Transient Analysis Method Research Articles

A comprehensive numerical investigation of bi-dimensional analysis of PVT system using square channel absorber

Abstract This paper offers a comprehensive numerical investigation of PVT solar thermal performance using the Finite Difference Method (FDM) for both longitudinal bi-dimensional transient and steady state analysis, which is the unique aspect of this study. Likewise, a thorough analysis of the use of two distinct cooling absorber PVT solar collectors is conducted under realistic climatic conditions. The current modeling methodology can be considered a useful tool that enables rapid bi-dimensional PVT system analysis. The findings show that, in comparison to the PVT tube configuration (587 kWh/m2, 178 kWh/m2), the direct flow square channel has more yearly thermal and electrical gain outputs (608 kWh/m2, 196 kWh/m2). Furthermore, the design of directly flow channels has the advantages of easier integration and effective conduction heat transfer between the fluid and absorber panel. A good agreement between the measured and predicted data was obtained once the current results were compared with theoretical and experimental data in the literature. 

Analysis of friction vibration characteristics of the end face of a T-slot sealing ring under thermal deformation

Aiming at the friction vibration problem caused by dry friction contact during the start-stop process of a dry gas sealing device, this paper takes the end face of a T-slot dry gas sealing ring as the research object and establishes a numerical calculation model of the end face of the T-slot sealing ring. The thermal coupling method is used to obtain the thermal deformation law of the seal ring end face. The transient dynamics analysis method was applied to study the frequency and vibration mode of the friction vibration instability of the seal ring end face under thermal deformation. A vibration test bench was set up for the friction ring, and the friction vibration signals of the test pieces were collected, and the characteristic frequencies were extracted. The results show that: After thermal deformation, the end face of the sealing ring changes from a parallel surface to an inward converging surface, and the friction system of the sealing ring will become unstable. When considering the influence of thermal deformation, there are more unstable frequencies and lower frequency values that are most prone to frictional vibration. As the thermal deformation of the sealing ring increases, the frictional vibration becomes greater. In areas where the characteristic frequency values of frictional vibration are concentrated during thermal deformation, the occurrence rate of frictional vibration noise is higher.

Multi-scale modeling: Finite element analysis of the thermophysical properties of carbon/carbon composites considering manufacturing defects and porosity at high temperature

Carbon/carbon (C/C) composites have strict requirements for their thermal properties in extreme environments, especially at high temperature, where their properties are crucial for long-term life. The structure of C/C composites is exceptionally complex and exhibits multi-scale characteristics, and their thermophysical properties are closely related to temperature. Therefore, exploring their thermal response and heat transfer mechanisms through experimental method is relatively costly. This paper constructs a multi-scale finite element model to investigate the influence of structure and manufacturing defects on performance, and analyzes the thermophysical properties of the composites at High-temperature. By constructing a micro-representative volume element (Micro-RVE) that includes fibers, matrix, and pores, and using a steady-state heat transfer analysis method, the influence of material phase distribution on performance is studied. At the same time, a Meso-RVE reflecting the layering form, needle punching effect and manufacturing defects is established, and the transient heat transfer analysis method is used to investigate the influence of the structural form on performance. Finite element analysis shows that, the simulation values of the three C/C composites of unidirectional fiber bundles, short-chopped fiber felts, and needle punched C/C composites show good consistency with the experimental results in the published literature. This paper uses numerical methods to calculate the thermophysical properties of C/C composites from room temperature to 900°C and explores their variation with temperature. The constructed multi-scale model provides an accurate and effective method for predicting the thermophysical properties of C/C composites and also provides new perspectives and insights for thermal-mechanical coupling analysis and structural design.

An improved two-phase rate transient analysis method for multiple communicating multi-fractured horizontal wells in shale gas reservoirs: Field cases study

