Thevenin Equivalent Research Articles

Digital Fault Locator for Double End Fed Transmission Lines

The paper presents a digital fault locator by dynamic system parameter estimation for a double end fed transmission line. The method uses about 1/6 cycle of recorded fault data and doesn‟t require filtering of dc offset and high-frequency components. The system differential equations are based on a lumped parameter line model, Thevenin equivalents at both ends of the line and an unknown fault resistance. The accuracy is demonstrated by a representative set of tests results obtained with computer simulation

Fast Assessment Method for Transient Voltage Stability of Photovoltaic Receiving‐End Grid

The incorporation of renewable energy on a broad scale into power grids increases the complexity to the issue of transient voltage stability in power systems. This research presents a rapid evaluation technique for assessing the stability of voltage fluctuations in power grids that receive electricity from photovoltaic sources. At first, a receiving‐end system model was developed, which includes photovoltaics, and an alternative circuit of the virtual induction motor (IM) is obtained by utilizing the Thevenin equivalent. Second, the torque balance equation and the Kirchhoff voltage equation are interconnected to determine the unstable slip of the IM following a malfunction. Finally, by merging the unstable slip with the conventional transient stability discriminant index, the effects of different photovoltaic outputs, IM ratios, and system contact impedances on transient voltage stability are investigated. The proposed method avoids the computational burden of solving the differential‐algebraic equations describing the complex transient processes of the IM. It also obviates the necessity of iteratively modifying the receiving load or fault clearance time in the simulation platform to achieve the constrained stability condition of the system’s transient voltage. The transient stabilization of voltage results is efficiently obtained by directly solving algebraic equations.

Accuracy analysis using the EMD and VMD for two-terminal transmission line fault location based on traveling wave theory

This paper presents an accuracy analysis from the application of techniques for the extraction of characteristic data from current and voltage signals in transmission line fault location based on traveling wave theory. The techniques used were the empirical mode decomposition and the variational mode decomposition associated with Teager energy operator, which helps to identify the instantaneous energy of the first intrinsic mode function. The simulation of the power system was carried out using the MATLAB/Simulink® software, for a test system consisting of a 200 km long transmission line between two Thevenin equivalents. Data is obtained from both terminals. The fault resistance was fixed at 100 Ω, but the incidence angle, the sampling rate and the fault location were varied for all fault types. The numerical and graphical results proved that the techniques can extract the characteristic data of the current and voltage signals and estimate the fault distance to the terminal with high accuracy, depending only on the sampling rate adopted.

КОМП’ЮТЕРНЕ МОДЕЛЮВАННЯ ТА ДОСЛІДЖЕННЯ ЕНЕРГОЕФЕКТИВНОСТІ ПРОЦЕСІВ ЗАРЯДЖАННЯ АКУМУЛЯТОРНОЇ БАТАРЕЇ ЕЛЕКТРОМОБІЛЯ ВІД БЕЗДРОТОВОГО ЗАРЯДНОГО ПРИСТРОЮ

In the paper, based on the method of computer simulation, the process of charging a lithium-ion battery for an electric car from a wireless charger of the inductive-resonance type was investigated. It is shown that when modeling this process, it is necessary to take into account the simultaneous flow of two processes of different scales in time and interconnected - a short-term high-frequency process in the inverter of the charger with a characteristic time of 10-5 s and a long-term process of charging the battery with a characteristic time of 104 s. Direct numerical calculation of these two processes simultaneously requires significant computer resources. To solve this problem, a new approach is proposed and implemented in the Matlab/Simulink package, according to which, at the first stage, when calculating high-frequency processes in the inverter, there are modified Thevenin and Norton equivalents for a wireless charging device, taking into account the total internal losses in this device, and at in the second stage, the long-term battery charging process is calculated first in the mode of a constant current source, using the constructed Norton equivalent, and then in the mode of a constant voltage source, using the constructed Thevenin equivalent. This approach makes it possible to take into account interrelated and time-varying processes in the inverter and in the battery and to investigate the efficiency of wireless transmission of electrical energy from a stationary power source to a battery located on board an electric vehicle. According to the results of the calculations, it is shown that for the developed device, the integral efficiency of the entire battery charging process when the battery parameter increases from 20% to 95% is 86%. References 9, figures 8.

