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This paper considers the sample-data-based consensus problem of multiagent systems with time-varying delay and packet losses. To distinguish the time delays caused by network-induced time-delay and packet losses, the switched system is utilized. A lower gain controller is designed based on the solution of a parametric algebraic Riccati equation. The Lyapunov stability theory is utilized to obtain the limitations on the frequency and the duration of packet losses which guarantees the consensus of multiagent systems. On the other hand, we theoretically prove that refined time-delay function can reduce the conservatism. A simulation example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a data-driven small-signal stability constrained optimal power flow (SSSC-OPF) method with high computational efficiency. Instead of repeating the computational expense small-signal stability analysis via differential and algebraic equations during the iterative OPF process, a computationally cheap surrogate constraint for small-signal stability is developed. To reduce the learning difficulty for small-signal stability boundaries, an efficient sample generation strategy is proposed with sampling space compression. This allows us to use the support vector machine (SVM) with a kernel function to derive the explicit data-driven surrogate constraint for small-signal stability. Penalty factor optimization is proposed to compensate for the error caused by SVM. The learned small-signal stability constraint is embedded into the OPF model for generator control. An examination strategy is also developed to avoid the small-signal instability of re-dispatch caused by the error of the data-driven surrogate model. Comparison results with other model-based and data-driven methods on the IEEE 39-bus and 118-bus systems demonstrate the high computational efficiency and economic benefits of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the dissipativity of singular time-delay systems. The objective is to derive a less conservative criterion with less computational demand. Throughout this paper, the augmented Lyapunov–Krasovskii functional (LKF) and the free-matrix-based integral inequality are used to realize less conservativeness. On the basis of these techniques, a less conservative criterion is first given. Then, by decomposing singular time-delay systems into differential equations and algebraic ones, state vectors of the systems are divided into two parts. To reduce redundant decision variables, each part of the state vectors is considered independently to construct a special augmented LKF with less decision variables. As a result, an improved criterion is deduced, and thus less conservativeness and less computational demand are achieved at the same time. Moreover, the presented state decomposition method provides a new research idea for singular time-delay systems not yet reported in the literatures. Finally, the above statements are demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

In recent years, the tracking problem of spherical inverted pendulum (SIP) system with multi-input, multi-output nature and unstable zero dynamics has been well addressed based on continuous-time nonlinear output regulation (NOR) theory. For the convenience of digital implementation, this paper further investigates the approximate NOR problem of the SIP system in discrete-time framework. The key for solving the discrete-time NOR problem lies in how to solve a set of algebraic functional equations known as discrete regulator equations (DRE). Since the equations are very complicated, the accurate solution of the DRE can not be obtained. In this paper, we first show that the DRE associated with the SIP system are solvable by center manifold theorem and then use neural network approach to tackle with the tracking problem. Finally, we compare our method with polynomial approximation method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, which is a mathematical tool able to obtain power series coefficients by transformation rules instead of calculating high order derivatives and has proved to be effective in solving state variables of nonlinear differential equations in our previous study. This paper further solves non-state variables, e.g., current injections and bus voltages, directly with a realistic DAE model of power grids. These non-state variables, nonlinearly coupled in network equations, are conventionally solved by numerical methods with time-consuming iterations, but their differential transformations are proved to satisfy formally linear equations in this paper. Thus, a non-iterative algorithm is designed to analytically solve all variables of a power system DAE model with ZIP loads. From test results on a Polish 2383-bus system, the proposed method demonstrates fast and reliable time performance compared to traditional numerical approaches including the implicit trapezoidal rule method and a partitioned scheme using the explicit modified Euler method and Newton Raphson method. [ABSTRACT FROM AUTHOR]

The paper presents a comprehensive study of small-signal stability analysis of power systems based on matrix pencils and the generalized eigenvalue problem. Both primal and dual formulations of the generalized eigenvalue problem are considered and solved through a variety of state-of-the-art solvers. The paper also discusses the impact on the performance of the solvers of two formulations of the equations modelling the power systems, namely, the explicit and semi-implicit form of differential-algebraic equations. The case study illustrates the theoretical aspects and numerical features of these formulations and solvers through two real-world systems, namely, a 1,479-bus model of the all-island Irish system, and a 21,177-bus model of the ENTSO-E network. [ABSTRACT FROM PUBLISHER]

