Graded Ring Research Articles

Design and Test of 500-kV Lightning Protection Insulator

In this paper, based on insulation coordination and simulation, a lightning protection composite insulator is proposed, made up of an insulation part and an arrester part connected in series, whose length is close to that of the standard composite insulator, which met the window size requirements of the tower. The arrester part contains zinc oxide resistors and an internal core rod, which has good explosion-proof performance and tensile strength, in the meantime overcomes the problem that arresters cannot bear the tensile load of transmission lines. Electrical simulations and experiments have shown that the shielding failure current can be released through the proposed lightning protection insulator to the ground and the counterattack current can be prevented from entering the line. The dry-arc distances of the arrester part and the insulation part are 2.4 and 2.2 m respectively, and the grading ring distance is 1.8 m. The maximum AC withstanding voltage reaches 700 kV, and the switching overvoltage impulse withstanding voltage reaches 1200 kV. The proposed insulator can prevent lightning accidents from happening. Moreover, its length, tensile load, and installation mode are the same as existing line insulators, which has the advantages of low cost and ease of installation and maintenance.

Research on overvoltage and minimum air clearance on 1000 kV AC side of converter transformer in ±1100 kV Guquan converter station

In the hierarchically connected ultra-high voltage (UHV) DC projects, the minimum air clearance on the 1000 kV AC side of converter transformer directly affects the layout and area of the valve hall. The minimum air clearance is determined by the overvoltage and the flashover characteristics of different electrodes. Since the UHV DC projects are hierarchically connected to the AC power grid, the overvoltage and the electrode flashover characteristics are different from that of general UHV AC projects, necessitating the relevant overvoltage calculation and test studies. The electromagnetic transients software PSCAD is used for modelling of the ±1100 kV Wannan convertor station and the related AC system. The power frequency overvoltage, switching overvoltage, time-to-crest value, and coefficient α of phase-to-phase overvoltage on the AC side of the 1000 kV converter transformer are calculated. Tests are carried out on air clearances between bundle conductors, tubular buses, and equipment grading rings under switching impulse with 1000 μs long wave-front. The minimum phase-to-earth and phase-to-phase air clearances on the 1000 kV AC side of the converter transformer are given.

Iris hooks versus a pupil expansion ring: Operating times, complications, and visual acuity outcomes in small pupil cases

To compare iris hooks and a pupil expansion ring (Malyugin ring) in eyes with a small pupil. Epsom and St. Helier University National Health Service Trust, London, United Kingdom. Retrospective case series. Patients who had primary phacoemulsification cataract surgery from January 1, 2012, to December 30, 2016, were included. Combined procedures and surgeons with fewer than 50 cases were excluded. Anonymized data were demographics, surgeon grade, case complexity, iris hooks or Malyugin ring use, posterior capsule rupture, zonular fiber rupture or dialysis, vitreous loss, operating time, postoperative complications, and visual acuity. Of the 9552 cases included, 425 (4.4%) had a small pupil, 314 of which required a pupil expansion ring and 95 iris hooks. Compared with no pupil expander, iris hooks were associated with an additional operating time of 14minutes for consultants and 24minutes for trainees. The pupil expansion ring was associated with an additional operating time of 4minutes and 6minutes, respectively. Neither pupil expander was associated with more intraoperative complications. The pupil expansion ring was associated with higher postoperative anterior uveitis and corneal edema rates. Pupil expander cases achieved equivalent visual acuity gains. The pupil expansion ring and iris hooks were safe and effective in minimizing intraoperative complications in eyes with a small pupil. The pupil expansion ring was faster to use than iris hooks. Monitoring for signs of postoperative anterior uveitis or cornea edema with careful insertion or removal of pupil expansion rings is advocated.