Impedance-frequency characteristic analysis of bypass damping filter in suppressing AC–DC system’s subsynchronous resonance

Recently, subsynchronous resonance (SSR) in HVDC transmission is considered to be related to electronic converter equipment and complex control systems. Aiming at the subsynchronous resonance problem caused by frequent topology changes of AC–DC systems, this paper firstly proposes an impedance-frequency characteristic analysis method based on Thevenin Equivalent and Fast Fourier Transform (FFT) algorithm. This method is used to analyze the impedance frequency characteristics of AC–DC systems after the bypass damping filter (BDF) is configured. Firstly, based on the IEEE first benchmark model, the mechanism of BDF in suppressing subsynchronous resonance is explained by quantitative analysis, and the BDF parameter setting method is proposed. Then, the time domain simulation model of a single-machine HVDC system with BDF is established in PSCAD/EMTDC. Finally, according to Thevenin’s theorem, the equivalent structure of each subsystem is simplified, and the FFT algorithm is used to solve the harmonic equivalent impedance of each subsystem. After BDF is configured, the mechanical resonance frequency ”transfers” from 16Hz to 10Hz, and the minimum electrical damping changes from -0.9637 to -0.4581. The results show that the BDF configuration can change the impedance-frequency characteristics of the system, thereby improving the electrical damping in the torsional vibration mode in a targeted manner, and has a certain effect on suppressing the subsynchronous resonance of AC–DC systems.

Static Voltage Stability of Distributed Power Access Distribution Network Based on Thevenin Equivalent

As part of the process of voltage regulation, a voltage stability analysis approach suitable for wind power system needs to be established. On equivalent Thevenin parameters, the ordinary equivalent black-box Thevenin method is unable to characterize the wind connection mechanism. Accordingly, this paper proposes an analytical method equivalent to Thevenin for analyzing the steady-state voltage of electricity systems with wind energy. The equivalent model is adopted in this method connected to the wind energy grid because of the equivalence of injected nowaday sources. The analytic expressions for the equivalent Thevenin parameters are then derived in two equivalent ways, and the wind connection mechanism affecting equivalent Thevenin parameters is revealed. Lastly, the enhanced IEEE 30 bus system with wind power is simulated and validated, and it is verified that the research contents of the study contents can enhance the voltage stability of Network connection point. On the other hand, the research content of this topic reduces the active power wastage of the distributed generation connection, so as to keep the balanced terminal voltage distribution.

Static Voltage Stability Assessment of Ethiopian power System Using Normalized Active Power Margin Index

Voltage stability assessments, made so far on the Ethiopian electric power system (EEP), are limited both in number and in methodology. Here, in this paper the static voltage stability of the Ethiopian power system is investigated using an index called normalized active power margin. The methodology starts from determining Thevenin equivalent of a system as viewed from the load buses. The Thevenin equivalent parameters help to determine the load bus maximum active power transfer limit and to draw the PV relation curves. The approach avoids the time-consuming method of PV curve based maximum active power transfer determination, which requires large number of power flow computations. The resulting maximum active power transfer and current operating active power load are used for the index calculation. The index is tested using IEEE 30 bus system and produced results matching with other previously established indices. The index is capable of ranking vulnerability of load buses to voltage instability. Then, scenarios of heavy load and light load EEP cases, with and without system reactive power compensation, are investigated. Results reveal weakest buses are supplied from 66kV transmission lines, load bus 232 being the weakest of all. On the other hand, the most stable buses are supplied from 132 kV transmission lines, bus 149 being the most stable bus. PV curves drawn, also, reveal the improvement that come with reactive power compensation and with operating in light load condition.

Critical Comparative Analysis of Measurement Based Centralized Online Voltage Stability Indices

In this paper, a detailed qualitative & quantitative comparative analysis of measurement based centralized voltage stability monitoring approaches using Thevenin equivalent is presented. These methods typically utilize the state estimation output, making them easily implementable at the control centers. The metrics for comparison are defined in terms of computation resources required, accuracy of identifying the critical loading point, critical contingency screening, and robustness to noise. These performance metrics are relevant for practical implementation and are presented on the IEEE 300 bus system and the MATPOWER 2383-bus system. To the best of our knowledge, this is the first systematic qualitative & quantitative comparison between various measurement based voltage stability methods using these performance metrics. The results will guide the utilities and operators about possible trade-offs between the various methods for large systems, enabling them to make an informed decision on the specific method to use for their needs.

