Discrete Time Domain Modeling Research Articles

SOC Balancing Control Based on Predictive Power Model Amongst Supercapacitor Packs in MMC With Embedded Energy Storage System

Modular multilevel converter with supercapacitor (SC) packs-based energy storage system (MMC-SESS) can play a role in energy transition and renewable energy consumption. However, SESS's imbalance problem is caused by the inconsistency of its packs, which has a negative effect on the utilization of the MMC-SESS and has become a hot research topic. Confronting this problem, this paper proposes a state of charge (SOC) balancing control strategy amongst SC packs based on a discrete time-domain predictive power model in MMC-SESS based medium-voltage direct-current (MVDC). It is a double-loop control to accurately control the charging and discharging power. The outer power control establishes a discrete time-domain predictive power model for the SOC differences. The inner current loop designs a hybrid controller based on the continuous control set-model prediction control (CCS-MPC) and the feedback control strategy to accurately track the dynamic current reference. Simulations in PSCAD/EMTDC have shown that the proposed control can achieve SOC balancing amongst SC packs and improve the dynamic response as well as mitigate the SC pack current ripples.

Fully discrete-time domain model and damping characteristics accurate analysis for grid-connected inverter with LCL filter

Fully discrete-time domain model and damping characteristics accurate analysis for grid-connected inverter with LCL filter

Discrete time domain modeling and design of current mode controlled flyback LED driver

In this paper, modeling for a current mode controlled (CMC) flyback LED driver with a stabilizing ramp is performed in a step-by-step procedure. Discrete time state equations for the system are derived and linearized with respect to a steady-state operating point. At this operating point, the switching control law, the condition that determines the duty ratio, is also linearized. In the next step, a closed-loop system model is derived by combining the two models of the flyback driver and the switching control law. The root locus analysis in the z-plane is used to investigate the characteristics of the combined linearized system and obtain design guidelines for feedback loops. The feasibility of the proposed design is confirmed through the experimental results for the CMC flyback LED driver.

An Eigenvalues Method for Stability Analysis of Power Grid with Energy Storage Devices Based on Discrete Time Domain Model

The eigenvalue analysis based on state space model is an important method to study stability of power grid. With the large-scale access of energy storage devices and power electronics converters in power grid, the conventional state space modelling method suffers from complicated process of determining state variables and large calculation amount of eigenvalues, and nonlinear stability characteristics of power grid cannot be accurately reflected. To obtain the eigenvalues of power grid with energy storage devices more efficiently, this paper proposes a method for constructing state space model of power grid based on discrete time domain model (DTDM) and presents the corresponding stability criterion. Compared with the conventional state space modelling method, the nonlinear characteristics of components under proposed method can be linearized, and the constructed state space model can capture a wider range of system information including energy storage devices. Besides, the complete state space model of power grid can be obtained only according to the connection between component's DTDM and grid. Moreover, because eigenvalue solution under proposed method relies on the sparse grid node voltage matrix, the calculation of eigenvalues is simple and efficient, and it visually presents variation trend of eigenvalue and investigates the stability of system. Simulation results in Simulink/Matlab verify the correctness and effectiveness of proposed method.

Discrete Time Domain Modeling and Control of a Grid-Connected Four-Wire Split-Link Converter

Distributed generation (DG) allows the production of renewable energy where it is consumed, avoiding transport losses. It is envisioned that future DG units will become more intelligent, not just injecting power into the grid but also actively improving the power quality by means of active power filtering techniques. In this manner, voltage and current harmonics, voltage unbalance or over-voltages can be mitigated. To achieve such a smart DG unit, an appropriate multi-functional converter topology is required, with full control over the currents exchanged with the grid, including the neutral-wire current. For this purpose, this article studies the three-phase four-wire split-link converter. A known problem of the split-link converter is voltage unbalance of the bus capacitors. This mid-point can be balanced either by injecting additional zero-sequence currents into the grid, which return through the neutral wire, or by injecting a compensating current into the mid-point with an additional half-bridge chopper. For both methods, this article presents a discrete time domain model to allow controller design and implementation in digital control. Both techniques are validated and compared by means of simulation results and experiments on a test setup.