The reduction in well spacing for multi-fractured horizontal wells (MFHWs) and the increase in infill drilling exacerbate the risk of fracture communication. This presents substantial challenges for the rate transient analysis of the parent–child well system. This study proposes an improved two-phase straight-line analysis method to evaluate the linear flow parameters of multiple communicating MFHWs in shale gas reservoirs. Considering shale gas adsorption–desorption mechanisms, nonuniform length of fractures, stress-dependent effects, and matrix shrinkage effects, two-phase productivity equation is established within the dynamic drainage area (DDA). Subsequently, we develop a three-well square root of time plot based on DDA correction and propose a rigorous workflow for evaluating linear flow parameters in single-well, two-well, and three-well systems. The straight lines on the parent well's square root of the time plot exhibit varying degrees of jumps, depending on the frequency of fracture communication. After communication, it is necessary to adjust the cumulative production and production time of the parent well to accurately recalculate the average pressure within the drainage area. Numerical simulations are employed to generate a series of cases under different reservoir conditions to validate the accuracy of the proposed model. The results show that the model estimates fracture half-lengths with errors within 8%, meeting the precision requirements for field applications. Additionally, the method exceeds numerical simulations in computational speed. Two field case studies in the WY Basin, China, further illustrate the effectiveness and practicality of the proposed method, providing theoretical support for hydraulic fracturing construction design and development planning.

Research Methods for Transient Stability Analysis of Power Systems under Large Disturbances

Transient stability analysis is critical for maintaining the reliability and security of power systems. This paper provides a comprehensive review of research methods for transient stability analysis under large disturbances, detailing the modeling concepts and implementation approaches. The research methods for large disturbance transient stability analysis are categorized into five main types: simulation methods, direct methods, data-driven methods, analytical methods, and other methods. Within the analytical method category, several common analytical strategies are introduced, including the asymptotic expansion method, intrusive approximation method, and other analytical methods. The fundamental principles, characteristics, and recent research advancements of these methods are detailed, with particular attention to their performance in various aspects such as computational efficiency, accuracy, applicability to different system models, and stability region estimation. The advantages and disadvantages of each method are compared, offering insights to support further research into transient stability analysis for hybrid power grids under large disturbances.

An efficient multiscale method for subwavelength transient analysis of acoustic metamaterials.

A reduced-order homogenization framework is proposed, providing a macro-scale-enriched continuum model for locally resonant acoustic metamaterials operating in the subwavelength regime, for both time and frequency domain analyses. The homogenized continuum has a non-standard constitutive model, capturing a metamaterial behaviour such as negative effective bulk modulus, negative effective density and Willis coupling. A suitable reduced space is constructed based on the unit cell response in a steady-state regime and the local resonance regime. A frequency domain numerical example demonstrates the efficiency and suitability of the proposed framework.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Research on thermal-solid coupling behavior of drum brake under emergency braking on slopes

Abstract When a truck makes emergency braking while driving on a slope, the transient impact force generated can easily cause personal injury to passengers and damage the vehicle’s braking system. In order to study the working state of the brake under this working condition, the ANSYS finite element thermal-solid coupling transient analysis method was used to establish the mechanical model and finite element model of the vehicle and brake under the slope emergency braking state, showing the temperature field and stress field distribution rules and interactions of the drum brake under this working condition, and compared with the flat road emergency braking condition. The results show that the maximum temperature of the brake reaches 184.26°C during emergency braking, and the stress field and temperature field are strongly coupled in two directions, which can easily lead to uneven wear of the linings and a reduction in the fatigue life of the brake.

Mode decomposition of core dynamics transients using higher-order DMD method

Accurately predicting three-dimensional power distribution within a reactor core during reactivity transients is crucial for optimizing reactor operational control. This paper proposes a higher-order dynamic mode decomposition (DMD) method for analyzing highly nonlinear dynamic systems in nuclear reactors. Through analysis of the 3-D LWR Core Transient Benchmark (3DLWRCT) with rod ejection accident, traditional DMD reconstruction techniques were found inadequate in accurately capturing the system’s dynamic evolution using the given simulation data, primarily due to the nonlinear features and local high-order characteristics of the reactor system. In contrast, the HODMD approach demonstrated its effectiveness in predicting future variations in the core’s state. These findings establish the feasibility of employing the HODMD method for transient analysis of core dynamics, leading to promising prospects for dynamic analysis in nuclear energy systems. Future research directions for improving the reconstructive accuracy of HODMD include capturing nonlinear characteristics, automating parameter selection, enabling multi-scale analysis, enhancing anomaly detection capabilities, and providing a broader context for analysis.

