Local Invertibility Research Articles

An enhanced sensitivity‐based combined control method of battery energy storage systems for voltage regulation in PV‐rich residential distribution networks

AbstractCommercial off‐the‐shelf (OTS) photovoltaic systems coupled with battery energy storage units (PV‐BES) are typically designed to increase household self‐consumption, neglecting their potential for voltage regulation in low voltage distribution networks (LVDNs). This work proposes an enhanced sensitivity‐based combined (ESC) control method for voltage regulation, using BES control as level 1 and reactive power compensation as level 2. A centralized controller manages charging/discharging intervals, while local inverters handle real‐time power rates and reactive power, ensuring effective LVDN voltage regulation. The BES set points are obtained concerning the measured local bus voltage and according to enhanced sensitivity coefficients. The enhancement algorithm ensures that the full capacity of BES is utilized and that there is adequate capacity during charging and discharging time intervals. The proposed method, tested on 8‐bus and 116‐bus LV test feeders, outperforms OTS and an adaptive decentralized (AD) control method by completely preventing overvoltage issues, minimizing various changes in the direction of BES power, and reducing voltage deviation without significantly affecting consumers' grid dependency.

SMILE: Siamese Multi-scale Interactive-representation LEarning for Hierarchical Diffeomorphic Deformable image registration

Deformable medical image registration plays an important role in many clinical applications. It aims to find a dense deformation field to establish point-wise correspondences between a pair of fixed and moving images. Recently, unsupervised deep learning-based registration methods have drawn more and more attention because of fast inference at testing stage. Despite remarkable progress, existing deep learning-based methods suffer from several limitations including: (a) they often overlook the explicit modeling of feature correspondences due to limited receptive fields; (b) the performance on image pairs with large spatial displacements is still limited since the dense deformation field is regressed from features learned by local convolutions; and (c) desirable properties, including topology-preservation and the invertibility of transformation, are often ignored. To address above limitations, we propose a novel Convolutional Neural Network (CNN) consisting of a Siamese Multi-scale Interactive-representation LEarning (SMILE) encoder and a Hierarchical Diffeomorphic Deformation (HDD) decoder. Specifically, the SMILE encoder aims for effective feature representation learning and spatial correspondence establishing while the HDD decoder seeks to regress the dense deformation field in a coarse-to-fine manner. We additionally propose a novel Local Invertible Loss (LIL) to encourage topology-preservation and local invertibility of the regressed transformation while keeping high registration accuracy. Extensive experiments conducted on two publicly available brain image datasets demonstrate the superiority of our method over the state-of-the-art (SOTA) approaches. Specifically, on the Neurite-OASIS dataset, our method achieved an average DSC of 0.815 and an average ASSD of 0.633 mm.

A continuous-time voltage control method based on hierarchical coordination for high PV-penetrated distribution networks

The photovoltaic (PV) integration brings both fast photovoltaic generation (PVG) variations and a large number of PV inverters to the distribution networks (DNs). The management of the PVG variation and the PV inverter is an urgent problem. The discrete-time model can’t describe PVG variations during the schedule interval and the regulation potential of the PV inverter is limited by a fixed dispatching value. This paper proposes a continuous-time voltage control method based on hierarchical coordination for high PV-penetrated DNs. In the central schedule, based on the Bernstein polynomial method, continuous-time models of PVGs are established and reference values of local inverter control curves are dispatched as continuous-time functions in a sub-hourly timescale. In the local control, reactive power and active power curtailment of PV inverters are set as the reference values, i.e., the corresponding values of the continuous-time functions, every 30 s to optimize the central dispatching objective under the voltage constrains, and deviate from the reference values according to both the local control curve and voltage measurement only when the real-time bus voltage violation occurs. In addition, the cooperation between inverter and mechanical equipment in the continuous-time framework is also considered, and the Bernstein polynomial method is developed to the continuous-time modeling of voltage control in DNs. The simulation shows that the proposed method has lower maximum voltage magnitude and lower energy loss compared with discrete-time central schedule method.

