High-voltage Solution Research Articles

An implicit Z-bus based sequential power flow algorithm for VSC AC/DC systems

AC/DC power flow algorithms have been proposed and developed as essential analysis tools for the Voltage Source Converter (VSC) based AC/DC hybrid grid. However, prevailing AC/DC power flow algorithms, e.g., the Newton-Raphson based algorithm, suffer from limitations in terms of convergence, multiple solutions, and high computational complexity. To address these issues, this paper presents a novel sequential AC/DC power flow algorithm based on the implicit Z-bus (IZB) method. We firstly provide a general AC/DC power flow model in real vector space, which takes into account the interface data, internal connection and various control modes of VSC stations. Then, simple and compact IZB iterative mappings in real vector space are derived for the AC solver and DC solver. A sequential algorithmic architecture and data exchange mechanisms are designed considering losses calculation, capacity limits and control strategy switching. The impacts of tolerance settings, initial value selections and load levels on the convergence and accuracy of the algorithm are theoretically analysed. Notably, rigorous convergence analyses substantiate the superior attributes of the proposed algorithm over existing models, guaranteeing convergence to high-voltage solutions (feasible and stable solutions). Numerical tests are performed to compare the proposed algorithm with existing works in terms of accuracy, efficiency, scalability and reliability.

Parameterized Linear Power Flow for High Fidelity Voltage Solutions in Distribution Systems

This paper introduces a new model for highly accurate distribution voltage solutions, coined as a parameterized linear power flow model. The proffered model is grounded on a physical model of linear power flow equations, and uses learning-aided parameterization to increase the fidelity of voltage solutions over a wide range of operating points. To this end, the closed-form analytic solution of the parameterization approach is obtained via a Gaussian Process using a deliberately small input sample and without the need for recomputation. The resulting "self-adjusting" parameter is system-specific and controls how accurate the proposed power flow equations are according to loading conditions. Under a certain value of the resulting parameter, the proposed model can fully recover the linearized formulation of a specialized branch flow model for radial distribution systems, the so-called simplified DistFlow model. Numerical examples are provided to illustrate the effectiveness of the proposed model as well as the improvement in solution accuracy for voltage magnitudes over the simplified DistFlow model and several other linear power flow models, at multiple loading levels. Simulations were carried out on six small- and medium-sized test systems.

DC Power Grids With Constant-Power Loads—Part II: Nonnegative Power Demands, Conditions for Feasibility, and High-Voltage Solutions

In this two-part article, we develop a unifying framework for the analysis of the feasibility of the power flow equations for dc power grids with constant-power loads. Part II of this article, explores further implications of the results in Part I. We present a necessary and sufficient linear matrix inequality (LMI) condition for the feasibility of a vector of power demands (under small perturbation), which extends a necessary condition in the literature. The alternatives of these LMI conditions are also included. In addition, we refine these LMI conditions to obtain a necessary and sufficient condition for the feasibility of nonnegative power demands, which allows for an alternative approach to determine power flow feasibility. Moreover, we prove two novel sufficient conditions, which generalize known sufficient conditions for power flow feasibility in the literature. Finally, we prove that the unique long-term voltage semistable operating point associated to a feasible vector of power demands is a strict high-voltage solution. A parametrization of such operating points, which is dual to the parametrization in Part I, is obtained, as well as a parametrization of the boundary of the set of feasible power demands.

Multistability and anomalies in oscillator models of lossy power grids

The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate a close correspondence between stable synchronous states in dissipatively coupled oscillators, and the winding partition of their state space, a geometric notion induced by the network topology. Leveraging this winding partition, we accompany this article with an algorithms to compute all synchronous solutions of complex networks of dissipatively coupled oscillators. These geometric and computational tools allow us to identify anomalous behaviors of lossy networked systems. Counterintuitively, we show that loop flows and dissipation can increase the system’s transfer capacity, and that dissipation can promote multistability. We apply our geometric framework to compute power flows on the IEEE RTS-96 test system, where we identify two high voltage solutions with distinct loop flows.