Hybrid method for hydraulic transient analysis of liquid pipe networks based on characteristic lines and equivalent circuits

Water hammer poses a significant concern in the transportation of pipelines and pipe networks. Due to the passage of reflection of water hammer waves at nodes, a large number of high-frequency pressure fluctuation signals appear in the pipe network, demanding an intensive computational workload. A novel hybrid method based on characteristic lines and equivalent circuits is proposed for the accurate and fast simulation of pipe networks. Multiple methods are employed for the simulation of pipelines and pipe networks, followed by a comparative analysis. The accuracy of the hybrid method is validated by comparing the proposed method with simulation results of commercial software. The hybrid method reduces the significant computational workload inherent in the classic method of characteristics and enhances the accuracy at high frequencies in the state-of-the-art elastic water column model. A trade-off between simulation accuracy and computation speed is achieved by adjusting the time step. The accuracy of calculating higher-frequency pressure fluctuations is further validated with an increase in the pipe diameter and a corresponding reduction in the friction loss. Generally, this method enables the simultaneous descriptions of high-frequency characteristics and nonlinear friction loss, enhancing calculation speed with little impact on the accuracy. The results demonstrate that the proposed model can be utilized for the transient analysis of pipe networks, providing support for predicting system performance and designing optimal strategies.

Modeling transient temperature coupled pressure behaviour for waterflooding well with induced fractures: Semi-analytical model, numerical model, and case studies

Waterflooding is a widely used technique for developing unconventional reservoirs. Long-term waterflooding can lead to the formation of multiple induced fractures. Accurately tracking the location, extent, and dynamic behavior of these induced fractures is crucial. To enhance monitoring capabilities, data obtained from distributed temperature sensors are used to track temperature variations within the wellbore and at the bottom of the well. Combining temperature and pressure inversion techniques helps mitigate the issue of multiple solutions while offering a more comprehensive characterization of multi-induced fractures from various perspectives. In this study, this work presents a model for temperature coupled pressure (TCP) transient analysis. Additionally, this work utilizes COMSOL Multiphysics software to develop and solve a dynamic wellbore temperature (DWT) model. This work proposes a workflow that describes the dynamic behaviour of multi-induced fractures. During model development and solution, this work employs both pressure and temperature transient analysis methods, examining time-dependent non-linear pressure drop and heat transfer variations. Our results reveal that induced fractures exhibit convective heat exchange with the wellbore, resulting in significantly higher temperatures at the induced fracture locations compared to other wellbore locations. By analyzing temperature-wellbore location curves, this work can accurately identify the locations of induced fractures. The TCP model successfully extracts characteristic parameters of induced fractures, while the DWT model allows for monitoring the locations and heights of these fractures. By combining the workflows of both models, this work achieves a comprehensive characterization of the physical properties of induced fractures. In conclusion, this advancement empowers engineers to manage the development of such fractures effectively, thereby averting potential adverse effects on production well performance and preventing the need for well abandonment.

Performance improvement evaluation of latent heat energy storage units using improved bi-objective topology optimization method

Latent heat thermal energy storage (LHTES) based on phase change materials is one of the key technologies to improve energy utilization efficiency and alleviate the mismatch between energy supply and demand. Heat storage capacity and charging/discharging rate are two core factors that determine the comprehensive performance of LHTES units. So a bi-objective transient topology optimization(TO) model is established to freely evolve the optimal structure and volume fraction of LHTES fins to maximize the heat transfer rate based on ensuring high storage capacity. The bi-objective optimization function coupling storage capacity and heat transfer rate is constructed by normalized SAW model. The TO model is formulated using variable density-based design variables of grid cells in physical governing equations, objective functions and constraints. Helmholtz PDE filtering and hyperbolic tangent projection methods are employed to achieve high-precision optimization solutions. Complex transient multi-physics field and bi-objective iterative calculations are performed using the transient adjoint-based sensitivity analysis method and GCMMA algorithm. Results demonstrate that the physical field dynamics response of the design variables at each iteration can more clearly exhibit the evolutionary direction and mechanism of seeking optimal structures. The Pareto frontier indicates TO model responds significantly to the changes in the bi-objective weight ratio ω1:ω2, which also reveals the physical mechanism of the trade-off game among fin topology formation, state parameters distribution and objective changes. Optimal configurations and its performance parameters change regularly with ω1:ω2 decreasing, and has an demonstrable performance mutations occurring at ω1 = 0.65(ω2 = 0.35). The scattered distribution and uniform multi-branch structure of TO fins are key factors in regulating the physical field state. Therefore, TO-fins LHTES exhibits extremely high heat transfer rate, and the charging/discharging time of traditional trapezoid fin LHTES is approximately three times longer than that of TO-fins LHTES under ω1:ω2 = 0.65:0.35.