Solving nonlinear algebraic equations is a core task in many fields of engineering and the sciences. Iterative methods such as Newton's method have been popular in solving power flow equations. Recently, the non-iterative holomorphic embedding (HE) methods that employ polynomial embedded systems have been proposed to solve power flow equations. It is advantageous for the solution functions obtained by the HE method to possess an algebraic property. The present paper points out that algebraic solution functions can have several desired properties for the HE method to work. This paper also exemplifies that the algebraic property cannot be ensured by the elimination process, which corrects an assertion in the literature. It is hence essential to study required conditions for ensuring the existence of algebraic solution functions. The present paper is devoted to the theoretical foundation of HE methods using a polynomial embedded system and develops a novel general theorem and sufficient conditions to ensure the required algebraic property. Examples and numerical results are presented to better explain the derived theoretical results. [ABSTRACT FROM AUTHOR]

A novel approach on the robust ${H_\infty }$ controller design for the doubly fed induction generator (DFIG)-based wind generation systems through the state-dependent Riccati equation (SDRE) technique is proposed in this paper. The control objective is to mitigate the impact of grid voltage dips to enhance the fault-ride-through capability of the wind generation system. A robust ${H_\infty }$ control problem using the fifth-order detailed DFIG model is formulated to mitigate the impact of voltage dips for the DFIG riding through the faults. The SDRE technique performs extended linearization of nonlinear systems, and the robust ${H_\infty }$ control problem can be solved through an algebraic Riccati equation like approach with state-dependent coefficient (SDC) matrices. The pointwise stabilizability and controllability of the extended linearized system are guaranteed by using the input-to-state stability theory. Accordingly, weighting matrices as well as the SDC matrices are designed with fully studied principles. The notion of controllability Gramian is used to optimize the choice of SDC matrices. The control performance of the proposed robust ${H_\infty }$ controller is verified through case studies. Comparisons with the proportional-integral controllers, the sliding mode control, and the exact linearization-based nonlinear control are performed, which demonstrate better dynamic performances and disturbance attenuation through the proposed controller. [ABSTRACT FROM AUTHOR]

The paper proposes a new adaptive approach to power system model reduction for fast and accurate time-domain simulation. This new approach is a compromise between linear model reduction for faster simulation and nonlinear model reduction for better accuracy. During the simulation period, the approach adaptively switches among detailed and linearly or nonlinearly reduced models based on variations of the system state: it employs unreduced models for the fault-on period, uses weighted column norms of the admittance matrix to decide which functions to be linearized in power system differential-algebraic equations for large changes of the state, and adopts a linearly reduced model for small changes of the state. Two versions of the adaptive model reduction approach are introduced. The first version uses traditional power system partitioning where the model reduction is applied to a defined large external area in a power system and the other area defined as the study area keeps full detailed models. The second version applies the adaptive model reduction to the whole system. The paper also conducts comprehensive case studies comparing simulation results using the proposed adaptively reduced models with the linearly reduced model and coherency-based reduced model on the Northeast Power Coordinating Council 140-bus 48-machine system. [ABSTRACT FROM AUTHOR]

Time delay is prejudicial to power system stability and generally worsens the performance of a control system. In this paper, the approaches for stability analysis and stabilization of a power system consisting of time-varying delay are established. The paper starts with the modeling of the power system according to time-delay differential algebraic equations. An integral quadratic constraints (IQC) method is constructed to guarantee the stability of the proposed feedback controller. The frequency-domain IQC and time-domain dissipation inequality are effectively combined to perform stability analysis and stabilization of the power system considering time delays, without complex numerical computation. A two-area four-machine system, an IEEE 10-machine 39-bus system, and a WECC 179-bus system are employed to support the stability criteria and the IQC method. The simulation results indicate that the combined methods effectively damp the oscillation and improve the performance. [ABSTRACT FROM AUTHOR]

In this paper, an improved dynamic state estimation (DSE) based protection (DSEBP) scheme is proposed for transmission lines in MMC-HVDC grids. Firstly, a dynamic model of the protection zone (DC line of interest) is constructed using differential and algebraic equations. The impact of frequency dependent line parameters is mitigated through the utilization of the “line mode” transmission line model. Then, a novel Runge-Kutta (RK) discretization scheme is proposed to consider the dynamics of the control variables during electromagnetic transients, yielding reduced discretization error as compared to the conventional RK scheme. Finally, the batch mode regression framework based DSE is developed to formulate the protection logic considering errors of both measurements and historical estimates. Numerical experiments have shown that the proposed DSEBP scheme can dependably detect and trip internal faults, and securely ignore the external faults. The proposed scheme achieves improved reliability and operational speed as compared with the existing DSEBP schemes. The proposed scheme only requires a typical sampling rate of 10k samples per second, has the robustness to measurement noises, and the calculation burden is low enough for practical implementations. [ABSTRACT FROM AUTHOR]

