Models Of Power System Components Research Articles

Feasibility Study of Neural ODE and DAE Modules for Power System Dynamic Component Modeling

In the context of high penetration of renewables, the need to build dynamic models of power system components based on accessible measurement data has become urgent. To address this challenge, firstly, a neural ordinary differential equations (ODE) module and a neural differential-algebraic equations (DAE) module are proposed to form a data-driven modeling framework that accurately captures components' dynamic characteristics and flexibly adapts to various interface settings. Secondly, analytical models and data-driven models learned by the neural ODE and DAE modules are integrated together and simulated simultaneously using unified transient stability simulation methods. Finally, the neural ODE and DAE modules are implemented with Python and made public on GitHub. Using the portal measurements, three simple but representative cases of excitation controller modeling, photovoltaic power plant modeling, and equivalent load modeling of a regional power network are carried out in the IEEE-39 system and 2383wp system. Neural dynamic model-integrated simulations are compared with the original model-based ones to verify the feasibility and potentiality of the proposed neural ODE and DAE modules.

Modeling and analysis approaches for small‐signal stability assessment of power‐electronic‐dominated systems

AbstractThe stability, operation, and control of power networks have been challenged due to the increased penetration of power electronic converters. New instability phenomena have appeared due to the interaction of the power converter controllers with other power network elements, including other power converters. Small‐signal tools have been proved effective to identify and mitigate stability issues but their development is still ongoing. This article presents the state of the art on small‐signal modeling and stability assessment of converter‐dominated networks. The modeling of converters and other power system components is reviewed, as well as the most common small‐signal analysis techniques employed in conventional and modern power systems with power electronics. Two case studies are introduced to exemplify the modeling and stability analysis, employing some of the techniques presented in the article.This article is categorized under: Energy and Power Systems > Distributed Generation

On the Choice of Methods for Numerically Integrating the Equations of Transients in Electric Power Systems

Algorithms for solving the system of differential-algebraic equations describing electromechanical transients in electric power systems are considered along with matters concerned with ensuring the reliability and required accuracy of the solution results. Classical explicit methods, methods for implicit numerical integration and simultaneous solution of differential-algebraic systems of equations are used to model dynamic processes in power systems. On the basis of the methods used, difference models of electric power system components are obtained. The equations of transients in electric power systems are written in a homogeneous coordinate basis with the use of nodal voltage equations. A comparative analysis of algorithms based on the explicit Runge-Kutta method and implicit methods of Euler, trapezoids, Euler with fitting coefficients is carried out. The analysis results have shown that in terms of stability and accuracy, the trapezoid method has the greatest advantages, which is not inferior to the 4th order Runge-Kutta method and allows calculations with a large integration step to be carried out. The effectiveness of the combined method is shown, in which the Euler method with fitting is used to solve the differential equations describing electromagnetic processes, and the trapezoid method is used to solve the equations of electromechanical motion.

Extending the Frequency Bandwidth of Transient Stability Simulation Using Dynamic Phasors

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 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.

Novel models of power system components for implicit solution of the adjusted power flow problem

AbstractThe solution of the adjusted power flow problem involves handling power system components whose control characteristics possess operational limits. Examples include generator reactive power limits, tap-changing and phase-shifting transformers, and FACTS devices. While the conventional method involves checking for limit violations in an outer loop drawn around the unadjusted power flow problem being solved by the Newton-Raphson (NR) method, for iterative processes, it is desirable to have smooth, continuously differentiable models implicitly handled within a single loop. A novel formulation for a subset of devices is presented for implicit handling within power flow. The steady state characteristics of tap-changing and phase-shifting transformers, and FACTS devices SVC and STATCOM, can be described using the “cut function”, a piecewise linear function traditionally employed in neural networks. A new approximation of the cut function is used for formulating novel equations describing the steady state characteristics. An augmented set of equations is formed and solved by the NR method, eliminating the need of an outer loop. The efficacy of the proposed method is demonstrated by employing it for plotting bus voltage profiles and determining maximum loadability of test systems. Comparisons with the conventional method show that significant savings in computation can be achieved.

