Reactance Matrices Research Articles

A method to control distributed energy resources in distribution networks using smart meter data

Voltage regulation has been one of the major challenges for distribution network operators (DNOs) due to the integration of distributed energy resources in the recent years. Control approaches mitigating over-voltage (OV) generally require full network model, which for low-voltage distribution networks (LVDNs), can be inaccessible to DNOs. This paper presents a novel data-driven model-free control framework for improving voltage regulation in 4-wire 3-phase LVDNs. In the proposed approach, first, using smart meter data, the aggregated resistance and reactance matrices of the network are estimated. Then, these matrices serve as an input for the proposed optimal power flow (OPF) method to control the DERs’ active and reactive power outputs. This method also lets the DNO adjust the fairness in prosumers’ generation curtailment. The performance of the proposed approach is evaluated in various case studies conducted on a real-world low-voltage test feeder. The simulation results exhibit significant effectiveness in solving the OV problem associated with DERs. For example, in the studied network, the proposed approach limits the maximum voltage of the network to 1.1 pu, while without having control over the DERs output power, it can even overpass 1.17 pu during the peak generation period. In addition, utilizing DERs’ reactive control capability reduces the amount of active power curtailment, and prosumers are able to collectively inject 5.66% more active power.

A hybrid approach for simulating fluid loading effects on structures using experimental modal analysis and the boundary element method.

Many structural acoustics problems involve a vibrating structure in a heavy fluid. However, obtaining fluid-loaded natural frequencies and damping experimentally can be difficult and expensive. This paper presents a hybrid experimental-numerical approach to determine the heavy-fluid-loaded resonance frequencies and damping of a structure from in-air measurements. The approach combines in-air experimentally obtained mode shapes with simulated in-water acoustic resistance and reactance matrices computed using boundary element (BE) analysis. The procedure relies on accurate estimates of the mass-normalized, in vacuo mode shapes using singular value decomposition and rational fraction polynomial fitting, which are then used as basis modes for the in-water BE analysis. The method is validated on a 4.445 cm (1.75 in.) thick nickel-aluminum-bronze rectangular plate by comparing natural frequencies and damping obtained using the hybrid approach to equivalent data obtained from actual in-water measurements. Good agreement is shown for the fluid-loaded natural frequencies and one-third octave loss factors. Finally, the limitations of the hybrid approach are examined.

A hybrid method for predicting heavy fluid loading of structures

Measuring the resonance frequencies and damping of structures in heavy fluids can be difficult and time consuming. To alleviate this burden, a hybrid approach is proposed by combining in-air experimental modal analysis with a boundary element estimate of the acoustic resistance and reactance matrices. The method was validated on a rectangular metal plate by comparing the natural frequencies estimated using the hybrid method to the natural frequencies measured in water. The modal parameters were first measured in air with the mass-normalized mode shapes estimated using the complex mode indicator function. The modal parameters were then updated using rational polynomials curve fitting. The measured modes were then used as in-vacuo basis functions to compute modal resistance and reactance matrices in water and the fluid-loaded vibration and sound radiation was estimated. The natural frequencies of the plate submerged in water were then measured and compared to the frequencies predicted by the hybrid method showing good agreement.

Effective Collision Strengths for Fine‐Structure Transitions from the 3s23p52PGround State of Chlorine–like Nixii

The R-matrix method is used to compute electron impact collision strengths for transitions in Ni XII from its ground-state fine-structure levels. Sophisticated configuration-interaction wave functions are used to represent the 14 lowest LS target states employed in the R-matrix expansion. By transforming the LS-coupled reactance matrices, and by assuming a Maxwellian velocity distribution for the incident electrons, the effective collision strengths are calculated for the 3s -->23p -->5 -->2P -->o1/2-3s -->23p -->5 -->2P -->o3/2 transition within the ground state and from both these fine-structure levels to the 29 excited levels arising from states obtained from 3s3p6 and 3s23p43d configurations. Effective collision strengths, obtained in the temperature range log Te = 3.2-6.6 (K), are expected to have an accuracy of better than 20%.

Effective collision strengths for fine structure transitions from the ground state to n = 3 levels in Ca XI

The R-matrix method is used to calculate electron impact collision strength in Ca XI from its ground state. Configuration interactions are used to represent the first fifteen LS coupled states which are retained in the R-matrix expansion. Effective collision strengths are calculated for transitions between the fine structure levels of the ground state and those of the excited states by employing a transformation of the LS-coupled reactance matrices, and by assuming a Maxwellian velocity distribution for the incident electrons.

Electron-impact fine-structure transitions in Cu XX from its ground state

The R-matrix method is used to calculate collision strengths for electron-impact excitation of Cu XX from its ground state. Configuration interaction wavefunctions are used to represent the lowest 15 LS coupled states which are retained in the R-matrix expansion. Effective collision strengths are calculated for transitions from the ground state to fine-structure levels of the excited states by employing a transformation of the LS coupled reactance matrices, and by assuming a Maxwellian distribution for the incident electron. This is the first detailed calculation on this ion in which the effects of exchange, channel couplings and short-range correlation effects are taken into account.