Forward Speed Prediction of a Free-Running Wave-Propelled Boat

Wave-propelled boats utilize submerged flapping foils to convert wave energy directly into propulsion. For platforms that are solely propelled using submerged flapping foils, predicting the forward speed is challenging as it is time varying and dependent on the coupled responses of the wave-induced hull motions (surge, heave, and pitch) and the foil flapping motion (driven by the wave-induced hull motions and incident wavy flow). To ascertain the free-running response of wave-propelled boats, this article presents a hybrid discrete time-domain numerical model and experimental results from a prototype wave-propelled autonomous surface vehicle (ASV) with forward and aft (tandem) flapping foils. Results from a series of free-running experiments in regular head waves, over a range of wave frequencies for three different foil locations, are presented and used to validate the numerical model. The model was found to show good agreement with the experimental results, capturing the coupled dynamics of the vessel and foils and oscillating forward speed, over a range of wave frequencies and foil locations. The model and results provide a valuable insight for the design of wave-propelled boats.

A Computational Analysis of Interfacing Converters with Advanced Control Methodologies for Microgrid Application

Power electronics converter and inverter systems for microgrid operations are always stochastic. When the system is operating in grid-tied mode, the attached load is not constant, so the current which drawn from the DC grid also varies leads to a voltage drop and that causes steady-state error in between the actual and desired output voltage in microgrid. DC-DC bidirectional converters are widely used in microgrid application that facilitates bidirectional energy convertion which having boost mode operation in one direction and bucking mode in other operation. The Interfacing converter is controlled by using the Maximum Power Point Tracking (MPPT) control technique for obtaining maximum power during different atmospheric conditions. In this work, a Model Predictive Control (MPC) strategy is proposed which having an improved cost function, single prediction horizon, and an observer to keep tracking the output voltage. Here, MPC is proposed for cumulative control in between the DC grid side converters and AC grid side inverter, and for improving the power quality and reliability of the utility grid. Both continuous time and discrete time domain models are formed for the whole system for applying different control strategies. Along with MPC, the system has been controlled by using other controllers like as PI controller, Sliding Mode Controller (SMC). Luenberger observer is used to check the DC grid voltage when disturbances are implemented. Here, all the computational results are compared for justifying and validate a better controlling method for microgrid application. These kind of work is first time reported in this manuscript.

A Model-Based Design Approach for Stability Assessment, Control Tuning and Verification in Off-Grid Hybrid Power Plants

This paper proposes detailed and practical guidance on applying model-based design (MBD) for voltage and frequency stability assessments, control tuning and verification of off-grid hybrid power plants (HPPs) comprising both grid-forming and grid-feeding inverter units and synchronous generation. First, the requirement specifications are defined by means of system, functional and model requirements. Secondly, a modular approach for state-space modelling of the distributed energy resources (DERs) is presented. Flexible merging of subsystems by properly defining input and output vectors is highlighted to describe the dynamics of the HPP during various operating states. Eigenvalue (EV) and participation factor (PF) analyses demonstrate the necessity of assessing small-signal stability over a wide range of operational scenarios. A sensitivity analysis shows the impact of relevant system parameters on critical EVs and enables one to finally design and tune the central HPP controller (HPPC). The rapid control prototyping and control verification stages are accomplished by means of discrete-time domain models being used in both off-line simulation studies and real-time hardware-in-the-loop (RT-HIL) testing. The outcome of this paper is targeted at off-grid HPP operators seeking to achieve a proof-of-concept on stable voltage and frequency regulation. Nonetheless, the overall methodology is applicable to on-grid HPPs, too.

Observer-Based Predictive Vector-Resonant Current Control of Permanent Magnet Synchronous Machines

In this paper, an observer-based predictive vector-resonant current control strategy for permanent magnet synchronous machines is proposed, which can effectively improve system performance in case of disturbances caused by converter dead-time effect and model mismatch. Taking the external periodic, nonperiodic disturbances, and system delay into consideration, the system model in discrete-time domain is built. This model is then embedded with vector-resonant scheme with the aim of suppressing periodic disturbances resulting from converter dead-time effect and rotor flux harmonics. An extended-state observer is constructed in order to predict system behavior and to estimate the nonperiodic disturbances caused by parameter variations. The overall control law is then derived on basis of cost function minimization. With the proposed method adopted, the undesired anomalous peak around the resonant frequency in the frequency responses can be avoided. Moreover, enhanced transient performances and wider stability margin can also be obtained. The effectiveness and advantages of the proposed strategy are verified by frequency-domain analysis and comparative experimental studies.