This paper describes a procedure that computes seeds for linear-feedback shift register-based diagnostic test generation. A conventional process first computes test cubes, and then computes seeds that produce them by solving sets of linear equations. With this process, a seed may not exists for a given test cube. To address this issue, the procedure described in this paper produces seeds directly. Staring from a seed for fault detection, it modifies the seed such that the test it produces will distinguish a pair of faults. The procedure is applied in two modes. The first mode does not require diagnostic test cubes. In this mode, the procedure attempts to modify a seed for fault detection so as to lose the detection of one of the faults on one of the outputs where the faults are detected. The procedure thus uses the concept of test elimination that was used earlier for diagnostic test generation. The second mode is guided by a diagnostic test cube for a fault pair that needs to be distinguished. The procedure modifies a seed so as to reduce the distance between the test that the seed produces and the test cube. Without the requirement to match all the specified values of the test cube, the procedure can produce a seed for distinguishing the pair of faults even when a seed for the given test cube does not exist. Experimental results are presented to demonstrate the effectiveness of the procedure. [ABSTRACT FROM PUBLISHER]

Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of Gerchberg and Saxton and Fienup is still the popular choice for solving many variants of this problem. The algorithm is based on alternating minimization; i.e., it alternates between estimating the missing phase information, and the candidate solution. Despite its wide usage in practice, no global convergence guarantees for this algorithm are known. In this paper, we show that a (resampling) variant of this approach converges geometrically to the solution of one such problem—finding a vector \bf x from \bf y, \bf A, where \bf y = \vert \bf A^T\bf x\vert and \vert\bf z\vert denotes a vector of element-wise magnitudes of \bf z—under the assumption that \bf A is Gaussian. Empirically, we demonstrate that alternating minimization performs similar to recently proposed convex techniques for this problem (which are based on “lifting” to a convex matrix problem) in sample complexity and robustness to noise. However, it is much more efficient and can scale to large problems. Analytically, for a resampling version of alternating minimization, we show geometric convergence to the solution, and sample complexity that is off by log factors from obvious lower bounds. We also establish close to optimal scaling for the case when the unknown vector is sparse. Our work represents the first theoretical guarantee for alternating minimization (albeit with resampling) for any variant of phase retrieval problems in the non-convex setting. [ABSTRACT FROM AUTHOR]

This paper is concerned with the optimal output synchronization control problem for a class of heterogeneous complex dynamical networks (CDNs) with partially unknown system dynamics. By defining a new quadratic performance index including the information of state couplings, an optimal controller consisting of a feedback control and a compensated feedforward control is then designed. A necessary and sufficient condition for the optimal control minimizing the quadratic performance index is established. Especially, an algebraic Riccati equation (ARE) associated with a discount factor is obtained, and a novel online iteration algorithm by iteratively solving the ARE is proposed to compute the optimal controller gain for the case that the CDNs are with partially unknown system dynamics. Moreover, it is proved that the output synchronization errors converge to zero asymptotically by applying the optimal control laws. Finally, two simulation examples are provided to verify the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

Power flow formulated with a distributed slack bus involves modeling the active-power output of each generator with three elements: a nominal injection modulated by a fraction of the net-load imbalance allocated via a participation factor. This setup acknowledges generator dynamics and system operations, but it has long been plagued by ambiguous and inconsistent interpretations of its constituent elemental quantities. In this paper, we establish that, with the: i) nominal active-power injections set to be the economic dispatch setpoints, ii) participation factors fixed to be the ones used in automatic generation control, and iii) net-load imbalance considered to be the total load and loss unaccounted in economic dispatch, the power flow solution best matches results from a simulation unto steady state of the system differential algebraic equation (DAE) model. Numerical case studies tailored to the New England test system validate the analysis by demonstrating that solutions obtained from a distributed slack formulation offer lower errors (with respect to DAE-model simulations) compared to the exhaustive set of all single slack bus choices. [ABSTRACT FROM AUTHOR]