The Method of “Characteristic” Currents and Countercurrents for Short Circuits Diagnosis

Many software are available to analyze the design of electrical power systems. Therefore, it becomes relevant to know the rules of thumb to be able to diagnose in an elementary and intuitive way the computerized results. For the short-circuit analysis, in most practical cases, it is sufficient to adopt simplified and standard-based calculation methods. This article introduces the parameter of the countercurrents and illustrates the approach of the short-circuit models of power system components based on the “characteristic” currents method. This article, at first, presents a short overview of the IEC Std 60909, assumed as a reference for the proposed approach.

Analysis of Frequency-Dependent Network Equivalents in Dynamic Harmonic Domain

Rational function-based models have proved to be very efficient for accurate frequency-dependent modeling of power system components. These models are able to characterize the components terminal behaviours (analysing the admittance matrix) for nodal analysis. This provides a fast convergence and inherent stability to the solution routine of the model. This work presents a general framework for interfacing the dynamic phasor method to the rational models. That would be promising for the electromagnetic transient analysis (under harmonic distortion), in the frequency domain. Therefore, Y-element rational pole-residue models (employing the vector fitting method) are developed. Moreover, the pole-residue model is converted into the state-space representation. Next, the dynamic harmonic approach (in the frequency domain) is employed for harmonic analysis. It is shown that the order of state-space system can become a major concern for frequency-dependent networks analysis. Therefore, to generate a reduced-order model, the balanced realization theory is applied. Moreover, (for the sake of simplicity and efficiency) the trapezoidal integration rule is employed to discretise the state-space equations. For validation of the modelling, it is applied on three test case studies and results of these studies are compared with their time-domain analysis results.

Parameters determination of time-delayed embedding with application to Koopman operator-based model predictive frequency control

Power systems around the world have been registering a degenerating inertial response in view of the growth of inverter-based resources along with the withdrawal of conventional coal units. Therefore, there is a need for swift frequency support and its control, preferably by means of power electronic-interfaced storage devices, owing to their beneficial capabilities. Despite being particularly efficient, pragmatically, the traditional model-based non-linear control techniques are not highly popular in power system control design, primarily due to the complications faced in obtaining accurately suitable models for certain power system components. Lately, the modelfree Koopman operator-based model predictive control (KMPC) has proven to be highly conducive for data-driven non-linear control design. The principle behind KMPC is to change the coordinates in a manner to get an approximately linear model, which can then be controlled using a linear model predictive control. In this study, we employed time-delayed embedding of measurements to reconstruct a new set of preferable coordinates, thereby suggesting an approach for finding the optimal number of time lags and the embedding dimensions which are the key parameters of this algorithm. The efficacy of this KMPC framework is established by adopting a decentralized frequency control problem through a decoupled synchronous machine system, which we proposed for both the Kundur two-area system as well as the IEEE 39-bus test system.

Software Solution for Modeling, Sizing, and Allocation of Active Power Filters in Distribution Networks

The paper is related to the problem of modeling and optimizing power systems supplying, among others, nonlinear loads. A software solution that allows the modeling and simulation of power systems in the frequency domain as well as the sizing and allocation of active power filters has been developed and presented. The basic assumptions for the software development followed by the models of power system components and the optimization assumptions have been described in the paper. On the basis of an example of a low-voltage network, an analysis of the selection of the number and allocation of active power filters was carried out in terms of minimizing losses and investment costs under the assumed conditions for voltage total harmonic distortion (THD) coefficients in the network nodes. The presented examples show that the appropriate software allows for an in-depth analysis of possible solutions and, furthermore, the selection of the optimal one for a specific case, depending on the adopted limitations, expected effects, and investment costs. In addition, a very high computational efficiency of the adopted approach to modeling and simulation has been demonstrated, despite the use of (i) element models for which parameters depend on the operating point (named iterative elements), (ii) active filter models taking into account real harmonics reduction efficiency and power losses, and (iii) a brute force algorithm for optimization.

Parallel-in-Time Object-Oriented Electromagnetic Transient Simulation of Power Systems

Parallel-in-time methods are emerging to accelerate the solution of time-consuming problems in different research fields. However, the complexity of power system component models brings challenges to realize the parallel-in-time power system electromagnetic transient (EMT) simulation, including the traveling wave transmission lines. This paper proposes a system-level parallel-in-time EMT simulation method based on traditional nodal analysis and the Parareal algorithm. A new interpretation scheme is proposed to solve the transmission line convergence problem. To integrate different kinds of traditional EMT models, a component-based EMT system solver architecture is proposed to address the increasing model complexity. An object-oriented C++ implementation is proposed to realize the parallel-in-time Parareal algorithm based on the proposed architecture. The results on the IEEE-118 test system show 2.30x speed-up compared to the sequential algorithm under the same accuracy with 6 CPU threads, and a high parallel efficiency around 40%. The performance comparison of various IEEE test cases shows that the system’s time-domain characteristics determine the speed-up of Parareal algorithm, and the delays in transmission lines significantly affect the performance of parallel-in-time power system EMT simulations.