Breakdown Characteristics of a 220-kV Composite Insulator String Under Short Tail Lightning Impulses Based on the Discharge Current and Images

There are two hypotheses in the leader progression model to illustrate the insulator breakdown process. One is the streamer onset time is relatively small that can be ignored. The other is the leader velocity at both sides of the composite insulator strings are equal. These assumptions are mostly based on the experimental results in rod-rod air gaps. In this paper, experiments were performed to study the breakdown process of a 220-kV composite insulator string with grading rings under positive short tail lightning impulses. The discharge current at the high-voltage side and the high-speed photographs were recorded synchronously. The method of identifying four typical stages of the breakdown process from the current waveform was proposed. The experimental results show that the streamer onset time should not be ignored when calculating the breakdown time, especially for the composite insulator string with grading rings. By fitting the experimental results, the relationship between the streamer onset time and U P / U ${}_{\text{50}}$ has been given. The results also indicate that the velocity of the positive leader is nearly 1.3 times than that of the negative leader during the breakdown process when the positive impulse is applied to the composite insulator string.

Criteria for the Validity of Goldie’s Theorems for Graded Rings

We specify conditions on a group G that are necessary and sufficient for analogs of Goldie’s theorems to hold in a class of G-graded rings, i.e., for every G-graded gr-prime (gr-semiprime) right Goldie ring to possess a completely gr-reducible graded classical right ring of quotients.

Optimisation of corona ring design for composite insulator strings

PurposeThe purpose of this paper is to propose an optimum design of a corona ring for insulator strings using optimisation techniques, which are gravitational search algorithm (GSA) and imperialist competitive algorithm (ICA).Design/methodology/approachAn insulator string model geometry with a corona ring was modelled in a finite element analysis software, and it was used to obtain the electric field distribution in the model. The design was optimised using GSA and ICA. The variables were the corona ring diameter, ring tube diameter and vertical position of the ring along the insulator string.FindingsUsing optimisation method, the minimum electric field magnitude on the insulator string with a corona ring design is lower than without using optimisation method. GSA yields better results than ICA in terms of the optimised corona ring design.Practical implicationsThe proposed methods can help in improvement of corona ring design in reducing the electric field magnitude on the energised end of insulator strings.Originality/valueA new method to design an optimum corona ring for insulator strings, which is using optimisation methods, has been developed in this work.

Injective DG-modules over non-positive DG-rings

Let A be an associative non-positive differential graded ring. In this paper we make a detailed study of a category Inj(A) of left DG-modules over A which generalizes the category of injective modules over a ring. We give many characterizations of this category, generalizing the theory of injective modules, and prove a derived version of the Bass–Papp theorem: the category Inj(A) is closed in the derived category D(A) under arbitrary direct sums if and only if the ring H0(A) is left noetherian and for every i<0 the left H0(A)-module Hi(A) is finitely generated. Specializing further to the case of commutative noetherian DG-rings, we generalize the Matlis structure theory of injectives to this context. As an application, we obtain a concrete version of Grothendieck's local duality theorem over commutative noetherian local DG-rings.

Stability of Valuations: Higher Rational Rank

Given a klt singularity $$x\in (X, D)$$ , we show that a quasi-monomial valuation v with a finitely generated associated graded ring is a minimizer of the normalized volume function $${\widehat{\text{vol}}}_{(X,D),x}$$ , if and only if v induces a degeneration to a K-semistable log Fano cone singularity. Moreover, such a minimizer is unique among all quasi-monomial valuations up to rescaling. As a consequence, we prove that for a klt singularity $$x\in X$$ on the Gromov–Hausdorff limit of Kahler–Einstein Fano manifolds, the intermediate K-semistable cone associated with its metric tangent cone is uniquely determined by the algebraic structure of $$x\in X$$ , hence confirming a conjecture by Donaldson–Sun.

A May-type spectral sequence for higher topological Hochschild homology

Given a filtration of a commutative monoid $A$ in a symmetric monoidal stable model category $\mathcal{C}$, we construct a spectral sequence analogous to the May spectral sequence whose input is the higher order topological Hochschild homology of the associated graded commutative monoid of $A$, and whose output is the higher order topological Hochschild homology of $A$. We then construct examples of such filtrations and derive some consequences: for example, given a connective commutative graded ring $R$, we get an upper bound on the size of the $THH$-groups of $E_{\infty}$-ring spectra $A$ such that $\pi_*(A) \cong R$.

