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This paper presents a novel approach to dynamic phasor-based transient stability simulation. The proposed method is based on the modified nodal analysis (MNA) approach to circuit simulation, which is used to construct continuous differential-algebraic equations (DAEs). The proposed method makes use of the stamp technique, which makes it possible to construct a general purpose MNA-based simulator. Stamp-based models for common power system components are derived in this work. A new MNA-based synchronous machine model is presented, which represents machines as nonlinear inductances instead of subtransient equivalents. The resultant continuous DAEs are numerically solved using the general purpose variable step and variable order library \texttt{IDA}. Simulation results from the IEEE 68 bus test system, a real 400 bus power system, and the IEEE 39 bus test system with an embedded HVdc transmission system demonstrate that the proposed method is suitable for large ac networks with power electronic devices. The results demonstrate good agreement between the proposed method and electromagnetic transient (EMT) simulation. The results also demonstrate that the proposed method is fast and scalable with CPU times that are up to 200 times faster than EMT simulation.

The modified nodal analysis (MNA) is probably the most widely used formulation for the modeling and simulation of electric circuits. Its conventional form uses electric node potentials and currents across inductors and voltage sources as unknowns, thus taking an electric viewpoint. In this paper, we propose an alternative magnetic oriented nodal analysis (MONA) for electric circuits, which is based on magnetic node potentials and charges across capacitors and voltage sources as the primary degrees of freedom, thus giving direct access to these quantities. The resulting system has the structure of a generalized gradient system which immediately ensures passivity in the absence of sources. A complete index analysis is presented showing regularity of the magnetic oriented formulation under standard topological conditions on the network interconnection. In comparison to conventional MNA, the differential‐algebraic index of MONA is smaller by one in most cases which facilitates the numerical solution. Some preliminary numerical experiments are presented for illustration of the feasibility and stability of the new approach.

This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation and the computation of corresponding consistent initial conditions later on. For differential algebraic equations with a special structure as, e.g. given in flux-charge modified nodal analysis, it is shown that the usage of the implicit Euler method as a time integrator suffices for the Parareal algorithm to converge. Both versions of the Parareal method are applied to numerical examples of nonlinear index 2 differential algebraic equations.

This paper presents a unified power flow algorithm for large and complex mixed ac/dc power systems based on the partitioning of power grids, a version of the two-level Newton method, and the modified nodal analysis formulation. Partitioning significantly increases numerical efficiency without altering the accuracy of the power flow solution. This approach can be applied to any combination of multiple dc and possibly non-synchronized ac systems. It considers the steady-state interaction of ac and dc systems for a wide range of converter representations and control functions. Simplification of elements within the converter stations is not required. Both dc and ac -side converter losses are adequately accounted for by using a generalized converter loss model. The steady-state converter equations are derived in their most general form, with the ac and/or dc -side power exchange or voltages defined as controlled quantities.

IntroductionCerebrovascular disease is a major public health challenge. An important biomarker is cerebral hemodynamics. To measure cerebral hemodynamics, however, only invasive, potentially harmful or time-to-treatment prolonging methods are available. We present a simulation-based alternative which allows calculation of cerebral hemodynamics based on the individual vessel con figuration of a patient derived from structural vessel imaging.MethodsWe implemented a framework allowing annotation of extracted brain vessels from structural imaging followed by 0-dimensional lumped modelling of cerebral hemodynamics. For annotation, a 3D-graphical user interface (GUI) was implemented. For 0D-simulation, we used a modified nodal analysis (MNA), which was adapted for easy implementation by code. The code was written in-house in java. The simulation GUI allows inspection of simulation results, identification of vulnerable areas, simulation of changes due to different systemic blood pressures. Moreover, sensitivity analysis was implemented allowing the live simulation of changes of variables such as vessel lumen to simulate procedures and disease courses. In two exemplary patients, simulation results were compared to dynamic-susceptibility-weighted-contrast-enhanced magnetic- resonance(DSC-MR) perfusion imaging.ResultsThe successful implementation of the framework allowing individualized annotation and simulation of patients is presented. In two exemplary patients, both the simulation as well as DSC- MRI showed the same results pertaining to the identification of areas vulnerable to ischemia. Sensitivity analysis allows the individualized simulation of changes in vessel lumen and the effect on hemodynamics.DiscussionWe present the first precision medicine pipeline for cerebrovascular disease which allows annotation of the arterial vasculature derived from structural vessel imaging followed by personalized simulation of brain hemodynamics. This paves the way for further development of precision medicine in stroke using novel biomarkers and might make the application of harmful and complex perfusion methods obsolete for certain use cases in the future.