Surface penalization of self-interpenetration in linear and nonlinear elasticity

We analyze a term penalizing surface self-penetration, as a soft constraint for models of hyperelastic materials to approximate the Ciarlet-Nečas condition (almost everywhere global invertibility of deformations). For a linear elastic energy subject to an additional local invertibility constraint, we prove that the penalized elastic functionals converge to the original functional subject to the Ciarlet-Nečas condition. The approach also works for nonlinear models of non-simple materials including a suitable higher order term in the elastic energy, without artificial local constraints. Numerical experiments illustrate our results for a self-contact problem in 3d.

Distribution Grid Optimal Power Flow in Unbalanced Multiphase Networks With Volt-VAr and Volt-Watt Droop Settings of Smart Inverters

High penetration of photovoltaic (PV) generators in active distribution networks (ADNs) cause overvoltage due to reverse power flow. Smart inverter (SI) functionalities can be configured to provide efficient voltage regulation and reactive power support in ADNs. Moreover, the mismatch between peak PV generation and peak demand make battery energy storage systems (BESSs) increasingly important assets in power grids, capable of enabling higher penetration of renewable energy resources by mitigating the system-wide effects of PV intermittency. In this work, we propose the inclusion of local piecewise Volt-VAr and Volt-Watt droop functions of PV (as per the IEEE-1547) as constraints in a multiperiod distribution grid optimal power flow (DOPF) formulation. This approach is an efficient voltage control method for unbalanced multiphase networks, making the inverter dispatch solutions abide by the IEEE-1547 standard and therefore suitable at the local inverter controller level. We adopt a well-known LinDist3Flow version of DOPF, and the resulting multiperiod DOPF becomes a mixed-integer linear programming problem. Simulations on the IEEE 123-node feeder with 15 utility-scale PV and BESS inverters validate the efficacy of the proposed formulation in performing effective voltage regulation and control that abide by the IEEE-1547 standard. The case studies show that SI droop-integrated DOPF can ensure reduced variation in bus voltages, reducing the risk of voltage violations, and net load smoothing can be achieved with BESS, reducing the disparity between inexpensive midday and expensive evening energy price.

Dynamic Model and Converter-Based Emulator of a Data Center Power Distribution System

Data centers have become a widespread power electronics (PE) load, which has significant impact on the power grid. In order to investigate the data center load characteristics, this article proposes a complete dynamic model for a typical data center ac power distribution system. A generalized model with mode transition is proposed to coordinate different power stages in the data center power system. Meanwhile, to help evaluate the grid dynamic performance and transient stability, an all-in-one load data center power emulator is developed on a reconfigurable PE converter-based hardware testbed (HTB). The dynamic power model is digitized and simplified to be implemented in two local voltage source inverters on the HTB. This proposed data center power emulator has been verified experimentally in a regional network. Dynamic performances during voltage sag events and server load variations are emulated and discussed. The article details the design, development, and verification of the data center model and power emulator. The proposed model and emulator provide an effective, easy-to-use tool to better design data centers and study the interaction with the power system.

On local invertibility of functions of an h-complex variable

The theory of functions of an h-complex variable is an alternative to the usual theory of functions of a complex variable, obtained by replacing the rules of multiplication. This change leads to the appearance of zero divisors on the set of h-complex numbers. Such numbers form a commutative ring that is not a field. h-Holomorphic functions are solutions of systems of equations of hyperbolic type, in comparison with classical holomorphic functions, which are solutions of systems of equations of elliptic type. A consequence of this is a significant difference between the properties of h-holomorphic functions and the classical ones. Interest in studying the properties of functions of an h-complex variable is associated with the need to search for new methods for solving problems in mechanics and the plane theory of relativity. The paper presents a theorem on the local invertibility of h-holomorphic functions, formulates the principles of preserving the domain and maximum of the norm.