The strong Rees property of powers of the maximal ideal and Takahashi–Dao's question

In this paper, we introduce the notion of the strong Rees property (SRP) for m-primary ideals of a Noetherian local ring and prove that any power of the maximal ideal m has its property if the associated graded ring G of m satisfies depthG≥2. As its application, we characterize two-dimensional excellent normal local domains so that m is a pg-ideal.Finally we ask what m-primary ideals have SRP and state a conjecture which characterizes the case when mn are the only ideals which have SRP.

On the computation of the Ratliff-Rush closure, associated graded ring and invariance of a length

Let $(R,\frak{m} )$ be a Cohen-Macaulay local ring of positive dimension $d$ and infinite residue field. Let $I$ be an $\frak{m} $-primary ideal of $R$, and let $J$ be a minimal reduction of $I$. In this paper, we show that, if $\widetilde {I^k}=I^k$ and $J\cap I^n=JI^{n-1}$ for all $n\geq k+2$, then $\widetilde {I^n}=I^n$ for all $n\geq k$. As a consequence, we can deduce that, if $r_J(I)=2$, then $\widetilde {I}=I$ if and only if $\widetilde {I^n}=I^n$ for all $n\geq 1$. Moreover, we recover some main results of \cite {Cpv, G}. Finally, we give a counter example for Puthenpurakal [Question 3]{P1}.

Torsion-free Aluffi algebras

A pair of ideals J⊆I⊆R has been called Aluffi torsion-free if the Aluffi algebra of I/J is isomorphic to the corresponding Rees algebra. We give necessary and sufficient conditions for the Aluffi torsion-free property in terms of the first syzygy module of the form ideal J⁎ in the associated graded ring of I. For two pairs of ideals J1,J2⊆I such that J1−J2∈I2, we prove that if one pair is Aluffi torsion-free the other one is so if and only if the first syzygy modules of J1 and J2 have the same form ideals. We introduce the notion of strongly Aluffi torsion-free ideals and present some results on these ideals.

Homogeneous prime elements in normal two-dimensional graded rings

We prove necessary and sufficient conditions for the existence of homogeneous prime elements in normal N-graded rings of dimension two, in terms of rational coefficient Weil divisors on projective curves.

A NOTE ON SIMPLE MODULES OVER QUASI-LOCAL RINGS

Matlis showed that the injective hull of a simple module over a commutative Noetherian ring is Artinian. Many non-commutative Noetherian rings whose injective hulls of simple modules are locally Artinian have been extensively studied recently. This property had been denoted by property $(\diamond)$. In this paper we investigate, which non-Noetherian semiprimary commutative quasi-local rings $(R, m)$ satisfy property $(\diamond)$. For quasi-local rings $(R,m)$ with $m^3=0$, we prove a characterisation of this property in terms of the dual space of $Soc(R)$. Furthermore, we show that $(R,m)$ satisfies $(\diamond)$ if and only if its associated graded ring $gr(R)$ does. Given a field $F$ and vector spaces $V$ and $W$ and a symmetric bilinear map $\beta:V\times V\rightarrow W$ we consider commutative quasi-local rings of the form $F\times V \times W$, whose product is given by $(\lambda_1, v_1,w_1)(\lambda_2,v_2,w_2) = (\lambda_1\lambda_2, \lambda_1v_2+\lambda_2v_1, \lambda_1w_2+\lambda_2w_1+\beta(v_1,v_2))$ in order to build new examples and to illustrate our theory. In particular we prove that any quasi-local commutative ring with radical cube-zero does not satisfy $(\diamond)$ if and only if it has a factor, whose associated graded ring is of the form $F\times V \times F$ with $V$ infinite dimensional and $\beta$ non-degenerated.

A filtration of the Sally module and the first normal Hilbert coefficient

The Sally module of an ideal is an important tool to interplay between Hilbert coefficients and the properties of the associated graded ring. In this paper we give new insights on the structure of the Sally module. We apply these results to characterize the almost minimal value of the first Hilbert coefficient in the case of the normal filtration in an analytically unramified Cohen–Macaulay local ring.

