Nodal Admittance Matrix Research Articles

The Formulation of a Power Flow Using $d\text{--}q$ Reference Frame Components—Part II: Unbalanced $3\phi$ Systems

This paper presents the formulation and testing of the extended $d\text{--}q$ -axis power flow (DQPF) method to analyze power systems that have buses with unbalanced $3\phi$ voltages. The extended DQPF method is based on converting a $3\phi$ system into three networks, which are defined using the $d$ -axis, $q$ -axis, and 0-axis voltage and current components. Each of the three networks is modeled by nodal equations, where the nodal voltages and admittance matrix determine the currents flowing in that network. Moreover, the apparent power mismatches are used (instead of active and reactive power mismatches) in order to reduce computational requirements. This approach offers an accurate representation of buses with unbalanced $3\phi$ voltages resulting from load unbalances or asymmetrical impedances of $3\phi$ transmission lines. The extended DQPF method is implemented for performance testing on different power systems that have buses with unbalanced $3\phi$ voltages. Performance results show good accuracy, fast convergence, and minor sensitivity to the source of voltage unbalance. In addition, performance results reveal that the extended DQPF requires less iterations and lower memory requirements to obtain power flow solutions than other methods.

Modelling, analysis and virtual parallel resistor damping control of VSC‐based DC grid using master–slave control mode

This study presents a generic linearised modelling method and a virtual parallel resistor damping control for a voltage source converter-based high-voltage direct current (HVDC) system including a direct current (DC) grid. The generic modelling method is composed of DC network's equivalent node-admittance matrix and the Thevenin equivalent matrix of all converters. A simplified two-terminal HVDC system is used to identify the key factors influencing the stability of the DC grid easily. Those key factors are proved by two methods, namely, root locus and participation factors analysis. The parameters of the virtual parallel resistor damping control are designed using the simplified HVDC system. The performance of the proposed damping control is studied employing the linearised model of the DC grid. Time simulations such as instability suppressing, power-controlled station N − 1 fault, and DC system faults are carried out to validate the effectiveness of the damping control.

On the Properties of the Compound Nodal Admittance Matrix of Polyphase Power Systems

Most techniques for power system analysis model the grid by exact electrical circuits. For instance, in power flow study, state estimation, and voltage stability assessment, the use of admittance parameters (i.e., the nodal admittance matrix) and hybrid parameters is common. Moreover, network reduction techniques (e.g., Kron reduction) are often applied to decrease the size of large grid models (i.e., with hundreds or thousands of state variables), thereby alleviating the computational burden. However, researchers normally disregard the fact that the applicability of these methods is not generally guaranteed. In reality, the nodal admittance must satisfy certain properties in order for hybrid parameters to exist and Kron reduction to be feasible. Recently, this problem was solved for the particular cases of monophase and balanced triphase grids. This paper investigates the general case of unbalanced polyphase grids. Firstly, conditions determining the rank of the so-called compound nodal admittance matrix and its diagonal subblocks are deduced from the characteristics of the electrical components and the network graph. Secondly, the implications of these findings concerning the feasibility of Kron reduction and the existence of hybrid parameters are discussed. In this regard, this paper provides a rigorous theoretical foundation for various applications in power system analysis

On the Properties of the Power Systems Nodal Admittance Matrix

This letter provides conditions determining the rank of the nodal admittance matrix, and arbitrary block partitions of it, for connected AC power networks with complex admittances. Furthermore, some implications of these properties concerning Kron Reduction and Hybrid Network Parameters are outlined.

Application of the Sherman–Morrison formula to short-circuit analysis of transmission networks with phase-shifting transformers

For transmission network with in-phase transformers only, the nodal admittance matrix is symmetric. For such networks the short-circuit calculations can be done using sparsity-oriented factorisation of large complex symmetric matrices. In some transmission networks the phase-shifting transformers are used in order to control the real power flows. The series branch of the π-port network modelling such transformer has directional property. When such anisotropic branches are included in the network model the admittance matrix becomes asymmetric. Typically the number of phase-shifting transformers installed in transmission network is very small when compared to the whole number of transformers. It means that very few asymmetric element of the matrix imposes a larger computational effort especially for factorisation, which is the most time consuming and memory using process. In this article it is shown that (in spite of the asymmetric elements) the short-circuit calculations can be done by factorisation performed by procedure applicable to symmetric matrices. A new calculation method is proposed where the admittance model of the phase-shifting transformer is divided into the isotropic π-port network and a series anisotropic branch. The network admittance matrix is formed only from the isotropic branches and is factorised by procedure for symmetric matrices. The anisotropic branches are taken into account by modification of the impedance matrix elements using the formulas derived in this paper on the basis of the Sherman–Morrison formula. Proposed method can be easily implemented in already existing computer programs originally developed for transmission networks without the phase-shifting transformers.