Cooperative Markov Decision Process for Voltage Control of Grid-Tied Photovoltaic Generators With Reactive Power Support

The problem of voltage control (VC) by means of inverter reactive support in distribution grids with photovoltaic (PV) generation is addressed. A novel decentralized approach for VC is proposed, which consists in heuristic specification of a distributed reactive support cooperative partially observable Markov decision process (DRS-C-POMDP) whose agents control groups of PV nodes clustered according to voltage correlation. The proposed method employs offline policy optimization, which yields closed-form reactive power setpoint control laws. Hence, the online processing time required by most VC methods is avoided and controller implementation is simplified. The method is validated via simulation on a 123-bus feeder, in which it is compared to other decentralized heuristic methods from the literature. The results indicate that, for identical local inverter controls, the proposed method yields superior performance.

Minimizing Neutral Current of Two Parallel STATCOMs

This paper proposes control augmentations to allow two Static Synchronous Compensators (STATCOMs) devices to operate in parallel from a shared DC bus. Two parallel connected four-wire STATCOMs will be shown to be highly susceptible to an uncontrolled circulating current in the neutrals when operating with a three degree of freedom current control scheme. The circulating current can be calculated from the local inverter phase currents and neutral current. This paper shows the circulating component is readily suppressed by a neutral voltage offset that is determined by a proportional controller (P). The controller is validated by both simulation and experimental results.

Differentiating between plant level and inverter level voltage control to bring about operation of 100% inverter based resource grids

Recent research has resulted in the emergence of so called grid forming inverter control architectures which behave as voltage sources. However, from a fundamental electric circuit theory perspective, there are no inherent limitations that restrict the continued operation of a network with pure current sources. In this paper, the ability of current sources to bring about stable operation of a zero inertia network will be shown. Such a stable operation will be brought about using appropriate auxiliary control loops and to the author’s knowledge, has not been illustrated elsewhere in research literature. Small signal stability analysis will be carried out to validate stability of this novel concept while time domain simulations carried out in electromagnetic transient (EMT) domain will be used to extend the concept to larger realistic networks. It will be shown that as the percentage of inverters increase in the power system, fast local inverter level voltage control will be crucial in dictating the stability of the power system. This signifies a paradigm shift in the manner in which voltage control is implemented in many conventional large solar and wind farms wherein today, voltage control is usually implemented in a slow manner at the plant controller level while the inverter level control is purely a reactive power control loop. With this paradigm shift, and without any further changes in inverter control structure, it will be shown that it is possible to achieve a stable and continued operation of a 100% inverter based resource grid.

Design and Implementation of PV Fed Local UPS Inverter

Locally manufactured Uninterruptible Power Supply (UPS) units are purchased as an alternative to rolling blackouts and load shedding in underdeveloped and developing countries like Pakistan. These locally manufactured UPS units are energy-inefficient, causing stress on the national grid and cost-intensive for the residential consumer in the form of high utility bills of electricity. In this regard, the authors have proposed the PV fed local UPS inverter to make the existing UPS unit more efficient through photovoltaic (PV) energy without disrupting its function of providing uninterrupted supply during load-shedding hours. In order to validate the performance of the proposed PV fed local UPS inverter, the maximum power point tracking (MPPT) PV charge controller module is designed and implemented practically in a hardware setup and simulated in MATLAB/Simulink and Proteus environment, respectively. Moreover, the installation of an MPPT PV charge controller module in an existing locally manufactured UPS unit is also discussed. The practical results demonstrate the superiority of the proposed PV fed local UPS inverter with an average efficiency of 81.51% and a lowest total harmonic distortion (THD) of 1.29% as compared to existing UPS inverters.

Local invertibility and sensitivity of atomic structure-feature mappings.