This paper addresses the control problem of the switched system with bounded actuators and average dwell-time. We present the switching rules for the designed controllers based on two kinds of parametric algebraic Riccati equation. The exponential stability of the switched system under the average-dwell time is ensured by the designed controllers and the switching rules. The dynamic performance of the control system is enhanced greatly by the proposed method. The simulation results illustrate the effectiveness and the usefulness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of electromagnetic field excited by a charge moving in a circular waveguide, which consists of two semi-infinite parts. The charge moves with a constant velocity along the waveguide axis from the partially dielectric section into the homogeneous one. It is assumed that Cherenkov radiation is generated in the bilayer section. The total field is represented as a sum of a known forced field that is the field of the charge in the infinite regular waveguide and a free field resulting from the presence of the transverse boundary. The infinite system of algebraic equations for amplitudes of the free-field modes is derived. The further analysis is conducted using numerical calculations. Special attention is given to the study of the so-called Cherenkov-transition radiation (CTR) within the homogeneous part of the waveguide volume. Typical distributions of CTR over frequencies and modes are presented for the case when the channel and the homogeneous area are free of medium. Analytical results obtained for the point charge are generalized for the charged bunch with an arbitrary profile and verified using direct simulations for the case of Gaussian bunch. [ABSTRACT FROM AUTHOR]

To determine the operating region of modular multilevel converter (MMC) station under unbalance grid conditions, this paper proposes the analytical and point-scanning methods. First, the imbalance of PCC voltages is expressed in terms of two proposed indexes for single phase fault (SPF), which can be directly calculated from the grid parameter and grounding impedance. Next, the algebraic equation to solve the PCC voltage for the given PCC power is presented. The existence of PCC voltage is considered as one constraint. Moreover, the other constraints for transformer rating, converter rating, ac current and output voltage are also analyzed to adapt the unbalance conditions. Based on the proposed method, the effect of the grid imbalance on the operating region of MMC is analyzed and then the common constraints to confine the operating region are determined. Following that, the boundary control is proposed to limit the operation of MMC on the boundary of the operating region under unbalanced conditions. The open and modular control structure allows more constraints to be considered for the boundary control. The simulation results validate the correctness of the proposed methods to define the operating region and the effectiveness of the boundary control. [ABSTRACT FROM AUTHOR]

The Cole model is widely used in bioimpedance spectroscopy (BIS) applications for evaluating the contents and status of biological tissues. Traditional frequency-domain fitting methods for Cole parameter estimation (CPE) often need wideband direct or indirect BIS measurements. The newly emerged time-domain fitting methods do not require BIS measurement, but they usually have unsatisfactory estimation accuracy and heavily rely on some specific excitations. This paper proposes a novel time-domain fitting method based on the fractional operational matrix (FOM) for CPE. First, the Cole model is represented as a FOM-based algebraic equation. Then, the model-based voltage response can be calculated as the product of the sampled current excitation and the FOM-based Cole equation. Finally, the Cole parameter can be estimated by minimizing the sum of squares error between the sampled voltage response and the model-based voltage response using an iterative nonlinear least-squares fitting algorithm. Experimental measurements are verified on three 2R1C circuits and in vivo leg muscle of a healthy volunteer. The results show that the Cole parameter can be accurately estimated by the proposed FOM-based fitting method directly using the sampled current and voltage signals. This paper establishes an effective time-domain fitting method for CPE, which could greatly simplify the hardware and software designs without the need for the BIS measurement. [ABSTRACT FROM AUTHOR]

A self-healing power grid can mitigate the impact of power outages and recover the affected area swiftly. To properly size the optimal amount and location of de-energized loads in the presence of both conventional and renewable sources, a precise optimization-based load recovery tool is proposed in this paper. The steady-state and transient behaviors of loads have been taken into account. The proposed tool contains three separate problems that interact with each other during the restoration period. The first-level problem determines the dispatching of generation units. The second-level problem comprises the non-linear algebraic equations, whose task is to provide the initial conditions for the third-level problem. Finally, the third-level problem intends to determine the optimal location and amount of load pickup through modeling the governor of generators as well as loads’ dynamic behaviors. To examine the effectiveness of the proposed tool, a modified IEEE 39-system under a partial blackout condition has been tested. The results are verified by a commercial time-domain simulation software (PSS/E) to demonstrate the accuracy of the proposed approach. Ultimately, the impact of wind turbine frequency control on the load recovery process has been studied under different penetration levels. [ABSTRACT FROM AUTHOR]

This paper proposes a systematic and general approach to model power systems as continuous stochastic differential-algebraic equations. With this aim, the paper provides a theoretical background on stochastic differential-algebraic equations and justifies the need for stochastic models in power system analysis. Then, the paper describes a general procedure to define stochastic dynamic models. Practical issues related to the numerical integration of the resulting power system model are also discussed. A case study illustrating the proposed approach is provided based on the IEEE 145-bus 50-machine system. The case study also illustrates and compares the reliability of the results obtained using stochastic and conventional probabilistic models. [ABSTRACT FROM PUBLISHER]

