Dynamic Average-value Modeling Research Articles

Dynamic Average-Value Modeling of Three-Level T-Type Grid-Connected Converter System

Three-level T-type converter (3LT2C) possesses the advantages of simple structure and high efficiency, which makes it appealing especially in low- and medium-voltage applications. Dynamic average-value modeling (AVM) has become an effective methodology for small-signal analysis and large-signal transients of power electronic subsystems in power systems applications. In this paper, a dynamic AVM for the three-phase 3LT2C is presented for the first time. The proposed model is derived using the state-space average approach, where the averaging process is implemented over each pulsewidth modulation switching period. The ac- and dc-side dynamics are represented by a fourth-order time-invariant system. The accuracy of the developed AVM is validated against the detailed switching model, while demonstrating its computational advantages. The new model is also verified using experimental tests on a prototype.

Dynamic modelling and long‐term simulation of ultracapacitor‐type ESS integration in power grid

A novel dynamic average-value model (AVM) of energy storage systems (ESS) integration in power grid for long-term control is developed and validated. It is expected to greatly improve the computational speed of power system dynamics in a long-term simulation. To end this, the development of the dynamic AVM of ESS integration including ultracapacitor, DC–DC converter, and voltage source converter is elaborated upon. A new control strategy which uses digital logic circuit is proposed to keep the ultracapacitors from overcharging without significantly increasing the charging time. To validate the proposed dynamic AVM and control strategy, case studies are carried out to perform the dynamics as affected by sudden changing of charging/discharging of ESS. The accuracy of the proposed model and controller is verified by the simulation results with that obtained from the detailed model implemented in MATLAB/Simulink. Moreover, the time-step size is enlarged greatly without sacrificing the accuracy, therefore the computational speed is improved significantly.

Using Multiple Reference Frame Theory for Considering Harmonics in Average-Value Modeling of Diode Rectifiers

Line-commutated converters (LCCs) are widely used in various high-power applications such as generator-rectifier systems, exciters, front-end rectifier loads, and classic high voltage dc systems. Among various techniques used for modeling LCC systems, the dynamic average value modeling (AVM) wherein the effect of switching is neglected or averaged over a prototypical switching interval has become indispensible since it results in continuous, linearizable, and computationally efficient models. The conventional AVMs can only predict the fundamental component of the ac voltages and currents, and neglect the harmonics injected at the ac side by the switching converter. In this paper, a recently proposed parametric average-value modeling (PAVM) approach is extended using multiple reference frame theory to include the significant harmonics of interest (e.g., fifth and seventh) for diode rectifiers. The new PAVM is verified against the detailed simulation in steady-state and transient studies, and is effective in predicting the transient waveforms, while achieving significant computational advantage (speed up) in time-domain simulation over conventional models.

A Generalized Methodology for Dynamic Average Modeling of High-Pulse-Count Rectifiers in Transient Simulation Programs

High-pulse-count rectifier systems (with more than six pulses) are often used in high-power applications. Dynamic average value modeling (AVM) has proven to be indispensable for simulation and analysis of such power electronic systems. However, developing accurate AVMs for such line-commutated converters is challenging due to the presence of complicated switching patterns (operating modes), configuration of multi-phase transformers and/or rotating machines, inter-phase transformers, filters, etc. This paper presents a generalized methodology for full-order dynamic average modeling of high-pulse-count line-commutated rectifiers, which is based on the recently proposed parametric AVM approach. Extensive simulation studies are carried out considering the 18-pulse rectifier example system. The accuracy and numerical advantages of the developed generalized AVM is verified against the detailed switching model, and a previously established average model in time and frequency domains.

Verification of Parametric Average-Value Model of Thyristor-Controlled Rectifier Systems for Variable-Frequency Wind Generation Systems

Line-commutated thyristor-controlled rectifiers are often used in many industrial and renewable energy applications where controllable dc voltage is required. The derivation of accurate dynamic average-value models for thyristor-controlled systems is challenging. The recently proposed parametric average value modeling (PAVM) avoids the discrete switching states of the converters and results in computationally efficient models that are suitable for system level studies. This paper extends the PAVM recently developed for synchronous-machine-fed thyristor-controlled-rectifier systems to a permanent magnet synchronous machine wind generation system where the operation in variable speed and frequency is required.

Dynamic Average-Value Modeling of Direct Power-Controlled Active Front-End Rectifiers

Active front-end (AFE) rectifiers are becoming widely used in medium-to-high-power adjustable speed drives (ASDs) to achieve regenerative operation and meet the energy efficiency and harmonic requirements. The typical control methods used with AFE rectifiers include voltage-oriented control (VOC), direct power control (DPC) and virtual-flux-based methods. This paper presents a dynamic average-value model (AVM) of the AFE rectifier system which is based on the voltage-source converter (VSC) operated with DPC. The developed AVM and the modeling methodology presented in this paper highlight the specifics of the hysteresis bang-bang type DPC that is used to track the real and reactive power references. The proposed AVM of the AFE rectifier system is demonstrated to significantly reduce the computing effort while accurately capturing the fast transient performance of the system.