A full frequency dependent line model based on folded line equivalencing and latency exploitation

This work proposes to improve the numerical performance in the rational modeling of full frequency dependent transmission lines. In this paper, latency is used to improve the numerical efficiency of time-domain implementation of the pole-residue representation of the nodal admittance matrix in the case of frequency dependent network equivalents. The idea of latency is to use different time-steps for distinct poles, i.e., fast poles are solved using a small time-step while slower poles may be solved using larger time-steps. For the separation of the slow and fast dynamics, a technique named Multiple Companion Networks (MCN) has been developed. The technique has been applied to transient tests of a transmission line modeled with a rational model. The results obtained indicated that a gain in numerical efficiency is possible without compromising accuracy.

Active filter synthesis based on nodal admittance matrix expansion

Active network synthesis is important for circuit designer to find new circuits with desired performance. In this paper, a method of Tow-Thomas (TT) Bi-quad band-pass filter circuit generation methods is proposed using nullor representation of the operational amplifier (OPA), and a method for synthesizing active band-stop filters is presented, both of which start from voltage transfer function and linked infinity variables to describe nullors in both nodal admittance matrix (NAM) and port admittance matrix of the circuit to be synthesized. The Tow-Thomas band-stop filter circuit and Åkerberg-Mossberg band-stop filter circuit are synthesized by nodal admittance matrix expansion on the same port admittance matrix.

Systematic Synthesis of High-Q T–T Filters Employing CCCIIs

This paper initially presents a modified T–T filter with high [Formula: see text] and derives two nodal admittance matrix (NAM) of the filter. Next, in accordance with the nullor-mirror models of the CCCII, 32 different forms of the Tow–Thomas (T–T) filter using various types of the CCCII are synthesized by bracket notation method. One of the synthesized circuits is analyzed to support the generation method.

Stability Analysis and Stability Enhancement Based on Virtual Harmonic Resistance for Meshed DC Distributed Power Systems with Constant Power Loads

This paper addresses the stability issue of the meshed DC distributed power systems (DPS) with constant power loads (CPLs) and proposes a stability enhancement method based on virtual harmonic resistance. In previous researches, the network dynamics of the meshed DC DPS are often ignored, which affects the derivation of the equivalent system impendence. In addition, few of them have considered the meshed DC DPS including multiple sources with voltage-controlled converters and CPLs. To tackle the aforementioned challenge, this paper mainly makes the following efforts. The component connection method (CCM) is employed and expanded to derive the stability criterion of the meshed DC DPS with CPLs. This stability criterion can be simplified to relate only with the network node admittance matrix, the output impendences of the sources, and the input admittances of the CPLs. A virtual harmonic resistance through the second-order generalized integrator (SOGI) is added in the source with the voltage-controlled converter to lower the peak of the source output impendence, which can enhance the stability of the meshed DC DPS. The effectiveness of the proposed stability criterion and stability enhancement method are verified by nonlinear dynamic simulations.

Systematic synthesis approach for floating gyrators employing single z ‐copy CCCCTA

A systematic synthesis approach for floating gyrators employing single z-copy current-controlled current conveyor trans-conductance amplifier (CCCCTA) is presented in this work. Initially, the pathological models of two types of the CCCCTA, namely z-copy z +-output CCCCTA (CCCCTA+) and z-copy z −-output CCCCTA (z-copy CCCCTA−), are derived by virtue of the nodal admittance matrix (NAM) expansion method. Moreover, these models are then used in the synthesis of floating gyrator using single z-copy CCCCTA. Two floating gyrators are acquired by expanding the NAM of floating gyrator. The synthesised gyrators employ one z-copy CCCCTA and a grounded admittance. Adjusting bias currents of the CCCCTA can tune the parameter of the gyrators. The hand analysis and PSPICE simulation show that the used synthesis method is simple, systematic and valid.