Balancibility: Existence and uniqueness of power flow solutions under voltage balance requirements

In distribution systems, power injection variability due to growing penetrations of distributed energy resources (DERs) and dispatchable loads can lead to power quality issues such as severe voltage unbalance. To ensure safe operation of phase-balance-sensitive components such as three-phase motor loads, the amount of voltage unbalance must be maintained within specified limits for a range of uncertain loading conditions. This paper builds on existing “solvability conditions” that characterize operating regions for which the power flow equations are guaranteed to admit a unique high-voltage solution. We extend these existing solvability conditions to be applicable to distribution systems and augment them with a “balancibility” condition that quantifies an operating region within which a unique, adequately balanced power flow solution exists. To build this condition, we consider different unbalance definitions and derive closed-form representations through reformulations or safe approximations. Using case studies, we evaluate these closed-form representations and compare the balancibility conditions associated with different unbalance definitions.

An efficient holomorphic embedded based approach for available transfer capability evaluation

Available Transfer Capability (ATC) is the additional power that can be securely and reliably transacted over and above the already committed transactions in a power network. In the electricity market, where every player (power producer and consumer) tries to earn higher profit, quick and accurate assessment of ATC of the power network is a prime concern. Holomorphic Embedding (HE) is a novel and non-iterative way of solving the Power Flow (PF) equations, which guarantees to find the operational High Voltage (HV) solution, in case it exists. Analytic continuation extends the domain of convergence of non-analytic functions to have voltage solutions. This paper, thus, proposes an extremely efficient and accurate approach for evaluation of ATC using the Holomorphic Embedded PF (HEPF) considering the intact system condition and N-1 contingency situations. This approach is successfully tested on IEEE 30 bus, IEEE 118 bus, and IEEE 300 bus systems for various bilateral and multilateral transactions. The results, thus, obtained prove the efficacy of the proposed approach in comparison with those obtained from the repeated Newton-Raphson PF (NRPF), Fast Decoupled PF (FDPF) and Continuation PF (CPF) based methods.

Online Partial Discharge Condition Monitoring of Complete Networks: Challenges and Solutions Explained through Case Studies for the Pulp and Paper Industry

Unplanned outages within the paper industry lead to significant costs to operators. To reduce unplanned outages and losses, condition monitoring (CM) techniques can be implemented to determine asset health and help target maintenance to where it is required most. The challenges faced by the paper industry to implement condition-based maintenance (CBM) on their medium-voltage (MV) and high-voltage (HV) networks and solutions for online partial discharge (OLPD) monitoring are due to the range and number of assets present and the geographical spread coupled with problems of retrofitting the technology on pre-existing plants. The implementation of OLPD testing or monitoring can vary based on several factors: network topology, connected assets, switchboard type, and the owner's budget and desired local engineer involvement. This article discusses different approaches to implementing an OLPD test program, ranging from simple handheld survey units to complete network monitoring. Its focus is on case studies of the deployment of OLPD testing and monitoring solutions at several U.S. paper sites. The case studies present diagnostic testing of unshielded MV cable at one paper mill up to full permanent OLPD monitoring systems at two others.

Power Flow Solvers for Direct Current Networks

With increasing smart grid direct current (DC) deployments in distribution feeders, microgrids, buildings, and high-voltage transmission, there is a need for better understanding the landscape of power flow (PF) solutions as well as for efficient PF solvers with performance guarantees. This paper puts forth three approaches with complementary strengths towards coping with the PF task in DC power systems. We consider a possibly meshed network hosting ZIP loads and constant-voltage/power generators. The first approach relies on a monotone mapping. In the absence of constant-power generation, the related iterates converge to the high-voltage solution, if one exists. To handle generators operating in constant-power mode at any time, an alternative Z-bus method is studied. For bounded constant-power generation and demand, the analysis establishes the existence and uniqueness of a PF solution within a predefined ball. Moreover, the Z-bus updates converge to this solution. Third, an energy function approach shows that under limited constant-power demand, all PF solutions are local minima of a function. The derived conditions can be checked without knowing the system state. The applicability of the conditions and the performance of the algorithms are numerically validated on a radial distribution feeder and two meshed transmission systems under varying loading conditions.

