A new algorithm for simulation of power electronic systems using piecewise-linear device models

Before manufacturing, designers of power electronic systems use more and more computer simulation. The reduced computing cost and precision of power component models are essential for the accurate simulation of the power electronic systems to predict their electrical behavior. The accurate simulations of power electronic systems are based on the one hand on the knowledge of power component design parameters not published by manufacturers and on the other hand on a very good description of the arrangement and position of devices including the electromagnetic compatibility (EMC) contributions. In this chapter, through a study considering an experimental circuit of a switching cell including a Thyristor under test controlled by a MOSFET transistor, it is checked that a simple wiring inductance as the circuit wiring representation is insufficient to obtain accurate simulation results. Therefore, a suitable wiring model of the switching cell circuit is developed taking into account the wiring parasitic inductances of the layout and the mutual effects between them. Then, using the accurate model of the switching cell circuit, a detailed extraction procedure of the Thyristor design parameters is developed. This extraction procedure is based on a comparative study between experimental and simulated results, considering the physics of component. Finally a good agreement is obtained between experimental and simulated results confirming the validity of the developed extraction procedure as well as the suitable wiring model of the switching cell circuit.

The literature review explores the evolution and advancements in the implementation of latency-based solvers for real-time simulation of power electronic systems using field-programmable gate arrays (FPGAs).The journey begins with Dr. Johnson, who highlights the exceptional capability of FPGAs to outperform traditional general-purpose processors in floating-point throughput for power flow computations.[1] This foundational work sets the stage for subsequent research that delves deeper into the acceleration of various computational tasks using FPGA technology.As the field continues to mature, new methodologies and algorithms are developed to harness the full potential of FPGAs.These innovations aim to not only improve the performance of power electronic simulations, but also to enhance the flexibility and reconfigurability of the systems.Researchers are exploring novel approaches such as adaptive solvers, where the latency of the system dynamically adjusts based on the complexity of the simulation.[2] This adaptive nature allows for efficient resource allocation and utilization in real-time applications, leading to improved overall system performance.Furthermore, advancements in FPGA architecture and design techniques enable the integration of multiple solvers on a single chip, catering to the increasing demand for multi-domain simulations.This integration paves the way for seamless co-simulation of diverse power electronic systems, including converters, inverters, and motor drives.Additionally, the emergence of high-level synthesis tools simplifies the development process, making it more accessible to researchers and practitioners alike.[3] These tools enable the conversion of high-level hardware description languages into FPGA-specific designs, alleviating the need for manual low-level coding.Moreover, the availability of FPGA development boards and development kits provides a testing ground for prototype implementations, allowing researchers to evaluate their designs in a real-world scenario.[1] In conclusion, the literature review highlights the evolutionary journey of latency-based solvers for real-time power electronic simulations using FPGAs.From the initial groundbreaking work to the current state-of-the-art advancements, researchers have continuously pushed the boundaries to achieve higher performance and accuracy.With ongoing research and innovation, the field is poised for further growth and development, promising even more efficient and versatile solutions for real-time power electronic simulations.[4] [5] build on this foundation by addressing the parallelization of the sparse Matrix-Solve phase in SPICE applications.Their findings indicate that reduced-precision floating-point datapaths can significantly enhance performance, achieving speedups of 2-18 times over single-core microprocessor implementations.This article emphasizes the importance of exploiting parallelism and optimizing resource usage in FPGA designs.The authors present an FPGA-based framework that effectively tackles and addresses the inherent challenges associated with simulating intricate physical phenomena utilizing unstructured spatial discretization.This innovative and pioneering approach significantly enhances data locality and memory access patterns, thereby showcasing a remarkable and astonishing 90 times speedup as compared to high-performance microprocessors.[1] The demonstrated outcomes and results of this work serve to underscore and emphasize the critical significance of efficient and effective memory management when harnessing and leveraging the immense computational power offered by FPGAs.This research proves to be a groundbreaking and pivotal advancement in the field, with far-reaching implications and potential for further exploration and application in diverse areas of study.[6] Introduce FPGA-SPICE, which is a state-of-the-art simulation-based power estimation framework that perfectly integrates seamlessly with cutting-edge architecture exploration tools.