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety of representations that can be used to convert them into a finite set of symmetric descriptors or features. Methods: Here, we analyze the sensitivity of the mapping to atomic displacements, using a singular value decomposition of the Jacobian of the transformation to quantify the sensitivity for different configurations, choice of representations and implementation details. Results: We show that the combination of symmetry and smoothness leads to mappings that have singular points at which the Jacobian has one or more null singular values (besides those corresponding to infinitesimal translations and rotations). This is in fact desirable, because it enforces physical symmetry constraints on the values predicted by regression models constructed using such representations.However, besides these symmetry-induced singularities, there are also spurious singular points, that we find to be linked to the incompleteness of the mapping, i.e. the fact that, for certain classes of representations, structurally distinct configurations are not guaranteed to be mapped onto different feature vectors. Additional singularities can be introduced by a too aggressive truncation of the infinite basis set that is used to discretize the representations. Conclusions: These results exemplify the subtle issues that arise when constructing symmetric representations of atomic structures, and provide conceptual and numerical tools to identify and investigate them in both benchmark and realistic applications.

Invertibility of multi-energy X-ray transform.

PurposeThe goal is to provide a sufficient condition for the invertibility of a multi‐energy (ME) X‐ray transform. The energy‐dependent X‐ray attenuation profiles can be represented by a set of coefficients using the Alvarez–Macovski (AM) method. An ME X‐ray transform is a mapping from N AM coefficients to N noise‐free energy‐weighted measurements, where N≥2.MethodsWe apply a general invertibility theorem to prove the equivalence of global and local invertibility for an ME X‐ray transform. We explore the global invertibility through testing whether the Jacobian of the mapping J(A) has zero values over the support of the mapping. The Jacobian of an arbitrary ME X‐ray transform is an integration over all spectral measurements. A sufficient condition for J(A)≠0 for all A is that the integrand of J(A) is ≥0 (or ≤0) everywhere. Note that the trivial case of the integrand equals 0 everywhere is ignored. Using symmetry, we simplified the integrand of the Jacobian to three factors that are determined by the total attenuation, the basis functions, and the energy‐weighting functions, respectively. The factor related to the total attenuation is always positive; hence, the invertibility of the X‐ray transform can be determined by testing the signs of the other two factors. Furthermore, we use the Cramér–Rao lower bound (CRLB) to characterize the noise‐induced estimation uncertainty and provide a maximum‐likelihood (ML) estimator.ResultsThe factor related to the basis functions is always negative when the photoelectric/Compton/Rayleigh basis functions are used and K‐edge materials are not considered. The sign of the energy‐weighting factor depends on the system source spectra and the detector response functions. For four special types of X‐ray detectors, the sign of this factor stays the same over the integration range. Therefore, when these four types of detectors are used for imaging non‐K‐edge materials, the ME X‐ray transform is globally invertible. The same framework can be used to study an arbitrary ME X‐ray imaging system, for example, when K‐edge materials are present. Furthermore, the ML estimator we presented is an unbiased, efficient estimator and can be used for a wide range of scenes.ConclusionsWe have provided a framework to study the invertibility of an arbitrary ME X‐ray transform and proved the global invertibility for four types of systems.

On some properties of p-holomorphic and p-analytic function

In this article the relationship between the conditions of p-differentiability, p-holomorphycity, and the existence of the derivative of a function of a p-complex variable is considered. The general form of a p-holomorphic function is found. The sufficient conditions for p-analyticity and local invertibility are obtained. The open mapping theorem and the principle of maximum of the norm for a p-holomorphic function and the uniqueness theorem are proved.