Analysis of Sliding Vibration of an Electric Shoegear Against a Conductor Rail in Medium- and Low-Speed Maglev Trains

In recent years, medium- and low-speed maglev trains have been put into use in China. It was discovered during testing that the electric shoegear and conductor rail system generate significant vibration and noise when the electric shoegear passes through expansion and intermediate joints. By analyzing the sound pressure level (SPL) of the noise signal, it was found that the A-weighted SPL of the noise was between 77.83 dBA and 91.80 dBA, when the maglev trains were running normally, which reached the level of annoyance. Based on the theory of self-excited frictional vibrations, the finite element models of an electric shoegear and conductor rail system (shoe–rail system) were established. The main frequency of the vibration signal calculated by the transient dynamic analysis method was 1510.05 Hz. The self-excited frictional vibrations of the system were further studied using the complex eigenvalue analysis (CEA), and the causes of the noise are analyzed. The results show that the system has unstable vibration when the friction coefficient was greater than or equal to 0.21. The parameter sensitivity analysis showed that the slip shoe material of the electric shoegear, vertical damping of the suspension device, and tuned mass damper (TMD) structure have an important influence on the generation of vibration and noise of the system. Installing an appropriately tuned mass damper structure can suppress or eliminate the unstable vibration of the system.

Calculation Method and Characteristic Analysis for Fault Current of Permanent Magnet Direct-Drive Wind Power System considering Positive and Negative Sequence Decomposition

In view of the fact that the influence of positive and negative sequence decomposition, which is widely used in positive and negative sequence decoupling control in control system, on the fault current calculation process is not deeply considered in the existing transient analysis methods of permanent magnet direct-drive wind farm short circuit current, this paper proposes a transient short circuit current calculation model that takes into account positive and negative sequence decomposition. The influence of the transient characteristics of positive and negative sequence decomposition on the control system is studied, and the mechanism of its action on the transient change of short circuit current is revealed. The positive and negative sequence decoupling processes of the circuit equation are modified, and the characteristics of the coupling equation are analyzed. The difference in the converter output voltage between the circuit equation and the control equation and the depth of its influence on the calculation process is revealed. On the basis of quantifying the difference at the converter output voltage, the circuit equation and the control equation are combined to form a short-circuit current calculation model with positive and negative sequence decomposition, which accurately characterizes the transient characteristics of fault current under different voltage drops and effectively improves the accuracy of the calculation results.

Temperature Evolution inside Hollow Core Wood Elements and Fire Resistance

The present study is focused on wall panels exposed to fire, with the construction building elements we used being made of wood and gypsum board materials. This type of configuration forms hollow core wood due to the constructive process. The aim is to present a numerical study to approach the calculation of the temperature inside hollow core wood elements and measure their fire resistance. The temperature evolution inside the cavities will be obtained with recourses to obtain the heat effect by convection and radiation through the wall elements. A numerical model, previously validated by the authors, will be used to carry out this process. The methodology includes the use of the finite element method in thermal and transient analysis with nonlinear materials to calculate temperature. To measure the fire resistance of the constructive model, the thermal insulation criterion, defined by the EN 1363-1:2020 standard, will be applied. Different results will be presented to discuss and ensure the verification of these fire-resistant elements.

Transient stability enhancement control strategy based on grid dispatching for multi-paralleled grid forming inverters during LVRT

In this article, the transient synchronization process of multi-paralleled grid forming (GFM) inverters is studied detailly. Firstly, based on the multi-paralleled inverters control structure and complementary cluster center of inertia relative motion (CCCOI-RM), the single machine infinite bus (SMIB) system is proposed. Subsequently, the power angle characteristic (PAC) equation of multi-paralleled inverters for different dispatching strategies with simplified damping coefficient is built. Meanwhile, a grid dispatching strategy considering communication delay is proposed, which avoiding the cascading failures of grid faults. Furthermore, according to the grid dispatching strategy, a cluster control strategy optimization method including critical cluster identification (CCI) method and transient stability prediction analysis method is designed, which is proposed to identify unstable cluster in multi-paralleled inverters. In addition, the synchronization stability criteria for dispatching strategies of multi-paralleled inverters are obtained based on the PAC equation, in which the transient instability phenomenon and mechanism for different fault stages is explained by extended equal area criterion (EEAC) method. Finally, the simulations results validate the effectiveness of the theoretical analysis and proposed method.