High Voltage Solution

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Controlling the Composition, Morphology, Porosity, and Surface Chemistry of Lignin-Based Electrospun Carbon Materials

Electrospinning is a suitable top-down technique for the preparation of polymeric fibers using high voltage electrical fields and solutions of the selected polymer of adequate viscosity and conductivity. The versatility of electrospinning allows accurate control of the morphology and composition of the fibers by a wide combination of operating conditions and small modifications of the spinneret and collector. Alcell lignin, which is extracted from lignocellulosic biomass using organic solvents through Organosolv process, is readily solved in ethanol, producing a solution that matches the requirements of the electrospinning process. This review summarizes the vast collection of carbon materials that can be obtained by processing lignin using electrohydrodynamic forces. The coaxial and triaxial electrospinning setups allow for obtaining fibers with two or more components hierchically arranged, the use of these configurations along with a carefully setting of the operating conditions (distance between needle and collector, voltage, flow rate,…) and the solution properties (conductivity, viscosity,…) facilitates the conformation of lignin into spheres, beaded fibers, straight fibers and fused meshes. All these morphologies can be implemented with solid or hollow bodies (i.e. enabling the production of tubes and hollow spheres) by using a sacrificial templating agent. Phosphoric acid can also be added in small amounts to the lignin solution, shortening the thermostabilization time of the fibers. The porosity of the phosphorus containing carbon fibers can be modified in the last stage of the preparation of carbon fibers by controlled gasification process, owing to the extended oxidation resistance of the P-doped fibers. Fibrillar carbon catalysts can be also obtained by one-pot preparation method, only solving small quantities of metallic salts in the lignin solution. In addition, alumina and silica-coated lignin fibers were produced by feeding a partially gelated solution of the respective alkoxide through the outer needle of the spinneret. The coated fibers can be carbonized without thermostabilization step, decreasing considerably the preparation time. All these carbon materials were successfully tested in different applications such as heterogeneous catalysis, energy storage and environmental protection, confirming that electrospinning is a powerful tool for maximizing the value of lignin as carbon precursor.

Efficient method to compute all the type‐1 low‐voltage power flow solutions in distribution systems

The power flow equations usually have multiple solutions including a high-voltage solution and many low-voltage solutions, among which only the type-1 solutions (where the power flow Jacobian matrix has only one positive real-part eigenvalue) are closely related to the voltage instability phenomenon. This study proposes an efficient method to compute all the type-1 low-voltage power flow solutions in distribution systems. First, the geometric properties of the power flow solution space of distribution systems have been studied. Second, the propositions which can guarantee to locate all the type-1 power flow solutions have been suggested and proved. Finally, the conventional implicit Z-bus method is modified to compute all the type-1 germ solutions, based on the suggested propositions; and then the Newton–Raphson method is utilised to trace all the type-1 low-voltage power flow solution branches which originate from the known type-1 germ solutions. The 7-node, 33-node, and 69-node systems are used to validate and demonstrate the proposed method.

Fabrication of Polyvinylpyrrolidone Fibers by Means of Rotary Forcespinning Method

Fibers made from polymer materials have been widely developed as a carrier medium of active ingredients in drug delivery systems. In this research, PVP polymer was chosen because of its wide and safe use in the medical field. The purpose of this study was to produce PVP fibers that can later be applied as a carrier of active ingredients in drug delivery systems. The rotary forcespinning (RFS) method was chosen to shorten the time of production and to overcome the limitations of electrospinning method such as the use of high voltage and dielectric solutions. The PVP solution was varied in several concentrations (8 wt%, 10 wt%, 12 wt%, 14 wt%, 16 wt%, and 18 wt%) to achieve the best fibers morphology. The morphology and the diameter of fibers were analyzed using a digital microscope. From the microscope images, it can be shown that beaded fibers were formed when the concentration of polymer in the precursor solution was low. The number of beads decreased as the concentration of polymer increased. Beads-free fibers were fully formed at above certain polymer concentration.