This paper proposes a new approach for power system transient stability simulation, which is based on a semi-analytical solution (SAS) of power system differential-algebraic equations. In this paper, an SAS is derived using the Adomian decomposition method as a closed-form explicit function of symbolic variables such as time, the initial state, and other variables on system conditions and; hence, it can directly give a power system's dynamic trajectory being accurate for a certain time window. Unlike a traditional numerical integration based simulation approach, the proposed new approach offline derives an SAS and online evaluates the SAS by plugging in values of symbolic variables for a series of time windows making up the desired simulation period. This paper further studies the maximum length of the time window for an SAS being accurate and proposes a divergence indicator for simulation using adaptive time windows. Implementation of this new approach on parallel computers is also studied. The new approach is validated through contingency simulation of the IEEE 10-generator 39-bus system with detailed generator models. [ABSTRACT FROM AUTHOR]

This paper proposes a method for the model order reduction (MOR) of large scale power system models that produces reduced order models (ROM) which preserve the access to selected parameters exactly like the original full order model (FOM). The preserved parameters are related to decentralized power system devices, including, but not limited to, power system stabilizers that are used for the damping control of system electromechanical oscillations. The problem formulation of this parametric MOR (PMOR) is described, as well as the implementation details regarding efficiency and flexibility. Test results are described for large practical power system models used in small-signal electromechanical stability studies. The ROM produced sufficiently accurate responses following parameters changes, when equivalently compared to the original FOM results. The proposed method allows preserving specified nonlinearities in chosen devices of the parameterized ROMs. It can also be applied to the reduction of differential algebraic equation models related to other areas of engineering. [ABSTRACT FROM AUTHOR]

Dual formulations are accurate in use for computing energy-related global quantities such as inductance and providing upper and lower bounds of the unknown true values of these global parameters, which is not possible if using a single formulation. Since traditional dual formulations result in totally different algebraic matrix equations, people have to develop two different finite element (FE) programs and solve the resultant two algebraic equation systems, respectively. In this paper, two practical dual formulations for open region magnetostatic problems, where the global FE matrices are exactly the same, are adopted for extracting the winding inductances. FE formulation and implementation details are presented. Practical examples having complex windings are solved using the proposed methods to showcase the effectiveness and accuracy. High-order FE basis functions are also used to enhance the solution accuracy. The proposed method is highly useful for medium-sized industrial applications by providing guaranteed inductance parameters. [ABSTRACT FROM AUTHOR]

The method of moments (MoM) discretization of volume integral equation (VIE) results in dense $N \times N$ matrix, $N$ being the number of MoM basis functions. Naïve solution of such a system of linear algebraic equations (SLAE) is expensive when problems become large scale. Recently, tensor decomposition has been introduced for solving the SLAE by folding its matrix and its vectors into high-dimensional tensors. In this paper, we present detailed explanations for tensor train (TT) decomposition of the SLAE matrices and vectors resulting from MoM discretization of VIE for scalar 2-D scattering problems under TM-polarization and magneto-quasi-static characterization of multiconductor transmission lines. For Toeplitz matrices resulted from MoM discretization on structured meshes, the extraordinary performance of TT with scaling of $\log (N)$ in CPU time and memory is shown to directly solve SLAE with millions of unknowns within a few minutes and few megabytes of memory. Such $\log (N)$ performance is limited, however, to the SLAE with purely Toeplitz matrices corresponding to the scattering problems on homogeneous dielectric scatterers of the rectangular cross section. To overcome this limitation and solve the problems with arbitrarily shaped inhomogeneous objects, we propose an iterative conjugate gradient-TT (CG-TT) scheme for solving MoM discretized VIE, which utilizes TT decomposition for the fast evaluation of the matrix-vector products. The CG-TT shows CPU and memory scaling in the low- and high-frequency regimes with $O(N)$ and $O(r^{2}~N \log N)$ , respectively, $r$ being the highest rank in the TT carriages. Detailed analysis of memory and CPU time scaling with respect to a number of unknowns and time-harmonic frequency is presented. [ABSTRACT FROM AUTHOR]