Comprehensive computer program for SSTI analysis of AC/DC power systems based on the component connection method

This paper presents a comprehensive methodology for the investigation of SSTI in AC/DC transmission networks. The main advantage of the proposed methodology is the modular modeling approach, where various complex components can be modeled in a comprehensive way while at the same time preserving the level of detail needed to capture the relevant dynamics. This is done by enhancing the CCM with an algorithm for the formulation of network state equations. All power system component models necessary for SSTI analysis are developed separately using the CCM principles and are connected according to their topological relations. A small-signal model of a point-to-point MMC-based VSC HVDC is developed to assess its influence on SSTI. The proposed methodology together with the developed models are implemented in a software framework called SNAP. The proposed methodology and the developed models are validated against time-domain simulations in PSS®NETOMAC.

A Three Phase Matlab Simulink Model of IEEE 57 Bus Power System Network

The Electrical power system, field engineers always strive to design a Real time power system model to anticipate the practical outcomes. The simulation software not only fixes the changes in power system, but also trying to perceive the potential impact of power system before construction. A realistic model of the power system is very essential for the future and present operations. Present, this paper makes center of attention on designing of 3-phase power system network of IEEE 57 bus power system network within the Matlab Simulink module. It supports GUI (Graphical User Interface) based models of power system components, which are used to design a dynamic model of the power system. The present design is based on the test case data and the one line diagram; so that the three-phase model is equivalent to single phase one line diagram. The simulation of this model allows for verification of voltage, current, active power and reactive power of each bus and variation of those parameters with respect to time domain waveform. The present model is also useful for learning the operation of the power system network under Steady state, Transient state and Dynamic state with the application of FACTS, Fuzzy, and ANN etc.

Implementation of the frequency dependent line model in a real-time power system simulator

In this paper is described the implementation of the frequency-dependent line model (FD-Line) in a real-time digital power system simulator. The main goal with such development is to describe a general procedure to incorporate new realistic models of power system components in modern real-time simulators based on the Electromagnetic Transients Program (EMTP). In this procedure are described, firstly, the steps to obtain the time domain solution of the differential equations that models the electromagnetic behavior in multi-phase transmission lines with frequency dependent parameters. After, the algorithmic solution of the FD-Line model is implemented in Simulink environment, through an S-function programmed in C language, for running off-line simulations of electromagnetic transients. This implementation allows the free assembling of the FD Line model with any element of the Power System Blockset library and also, it can be used to build any network topology. The main advantage of having a power network built in Simulink is that can be executed in real-time by means of the commercial eMEGAsim simulator. Finally, several simulation cases are presented to validate the accuracy and the real-time performance of the FD-Line model.

Large Multi-Machine Power System Simulations Using Multi-Stage Adomian Decomposition

Multi-stage Adomian decomposition method (MADM) is a proven semi-analytical approximation solution technique for ordinary differential equations (ODEs), which provides a rapidly convergent series by integrating over multiple time intervals. Applicability of MADM for large nonlinear differential algebraic systems (DAEs) is established for the first time in this paper using the partitioned solution approach. Detailed models of power system components are approximated using MADM models. MADM applicability is verified on 7 widely used test systems ranging from 10 generators, 39 buses to 4092 generators, 13659 buses. Impact of the step size and the number of terms is investigated on the stability and accuracy of the method. An average speed up of 42% and 26% is observed in the solution time of ODEs alone using the MADM when compared to the midpoint-trapezoidal (TrapZ) method and the modified-Euler (ME) method, respectively. MADM accuracy is found to be similar to the ME and comparable to the TrapZ method. MADM stability properties are found to be better than the ME and weaker than the TrapZ method. An average speed up of 13% and 5.85% is observed in the overall solution time using MADM w.r.t. TrapZ and ME methods, respectively.