High-Voltage Solution in Radial Power Networks: Existence, Properties, and Equivalent Algorithms

The ac power flow equations describe the steady-state behavior of the power grid. While many algorithms have been developed to compute solutions to the power flow equations, few theoretical results are available characterizing when such solutions exist, or when these algorithms can be guaranteed to converge. In this letter, we derive necessary and sufficient conditions for the existence and uniqueness of a power flow solution in balanced radial distribution networks with homogeneous (uniform R/X ratio) transmission lines. We study three distinct solution methods: 1) fixed point iterations; 2) convex relaxations; and 3) energy functions—we show that the three algorithms successfully find a solution if and only if a solution exists. Moreover, all three algorithms always find the unique high-voltage solution to the power flow equations, the existence of which we formally establish. At this solution, we prove that: 1) voltage magnitudes are increasing functions of the reactive power injections; 2) the solution is a continuous function of the injections; and 3) the solution is the last one to vanish as the system is loaded past the feasibility boundary.

Theoretical convergence guarantees versus numerical convergence behavior of the holomorphically embedded power flow method

The holomorphic embedding load flow method (HELM) is an application for solving the power-flow problem based on a novel method developed by Dr. Trias. The advantage of the method is that it comes with a theoretical guarantee of convergence to the high-voltage (operable) solution, if it exists, provided the equations are suitably framed. While theoretical convergence is guaranteed by Stahl’s theorem, numerical convergence is not; it depends on the analytic continuation algorithm chosen. Since the holomorphic embedding method (HEM) has begun to find a broader range of applications (it has been applied to nonlinear structure-preserving network reduction, weak node identification and saddle-node bifurcation point determination), examining which algorithms provide the best numerical convergence properties, which do not, why some work and not others, and what can be done to improve these methods, has become important. The numerical Achilles heel of HEM is the calculation of the Padé approximant, which is needed to provide both the theoretical convergence guarantee and accelerated numerical convergence. In the past, only two ways of obtaining Padé approximants applied to the power series resulting from power-system-type problems have been discussed in detail: the matrix method and the Viskovatov method. This paper explores several methods of accelerating the convergence of these power series and/or providing analytic continuation and distinguishes between those that are backed by the theoretical convergence guarantee of Stahl’s theorem (i.e., those computing Pade approximants), and those that are not. For methods that are consistent with Stahl’s theoretical convergence guarantee, we identify which methods are computationally less expensive, which have better numerical performance and what remedies exist when these methods fail to converge numerically.

Readout electronics of a prototype spectrometer for measuring low-energy ions in solar wind plasma

Readout electronics is developed for a prototype spectrometer for in situ measurement of low-energy ions of 30 eV/e–20 keV/e in the solar wind plasma. A low-noise preamplifier/discriminator (A111F) is employed for each channel to process the signal from micro-channel plate (MCP) detectors. A high-voltage (HV) supply solution based on a HV module and a HV optocoupler is adopted to generate a fast sweeping HV and a fixed HV. Due to limitation of telemetry bandwidth in space communication, an algorithm is implemented in an FPGA (field programmable gate array) to compress the raw data. Test results show that the electronics achieves a 1 MHz event rate and a large input dynamic range of 95 pC. A slew rate of 0.8 V/μs and an integral nonlinearity of 0.7-LSB for the sweeping HV, and a precision of less than 0.8 % for the fixed HV are obtained. A vacuum beam test shows an energy resolution of 12 ± 0.7 % full width at half maximum (FWHM) is achieved, and noise counts are less than 10/sec, indicating that the performance meets the physical requirement.