Power system reliability evaluation (PSRE) typically involves with finding the system (or bus) reliability index from known component reliability parameters. In this paper, we consider the case of using the system (or bus) reliability index to obtain the unknown component reliability parameter (UCRP). This problem is called the inverse PSRE problem. Analytical model of the inverse PSRE problem is constructed and formulated as the nonlinear algebraic equations. In particular, analytical models for the composite generation and transmission system and the generating system are developed based on the state enumeration method. Solution method using the interval analysis is developed by transforming the nonlinear algebraic equations into the interval nonlinear equations with UCRPs represented by the interval numbers. A modified Krawczyk-operator algorithm based on interval bisection elimination scheme is developed to overcome the difficulty of selecting the appropriate initial interval in the problem-solving process. The RBTS, IEEE-RTS, and a 91-bus system are used for the case study to verify the effectiveness of the proposed model and the solution method. In addition, an application to power system planning is investigated to examine how the component reliability parameters can be modified quantitatively to achieve the desired system reliability improvement. [ABSTRACT FROM AUTHOR]

As time delays of some remote signals cannot be ignored, the power system model must be represented as time-delay differential and algebraic equations. For this case, we can analyze the local dynamical characteristic of the system by calculating the eigenvalues of the related linearized system. In this paper, we present some practical tools to evaluate the impact of the delays on system modes. First, we derive an analytical method for computing the eigenvalue sensitivity. A Newton method for computing the exact eigenvalues of the time-delay system is then proposed, followed by an eigenvalue tracing method to obtain the eigenvalue trajectory when the delay varies. To realize the methods, a general linearized model and the generalized eigenvalue problem formulation are adopted. The proposed methods are applied to analyze the oscillation modes of two power systems with wide-area controllers. [ABSTRACT FROM AUTHOR]

Transient stability simulation of a large-scale and interconnected electric power system involves solving a large set of differential algebraic equations (DAEs) at every simulation time-step. With the ever-growing size and complexity of power grids, dynamic simulation becomes more time-consuming and computationally difficult using conventional sequential simulation techniques. To cope with this challenge, this paper aims to develop a fully distributed approach intended for implementation on High Performance Computer (HPC) clusters. A novel, relaxation-based domain decomposition algorithm known as Parallel-General-Norton with Multiple-port Equivalent (PGNME) is proposed as the core technique of a two-stage decomposition approach to divide the overall dynamic simulation problem into a set of subproblems that can be solved concurrently to exploit parallelism and scalability. While the convergence property has traditionally been a concern for relaxation-based decomposition, an estimation mechanism based on multiple-port network equivalent is adopted as the preconditioner to enhance the convergence of the proposed algorithm. The proposed algorithm is illustrated using rigorous mathematics and validated both in terms of speed-up and capability. Moreover, a complexity analysis is performed to support the observation that PGNME scales well when the size of the subproblems are sufficiently large. [ABSTRACT FROM AUTHOR]

Active research activity in power systems areas has focused on developing computational methods to solve load flow equations where a key question is the maximum number of solutions. Although several upper bounds exist, recent studies have hinted that much sharper upper bounds that depend on the topology of underlying power networks may exist. This paper provides a significant refinement of these observations. We also develop a geometric construction called adjacency polytope that accurately captures the topology of a power network and is immensely useful in the computation of the solution bound. Finally, we highlight the significant implications of the development of such solution bounds in numerically solving load flow equations. [ABSTRACT FROM PUBLISHER]

This paper presents a new algorithm, termed truncated amplitude flow (TAF), to recover an unknown vector x from a system of quadratic equations of the form yi=|\langle {a}i, {x}\rangle |^{2} , where ai ’s are given random measurement vectors. This problem is known to be NP-hard in general. We prove that as soon as the number of equations is on the order of the number of unknowns, TAF recovers the solution exactly (up to a global unimodular constant) with high probability and complexity growing linearly with both the number of unknowns and the number of equations. Our TAF approach adapts the amplitude-based empirical loss function and proceeds in two stages. In the first stage, we introduce an orthogonality-promoting initialization that can be obtained with a few power iterations. Stage two refines the initial estimate by successive updates of scalable truncated generalized gradient iterations, which are able to handle the rather challenging nonconvex and nonsmooth amplitude-based objective function. In particular, when vectors x and ai ’s are real valued, our gradient truncation rule provably eliminates erroneously estimated signs with high probability to markedly improve upon its untruncated version. Numerical tests using synthetic data and real images demonstrate that our initialization returns more accurate and robust estimates relative to spectral initializations. Furthermore, even under the same initialization, the proposed amplitude-based refinement outperforms existing Wirtinger flow variants, corroborating the superior performance of TAF over state-of-the-art algorithms. [ABSTRACT FROM PUBLISHER]