Full Discrete Modeling, Controller Design, and Sensitivity Analysis for High-Performance Grid-Forming Converters in Islanded Microgrids

Recent works have shown that the state-feedback decoupling of capacitor voltage allows for drastic bandwidth enlarging of current controllers for grid-forming converters in islanded microgrids. Furthermore, Smith predictor and lead compensation have been also proved as very effective implementations for compensating the controller delays. These features are key to fulfill demanding requirements in terms of voltage regulation in islanded applications. This work deepens in the discrete-time domain modeling and implementation issues of the above-mentioned techniques. A full discrete-time and sensitivity analyses reveal phenomena not properly modeled in previous works, which limits the performance: the presence of high-frequency oscillations due to discrete poles with negative real part. Subsequently, proper design countermeasures (i.e., limit bandwidth) are proposed. Discrete implementation of the voltage controller is also addressed, and design guidelines are provided. Experimental tests in accordance with the high demanding standards for uninterruptible power supply systems verify the theoretical analysis.

High-Performance Current-Mode-Controller Design of Buck LED Driver With Slope Compensation

A discrete time domain modeling and analysis for the current-mode-controlled (CMC) buck LED driver with slope compensation is presented in this paper. The discrete time domain equation representing the buck LED driver is derived and linearized about the equilibrium state. Also, the switching control law, the proportional-integral compensator is used here as an example of the error amplifier, is linearized about the equilibrium state. The linearized buck LED driver and the control law are then combined to arrive at a linearized CMC buck LED driver. The root-locus method is employed to analyze the closed-loop system. The design guidelines and experimental results for the CMC buck LED driver are presented.

Discrete-Time Adaptive Control Design for Ionic Polymer-Metal Composite Actuators

Discrete-time adaptive control for ionic polymer-metal composite (IPMC) actuator is studied in this paper. First, a new mathematical model in discrete-time domain is proposed for IPMC actuator. Then, based on the obtained model, a discrete adaptive control law is synthesized for IPMC actuators. The proposed discrete adaptive controller can guarantee the global stability of the closed-loop system, and the position tracking error of the IPMC actuator can be controlled by the design parameters. Finally, the proposed model and control law are verified by IPMC actuator experiments.

Identification of Discrete-Time Model With Integer Delay and Control Design for Cooling Processes With Application to Jacketed Crystallizers

Motivated by the cooling process control of industrial jacketed crystallizers, this paper proposes a discrete-time domain model identification method and a model-based control scheme for such a cooling process based on a computer-aided control device. By using an input excitation of a rectangular wave to comply with practical constraints of a cooling circulator for implementation, a bootstrapping identification method is developed to establish a discrete-time integrating-type model with integer delay for describing the temperature response of the cooling process. Consistent parameter estimation against measurement noise is addressed with a proof. Correspondingly, a discrete-time two-degree-of-freedom control design is developed for the convenience of implementation in a sampled control system, which can improve the set point tracking without overshoot and load disturbance rejection. Illustrative examples from the literature and an application to a 4-L crystallizer are given to show the effectiveness and merit of the proposed model identification algorithm and control method.

Stability and Dispersion Analysis of a TLM Unified Approach for Dispersive Anisotropic Media

With the advancement of technology, modern equipment involves new functionalities that require complex media (e.g., anisotropic dispersive media such as ferrite, lossy dielectrics, or graphene) for a variety of applications. This imposes the necessity to extend simulation techniques capable of solving Maxwell’s equations in such media. However, as far as discrete time-domain models are concerned, their performance in terms of dispersion and stability criterion has not been thoroughly investigated in the presence of complex media. More particularly, a question arises about which maximum mesh size can be used and the resulting time step to ensure stability. Starting from a transmission-line matrix method algorithm for the general linear media, procedures for dispersion and stability analysis are given and special cases are presented. It is found that the proposed approach allows, in certain cases, some significant reduction in the computer cost compared to the approximate rules generally used. The same procedures can be easily extended to other time-domain schemes such as FDTD.

Discrete-Time Domain Modeling of Voltage Source Inverters in Standalone Applications: Enhancement of Regulators Performance by Means of Smith Predictor

The decoupling of the capacitor voltage and inductor current has been shown to improve significantly the dynamic performance of voltage source inverters in standalone applications. However, the computation and pulse width modulation delays still limit the achievable bandwidth. In this paper, a discrete-time domain modeling of an LC plant with consideration of delay and sample-and-hold effects on the state feedback cross-coupling decoupling is derived. From this plant formulation, current controllers with wide bandwidth and good relative stability properties are developed. Two controllers based on lead compensation and Smith predictor design, respectively, are obtained. Subsequently, the voltage regulator is also designed for a wide bandwidth, which permits the inclusion of resonant filters for the steady-state mitigation of odd harmonics at nonlinear unbalance load terminals. Discrete-time domain implementation issues of an antiwind up scheme are discussed as well, highlighting the limitations of some discretization methods. Extensive experimental results, including a short-circuit test, verify the theoretical analysis.