A Review of the Dynamic Modelling of Pollution Flashover on High Voltage Outdoor Insulators

In this paper, a dynamic model that simulated and tested the flashover of polluted insulators with HV voltage is presented. Generally, developing the performance of the transmission line depends on the improvement of the insulators due to the pollutants deposited on its surface. This study focused on the classification of insulators and the factors that affect the insulators to cause flashover as well as the analysis of the insulator’s electric properties. The electric field and voltage distribution along with composite insulators used in transmission systems under different conditions were also presented. The problem of nonlinearity of the electric field and voltage distribution, especially along insulators used for HV transmission systems, was investigated and a solution for improving the electric field and voltage distribution along the insulators was suggested. Findings showed that the presence of water droplets and pollution layer distributed on weather sheds enhanced the local electric field but it did not really affect the electric field distribution inside the fibre reinforced plastic core. Moreover, for the pollution case, the effect of pollution layer conductivity was significant to the electric field. For thicker pollution layers, the maximum electric field point moved from the triple junction point. Finally, the study also found that the corona ring might be necessary for the HV insulator for both ends (HV and ground) and its behaviour was affected under polluted and wet conditions.

Electrical Property Test and Research of Insulated Operating Rods with Metal Joint for Live Working

Sectional structure with metal joint is commonly found in an insulated operating rod for live working in an extra- or ultra-high voltage power transmission line but the metal joint is inclined to discharge because uneven distribution of electric fields around the metal joint. In this paper, power frequency discharge tests are made on operating rods with metal joint and insulated joint, including even boost and discharge test and 300s power frequency voltage withstand test and test results are analyzed and studied. Results show: operating rods with two types of joints in the even boost test have basically the same discharge voltage values; the operating rod with insulated joint has significantly higher discharge voltage value than that with metal joint in the 300s voltage withstand test; the metal joint causes local electric field concentration and internode capacitance effect, leading to uneven electric field point position distribution of the insulated operating rod and reduced electrical property. However, the electrical property of the operating rod may be enhanced by mounting a grading ring at the end of the operating rod or coating functional coating outside the operating rod.

Cayley graphs of graded rings

Let [Formula: see text] be a subset of a commutative graded ring [Formula: see text]. The Cayley graph [Formula: see text] is a graph whose vertex set is [Formula: see text] and two vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. The Cayley sum graph [Formula: see text] is a graph whose vertex set is [Formula: see text] and two vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. Let [Formula: see text] be the set of homogeneous elements and [Formula: see text] be the set of zero-divisors of [Formula: see text]. In this paper, we study [Formula: see text] (total graph) and [Formula: see text]. In particular, if [Formula: see text] is an Artinian graded ring, we show that [Formula: see text] is isomorphic to a Hamming graph and conversely any Hamming graph is isomorphic to a subgraph of [Formula: see text] for some finite graded ring [Formula: see text].

On graded special radicals of graded rings

In this paper, a graded ring is a ring which is the direct sum of a family of its additive subgroups indexed by a nonempty set under the assumption that the product of homogeneous elements is again homogeneous. We study graded special radicals and special radicals of graded rings, but which contain the corresponding Jacobson radicals. There are two versions of this graded radical, which we name the graded over-Jacobson and the large graded over-Jacobson radical. We establish several characterizations of the graded over-Jacobson radical of a graded ring and also prove that the largest homogeneous ideal contained in the corresponding classical radical of a graded ring coincides with the large graded over-Jacobson radical of that ring.

Extensions of Valuations to the Henselization and Completion

We show that if R is a local domain which is dominated by a valuation $\nu $ , then there does not always exist a regular local ring $R^{\prime }$ which birationally dominates R and is dominated by v and an extension of $\nu $ to the Henselization $(R^{\prime })^{h}$ of $R^{\prime }$ such that the associated graded rings of $R^{\prime }$ and $(R^{\prime })^{h}$ along the valuations are equal. We also show that there does not always exist $R^{\prime }$ , a prime ideal p of the completion of $\widehat R^{\prime }$ such that $p^{}\cap R^{\prime }=(0)$ and an extension of $\nu $ to $\widehat R^{\prime }$ such that the associated graded rings of $R^{\prime }$ and $R^{\prime }/p$ along the valuation are equal.