This paper analyses the frequency stability of ac grids in the presence of non-dispatchable generation and stochastic loads. Its main goal is to evaluate conditions in which the system is robust to large, persistent active power disturbances without recurring to time-domain simulations. Considering the ongoing energy transition to more renewable sources, defining robustness boundaries is a key topic for power system planning and operation. However, much of the research on long-term studies has not dealt with robust dynamic constraints, while short-term analyses usually depend on time-consuming simulations to evaluate nonlinearities. To bridge this gap, the authors derive an algebraic equation that provides sufficient conditions for robust frequency stability in ac power systems and a relationship among four key quantities: the maximum active power perturbation, the minimum system damping, the steady-state and the transient frequency limits. To achieve this goal, it uses a nonlinear average-model of the ac grid and Lyapunov's direct method extended by perturbation analysis requiring only limited knowledge of the system parameters. The algebraic calculations are validated using time-domain simulations of the IEEE 39-bus test system and results are compared to the traditional Swing Equation model. [ABSTRACT FROM AUTHOR]

Power system stability is widely assessed based on tools that rely on the representation of voltages and currents through quasi-static phasor calculus, implying that the network itself and the synchronous machine stators are modeled by algebraic equations. Accordingly, the associated fast transients are neglected, assuming those decay rapidly. However, with the increasing penetration of converter interfaced generation in power systems, the reliance on quasi-static phasor calculus is to be questioned. In this paper, the validity of quasi-static phasor calculus models is verified, and dynamic phasor calculus is considered as the alternative. A methodology to systematically compare quasi-static and dynamic phasor calculus is developed. It includes frequency response, modal, and sensitivity analyses. The methodology is applied to an IEEE test network considering penetrations of converter interfaced generation of up to 100%. The models are implemented in MATLAB. The H-infinity norm is proposed as an indicator to identify differences in the applicability of the models. The results show that the quasi-static phasor calculus is suitable for stability analysis only if low bandwidths of converter controls are given. Dynamic phasor calculus instead is suitable and applicable to generic stability studies of integrated power electric and electronic systems with high penetration of renewables. [ABSTRACT FROM AUTHOR]

Frequency dynamics during primary frequency control is closely related to pre-disturbance operating conditions, the disturbance, and equipment characteristics. How to rigorously express such a relation in a frequency stability constrained optimal dispatch problem is still an open question. This paper presents an optimal power flow (OPF) model for generation re-dispatch that considers dynamic frequency response constraints to ensure frequency stability during primary frequency regulation. The distinct feature of the model is that the dynamic frequency response is formulated as a set of differential algebraic equations (DAEs), which allows considering the transient behavior of frequency and mechanical/electromagnetic power for each generator during primary frequency control period. Based on the solution of the optimization problem, a definition of the primary reserve for each unit is proposed according to the maximum of incremental mechanical power. This definition helps meet the adequacy requirement of primary frequency response and achieve partial frequency restoration. Simulation results on WSCC 3-machine 9-bus system, New England 10-machine 39-bus system and the modified IEEE 54-machine 118-bus system validate the effectiveness of the proposed model and reveal the strong coupling between frequency dynamics and the pre-disturbance generation. [ABSTRACT FROM AUTHOR]

Photovoltaic cells are characterized via a static relationship that describes their current–voltage relationship. This relationship is a complicated implicit algebraic equation that depends, in a nonlinear way, on two critical uncertain parameters: temperature and solar irradiance. The efficient operation of the panel relies on the knowledge of these key parameters. While it is technologically feasible to measure the former, a sensor for the latter is usually expensive and difficult to calibrate. In this paper, we propose a globally convergent estimator for solar irradiance which is developed using the principles of immersion and invariance recently reported in the control literature. To design the estimator, a suitable reparameterization of the current–voltage characteristic, which effectively exhibits a monotonic behavior, is introduced. The approach is validated through detailed computer simulations and experimental prototyping using real outdoor measurements. [ABSTRACT FROM PUBLISHER]

We present a numerical method named mixed high order (MHO) to obtain high order of convergence for electrostatic problems solved on general polyhedral meshes. The method, based on high-order local reconstructions of differential operators from face and cell degrees of freedom, exhibits a moderate computational cost thanks to hybridization and static condensation that eliminate cell unknowns. After surveying the method, we assess its effectiveness for 3-D problems by comparing, for the first time in literature, its performances with classical conforming finite elements. Moreover, we emphasize the algebraic equivalence of MHO in the lowest order with the analog formulation obtained with the discrete geometric approach or the finite-integration technique. [ABSTRACT FROM AUTHOR]