Reservoir Modeling Predicts Effect of Cold-Water Injection on Geothermal PTA

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 212615, “Reservoir Modeling To Predict the Effect of Cold-Water Injection in Geothermal Pressure Transient Analysis,” by Purnayan Mitra, SPE, University of Petroleum and Energy Studies, and Nihal Mounir Darraj, SPE, Imperial College London. The paper has not been peer reviewed. _ Geothermal reservoirs are one of the cleanest renewable sources of energy poised to address the global energy challenge. A major issue in the exploitation of geothermal reservoirs, however, is to find best-fit analytical methods for pressure transient analysis (PTA). This is because the assumptions made to predict PTA in hydrocarbon reservoirs are not satisfied by geothermal reservoirs. In the complete paper, the effect of cold-water injection on PTA of geothermal reservoirs is studied by varying the temperature of the injected cold water from room temperature to reservoir temperature. Introduction A major method of extracting heat energy from the Earth is the injection of water. Cold water is injected deep into geothermal reservoirs at a depth of 2–4.5 km. In this environment, cold water is essentially heated by the hot granite rock. Hydraulic fracturing is used to produce a large crack within the geothermal reservoir. Two boreholes intercept the crack. These boreholes are used for passing the cold fluid stream and the hot stream, respectively. In many scenarios, the gradient within the geothermal reservoir is so strong that a dry stream is produced. The greater the temperature difference between the injected fluid and the interior of the Earth, the greater the heat transfer. Therefore, it is always desirable to inject cold water inside geothermal reservoirs to maximize heat transfer and extract more heat. The steam coming out from the reservoir after heat transfer is used to run turbines to generate electricity. The steam also is used for a variety of other purposes. However, instances exist in which the temperature gradient is not as high, and it is difficult to produce a sufficiently heated dry stream. In such cases, an organic Rankine cycle is used for heating the steam on the surface. In such a case, the hot water or steam mixture is passed through a heat exchanger for heating the fluid to a desired temperature. When cold water is injected into the reservoir, a need exists to analyze the pressure transience throughout the reservoir. Different formations affect PTA in different ways. PTA across the geothermal reservoir currently is performed using the empirical correlations available for hydrocarbon reservoirs. Although the method is not 100% effective because of differences in reservoir parameters, PTA provides an idea about reservoir conditions. To reduce imperfection, it is often preferred to use reservoir parameters rather than injectate properties. In the complete paper, the authors study the effect of injected water on geothermal reservoirs while varying temperature from 14 to 312°C.

CO2 Injectivity Test Proves Concept of CCUS Field Development

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 216673, “CO2 Injectivity Test Proves the Concept of CCUS Field Development,” by Yermek Kaipov, SPE, and Bertrand Theuveny, SLB, and Ajay Maurya, Saudi Aramco, et al. The paper has not been peer reviewed. _ The complete paper presents a unique case study on injectivity tests done in Saudi Arabia to prove the concept of carbon capture, use, and storage (CCUS) capability. It describes the design of surface and downhole testing systems, lessons learned, and recommendations. The injectivity tests were effective in identifying and confirming the best reservoir for CO2 injection and defining the best completion strategy. Creating injection conditions close to CCUS is vital, especially in heterogeneous carbonate reservoirs where the petrophysical correlations for the reservoir model require calibration with dynamic data. Introduction The energy company has conducted an extensive evaluation campaign by drilling appraisal wells through multizone saline aquifer reservoirs on different sites close to potential sources of CO2 at the surface. The evaluation program included coring, openhole logging, formation testing for stress-test and water sampling, and injectivity testing in the cased hole. Apart from reservoir characterization, different completion strategies were evaluated by performing injectivity tests in both vertical and horizontal wells. The lower completion was represented by perforated casing and an open hole. Injectivity Testing Injection tests are a commonly used method in waterflood projects to evaluate the injectivity capacity of the well and reservoir. The test involves an injection period with one or more injection rates, followed by a falloff period (Fig. 1). During the injection period, the liquid is injected at a stable rate to reduce the risk of near-wellbore formation damage caused by fluid incompatibility or exceeding the fracture gradient and inducing formation fracturing. The bottomhole-pressure data acquired during the test is analyzed using the pressure transient analysis method to estimate the permeability thickness, skin factor, and lateral heterogeneities. Additionally, the injection logging profile can be conducted along the sandface to assess completion efficiency and formation heterogeneity. By interpreting the results of the injection test, engineers can optimize the injection rate and improve the performance of the well and reservoir, ultimately leading to more-efficient oil recovery. Injectivity Test: Case Study The injectivity tests were conducted on virgin reservoirs using vertical appraisal wells that were sidetracked horizontally into the reservoirs with the greatest potential for storage. The reservoirs’ depths varied from 4,000 to 8,000 ft, with a normal gradient of reservoir pressure and temperature. The injectivity test design used reservoir properties estimated from the openhole evaluation, such as porosity, permeability, reservoir pressure, temperature, reservoir fluid sample, and fracture gradient. These data were used to set injectivity-test objectives, calculate expected well parameters, select equipment, and plan operations. The primary goal of the tests was to assess reservoir injectivity by injecting water, nitrogen, and CO2 to prove the concept for a CO2-injection project. While water and nitrogen injections are well-known in the industry, the CO2 injectivity test was new and required more attention during the design phase to evaluate all possible risks.