Advanced control methods for power electronics systems

Analysis of new converter topologies, large converters, multi-converter systems, line commutated converters and electrical drive systems requires an appropriate global simulation tool. Because the dynamic model of AC machines is very complex due to the nonlinearities of the system, it is necessary to simulate the whole system containing an AC machine. A user friendly simulator must be able to handle complex systems as such electrical drives by dividing them in small interconnected sub-systems (converter-machine-regulator) assembled in a modular structure. The interconnection of these sub-systems must be done in a simple manner, without additional programming, using a graphic interface. The aim of this paper is to present a new interactive power electronic systems simulation package SIMUSEC "SIMUlation des Systemes Electrotechniques en Commutation", developed in the SIMULINK environment. This package permits simulation of power converters feeding passive loads or electrical machines either in open loop or in closed loop configurations. It also permits simulation of interaction between the converter-machine setups and between converters in a multiconverter system in order to study the conducted emissions. The built-in functions and tool boxes of SIMULINK facilitate the design and the analysis of high performance AC drive systems using this package.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fast time-domain simulation of power electronic systems by using waveform-relaxation methods is presented. Algorithms for circuit partitioning, time windowing, and simulation scheduling are developed. Practical implementation of the partitioning algorithm based on modal analysis is also discussed. Feasibility and advantages of applying these methods to power electronic systems are demonstrated by simulation results for a series resonant converter and a boost zero-voltage-transition PWM converter.

With the increasingly high level of system integration it is becoming necessary to model not only electronic behavior of systems, but also interfaces to real world applications and the detailed physical behavior of elements of the system in question. The emergence of standard languages such as VHDL-AMS has made it possible to now describe a variety of physical systems using a single design approach and simulate a complete system. Application areas where this is becoming increasingly important include mixed-signal electronics, electro-magnetic interfaces, integrated thermal modeling, electro-mechanical and mechanical systems (including MEMS), fluidics (including hydraulics and micro-fluidics), power electronics with digital control and sensors of various kinds. In this paper, we will show how the behavioral modeling of multiple energy domains is achieved using VHDL-AMS, demonstrating with the use of examples how the interactions between domains takes place, and provide an insight into design techniques for a variety of these disciplines. The basic framework is described, showing how standard packages can define a coherent basis for a wide range of models, and specific examples used to illustrate the practical details of such an approach. Examples such as integrated simulation of power electronics systems including electrical, magnetic and thermal effects, mixed-domain electronics and mechanical systems are presented to demonstrate the key concepts involved in multiple energy domain behavioral modeling.

In the simulation of power electronics systems, for reasons of computing time and convergence, it may be necessary to use ideal components which generate ideal voltage switchings (steep edges). However, in reality, these voltage variations are far from ideal and to reproduce a voltage closer to reality, it is necessary to model these variations. This is especially important for the study of residual voltage obtained by simultaneous switching, which are present in PWM strategies developped to reduce the impact of the common-mode voltage generated by 3-phase inverters. This paper is focused on the required model accuracy, in order to take into account these residues obtained by the synchronization of switching voltages.

In this work we present a FPGA implementation of the Latency Insertion Method (LIM) to perform simulation of power electronics systems with high switching frequencies (e.g. SiC based power converter with ƒ sw = 100 − 200kHz). We describe how LIM is used to model a buck and a three phase AC/DC converter and how a FPGA solver based on this approach is implemented. Simulation test performed on a Virtex-7 are presented. All real-time simulations are performed with time steps of 40ns and smaller.