Digital current control in a rotating reference frame - Part I: System modeling and the discrete time-domain current controller with improved decoupling capabilities

Digital current control of three-phase voltage-source power electronic converters is analyzed. Special attention is paid to the exact discrete time-domain modeling of inductive-resistive current dynamics in the rotating reference frame whereas three different regular sampling strategies are incorporated to the analysis. The exact system model motivates the development of a new current control structure in the rotating reference frame that is based on discrete time-domain analysis. Ideally, the new discrete time-domain current controller leads to a full compensation of all cross-coupling effects that appear in the controlled system. The experimental results (performed on a 22 kW test-bench) reveal that even under test conditions an excellent decoupling capability of the presented controllers is achieved.

A Novel Continuous and Structural VAR Modeling Approach and Its Application to Reactor Noise Analysis

A vector autoregressive model in discrete time domain (DVAR) is often used to analyze continuous time, multivariate, linear Markov systems through their observed time series data sampled at discrete timesteps. Based on previous studies, the DVAR model is supposed to be a noncanonical representation of the system, that is, it does not correspond to a unique system bijectively. However, in this article, we characterize the relations of the DVAR model with its corresponding Structural Vector AR (SVAR) and Continuous Time Vector AR (CTVAR) models through a finite difference method across continuous and discrete time domain. We further clarify that the DVAR model of a continuous time, multivariate, linear Markov system is canonical under a highly generic condition. Our analysis shows that we can uniquely reproduce its SVAR and CTVAR models from the DVAR model. Based on these results, we propose a novel Continuous and Structural Vector Autoregressive (CSVAR) modeling approach to derive the SVAR and the CTVAR models from their DVAR model empirically derived from the observed time series of continuous time linear Markov systems. We demonstrate its superior performance through some numerical experiments on both artificial and real-world data.

Proportional-Integral (PI) Compensator Design of Duty-Cycle-Controlled Buck LED Driver

A discrete time-domain modeling and design for the duty-cycle-controlled buck light-emitting diode (LED) driver is presented in this paper. The discrete time-domain equation representing the buck LED driver is derived and linearized about the equilibrium state. Also the switching control law, the proportional-integral (PI) compensator is used here as an example of the error amplifier, is linearized about the equilibrium state. The linearized buck LED driver and the control law are then combined to arrive at a linearized duty-cycle-controlled buck LED driver. The root-locus method is employed to analyze the dynamic performance of the closed-loop system. Based on the modeling result, a practical design equation for the PI compensator is derived. Experimental results are presented to verify the validity of the proposed PI compensator design.

Error Amplifier Design of Peak Current Controlled (PCC) Buck LED Driver

A discrete time-domain modeling and analysis for the peak current controlled (PCC) buck light-emitting diode (LED) driver is presented in this paper. The discrete time-domain equa- tion representing the buck LED driver is derived and linearized about the equilibrium state. Also the switching control law, the proportional-integral compensator is used here as an example of the error amplifier, is linearized about the equilibrium state. The linearized buck LED driver and the control law are then combined to arrive at a linearized PCC buck LED driver. The root-locus method is employed to analyze the closed-loop system. The design guidelines and experimental results for the PCC buck LED driver are presented. Index Terms—Buck light-emitting diode (LED) driver, discrete time-domain modeling, error amplifier design, root-locus stability analysis.

Time-Domain Calibration of the LEMP Sensor and Compensation for Measured Lightning Electric Field Waveforms

The instrument decay time constant is an important parameter for a lightning electromagnetic pulse (LEMP) measuring system. So a LEMP sensor with different decay time constants (RC) will demonstrate different frequency response features of the lightning electric field instrument, and the time constant is easily affected by the environment and changes with time. To improve the performance of the lightning electric field instrument, a discrete time-domain model is established through the system identification method. On the basis of the analysis of the calibration method in the time domain and the excitation source selection, the problems of identification modeling within a broadband range of the lightning electric field instrument are discussed. A discrete time-domain model to represent the whole wideband characteristic of an LEMP measurement system can be established by the proposed method. The method can be used to correct the distorted output signal of the lightning electric field instrument. The feasibility of this identified model is verified by laboratory data as well as experimental data of an intracloud flash.