Model Of Synchronous Generator Research Articles

Nonlinear Dynamic Systems Parameterization Using Interval-Based Global Optimization: Computing Lipschitz Constants and Beyond

Numerous state-feedback and observer designs for nonlinear dynamic systems (NDS) have been developed in the past three decades. These designs assume that NDS nonlinearities satisfy one of the following <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">function set classifications:</i> bounded Jacobian, Lipschitz continuity, one-sided Lipschitz, quadratic inner-boundedness, and quadratic boundedness. These function sets are characterized by <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">constant</i> scalars or matrices bounding the NDS’ nonlinearities. These constants depend on the NDS’ operating region, topology, and parameters and are utilized to synthesize observer/controller gains. Unfortunately, there is a near-complete absence of algorithms to compute such bounding constants. In this article, we develop analytical and computational methods to compute such constants. First, for every function set classification, we derive analytical expressions for these bounding constants through global maximization formulations. Second, we utilize a derivative-free interval-based global maximization algorithm based on the branch-and-bound framework to numerically obtain the bounding constants. Third, we showcase the effectiveness of our approaches to compute the corresponding parameters on some NDS such as highway traffic networks and synchronous generator models.

Improvement of Low-Voltage Ride-Through Capability for Wave Energy Conversion System

With the wave energy conversion system (WECS) integrated to grid, the lack of satisfactory ability to ride through transient voltage faults will reduce the stability and reliability of the grid. In this article, in order to enhance the low-voltage ride-through (LVRT) capability of the WECS, the structure and the mathematical model of a magnetic-gear permanent magnet synchronous generator (MG_PMSG) and a float-type wave energy converter are introduced first. The output power characteristic of the WECS is analyzed. Then, a novel coordinative LVRT control scheme based on supercapacitor energy storage system (SC_ESS) is proposed. The control scheme includes four modes, which are determined by the severity of voltage sags and active power deviation of the WECS. Machine-side converter control, grid-side converter, control and SC_ESS control are used coordinately in the four operation modes. The results of simulation and experiment have verified the effectiveness of the proposed control scheme in normal running conditions.

Variable parameter practical model of synchronous generator for precise simulation of power system

The model of synchronous generator (SG) plays an important role in the simulation of power system and planning of power grid. With the constant parameter practical model (CPPM), it is difficult to consider the time-varying characteristic of the parameters affected by the complex non-linear factors, such as the saturation, distortion, skin effect and various spatial harmonics; thus, it cannot guarantee the precision of the simulation. In this paper, a variable parameter practical model (VPPM) of SG is proposed by coupling the CPPM with the three-dimensional parameter database and the parameter addressing model. The three-dimensional parameter database containing the steady-state, transient and sub-transient reactances and time constants is established with the terminal voltage, active power and reactive power as the variables. The parameters of the VPPM are selected through linear inter-polation according to the operating states of the generator. In order to verify the precision of the VPPM, a single-machine infinite system and a real power system with 204 buses and 107 generators are simulated. The result indicates that the VPPM is more accurate than the CPPM, and the stability limit and damping ratio calculated by the VPPM are larger than that by the CPPM. The study can provide important support for the precise simulation of the power system.

Dynamic Performance Enhancement of a Direct-Driven PMSG-Based Wind Turbine Using a 12-Sectors DTC

This paper focuses on the performance analysis, modeling, and control of permanent magnet synchronous generator (PMSG)-based wind energy conversion. This work analyzes controllers for the machine-side converter (MSC) and grid-side converter (GSC) and presents a new direct torque control (DTC) scheme based on a 12-sectors polygonal DTC for variable speed control of the PMSG. The proposed method solves the drawbacks faced by conventional six-sectors DTC control. The proposed method utilizes 12 sectors of 30° each compared to 60° in the conventional 6-sectors DTC. The 12-sectors technique was applied to voltages and flux vectors to increase the degrees of freedom for the selection of optimal vectors and, thus, reduce the torque ripple. This work analyzed the aforementioned DTC methods using MATLAB/Simulink, comparing the dynamic response of the proposed 12-sectors DTC with the conventional 6-sectors DTC control, and the results verified the effectiveness of the proposed DTC control.