Collisonal excitation of Fe X due to electron impact using the R-matrix method

view Abstract Citations (28) References (22) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Collisional Excitation of Fe X due to Electron Impact Using the R-Matrix Method Mohan, M. ; Hibbert, A. ; Kingston, A. E. Abstract The R-matrix method is used to calculate electron impact collision strengths of chlorine-like Fe X for transitions among the 14 lowest LS states, i.e., up to the 3s334(p-3) 3d state. Configuration interaction wave functions are used to represent the target states included in the R-matrix expansion. Effective collision strengths are calculated among the fine structure levels of ground state and from the ground to excited states by employing a transformation of the LS-coupled reactance matrices, and by assuming a Maxwellian velocity distribution for the incident electron. The results are tabulated for electron temperatures in the range log Te = 4.0 to log Te = 6.4 with Te expressed in kelvins. Publication: The Astrophysical Journal Pub Date: October 1994 DOI: 10.1086/174738 Bibcode: 1994ApJ...434..389M Keywords: Atomic Excitations; Electron Scattering; Electron Transitions; Iron; Matrices (Mathematics); Electron Energy; Fine Structure; Velocity Distribution; Wave Functions; Atomic and Molecular Physics; ATOMIC DATA; ATOMIC PROCESSES full text sources ADS |

Complex conjugate pairs in stationary Sturmian eigenstates.

Sturmian eigenstates specified by stationary scattering boundary conditions are particularly useful in contexts such as forming simple separable two nucleon t matrices, and are determined via solution of generalized eigenvalue equation using real and symmetric matrices. In general, the spectrum of such an equation may contain complex eigenvalues. But to each complex eigenvalue there is a corresponding conjugate partner. In studies using realistic nucleon-nucleon potentials, and in certain positive energy intervals, these complex conjugated pairs indeed appear in the Sturmian spectrum. However, as we demonstrate herein, it is possible to recombine the complex conjugate pairs and corresponding states into a new, sign-definite pair of real quantities with which to effect separable expansions of the (real) nucleon-nucleon reactance matrices.

Improved adiabatic calculation of muonic-hydrogen-atom cross sections. II. Hyperfine transitions and elastic scattering in symmetric collisions.

The improved adiabatic representation is used in calculations of elastic and hyperfine-transition cross sections for symmetric collisions of {ital p}{mu}, {ital d}{mu}, and {ital t}{mu} with bare {ital p}, {ital d}, and {ital t} nuclei and with H, D, and T atoms, respectively. The cross sections for {ital d}{mu}+{ital d} and {ital t}{mu}+{ital t} are in excellent agreement with other recent determinations, while those for {ital p}{mu}+{ital p} are about 30% larger at low energies. The electronic screening is calculated nonperturbatively and found to be about 30% smaller in magnitude than the previously calculated value at large internuclear distances, and to deviate considerably from the asymptotic form in the molecular region. The resulting screened elastic cross sections are up to 60% smaller than those obtained using the old screening potential. The reactance matrices, needed for calculations of molecular-target effects, are given in tables.

Improved adiabatic calculation of muonic-hydrogen-atom cross sections. I. Isotopic exchange and elastic scattering in asymmetric collisions.

The improved adiabatic representation is used in calculations of elastic and isotopic-exchange cross sections for asymmetric collisions of {ital p}{mu}, {ital d}{mu}, and {ital t}{mu} with bare {ital p}, {ital d}, and {ital t} nuclei and with H, D, and T atoms. This formulation dissociates properly, correcting a well-known deficiency of the standard adiabatic method for muonic-atom collisions, and includes some effects at zeroth order that are normally considered nonadiabatic. The electronic screening is calculated directly and precisely within the improved adiabatic description; it is found to be about 30% smaller in magnitude than the previously used value at large internuclear distances and to deviate considerably from the asymptotic form at small distances. The reactance matrices, needed for calculations of molecular-target effects, are given in tables.

Electron impact excitation of the 3s23p4 levels of Ar III

The authors have calculated collision strengths for electron excitation of the 3s23p4 3Pe0.1,2, 1De2 and 1Se0 levels of Ar III using the R-matrix method. They included the five states 3s23p4 3Pe, 1De, 1Se and 3s3p53P0, 1P0, which they represented by configuration interaction wavefunctions. These wavefunctions yield oscillator strengths for allowed transitions between the levels which are in good agreement with the experimental values. Reactance matrices were obtained in LS coupling and were transformed using JAJOM to give the fine-structure collision strengths. The latter have been averaged over a Maxwellian electron velocity distribution to give the effective collision strengths, for temperatures from 4000 to 24000 K. The calculated electron excitation rates are up to 50% larger than previous values at 10000 K due to resonance structure in the collision strengths.