The method for modeling switching converters plays a key role in real-time simulators. Associate discrete circuit (ADC) modeling technique is a commonly used method for modeling the switching converter. However, the optimal selection of the ADC-based switch model parameters has great importance in the accuracy of the real-time simulator. In this paper, the design of a real-time simulator for a switching power converter has been done, in which a novel method for detecting optimum values of the switch model parameters has been expressed. Particle swarm optimization (PSO) algorithm is used to find these optimum values using state-space analysis of the modeled circuit in the z-domain. The modified nodal analysis (MNA) method solves the real-time model at each simulation time-step. Case studies are a single-phase 5-level Cascaded H-Bridge (CHB), three-phase 9-level CHB inverter, and a Transmission line. Field-programmable gate array (FPGA) has been used as a platform for implementing the real-time simulator. Experimental result of the real-time simulator of the 5-level CHB inverter on a SPARTAN-6 FPGA and its comparison with the result of a prototype of a 5-level CHB inverter confirms not only the performance of the real-time simulator, but also the effectiveness of the proposed method for confirming the real-time simulator accuracy.

We consider the differential-algebraic systems obtained by modified nodal analysis of linear RLC circuits from a systems theoretic viewpoint. We derive expressions for the set of consistent initial values and show that the properties of controllability at infinity and impulse controllability do not depend on parameter values but rather on the interconnection structure of the circuit. We further present circuit topological criteria for behavioral stabilizability.

The widely applied Structure-Preserving Reduced-order Interconnect Macromodeling (SPRIM) algorithm cannot retain the reciprocity or the block structure of the circuit matrices of the original system, being inherent to RCL circuits; and consequently it is harder to synthesize a Passive Reduced-order Interconnect Macromodeling Algorithms (PRIMA) model into a practical circuit. In order to overcome this deficiency, this paper proposes an improved SPRIM algorithm to maintain the structure features of the input-output correlation matrix. Firstly, the algorithm in this paper reorders the modified nodal analysis (MNA) equations. An Input-Output structure Preserving Order Reduction (IOPOR) technique applicable to SPRIM is then proposed. Also, one combines the IOPOR technique with the conventional SPRIM algorithm to obtain a new projection matrix that can maintain the input and output correlation matrix of the original system. The feasibility and effectiveness of the proposed algorithm are verified through numerical analysis and calculation of typical problems.

This article presents a method for integrating traveling wave models (TWMs) into an optical circuit simulator based on modified nodal analysis (MNA) techniques previously developed for electrical circuit simulation. TWMs of optical propagation through waveguides provide flexible distributed descriptions of optical devices from simple waveguides to lasers. The model is, however, by definition an explicit time marching method and does not fit naturally into an MNA formulation. This article will show a method of integrating the TWM into a fully implicit multidomain (electrical/optical) circuit simulator based on MNA techniques. It will first describe the TWM for simple optical propagation and then its extension for optical gratings, amplifiers, and lasers. The integration of the TWM model into the MNA-based engine will then be specified, showing how the model is implemented using nonlinear optical sources. Finally, a set of examples, including waveguides, filters, and electro-optic devices will be used to show the effectiveness of the technique.

We present an enhanced partial element equivalent circuit (PEEC) model based on Voronoi decomposition of triangular meshes. A complex geometry is accurately represented by many surface triangles, while keeping the number of elements in the corresponding equivalent circuit far less than the number of triangles. To do this, the triangular geometry is automatically decomposed into surface partitions using Voronoi's algorithm. These partitions describe capacitance cells, while inductance elements are set between all neighboring partition pairs. The inductance ( L ) and capacitance ( C ) matrix calculations are done independently using solvers based on quasi-static electric and magnetic full-wave method of moments (MoM). To get the current and charge distribution over the triangles, the MoM results during LC evaluation are combined with the results of modified nodal analysis. We validated our method against the standard PEEC and MoM results as well as measured data. Then, we used our method to simulate conducted emission for a real automotive LED brake-light module.

This article presents the improved formulations for the latency insertion method (LIM) for diodes and MOSFETs utilizing the voltage-in-current framework. LIM is a fast circuit simulation algorithm, which computes the solutions to the voltages and currents in a circuit in a leapfrog manner, instead of a simultaneous matrix solution typically performed in the modified nodal analysis formalism. This allows LIM to have a far superior scaling with respect to the dimensions of the circuit. The formulations presented here have the advantage of not being limited by the stability condition in LIM and thus allow the simulations to be performed at larger time steps. Numerical examples are presented, which illustrate the improved performances of the developed formulations.

Adding mushroom-like electromagnetic band-gap (EBG) structures to split power planes can produce wideband suppression of ground bounce noise in high-speed printed circuit boards. Practical equations are used to estimate the stop-band performance of EBG structures within parallel power planes. In this article, a mushroom-like EBG and power-bus structure are derived using the modified nodal analysis (MNA) method. Equations calculated using the MNA method are easily programmable. The partial EBG structures developed in this article can suppress noise from electromagnetic (EM) interference within parallel plates in the power bus. Several examples below show that similar results can be obtained in measurements, in EM simulations software, and in derived equations. The proposed structure enhanced the suppression of simultaneous switching noise coupling (≤−40 dB) within the range of 260 MHz to 10 GHz.