Dynamic Average-Value Modeling of CIGRE HVDC Benchmark System

High-voltage direct-current (HVDC) systems play an important role in modern energy grids, whereas efficient and accurate models are often needed for system-level studies. Due to the inherent switching in HVDC converters, the detailed switch-level models are computationally expensive for the simulation of large-signal transients and hard to linearize for small-signal frequency-domain characterization. In this paper, a dynamic average-value model (AVM) of the first CIGRE HVDC benchmark system is developed in a state-variable-based simulator, such as Matlab/Simulink, and nodal-analysis-based electromagnetic transient program (EMTP), such as PSCAD/EMTDC. The 12-pulse converters in the HVDC system are modeled with a set of nonlinear algebraic functions that are extracted numerically. The results from the average-value models are compared with the results of the detailed simulation to verify the accuracy of the AVMs in predicting the large-signal time-domain transients. The developed dynamic average models are shown to have computational advantages.

Direct Interfacing of Dynamic Average Models of Line-Commutated Rectifier Circuits in Nodal Analysis EMTP-Type Solution

Dynamic average-value models (AVMs) for AC-DC rectifier circuits are generally formulated in state-space form and hence are straightforward to implement in state-variable-based simulation languages. In the nodal analysis-based approach used in electromagnetic transient (EMTP-type) simulation packages, the development of AVMs requires additional effort to reformulate and interface the models with the external ac and dc networks. This paper proposes a new averaged-circuit model for three-phase line-commutated rectifiers which is directly interfaced with the ac and dc networks, thereby achieving a simultaneous solution of the respective variables in EMTP-type solution. The proposed model is verified against conventionally interfaced model, as well as detailed switching model of the original rectifier circuit. A significant improvement of numerical accuracy and stability of the solution is demonstrated even at fairly large time steps.

Steady-State and Dynamic Performance of Front-End Diode Rectifier Loads as Predicted by Dynamic Average-Value Models

The detailed switch-level models of front-end diode rectifier loads can be readily implemented using a number of transient simulation programs, such as PSCAD/EMTDC, and the toolboxes in Matlab/Simulink. To improve the simulation efficiency for the system-level studies, the so-called dynamic average models have been widely used by researchers and engineers. Recently, several average-value modeling methodologies for the conventional three-phase (six-pulse) front-end rectifier loads have been discussed, and the dynamic performance of several developed models has been demonstrated in discontinuous and continuous modes. In this paper, the effects of topological variations of the ac-side filters on the system performance are investigated. Also, the steady-state and dynamic impedances predicted by the average models under balanced and unbalanced operation are compared. The studies and analyses presented here extend and complement those set forth in the preceding companion publication.

Dynamic Average-Value Modeling of 120° VSI-Commutated Brushless DC Motors With Trapezoidal Back EMF

The 120° voltage source inverter driven brushless dc (BLDC) motors are very common in many applications. This paper extends the previous work and presents an improved dynamic average-value model for such BLDC motor-drive systems. The new model is explicit and uses a proper qd model of the permanent magnet synchronous machine with nonsinusoidal rotor flux. The model utilizes multiple reference frame theory to properly include the back EMF harmonics as well as commutation and conduction intervals into the averaged voltage and torque relationships. The commutation angle is readily obtained from the detailed simulation. The proposed model is demonstrated on a typical industrial BLDC motor with trapezoidal back EMF waveforms. The results of studies are compared with experimental measurements as well as previously established models, whereas the new model is shown to provide appreciable improvement.

Dynamic Average-Value Modeling of Hybrid-Electric Vehicular Power Systems

This paper extends the concept of dynamic average-value modeling to power-electronic-intensive hybrid-electric vehicular power trains. Hybrid vehicles with plug-in capability are becoming increasingly important in the study of emerging smart power grids, and their simulation using digital programs has gained widespread attention. This paper demonstrates the usefulness of averaging in preserving the dynamic characteristics of the vehicular system while reducing the computational intensity of its simulation on an Electromagnetic Transients Program-type simulator. This paper presents an example of averaging for modeling, simulation, and system-level studies of a power-split gear hybrid drive-train.

Definitions and Applications of Dynamic Average Models for Analysis of Power Systems

Modeling and analysis of power and power-electronic systems' transients using digital programs enables testing new design concepts in modern electric grid and many industrial and commercial products and applications. This paper gives an overview of dynamic average-value modeling techniques for representing static switching converters for the system-level studies. Concepts and desirable properties of averaged models for conducting large-signal time-domain transient studies and small-signal frequency-domain analysis for control design tasks are discussed. Basic approaches for developing average models for dc/dc and dc/ac converters are briefly reviewed and summarized. Finally, the desirable properties of the average-value models are demonstrated through an example system.