Smart-Grid Topology Identification Using Sparse Recovery

Smart grid (SG) technology reshapes the traditional power grid into a dynamical network with a layer of information that flows along the energy system. Recorded data from a variety of parameters in SGs can improve the analysis of different supervisory problems, but an important issue is their cost and power efficiency in data analysis procedures. This paper develops an efficient solution for power network topology identification and monitoring activities in SG. The basic idea combines optimization-based sparse-recovery techniques with a graph theory foundation. The power network (PN) is modeled as a large interconnected graph, which can be evaluated with the dc power-flow model. It has been shown that topology identification for such a system can mathematically be reformulated as a sparse-recovery problem (SRP), and the corresponding SRP can efficiently be solved using SRP solvers. In this study, we especially exploit the concentration of nonzero elements in the corresponding sparse vectors around the main diagonal in the nodal admittance or structure matrix of the PN to improve the results. The network models have been generated with the MATPOWER toolbox, and MATLAB-based simulation results have indicated the promising performance of the proposed method for real-time topology identification (TI) in SGs.

Tunable Voltage-Mode Bandpass Biquad Synthesis Using NAM Expansion Method

The synthesis of voltage-mode parameter tunable biquadratic bandpass filters using grounded capacitors is presented. To easily construct high-order filters, the synthesis of voltage-mode cascadable tunable biquadratic bandpass filters is also indicated. The synthesis procedure is based on the nodal admittance matrix (NAM) expansion method using nullor–mirror pathological elements. The synthesis of filters using grounded capacitors is considered since it is helpful for easing the elimination/accommodation of various parasitic effects for monolithic integration. The Q factor of the derived filters can be adjusted without changing the natural frequency, so the high-Q bandpass filters are attainable. The workability of some synthesized circuits is verified by HSPICE simulations.

Systematic synthesis of CCCCTA-based T-T filters using NAM expansion method

ABSTRACTIn the light of nullor-mirror models for current-controlled current conveyor trans-conductance amplifier (CCCCTA), initiating the admittance matrices of the Tow-Thomas (T-T) filter, three different types of the T-T filter are synthesised by means of the nodal admittance matrix (NAM) expansion method. The type A filter, which employ one CCCCTA, one grounded resistor and two grounded capacitors, has eight different forms, the type B filter, which employ one CCCCTA, two grounded capacitors and a second-generation current-controlled conveyor (CCCII) or an second-generation inverting current-controlled conveyor (ICCCII) or an operational trans-conductance amplifier (OTA), has 64 different forms and the type C filter employing one CCCCTA and two grounded capacitors has eight different forms. In all, 80 voltage-mode/current-mode T-T filter circuits are obtained. Because of using canonic number components, the circuits are highly desirable from the viewpoint of IC fabrication and their parameters can be electronically tuned through tuning bias currents of CCCCTAs. The hand analysis and computer simulation results have been provided to support the synthesis method.

Synthesis of Cascadable DDCC-Based Universal Filter Using NAM

A novel systematic approach for synthesizing DDCC-based voltage-mode biquadratic universal filters is proposed. The DDCCs are described by infinity-variables’ models of nullor-mirror elements which can be used in the nodal admittance matrix expansion process. Applying the proposed method, the obtained 12 equivalent filters offer the following features: multi-input and two outputs, realization of all five standard filter functions, namely lowpass, bandpass, highpass, notch and allpass, high-input impedance, employing only grounded capacitors and resistors, orthogonal controllability between pole frequency and quality factor, and cascadable, low active and passive sensitivities. The workability of some synthesized filters is verified by HSPICE simulations to demonstrate the feasibility of the proposed method.

The minimization of voltage sag effect for specially connected transformers with a sensitive load and distributed generation systems

Abstract This paper improves the voltage sag for a distributed generation (DG) system with three-phase to two-phase connected transformers. The proposed connection system is compared with the systems designed by Scott and Le Blanc. A particle swarm optimization method with nonlinear time-varying evolution (PSO-NTVE) is used to determine the design values. This analysis considers sensitive loads and the coordination of over-current relays. The model uses a node admittance matrix for voltage sag calculation, in order to calculate the severity of system sag after single or two-phase faults. The analytical equations are useful in the mathematical optimal planning method. The PSO-NTVE is then used to derive suitable transformer impedances and relay time multiplier parameter values. The search for a global optimal solution for the voltage sag problems involves tests on the Scott and Le Blanc connected transformer power systems, in order to verify the effectiveness of the proposed method. Finally, the results show that the severity of the voltage sag is reduced by tuning the transformer impedances and relay settings.