A decentralized approach for frequency and voltage regulation in islanded PV-Storage microgrids

This paper proposes a novel decentralized and communication-less control strategy for frequency and voltage regulation in Photovoltaic (PV)-Storage islanded Microgrids (MGs). The developed approach aims at achieving a suitable management of the different operational assets of the PV-Storage islanded MGs providing seamless transitions among them and guaranteeing a continuous and effective power supply to the loads. Local inverter controllers are designed exploiting the capabilities of the Model Predictive Control; the resulting control architecture is a composition of local Distributed Generating (DG) unit controller relies only on measurements available on the DG unit site that allows nullifying both frequency and voltage errors providing a suitable repartition of the power request. This way, the proposed approach can combine the advantages of the classic droop and master/slave controllers as it needs neither communication among devices nor a secondary centralized control loop. Moreover, it is able to account for the Storage characteristics imposing a power curtailment of the PV units whenever either the power absorption or the State of Charge limit is reached.

Invertible field transformations with derivatives: necessary and sufficient conditions

We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating such a transformation as differential equations that give new variables in terms of original ones. The obtained results generalise the well-known and widely used inverse function theorem. Taking into account that field transformations are ubiquitous in modern physics and mathematics, our criteria for invertibility will find many useful applications.

A Droop Approach for the Passivity–based Control of Microgrids

Abstract In this paper, the stability properties of a microgrid in closed-loop with local inverters’ controllers and a droop power-sharing scheme are studied. The main result is the formal statement that this system is asymptotically stable concerning the equilibrium point that satisfies desired operating conditions. In contrast to the results reported in the literature, neither the stability analysis of the inverter’s dynamics is omitted, nor is it assumed that the only dynamic behavior is that corresponding to the droop scheme. The contribution exploits the inclusion of a passivity-based control law for the inverters and the input-to-state stability properties exhibited by the considered droop algorithm. The validity of the analysis is illustrated via a numerical evaluation.

Passivity Conditions for Plug-and-Play Operation of Nonlinear Static AC Loads

The complexity arising in AC microgrids from multiple interacting distributed generation units (DGUs) with intermittent supply behavior requires local voltage-source inverters (VSIs) to be controlled in a distributed or decentralized manner at primary level. In (Strehle et al., 2019a), we use passivity theory to design decentralized, plug-and-play voltage and frequency controllers for such VSIs. However, the stability analysis of the closed-loop system requires a load-connected topology, in contrast to real grids where loads are arbitrarily located. In this paper, we expand our former approach by considering the more realistic and general case of nonlinear static AC loads (ZIP and exponential) at arbitrary locations within an AC microgrid. Investigating the monotonicity of differentiable mappings, we derive sufficient inequality conditions for the strict passivity of these nonlinear static AC loads. Together with our plug-and-play VSI controller, this allows us to use passivity arguments to infer asymptotic voltage and frequency stability for AC microgrids with arbitrary topologies. An illustrative simulation validating our theoretical findings concludes our work.

Minimizing observation spillover for pose control of elastic bodies using optimal sensor placement

The impact of elastic modes limits the performance of position control of elastic bodies in a significant way. Local dampers are a typical way to suppress this issue, but lead to non-proportional damping and complex oscillation modes with varying nodal lines. To this end, the placement of the sensors is of major importance in high-precision applications. In this contribution, we present an optimal sensor placement algorithm which uses Gramian-based observability measures to overcome this issue. Singular sensing configurations with respect to the pose are avoided by considering the mappings’ local invertibility explicitly. Furthermore, we are in the position to cope with the highly relevant issue of constrained installation space and to handle complex 2D and 3D geometries by using model order reduction techniques. By means of an illustrative example, the significantly reduced influence of the elastic deformations on the controller is demonstrated at last.

Inverting the local geodesic ray transform of higher rank tensors

Consider a Riemannian manifold in dimension with a strictly convex boundary. We prove the local invertibility, up to potential fields, of the geodesic ray transform on tensor fields of rank four near a boundary point. This problem is closely related to elastic qP-wave tomography. Under the condition that the manifold can be foliated with a continuous family of strictly convex hypersurfaces, the local invertibility implies a global result. One can straightforwardedly adapt the proof to show similar results for tensor fields of arbitrary rank.