Validation of single-phase transformer model for ferroresonance analysis

The validation of power system component models for transient analysis implies the use of data recorded from either field measurements or laboratory tests. This task can be particularly difficult when the transient process is quite nonlinear, as it occurs in ferroresonance phenomena. Up-to-date research has proved that the \({\uppi }\) model can be more accurate than the classical T model for representing the transient response of transformers with a high level of saturation. This paper proposes a new technique for representing and implementing hysteresis in low-frequency transformer models using the \({\uppi }\) approach. The ultimate goal is to validate the addition of hysteresis effects in the \({\uppi }\) model for single-phase transformer representation in ferroresonance studies.

Dynamic Modeling of Networks, Microgrids, and Renewable Sources in the dq0 Reference Frame: A Survey

With increasing the penetration of distributed and renewable sources into power grids, and with increasing the use of power electronics-based devices, the dynamic behavior of large-scale power systems is becoming increasingly complex. These recent developments have led to several models attempting to simplify the analysis of dynamic phenomena, among them are models based on the dq0 transformation. Many recent works present dq0-based models of various power system components, ranging from small renewable sources to complete networks. The purpose of this paper is to review and categorize these works, with an objective to promote a straightforward modeling and the analysis of complex systems, based on dq0 quantities. This paper opens by recalling basic concepts of the dq0 transformation and dq0-based models. We then review several recent works related to dq0 modeling and analysis, considering the models of passive components, complete passive networks, synchronous machines, wind turbine systems, photovoltaic inverters, and others.

A Constant-Parameter Voltage-Behind-Reactance Synchronous Machine Model Based on Shifted-Frequency Analysis

Recently, the concepts of dynamic phasors and shifted-frequency analysis (SFA) have received renewed attention as a possible solution framework for the modeling of power system components and transients, as opposed to using instantaneous time-domain variables or conventional phasors. In this paper, a new voltage-behind-reactance (VBR) synchronous machine model based on SFA is presented. Using dynamic phasors, the proposed model permits the use of a much larger range of step sizes to efficiently simulate electromagnetic and electromechanical transients. Moreover, the proposed model has a constant-parameter (CP) stator interface, which is simple to implement and numerically more efficient compared with the prior state-of-the-art models with rotor-position-dependent stator inductance matrices. Rigorous transient case studies demonstrate that the new model requires significantly fewer time steps than the conventional time-domain models, and is more efficient than the previously established variable-parameter SFA model.

A novel simplified approach to complexity of power system components including nonlinear controllers based model reduction

Abstract Based on differential algebraic (DA) subsystem models of power system components including the nonlinear controllers, which are called component structural complex models, this paper presents a model reduction method (MRM). For the dynamic differential equations, based on the property that the nonlinearity of the controller compensates that of the component completely (or partially), the presented method uses the linear dynamic equations to describe the compensated dynamics. For the algebraic connection equations, the new defined state variables are used to substitute the original state variables for keeping the connection relation invariable. By selecting generators and static var compensators (SVC) as examples, the paper presents the basic procedure of the proposed reduction method for power system component complex models in detail. The numerical simulation indicates that the derived simplified models matches the original one very well in both dynamic response behaviors and the connection relation with the external system.

Modeling and Simulation of the Protection of Distribution Feeders in ATP

This article presents the modeling and simulation in the ATP (Alternative Transients Program)/MODELS of devices used in overcurrent protection of distribution networks such as reclosers , sectionalisers , fuses , digital relays and current transformers. A radial feeder with 63 buses was used in the study case. Numerous tests of short - circuits involving single-phase, two phases and three phases at various points of the feeder, were performed, with the purpose of validating the developed models and check the performance of the protection system. The results show the advantages of this type of modeling through which it is possible to evaluate the behavior of the power system against the operation of the protection and the protection front to diverse operating situations to which it is subjected. This study may contribute to the solution of problems of adjustment, coordination and analysis of the behavior of the distribution network using it for more elaborate models of power system components that are available in the ATP software.

Switching Overvoltage Measurements and Simulations—Part I: Field Test Overvoltage Measurements

This paper presents the work carried out by the IEEE Working Group on field-measured overvoltages and their analysis for validating power system component models to be used in switching transients studies. The work uses measurement data obtained from field tests performed by Bonneville Power Administration in June 1995 where switching overvoltages were measured on one of its 230 kV lines. This paper includes a description of the switching tests and the main results derived from field measurements. Details of the switching procedures that were followed to calibrate component models used to match field-recorded waveforms can be found in the Part II paper.