Identify Resonant Frequencies in AC Distribution Networks – A Numerical Example Part I – Harmonic Nodal Admittance Matrix Method

The subject of the paper is part of the general issue, particularly complex, establishing the means and methods of intervention for maintaining an appropriate quality of power supplied to consumers connected to existing distribution networks, which are subject to more pronounced harmonic pollution. In this context, the analysis in the frequency domain of the normal operating regimes of electrical distribution networks is a mandatory operation, the main instrument being the harmonic impedance seen in the network buses nodes. A typical application of this tool of analysis refers to reactive power compensation in distribution network harmonic polluted, operation that may lead to increased non-sinusoidal regime and consequently to increased negative effects on the operating of installations belonging to the supplier or consumers. Avoidance of harmonic resonances is possible only by knowing the frequency response of the network, more exactly the change of harmonic impedance seen in the network buses. This paper presents, in two parts, the numerical examples carried out on the same area of a real distribution network, two analytical methods: harmonic nodal admittance matrix method, respectively state matrix method. The results are analyzed and compared with the values obtained by the two methods.

Identify Resonant Frequencies in AC Distribution Networks – A Numerical Example Part II – The State Matrix Method

One of the most important issues regarding the operation of electrical distribution networks which is harmonic polluted is to avoid parallel resonance frequencies of relatively high harmonic currents, that are present in the network. For this is absolutely necessary to know the frequency response of the network or its harmonic impedance, more exactly, the frequencies which can produce parallel harmonic resonance. This article is the second part of the paper which presents two methods of calculating the parallel resonance frequencies corresponding to peaks (poles) harmonic impedance seen in the buses: harmonic nodal admittance matrix method (in the first part), respectively that state matrix method (in the second part). The results obtained by the two methods are compared and a qualitative and quantitative analysis is done.

Voltage Sag Planning of a Power System with Specially Connected Transformers Using Hybrid Differential Evolution Considering ITI Curve

This paper outlines the voltage sag planning of a power system with a three-phase to two-phase transformer. We compared systems with V-V and Scott connection schemes using the hybrid differential evolution (HDE) method to determine the design parameters by taking into account the ITI curves and coordination of over-current relays. The proposed model comprises a node admittance matrix for the calculation of voltage sag in order to determine the severity of system sag after single or two-phase faults. These analytical equations are useful in the mathematical determination of optimal design parameters. We also used the proposed method to obtain suitable values for the relay time multiplier and transformer impedance. Experiment results on V-V and Scott power systems demonstrate that the severity of voltage sag can be reduced through the tuning of relay settings and transformer impedance.

High-Q biquadratic notch filter synthesis using nodal admittance matrix expansion

A systematic method for synthesizing voltage-mode high-Q biquadratic notch filters is proposed. The proposed approach is based on the nodal admittance matrix expansion method using nullor-mirror pathological elements. The obtained circuits require no component-matching constraints and present low active and passive sensitivities. The Q factor of the derived filters can be adjusted without changing the pole frequency, so the tunable high-Q notch filters are attainable. The workability of some synthesized filters is verified by HSPICE simulations.

Enhancing the frequency-domain calculation of transients in multiconductor power transmission lines

In this paper numerical improvements are proposed to enhance the accuracy and efficiency of frequency-domain transient transmission line modeling. The adopted procedure is based on a robust eigenvector tracking algorithm and an accurate shape-preserving interpolation routine, formulating the highly resonant nodal admittance matrix from a minimal number of frequency data. The proposed method is integrated with the numerical Laplace transform and its performance is demonstrated in a configuration, consisting of an underground cable and an overhead line. Results are validated with the corresponding obtained from a frequency-domain model with regular sampling, revealing the high accuracy of the proposed formulation. The computational efficiency of the proposed numerical improvements is highlighted by comparisons of the execution times in cases of high sampling rates.