Numerical Dynamic Characterization of Peak Current-Mode-Controlled DC–DC Converters

Peak current-mode (PCM) control of pulsewidth-modulated (PWM) dc-dc converters is highly desired for its fast dynamic response and automatic overload protection. Dynamic characterization of PCM converters is mainly conducted via average-value modeling. However, deriving the average-value models of PCM converters is challenging when the component parasitics and different conduction modes are considered. This paper extends a recently developed computer-aided methodology to the PCM converters and presents an accurate dynamic average-value model that considers the parasitics and true averages of nonlinear waveforms. The proposed model is functional in all operational modes and is validated in large-signal transient studies and small-signal characterizations.

Numerical Validation of Parametric Average-Value Modeling of Synchronous Machine--Rectifier Systems for Variable Frequency Operation

The derivation of accurate dynamic average-value models for synchronous machine-rectifier systems is challenging. A recently proposed parametric approach uses a computer-aided procedure for constructing the required averaged models, wherein the key nonlinear functions are extracted from a detailed (valve-by-valve) simulation. This letter shows that by using a judicious selection of parametric functions, a model obtained at a fixed generator speed is also valid for variable speeds. This is an important feature that makes this approach applicable to systems where electromechanical dynamics and variable speed operation is required.

Numerical Validation of Parametric Average-Value Modeling of Synchronous Machine–Rectifier Systems for Variable Frequency Operation

The derivation of accurate dynamic average-value models for synchronous machine-rectifier systems is challenging. A recently proposed parametric approach uses a computer-aided procedure for constructing the required averaged models, wherein the key nonlinear functions are extracted from a detailed (valve-by-valve) simulation. This letter shows that by using a judicious selection of parametric functions, a model obtained at a fixed generator speed is also valid for variable speeds. This is an important feature that makes this approach applicable to systems where electromechanical dynamics and variable speed operation is required.

Averaged-Switch Modeling of Fourth-Order PWM DC–DC Converters Considering Conduction Losses in Discontinuous Mode

This manuscript addresses dynamic average-value modeling for fourth-order pulse-width modulation (PWM) DC-DC converters in discontinuous capacitor-voltage mode. Although significant literature is devoted to analysis of the inductor-based switching stage of second-order DC-DC converters in discontinuous current mode, much less has been published regarding the discontinuous voltage mode in the capacitor-based switching stage in fourth-order converters. Accurate average-value models are further complicated by the presence of non-ideality in the switching stage components. This manuscript presents a full-order average-value model for the capacitor-based switching stage, taking into account conduction losses according to the energy conservation principle. The proposed model is validated with a hardware prototype and detailed simulation and is shown to accurately predict large-signal time-domain transients as well as small-signal frequency-domain characteristics.

Fast Procedure for Constructing an Accurate Dynamic Average-Value Model of Synchronous Machine-Rectifier Systems

The analytical derivation of the average-value models (AVMs) for synchronous-machine-fed rectifier systems depends on many factors and is challenging in general. Various models presented in the literature rely on a single operating mode and a dc filter configuration. A recently proposed parametric approach utilizes a detailed simulation as a basis to establish an AVM that uses a proper full-order qd generator model. This paper presents a procedure to extract the appropriate nonlinear algebraic functions to represent the rectifier averaged behavior. In contrast to existing methods, the proposed procedure does not require significant analytical derivations and/or computational resources and results in a highly accurate dynamic AVM. The proposed methodology is validated with the results of detailed simulation and hardware experiment, and is shown to be very accurate in predicting the large-signal time-domain transients as well as the small-signal frequency-domain characteristics.

Dynamic average-value modeling of a four-level drive system

Multilevel power converters have gained much attention in recent years due to their high power quality, low switching losses, and high-voltage capability. These advantages make the multilevel converter a candidate for the next generation of naval ship prolusion systems. Evaluation of these systems is typically assisted with a dynamic average-value models in order to rapidly predict system performance under several operating scenarios. In this paper, an average-value model is developed for the four-level diode-clamped converter which takes into account the active capacitor voltage balancing control. This model performance prediction is compared to a detailed model and laboratory measurements on an 18 kW rectifier/inverter test system.

Steady-state characteristics of synchronous machine-line-commutated converter systems

A steady-state model of a synchronous machine-line-commutated converter pair is obtained from a dynamic average-value model of the system that accurately accounts for subtransient saliency of the machine. This steady-state model is comprised exclusively of linear and nonlinear algebraic equations that relate key variables of the system. Various algorithms for solving these equations to generate characteristics that relate two or three of these variables at a time are described. Specific characteristics that are illustrated include machine torque versus firing angle for constant dc current and dc voltage versus dc current for constant firing angle.

Steady-State Characteristics of Synchronous Machine-Line-Commuted Converter Systems

A steady-state model of a synchronous machine-line-commutated converter pair is obtained from a dynamic average-value model of the system that accurately accounts for subtransient saliency of the machine. This steady-state model is comprised exclusively of linear and nonlinear algebraic equations that relate key variables of the system. Various algorithms for solving these equations to generate characteristics that relate two or three of these variables at a time are described. Specific characteristics that are illustrated include machine torque versus firing angle for constant dc current and dc voltage versus dc current for constant firing angle.