Using of a single-phase synchronous multi-winding generator with permanent magnets for the power supply of an autonomous consumer

THE PURPOSE. Consider the existing ways of using electromechanical converters for power supply of an autonomous consumer. Conduct a comparative analysis of electromechanical converters, scenarios and conditions for their use in the power supply of an autonomous consumer. To develop a proposal to eliminate the shortcomings in existing models of synchronous generators in order to increase their controllability. To develop a mathematical description of a synchronous generator with magnetoelectric excitation from permanent magnets of a single-phase type with a simplified design as a universal example of the functioning of the entire proposed line of synchronous generators. Carry out mathematical modeling of the generator proposed for consideration in order to confirm the proposed method of regulating the generated parameters, such as current and voltage, without the need to change the generator shaft rotation speed.METHODS. When solving the problem, the method of describing an electric machine in a dq-coordinate system using a multi-winding description of the machine was used; to confirm the proposed control method, mathematical modeling with the SimInTech environment was used.RESULTS. The article describes the relevance of the topic, considers the features of the operation of various electromechanical converters for power supply of an autonomous consumer, indicates the conditions for the use of one type or another of the architects of the power supply system in conjunction with electromechanical converters. A line of synchronous generators with magnetoelectric excitation is proposed in order to improve their controllability, namely, the ability to regulate the output generated parameters.CONCLUSION. Using of the proposed synchronous generators with excitation from permanent magnets will allow for additional regulation of the generated parameters, thereby allowing either completely or partially to exclude additional semiconductor converting equipment, thereby reducing losses during the conversion of electrical energy. Moreover, it is possible to regulate the generated current and voltage discretely by two times increasing one of these values, this method of regulation depends on the design of the generator.

A comprehensive assessment of the state-of-the-art virtual synchronous generator models

The large-scale penetration of renewable energy sources has a significant impact on the steady-state operation and emergency control of modern electric power systems (EPS). Moreover, as a rule, the mentioned impact is negative. Therefore, the challenge associated with the development of a ‘comprehensive’ control strategy for renewables becomes extremely relevant. Such a strategy should ensure the same reliable operation of EPSs, as in the case of conventional synchronous generation. Among the existing directions, the concept of a virtual synchronous generator (VSG) is the most preferable. Within this paper, the synthesis and combination of the state-of-the-art concepts of VSG into generic structures has been performed. For the obtained structures, a comprehensive assessment and an experimental comparison were performed. On the basis of the results obtained, the benefits and drawbacks of the generic structures are highlighted, and a conclusion is made about the VSG structure, demonstrating the most effective and reliable operation.

Air-gap eccentricity fault detection, isolation, and estimation for synchronous generators based on eigenvalues analysis

Air-gap eccentricity fault causes rotor–stator rub and consequently damage to Synchronous Generators (SGs). In this paper, a fault diagnosis approach to diagnose the eccentricity fault for SGs is presented. In this approach, the state matrix eigenvalues based on the subspace identification are estimated, and those are used for fault diagnosis. Two dq models of SGs in faulty and healthy conditions are employed to present the theoretical foundation of the method. As the main advantage, the introduced fault diagnosis method is working properly for either linear or nonlinear loads of SGs. The stator and field currents and voltages, and rotor rotational speed are required signals in the introduced approach. The method is validated using experimental data of SGs in Iran-Safir (ER24) diesel–electric locomotives.