This paper focuses on the balancedness of symmetric Boolean functions. We prove a conjecture presented by Canteaut and Videau, which states that the balanced symmetric Boolean functions of fixed algebraic degree are trivially balanced when the number of variables is large enough. Denoted by \sigma n,d , the n -variable elementary symmetric Boolean function of degree d . As an application of this result to elementary symmetric Boolean functions, we show that all the trivially balanced elementary symmetric Boolean functions are of the form \sigma 2^{t+1l-1,2^{t}} , where t and $l$ are any positive integers. It implies that Cusick et al.’s conjecture, which claims that \sigma _{2^{t+1}l-1,2^{t}} is the only nonlinear balanced elementary symmetric Boolean functions, is equivalent to the conjecture that all the balanced elementary symmetric Boolean functions are trivially balanced. [ABSTRACT FROM PUBLISHER]

This paper proposes two methods to reduce the bias of the well-known algebraic explicit solution (Chan and Ho, “A simple and efficient estimator for hyperbolic location,” IEEE Trans. Signal Process., vol. 42, pp. 1905–1915, Aug. 1994) for source localization using TDOA. Bias of a source location estimate is significant when the measurement noise is large and the geolocation geometry is poor. Bias also dominates performance when multiple times of independent measurements are available such as in UWB localization or in target tracking. The paper starts by deriving the bias of the source location estimate from Chan and Ho. The bias is found to be considerably larger than that of the Maximum Likelihood Estimator. Two methods, called BiasSub and BiasRed, are developed to reduce the bias. The BiasSub method subtracts the expected bias from the solution of Chan and Ho's work, where the expected bias is approximated by the theoretical bias using the estimated source location and noisy data measurements. The BiasRed method augments the equation error formulation and imposes a constraint to improve the source location estimate. The BiasSub method requires the exact knowledge of the noise covariance matrix and BiasRed only needs the structure of it. Analysis shows that both methods reduce the bias considerably and achieve the CRLB performance for distant source when the noise is Gaussian and small. The BiasSub method can nearly eliminate the bias and the BiasRed method is able to lower the bias to the same level as the Maximum Likelihood Estimator. The BiasRed method is extended for TDOA and FDOA positioning. Simulations corroborate the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Metasurfaces are thin metamaterials used for manipulating propagation of plane waves and surface-waves (SWs). They can be characterized by homogenized–boundary conditions, which, in absence of losses, can be represented through an equivalent reactance. In this paper, we introduce a general representation of isotropic frequency-dependent reactance which is valid along the dispersion curve of the relevant TM SW. This representation is written in terms of a transition function derived from a manipulation of the Cardano’s formula for third-degree algebraic equations. Throughout a large portion of the dispersion curve, this transition function depends on one parameter only, which is an equivalent quasi-static capacitance. Approaching the Floquet–Bloch region, where many higher order Floquet modes are excited, two additional parameters should be extracted from the full-wave data to complete the transitional representation of the reactance until the upper boundary of the Brillouin region. The final formula is valid for a generic isotropic reactance and for an anisotropic reactance when the direction of propagation is along a symmetry axis of the unit cell element. [ABSTRACT FROM AUTHOR]

It is of paramount importance that power system operators be able to assess transient stability in order to realize a reliable and stable power supply. Transient stability analysis can be formulated as a large-scale system of differential and algebraic equations (DAE). However, as power systems are becoming larger and more complex, it is becoming difficult to solve DAE in a practical amount of time for system operations. Parallel computing based on the waveform relaxation method is an effective solution to achieve faster calculations for transient stability analysis. To enhance the performance of the waveform relaxation method, a proper partitioning of the original problem is essential. Although various partitioning approaches have been used, those approaches might not be effective when analyzing a weakly damped low-frequency oscillation. In particular, in the Japanese 60-Hz power system, this oscillation becomes an important problem. To resolve this issue, in this paper we have developed a new partitioning method that is better suited to analyzing a weakly damped low-frequency oscillation based on eigenvalue analysis. Specifically, effective partitioning can be automatically determined by the proposed index, which can evaluate the validity of the partitioning. The proposed method was tested using the Japanese standards of the IEEJ WEST10 system model and the WEST30 system model. [ABSTRACT FROM PUBLISHER]