can optimize the Q-table initialization operation before the agent learning and the action selection strategy during learning. The greedy coefficient is dynamically adjusted through the improved greedy strategy. Finally, according to different scenarios, our algorithm is verified by the road network model and epidemic historical data in the surrounding areas of Xinfadi, Beijing, China, and comparisons are made with common Q-Learning, the Sarsa algorithm and the artificial potential field-based reinforcement learning (RLAFP) algorithm. The results indicate that our algorithm improves convergence speed by 35% on average and the travel distance is reduced by 4.3% on average, while avoiding risk areas, compared with the other three algorithms.

An exact solution for vibration analysis of pipe coupled with conical-ring stiffened cylindrical shells with arbitrary boundary condition

In this paper, an analytical impedance synthesis method (ISM) is proposed to analyze the vibration characteristics of a pipe-hull coupled system, in which the hull of a submarine can be simplified to a combined conical-stiffened cylindrical-hemisphere shell. Wave solution and power series solution are used to describe the displacement of cylindrical and conical shell respectively. Rib stiffened and bulkhead are modeled as annular plate and circular plate. Based on exact general solutions, the impedance matrix of each segment is established separately and assembled in the global coordinate by displacement continuity and force balance boundary conditions. Natural frequency and forced responses are compared with open literature and FEM results to verify the correctness of the method. In the numerical examples, the effects of direction of external force and stiffness of support on the forced vibration characteristics are discussed, which can provide some guides for acoustic design of pipe in submarine.

Influence mechanism of solder aging and thermal network model optimization of multi-chip IGBT modules

With the continuous increase in the scale of new energy grid-connected, high-power converter IGBT modules are widely used in wind, solar, and other new energy power generation systems. The safe and reliable operation of IGBT modules with parallel chips is becoming more and more important. In the multi-chip module, uneven solder aging will increase the thermal resistance of some chips, which will lead to an inaccurate estimation of the junction temperature of the multi-chip IGBT power module. To this end, this paper proposes to use the reconstructed thermal impedance matrix to modify the multi-chip thermal network model and estimate the junction temperature. By analyzing the nonlinear accelerated deterioration law between the aging degree of the solder layer and the self-thermal impedance and coupled thermal impedance of the IGBT module, the influence mechanism of different solder layer aging degrees inside the module on the thermal conduction radius and thermal diffusion angle is clarified. The thermal impedance matrix is reconstructed with the modified thermal diffusion angle, thus realizing the optimization of the thermal network model of the multi-chip IGBT module. The experimental results show that the junction temperature calculation results of the improved multi-chip IGBT module thermal network model are more in line with the finite element simulation than the traditional unimproved method, thus verifying the validity and accuracy of the model, and laying a solid foundation for the large-scale integrated multi-chip thermal analysis. Theoretical basis.

A New Approach for Calculation of Metamaterial Printed Fractal Antenna Using Galerkin’s Method

This work provides a new approach for computing the impedance of a proposed multiband printed fractal antenna for wireless applications. Galerkin’s method is applied to deduce the impedance relationship of the proposed structure and then compute the return loss verses frequency by converting the impedance matrix of the proposed antenna [Z] to the scattering matrix [S]. This model is developed in order to study the impedance of the proposed antenna after adding a metamaterial structure in the antenna substrate. The obtained model is able to determine the resonant frequencies and the return loss of the proposed antenna. The model is also able to define the changes in these values when the dimensions of the proposed structure change. The proposed antenna provides multiband wireless applications in the (1–10) GHz frequency band, and the return loss of the proposed fractal antenna has been improved using negative permittivity and negative permeability metamaterial structure.

Direct Calculation of ZZ Interaction Rates in Multimode Circuit Quantum Electrodynamics

Hamiltonians of the superconducting qubits of Transmon type involve non-zero ZZ-interaction terms due to their finite and small anharmonicities. These terms might lead to the unwanted accumulation of spurious phases during the execution of the two-qubit gates. Exact calculation of the ZZ-interaction rates requires the full diagonalization of the circuit Hamiltonians which very quickly becomes computationally demanding as the number of the modes in the coupler circuit increases. Here we propose a direct analytical method for the accurate estimation of the ZZ-interaction rates between low-anharmonicity qubits in the dispersive limit of the multi-mode circuit-QED. We observe very good agreement between the predictions of our method and the measurement data collected from the multi-qubit devices. Our method being an extension of our previous work in [1] is a new addition to the toolbox of the quantum microwave engineers as it relates the ZZ-interaction rates directly to the entries of the impedance matrix defined between the qubit ports.

Reinforcement Learning of Impedance Policies for Peg-in-Hole Tasks: Role of Asymmetric Matrices

Robotic manipulators are playing an increasing role in a wide range of industries. However, their application to assembly tasks is hampered by the need for precise control over the environment and for task-specific coding. Cartesian impedance control is a well-established method for interacting with the environment and handling uncertainties. With the advance of Reinforcement Learning (RL) it has been suggested to learn the impedance matrices. However, most of the current work is limited to learning diagonal impedance matrices in addition to the trajectory itself. We argue that asymmetric impedance matrices enhance the ability to properly correct reference trajectories generated by a baseline planner, alleviating the need for learning the trajectory. Moreover, a task-specific set of asymmetric impedance matrices can be sufficient for simple tasks, alleviating the need for learning variable impedance control. We learn impedance policies for small (few mm) peg-in-hole using model-free RL, and investigate the advantage of using asymmetric impedance matrices and their space-invariance. Finally, we demonstrate zero-shot policy transfer from the simulation to a real robot, and generalization to new real-world environments, with larger parts and semi-flexible pegs.