Saturated full model capability of virtual synchronous generator to improve transient stability of hybrid power system

In hybrid power system (HPS), there are many inverter-based generators (IBGs) that inject renewable energy into the system as electrical power. Transient stability analysis of HPS in which synchronous generators (SGs) are operated in parallel with IBGs is necessary to operate the network safely under large disturbances. This paper examines the transient behaviour of IBGs with effective strategies, in which constraint on output current of IBGs is strictly considered to bring the results closer to reality. The control strategy is based on reference model tracking and substitution theory for networks, including parallel SG-IBGs to full IBGs. First, for a network with full IBGs, a constant power model reference is proposed as a static model. Then a dynamic reference model called saturated full model of virtual synchronous generator (VSG) or simply SFMVSG is introduced as the final solution for the controller of IBG in HPS. The SFMVSG has all existing VSG features and provides virtual damping torque created by the interaction of virtual damping fluxes. The simulation results confirm that the study is efficient.

The Implementation of Fuzzy PSO-PID Adaptive Controller in Pitch Regulation for Wind Turbines Suppressing Multi-Factor Disturbances

The stability of wind turbine output is affected by multi-factor disturbances, which makes traditional proportion-integral-differential (PID) control strategy hardly achieve a satisfactory effect. Hence, a pitch control strategy based on fuzzy adaptive particle-swarm-optimization (PSO)-PID is proposed in this paper. Firstly, the models of wind turbine, pitch regulator, and permanent magnet synchronous generator (PMSG) are built. Then, the influence of various disturbances, such as blade deformation, installation errors, and external wind speed, on the wind wheel speed is analyzed. Furtherly, a wind turbine pitch control strategy is devised in detail, in which the PID parameters are initially optimized by PSO and adaptively adjusted by fuzzy controller. Simulations under gust wind and turbulent wind conditions are carried out, and the results show that compared with fuzzy PID and PID, the fuzzy adaptive PSO-PID could reduce errors of wind wheel speed and wind turbine output power effectively.

Design of HHO-PID Controllers for Load Angle of Power Plant Synchronous Generators

Accurate analysis of load angle stability of the synchronous generator depends on considering mechanical parameters in addition to electrical parameters in synchronous generator modeling, which leads to increasing state-space variables and model complexity and ultimately reduces the accuracy and performance of conventional controllers. Therefore, an intelligent controller is required for the stable and reliable operation of the synchronous load angle generator. With this approach in this paper, first considering the electrical and mechanical parameters, a complete 14-order model of the synchronous generator is obtained. Then, a PID controller based on the Harris optimization algorithm is proposed to stabilize the load angle of the synchronous generator. The HHO optimization algorithm is a population-based optimization technique that optimizes PID controller coefficients. The effectiveness of the new HHO technique in optimizing the controller PID coefficients over known optimization techniques such as GA-PID and Modified GA-PID has been confirmed using simulation results. The simulation results show that the proposed controller has a higher performance in load angle stability compared to the sliding mode and fuzzy-PID controllers.

A Novel Energy Flow Analysis and Its Connection With Modal Analysis for Investigating Electromechanical Oscillations in Multi-Machine Power Systems

In this paper, a novel energy flow analysis (EFA) is proposed based on the signal reconstruction and decomposition to investigate the electromechanical oscillations. In contrast to the conventional EFA, the connection between the proposed EFA and modal analysis (MA) can be quantitatively revealed for arbitrary models of synchronous generators in multi-machine power systems. Firstly, the time-domain implementation (TDI) of the proposed EFA is designed. Specifically, the measurements at the terminal of a local generator are reconstructed through an exponential operator and then decomposed with respect to an angular frequency. Then, the mode-screened damping torque coefficient is defined to extract the damping feature with respect to an electromechanical oscillation mode. After that, the frequency-domain implementation (FDI) is derived. Specifically, the Parseval's Theorem is applied to transform the proposed EFA from the time domain to frequency domain. On this basis, the consistency between the proposed EFA and MA is strictly proved, which is applicable for arbitrary models of synchronous generators in multi-machine power systems. Additionally, the application procedure of the proposed EFA in investigating electromechanical oscillations is given. Finally, the proposed EFA are substantially demonstrated in multiple case studies.