Elaborate treatment of the inelastic collisions of positrons with alkali atoms and alkaline-earth positive ions using a restricted coupled-static approximation

We present the results of a very elaborate investigation of the inelastic collisions of positrons with the ground states of the first four alkali atoms (3Li,11Na,19K and38Rb) and their electronically resemblant alkaline-earth positive ions,i.e.4Be+,12Mg+,20Ca+ and39Sr+, respectively, using a restricted coupled-static approximation in which the reactance matrices are adjusted to be symmetrical. Our interest is concentrated on the calculation of the total elastic and positronium formation cross-sections and their behaviour in the low-energy region (below 10 eV for the atoms) or the regions above the positronium formation thresholds (when the ions are considered). Our results are the most accurate cross-sections expected from the approximation employed. They reveal, within their limits, the most important characteristics of these cross-sections and provide us with a satisfactory comparison between the main features of positron-atom and positron-ion collisions.

Electron impact excitation of Fe XVIII from its ground state

The R-matrix method is used to calculate electron impact collision strengths for transitions in fluorine-like Fe XVIII from its ground 2PO state. All states of the form 2p5, 2s2p6, 2p43l are included as target states and are represented by configuration interaction wavefunctions constructed in LS coupling. Effective collision strengths are calculated for transitions between the fine-structure levels of the ground state and those of the excited states by employing a transformation of the LS-coupled reactance matrices using term coupling coefficients, and by assuming a Maxwellian velocity distribution for the incident electrons.

Electron excitation of the 1s22s22p52Po3/2-2Po1/2transition and analysis of the 1s22s2p6nl resonances for Ne II and Mg IV

The author has calculated collision strengths for electron excitation of the 1s22s22p5 2Po3/2-2Po1/2 transition in Ne II and Mg IV using the R-matrix method. The author has included the 1s22s22p5 2Po and 1s22s2p6 2Se states, which were represented by sophisticated configuration interaction wavefunctions. Reactance matrices were obtained in LS coupling and transformed using JAJOM to give the fine-structure collision strengths. These have been averaged over a Maxwellian electron velocity distribution to give the effective collision strengths, which we have fitted as analytic functions of temperature between 0 and 40000 K. To estimate the accuracy of the results the author has calculated the positions and widths for the lower members of the 1s22s2p6ns and 1s22s2p6np resonance series. The results are in good agreement with experiment and with previous theory for both Ne II and Mg IV.

Some remarks on the calculation of Born partial wave integrals

The Born partial wave integrals of Seaton [3] are considered. It is shown that the treatment of Whelan [5] may be further simplified and that these integrals may be expressed as a finite sum of associated Legendre polynomials of the second kind. This provides a convenient method for their numerical evaluation and allows the relationship between the Born and Bethe reactance matrices to be given in explicit analytic form.

The S matrix for absorptive Hamiltonians

The existence of a matrix S ̃ such that S S ̃ = 1 in the presence of absorption is demonstrated. In the limit of a hermitian Hamiltonian the unitarity condition SS dg = 1 is recovered. A dispersion relation for forward seattering is derived and the properties of the reactance matrices K and K ̃ are obtained. It is shown that K = K ̃ .

Theory of phonon inelastic atom–surface scattering. I. Quantum mechanical treatment of collision dynamics

We present a systematic formulation of the atom–surface scattering dynamics which includes the vibrational states of the atoms in the solid (phonons). The properties of the total scattering wave function of the system, a representation of the interaction potential matrix, and the characteristics of the independent physical solutions are all derived from the translational invariance of the full Hamiltonian. The scattering equations in the integral forms as well as the related Green functions were also obtained. The configurational representations of the Green functions, in particular, are quite different from those of the conventional scattering theory where the collision partners are spatially localized. Various versions of the integral expression of scattering, transition, and reactance matrices were also obtained. They are useful for introducing approximation schemes. From the present formulation, some specific theoretical schemes which are more realistic compared to those that have been employed so far and at the same time capable of yielding effective ab initio computation are derived in the following paper. The time reversal invariance and the microscopic reversibility of the atom–surface scattering were discussed. The relations between the in and outgoing scattering wave functions which are satisfied in the atom–surface system and important in the transition matrix methods were presented. The phonon annihilation and creation, and the adsorption and desorption of the atom are related through the time reversal invariance, and thus the microscopic reversibility can be tested by the experiment.

Fine structure cross sections from reactance matrices — A more versatile development of the program JAJOM

Title of program: JAJOMPRE Nature of physical problem Results from calculations with LS-coupled wave functions Catalogue number: ACYG (reactance matrices and term coupling coefficients) are used to compute collision strengths for transitions between fine Program obtainable from: CPC Program Library, Queen’s structure levels. University of Belfast, N. Ireland (see application form in this issue) Method of solution Computer: IBM 360/65, IBM 360/195, CDC 6400; InstallaThe input is carefully checked. The algebraic transformation tion: University College London, SRC/Rutherford Laboratory, uses Racahalgebra, the coefficients are computed as required. UK, JILA, University of Colorado An optional further transformation to allow for intermediate coupling in the target requires term coupling coefficients to Operating system: OS 360, scope 34 be supplied by the user. The collision strengths are computed using either of two formulae, corresponding to weak or strong coupling respectively. Programming language used: FORTRAN IV

Collision strengths from reactance matrices

Collision strengths from reactance matrices

Fine structure cross sections from reactance matrices

Fine structure cross sections from reactance matrices