Estimating the saddle-node bifurcation point of static power systems using the holomorphic embedding method

Voltage stability studies have been progressively gaining importance in the power engineering community. Predicting the saddle-node bifurcation point (SNBP) of a power system has become more critical as the power-system loading has increased in many places without a concomitant increase in transmission resources. Since a Newton–Raphson power-flow method is inherently unstable near the SNBP, adaptations such as continuation methods have been used as stabilizers. A new class of nonlinear equation solvers known as the holomorphic embedding method (HEM) is theoretically guaranteed to find the high-voltage solution to the power-flow problem, if one exists, up to the SNBP, provided sufficient precision is used and the conditions of Stahl’s theorem are satisfied by the equation set. In this paper, four different HEM-based methods to estimate the saddle-node bifurcation point of a power system, are proposed and compared in terms of accuracy as well as computational efficiency.

Non-thermal plasma treatment of Radix aconiti wastewater generated by traditional Chinese medicine processing

The wastewater effluent from Radix aconiti processing, an important step in the production processes of traditional Chinese medicine (TCM), is a type of toxic wastewater and difficult to treat. Plasma oxidation methods have emerged as feasible techniques for effective decomposition of toxic organic pollutants. This study examined the performance of a plasma reactor operated in a dielectric barrier discharge (DBD) to degrade the effluent from R. aconiti processing. The effects of treatment time, discharge voltage, initial pH value and the feeding gas for the reactor on the degradation of this TCM wastewater were investigated. A bacterium bioluminescence assay was adopted in this study to test the toxicity of the TCM wastewater after non-thermal plasma treatment. The degradation ratio of the main toxic component was 87.77% after 60min treatment with oxygen used as feed gas and it was 99.59% when the initial pH value was 8.0. High discharge voltage and alkaline solution environment were beneficial for improving the degradation ratio. The treatment process was found to be capable of reducing the toxicity of the wastewater to a low level or even render it non-toxic. These experimental results suggested that the DBD plasma method may be a competitive technology for primary decomposition of biologically undegradable toxic organic pollutants in TCM wastewater.

The Holomorphic Embedding MethodApplied to the Power-Flow Problem

The Holomorphic Embedding Load-Flow Method (HELM) solves the power-flow problem to obtain the bus voltages as rational approximants, that is, a ratio of complex-valued polynomials of the embedding parameter. The proof of its claims (namely that: 1) it is guaranteed to find a solution if it exists; 2) it is guaranteed to find only a high-voltage (operable) solution; and 3) that it unequivocally signals if no solution exists) are rooted in complex analysis and the theory developed by Antonio Trias and Herbert Stahl. HELM is one variant of the holomorphic embedding method (HEM) for solving nonlinear equations, the details of which may differ from those available in its published patents. In this paper we show that the HEM represents a distinct class of nonlinear equation solvers that are recursive, rather than iterative. As such, for any given problem, there are an infinite number of HEM formulations, each with different numerical properties and precision demands. The objective of this paper is to provide an intuitive understanding of HEM and apply one variant to the power-flow problem. We introduce one possible PV bus model compatible with the HEM and examine some features of different holomorphic embeddings, giving step-by-step details of model building, germ calculation, and the recursive algorithm.

High-voltage solutions in CMOS technology

This paper presents trends on CMOS high-voltage techniques for power integrated circuits (PICs). Several fully CMOS compatible drain engineering techniques will be presented. Experimental devices were fabricated in standard CMOS processes from three different lithography generations (2, 0.7 and 0.5μm) without resorting to any extra processing steps. MOS devices layout specificity towards performance improvement, namely breakdown, parasitic effects and degradation, will be emphasized.A recently developed technique used to enlarge high-voltage devices safe-operating area and reduce leakage current will also be presented due to the very promising experimental results.Comparison with more sophisticated and expensive technologies still reveals CMOS as a highly accessible and versatile technology for future PICs.

Discrete voltage states in one-dimensional parallel array of Josephson junctions

We study low-voltage dynamics in highly discrete one-dimensional arrays of Josephson junctions. In particular, we focus on the resonant solutions emerging from the locking between the time period of the oscillations of the single junction with the spatial period of the wave propagating across the array. We find that the average voltage across the array scales as V∝(κ−κc)1/2, where κc is the critical value of the coupling. The connections to high voltage solutions are discussed.