Modeling the synchronous permanent magnet generator with RLC load

This paper is concerned with the modeling of the three-phase permanent magnet synchronous generator (PMSG) and its load in the dq0 reference system. The generator was considered to be directly connected to a balanced three-phase load. The loads under consideration were R and RLC type loads. The connection to the R load can be simulated using the standard PMSG dq model and Park transformations, but the connection to the RLC load requires the modeling of the system as a whole. LabVIEW simulations of these models were used in order to study the behavior of the PMSG under various load conditions (R, RL and RC). These models can be used to simulate the behavior of the PMSG in a conventional (natural gas, coal, etc.) or renewable (wind energy, hydropower, etc.) energy conversion system. They can also be used in designing the control of the energy conversion system (MPPT control, Droop control, etc.).

A review and comparison of current trends in virtual synchronous generator's models

The penetration of renewables-based converter-interfaced generation (CIG) has a great impact on the dynamic properties and characteristics of modern power grids. At the same time, certain challenges arise that are associated with ensuring the stable operation of both the CIG itself and the external power grid in general. The defining moment in this case is the approach to the CIG control. In a case of the conventional structure of the control system based on the use of phase-locked loop, it is currently infeasible to achieve a comprehensive solution that would allow performing all the ancillary services assigned to the conventional synchronous generation with the help of CIG. Thus, this paper discusses one of the most promising areas in the field of CIG control – the concept of a virtual synchronous generator (VSG). The presented review of the existing VSG concepts made it possible to highlight the main approaches to its implementation, for which an experimental comparison was carried out. As a result of the comparison, the main features of the VSG models operation were revealed, and general conclusions were made about the applicability of specific VSG concepts in the structure of the CIG control system.

Machine Learning Based Transient Stability Emulation and Dynamic System Equivalencing of Large-Scale AC-DC Grids for Faster-Than-Real-Time Digital Twin

Modern power systems have been expanding significantly including the integration of high voltage direct current (HVDC) systems, bringing a tremendous computational challenge to transient stability simulation for dynamic security assessment (DSA). In this work, a practical method for energy control center with the machine learning (ML) based synchronous generator model (SGM) and dynamic equivalent model (DEM) is proposed to reduce the computational burden of the traditional transient stability (TS) simulation. The proposed ML-based models are deployed on the field programmable gate arrays (FPGAs) for faster-than-real-time (FTRT) digital twin hardware emulation of the real power system. The Gated Recurrent Unit (GRU) algorithm is adopted to train the SGM and DEM, where the training and testing datasets are obtained from the off-line simulation tool DSAToolsTM/TSAT®. A test system containing 15 ACTIVSg 500-bus systems interconnected by a 15-terminal DC grid is established for validating the accuracy of the proposed FTRT digital twin emulation platform. Due to the complexity of emulating large-scale AC-DC grid, multiple FPGA boards are applied, and a proper interface strategy is also proposed for data synchronization. As a result, the efficacy of the hardware emulation is demonstrated by two case studies, where an FTRT ratio of more than 684 is achieved by applying the GRU-SGM, while it reaches over 208 times for hybrid computational-ML based digital twin of AC-DC grid.

Bayesian Inference for Thermal Model of Synchronous Generator—Part I: Parameter Estimation

Due to the increasing injection of intermittent power sources (solar+wind) into a common grid, dispatchable sources such as hydro power should be able to help reduce the variability in load and the variability in generation caused by the intermittent sources. A hydro generator should be able to operate short-term beyond its thermal capability limit. This requires the monitoring of internal temperatures in the hydro generator. In this paper, a thermal model of an air-cooled synchronous generator is presented, emphasizing the various aspects of parameter estimation and identifiability using Bayesian inference. Inferences are drawn from the posterior distributions of the parameters and initial conditions, dispersion (spreading) of particles and sampling efficiency, practical parameter identifiability, and model mismatch with experiments. Results show extremely narrow parameter distributions. It is early to generalize about the posterior distribution of air-related and metal-related parameters of the air-cooled synchronous generator based on the single experimental data presented here.