This brief presents an alternative to the well know LU factorization technique dominantly used in modified nodal analysis (MNA) circuit solutions. The method, called upper and lower decomposition, is proven to be computationally efficient as well as less prone to round off errors compared to the traditional LU factorization. The method is developed for three cases of circuit analysis. First, for situations where the excitation sources are all current sources, as traditionally is the case for MNA representation. In the second and third cases we allow input voltage sources in the circuit, making it the most general case of mixed sources. It is shown that a combined sources representation can generalize all three cases into one category. In terms of accuracy, because of the capability of the method to find the common factors (pivots) and remove them before hand, all divisions with remainders are categorically eliminated. This removes possible round off errors, adding to the precision of the technique, particularly for symbolic analysis.

Purpose The purpose of this paper is to show that the computation of time-periodic signals for coupled antenna-circuit problems can be substantially accelerated by means of the single shooting method. This allows an efficient analysis of nonlinearly loaded coupled loop antennas for near field communication (NFC) applications. Design/methodology/approach For the modelling of electrically small coupled field-circuit problems, the partial element equivalent circuit (PEEC) method shows to be very efficient. For analysing the circuit-like description of the coupled problem, this paper developed a generalised modified nodal analysis (MNA) and applied it to specific NFC problems. Findings It is shown that the periodic steady state (PSS) solution of the resulting differential-algebraic system can be computed very time efficiently by the single shooting method. A speedup of roughly 114 to conventional transient approaches can be achieved. Practical implications The proposed approach appears to be an efficient alternative for the computation of time PSS solutions for nonlinear circuit problems coupled with discretised conductive structures, where the homogeneous solution is not of interest. Originality/value The present paper explores the implementation and application of the shooting method for nonlinearly loaded coupled antenna-circuit problems based on the PEEC method and shows the efficiency of this approach.

This paper presents an FPGA-based Digital Real-Time Simulation (DRTS) environment for the analysis of Electromagnetic Transients (EMTs) of power systems that include multiple Power Electronic Converters (PECs). The main features of the proposed DRTS platform are that it i) employs two-value resistor switch model for PECs and thus avoids inaccuracies of Associate Discrete Circuit (ADC) model and ii) does not require separation of PECs by transmission lines (stub lines) and thus accurately represents PECs in close electrical proximity of each other. These features respectively result in a time-variant and large system admittance matrix which significantly increases the computation burden in each simulation time-step and can render it infeasible for real-time applications. To overcome this problem this paper introduces i) Switching-Network Partitioning (SNP) method which is tailored for PECs representation in FPGA and ii) Reformulated Modified Nodal Analysis (RMNA) method to enable computational parallelism between the solution of network and component models in FPGA. SNP enables solution-level partitioning of the PECs and the rest of the system. The developed DRTS platform enables sub-microsecond simulation time-step and provides a fixed hardware irrespective of the system configuration. Performance of the platform is evaluated for a study system and verified versus off-line simulation studies.

The effect of the surface tension–viscosity dissipation driving liquid Ti flow into a B4C packed bed was analyzed at 1941 K and 2573 K. The model consisted of randomized size distributions of pores (1 to 10 µm) mimicking a packed bed to determine the depth of infusion. Statistical uncertainty was determined as a function of viscosity and pore geometry. The computations were performed with our in-house software, which incorporates a directed acyclic graph and modified nodal analysis algorithms.

Optimal power flow (OPF) approaches employing such methods as semi-definite programming (SDP) have garnered considerable interest in the literature of the last decade. The OPF formulations for these approaches have almost universally relied on Ybus admittance matrix representations, which derive from nodal analysis, and restrict allowable network elements to be voltage-controlled only. Limitations of nodal analysis long been recognized, and to overcome these, commercial power system software often employs modified nodal analysis (MNA). Here, we consider a novel general power system modeling approach based on multi-port representation of individual components with Sparse Tableau Formulation (STF) of network constraints, which is more versatile than MNA for OPF requiring many monitored links with constrained flows. In STF, one is better able to exploit the fact that the vast majority of power grid network elements have voltage-current behavior that is well-modeled as linear. This opens the door to simple, engineering-based convex relaxations. We discuss two relaxations, admittance-based and current-based. The tightness of the relaxation is shown to improve when angle constraints and narrow bounds for active power generation are provided. Sequential bound tightening and reduced spatial branch-and-bound are discussed to obtain stronger relaxation solution. We conduct case studies to show the effectiveness of our relaxations with standard test cases.

A new circuit-field coupling methodology for a single-phase transformer connected to a half-wave rectifier is presented. The rectifier is composed of switched electronic devices (EDs) which can be modeled through a piecewise-linear approximation technique. The modified nodal analysis (MNA) is used to solve the circuit where the EDs are represented with stamps that are systematically incorporated into the system of differential equations. The transformer is modeled using a 2-D finite-element (FE) approach, leading to a coupled circuit-field system, which is solved using proprietary software. The system is also implemented experimentally using an xPC-Target data acquisition system, showing close correspondence with simulation results. Thus, this paper provides the basis for implementing multi-level power converters connected to transformers.