A new MIB-based time integration method for transient heat conduction analysis of discrete and continuous systems

By incorporating the matched interface and boundary (MIB) method into time integration computation, a new MIB-based time integration (MIBTI) approach is proposed for solving transient heat conduction problems in this work. Indeed, this is a truly effective time-domain MIB method that can directly discretize space and time derivatives, and the transient heat conduction problem (an initial-value problem) is transformed into a pseudo-space boundary-value problem. The initial and final time points are regarded as boundary points in the transformed space domain. Two algorithms are developed to deal with the final time point. Unlike conventional recursive schemes for time integration, all unknown variables can be determined by solving the transformed boundary-value problem in the present approach. Various discrete and continuous systems without and with internal heat sources under different boundary conditions are considered to examine the working performance of the proposed method. The applicability of the time stability criterion in the conventional recursive schemes to the proposed method is also discussed. It is found that excellent numerical stability and convergence can be achieved by using the present MIBTI method for solving transient heat conduction problems.

Influence of changes in tip structure on wind wheel vibration characteristics under wind wheel-tower coupling

This study conducted modal and vibration-characteristic tests using transient excitation and spectrum analysis methods to find the variation law of vibration characteristics of wind wheels with bifurcated tip structures as compared to wind wheels with unmodified tips when the coupling between a wind wheel and its tower is considered. Additionally, a finite element analysis was used to calculate the mechanical characteristics of wind power manoeuvres. The following are the major results of this study. As compared to the non-trailer state, the coupling action of the wind wheel and the tower reduced the static frequency of the unmodified wind wheel and the bifurcated blade tip structure wind wheel under the trailer state. The static frequency of the bifurcated blade tip structure wind wheel under the coupling action decreases more significantly. Compared with the single wind wheel which is not affected by coupling, the dynamic frequency of the whole machine decreases after being affected by coupling, and the bifurcated blade structure has less influence on the coupling effect. Compared with the non-trailer state, the dynamic frequency curves of the two blade tip structure wind wheels in the trailer state decrease, the speed range in the resonance area is shortened, and the corresponding speed in the resonance area is reduced. The results of this study provide data support and design reference for reliable design of wind turbines.

An Iterative Equal Area Criterion for Transient Stability Analysis of Grid-Tied Converter Systems With Varying Damping

With the increasing penetration of renewable energy generators, the stability issues of grid-tied converter systems become much more important. However, due to the high nonlinearity and varying damping of converter systems, conventional transient stability analysis methods are not applicable, which may bring to conservativeness or misjudgment on stability assessment. In this paper, the transient stability of grid-tied converter systems with varying damping is investigated to provide stability boundary estimation. Firstly, considering the frequency mutation of the phase-locked loop (PLL) caused by various perturbations, a modified swing equation model of grid-tied converter systems is built, which greatly improves the mathematical model accuracy under transient disturbances. To evaluate the impacts of varying damping and frequency mutation, an iterative equal area criterion (ITEAC) method is proposed with the iterative calculation of the accelerating and decelerating area, which renders stability boundaries with high accuracy. Moreover, the impacts of controller and system parameters on stability boundaries are quantitatively analyzed. Eventually, simulation and hardware-in-loop experiments are performed to verify the effectiveness and superiority of the proposed ITEAC.