Connection Between Damping Torque Analysis and Energy Flow Analysis in Damping Performance Evaluation for Electromechanical Oscillations in Power Systems

The damping performance evaluation for electro-mechanical oscillations in power systems is crucial for the stable operation of modern power systems. In this paper, the connection between two commonly-used damping performance evaluation methods, i.e., the damping torque analysis (DTA) and energy flow analysis (EFA), are systematically examined and revealed for the better understanding of the oscillatory damping mechanism. First, a concept of the aggregated damping torque coefficient is proposed and derived based on DTA of multi-machine power systems, which can characterize the integration effect of the damping contribution from the whole power system. Then, the pre-processing of measurements at the terminal of a local generator is conducted for EFA, and a concept of the frequency-decomposed energy attenuation coefficient is defined to screen the damping contribution with respect to the interested frequency. On this basis, the frequency spectrum analysis of the energy attenuation coefficient is employed to rigorously prove that the results of DTA and EFA are essentially equivalent, which is valid for arbitrary types of synchronous generator models in multi-machine power systems. Additionally, the consistency between the aggregated damping torque coefficient and frequency-decomposed energy attenuation coefficient is further verified by the numerical calculation in case studies. The relationship between the proposed coefficients and the eigenvalue (or damping ratio) is finally revealed, which consolidates the application of the proposed concepts in the damping performance evaluation.

Small-signal modeling and analysis of a three-phase virtual synchronous generator under off-grid condition

The current small-signal models of inverters that mimic synchronous generators usually use the steady-state equation of feeder line and load, and ignore the dynamic characteristics of voltage and current controller of inner loop. Thus, some important dynamics of the system will be omitted. To capture the dynamics more accurately, firstly, a small-signal model of a three-phase isolated inverter that mimics a synchronous generator was developed in this paper, and a comparison between the corresponding simulink model and the small-signal model was presented to validate the model correctness. Then, participation factor was calculated, which showed the relation between the state variables and eigenvalues. Based on the model, several root locus plots as a function of the system parameters was obtained. An individual eigenvalue sensitivity analysis of a certain eigenvalue close to the real axis disclosed different parameters’ contribution to the oscillation mode. Finally, a disturbance test with simulink model and the small-signal model under multiple sets of parameters was carried out and the results can accurately reflect the oscillation mode, which verified the correctness of the parameters effect on the conjugate eigenvalues.

Observability Analysis of a Power System Stochastic Dynamic Model Using a Derivative-Free Approach

Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. Facing these challenges, we propose a novel polynomial-chaos-based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">derivative-free</i> observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.

Adaptive damping control strategy of virtual synchronous generator based on fuzzy control

Based on the topology and small signal model of virtual synchronous generator, the influence of virtual inertia and damping coefficient on transient process is analysed. In order to solve the problem of overshoot with small damping coefficient and slow response with large damping coefficient, a fuzzy control method is introduced, which can completely eliminate overshoot without affecting the response speed. Another fuzzy controller is designed to optimize the output of the virtual synchronous generator in the primary frequency modulation process according to the SOC of the energy storage system.

Design and Modeling of a High-Speed Permanent Magnet Synchronous Generator with a Retention Sleeve of Rotor

In this paper, the authors present a novel approach to design a high-speed permanent magnet synchronous generator (HS-PMSG) with a retention sleeve. The importance of the retention sleeve becomes conspicuous when the rotor suffers from the radial and tangential stresses derived from a high speed say 60 krpm. With respect to the mechanical property of Titanium, this material has been demonstrated that it could be a proper material for the retention sleeve. The investigations of this paper are concentrated on the electromagnetic coupled with mechanical design of a 2-poles, 18-slots, 40 KW HS-PMSG which is carried out through FEM analysis using JMAG 17.1 and ABAQUS CAE and optimized through the well-known Taguchi optimization method. The obtained results assure the robust mechanical behaviour of the HS-PMSG at a rotational speed of about 60 krpm meanwhile the cogging torque, the Joule loss, and the total weight of the optimally designed HS-PMSG are reduced 44.71%, 27.87%, and 2.78%, respectively compared with the initial design.