Electro-thermal simulation of power electronic systems

An essential challenge in generation scheduling (GS) problems of hydrothermal power systems is the inclusion of adequate modeling of the hydroelectric production function (HPF). The HPF is a nonlinear and nonconvex function that depends on the head and turbined outflow. Although the hydropower plants have multiple generating units (GUs), due to a series of complexities, the most attractive modeling practice is to represent one HPF per plant, i.e., a single function is built for representing the plant generation instead of the generation of each GU. Furthermore, due to the computation time constraints and representation of nonlinearities, the HPF must be given by a piecewise linear (PWL) model. This paper presented some continuous PWL models to include the HPF per plant in GS problems of hydrothermal systems. Depending on the type of application, the framework allows a choice between the concave PWL for HPF modeled with one or two variables and the nonconvex (more accurate) PWL for HPF dependent only on the turbined outflow. Basically, in both PWL models, offline, mixed-integer linear (or quadratic) programming techniques are used with an optimized pre-selection of the original HPF dataset obtained through the Ramer-Douglas-Peucker algorithm. As a highlight, the framework allows the control of the number of hyperplanes and, consequently, the number of variables and constraints of the PWL model. To this end, we offer two possibilities: (i) minimizing the error for a fixed number of hyperplanes, or (ii) minimizing the number of hyperplanes for a given error. We assessed the performance of the proposed framework using data from two large hydropower plants of the Brazilian system. The first has 3568 MW distributed in 50 Bulb-type GUs and operates as a run-of-river hydro plant. In turn, the second, which can vary the reservoir volume by up to 1000 hm3, possesses 1140 MW distributed in three Francis-type units. The results showed a variation from 0.040% to 1.583% in terms of mean absolute error and 0.306% to 6.356% regarding the maximum absolute error even with few approximations.

Defining the Relationship of Oxygen Delivery and Consumption: Use of Biologic System Models

A linearization method suitable for smart sensors and intelligent transducers with highly nonlinear transfer curve of sensors is proposed here. The first, abscissa, is transformed by one piece-wise linear approximation, and then the standard piece-wise approximation of attained function is performed. The method is compared with the standard piece-wise polynomial and linear approximation, based on the example of the negative temperature coefficient sensor.

FPGA implementation of memristive Hindmarsh–Rose neuron model: Low cost and high-performing through hybrid approximation

This paper aims to design a stabilized Adaptive Model Predictive Control (MPC) for nonlinear continuous systems with unknown dynamics at the start time. The proposed method is based on the Lyapunov MPC (LMPC) where the derivative of the Lyapunov function of the closed-loop system is limited to be less than that under an auxiliary Lyapunov controller. Different from the existing LMPC methods, this paper provides an online constraint updating strategy, which gradually reduces the conservation of the constraint. Specifically, the piece-wise linear (PWL) model updated by the Set-Membership (SM) identification method is adopted in the constraint and the auxiliary controller design, which can result in a non-increasing boundary of the model error. Then, a sufficient condition that guarantees the stabilization of the closed-loop system is deduced, which takes the effect of sample-and-hold implementation and the error boundary of the PWL model into account. By this condition, an optimization problem to update the Lyapunov controller for relaxing the constraints of MPC is proposed. We prove that, by the proposed method, the states will eventually converge to a small region around the equilibrium, both this small region and the conservatism of MPC decrease with the increasing of the accuracy of the PWL model. The application of the proposed method to a chemical process demonstrates the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The control problem of nonlinear continuous systems with unknown dynamics has attracted the attention of researchers. This article develops an Adaptive MPC for this kind of system, which updates the boundary of uncertainties according to the measurement, and updates the constraints of MPC according to the updated uncertainty boundary. It provides a guaranteed stabilization and continuously relaxed constraint design for MPC where machine learning-based models are employed to predict the future trajectory. In the process of implementation, the method solves two optimization problems: one is to get the parameters of constraints which is based on the PWL model, and the other is used to optimize the future trajectory with the updated constraints. To proceed, the initial boundary of the uncertainty should be given at the initial instant, the initialization of PWL models and constraints can be configured based on it. The proposed method can be used for tracking control of chemical processes, power systems, robots, etc., where the accurate dynamics are not provided in advance and an improved performance is required.

In this paper we analyze the collective behaviors of networks of Hindmarsh-Rose (HR) neurons and compare them with the behaviors of networks of piecewise-linear (PWL) approximations of the HR neurons. In all cases, the neurons are assumed to be symmetrically and diffusively coupled, with different topologies. The analysis is based on the master stability function (MSF) approach. The obtained results are verified by numerical time domain simulations of networks of 100 neurons. The synchronization properties of the PWL networks turn out to be very similar to those of the HR networks, as well as the dynamical properties of the single neurons (analyzed elsewhere).