A Real-Time Enhanced Thevenin Equivalent Parameter Estimation Method for PLL Synchronization Stability Control in VSC

The real-time estimation of the AC power system equivalent parameters enables the grid-connected Voltage Source Converter (VSC) to achieve more effective stability control during a short-circuit fault. In this paper, a novel Thevenin Equivalent (TE) parameter estimation method based on local synchronous Phasor Measurement Units (PMUs) is proposed and applied to the Phase-Locked Loop (PLL) synchronization stability control of VSC. First, the relationship between the variation of the measured voltage and the error of the estimated impedance is strictly derived based on the rules of norm inequality. Then, according to the analysis of the upper bound of the system voltage change, a voltage threshold is proposed to select the PMU measurements to ensure the accuracy of the estimation during the large disturbance. Finally, using the estimated TE parameters, the current control instruction of VSC during the fault is calculated in real-time to ensure a synchronous and stable operation. The simulations reveal that the proposed estimation method can accurately track the TE parameters after a fault. Furthermore, the associated current control actions during a fault can ensure the PLL synchronization stability of VSC.

A Novel Bi-LSTM-Based Method for Thevenin Equivalent Parameter Identification

Insufficient power system operation data sets hinder the extensive application of various artificial intelligence algorithms. The solution of the Thevenin equivalent parameters especially depends on the power flow data of the grid. This article proposes a Kirchhoff circuit law-based power flow sample generation method, which can overcome the operation state observation difficulty and power flow calculation complexity of the power system. To a large extent, the quality of the sample determines the effect of the machine learning algorithm. This method is different in mechanism from traditional power flow calculations, which is applied to generate the state-based power flow sample data sets by using Kirchhoff circuit laws instead of the iterative calculation of power flow starting from the initial value. In this way, the efficiency of power system sample generation required by machine learning algorithms is enhanced significantly. Besides, this article finds the power characteristic parameter suitable for Thevenin’s equivalent parameter machine learning, that is, the load power differential ratio. A clustering method suitable for the Bi-LSTM (bidirectional long short-term memory) model for processing power state samples, which can improve learning performance, was studied. The case studies demonstrate the sample generation efficiency of this method and verify the learning effect of the Bi-LSTM algorithm.

Voltage Stability Analysis of a Power System with Wind Power Based on the Thevenin Equivalent Analytical Method

The traditional black-box Thevenin equivalent method cannot analyze the influence mechanism of wind power integration on Thevenin equivalent parameters. With the increase in wind power penetration, it will be difficult to accurately assess the voltage stability of power systems with wind power. Therefore, a Thevenin equivalent analytical method is proposed to analyze the voltage stability of a power system with wind power. This method adopts the equivalent model of wind power integration based on the current source model. It establishes the Thevenin equivalent analytical model for power systems with wind power by dividing the node types. Then, the analytical expressions of the Thevenin equivalent parameters are derived based on two equivalent modes to characterize the mechanism of wind power integration on the Thevenin equivalent parameters. In addition, the calculation flow chart of the voltage stability criterion is formulated based on the analytical value of the Thevenin equivalent impedance under different load growth ratios and wind power penetrations. Finally, a case study is conducted on the improved IEEE 39 node system with wind power. The results demonstrate the feasibility and effectiveness of the proposed Thevenin equivalent analytical method, which can more accurately judge the voltage stability of the power system with wind power.

Design and Experimentation Guidelines for DER’s Emulation Testbed

Due to the increasing integration of distributed energy resources (DERs) into the national grid, research is needed to understand high DER penetration in relation to grid reliability and stability. Emulation-based research is a viable option to consider hardware intensive investigations. Indeed, DER emulation-based research has advantages over DER software-based simulation and real DER implementation research. Some of these advantages are more realistic performance and boundaries and considerably less expense, higher safety, and modularity. While the downside of DER emulation-based research is the complexity of modeling large scale grid systems. This paper provides a rationalization for the selection of an emulation-based DER laboratory and description of the DER laboratory's capabilities. Additionally, guidelines for running experiments are discussed and two approaches, power scaling using rescaling coefficients and system sizing using Multi-Port Thevenin Equivalence (MPTE), are proposed to emulate realistic complex interconnected DER grid connected systems.

Distributed Frequency Divider for Power System Bus Frequency Online Estimation Considering Virtual Inertia From DFIGs

In this paper, a distributed frequency divider is proposed to estimate power system bus frequency with a limited number of PMUs while considering the inertial contributions from double-fed induction generators (DFIGs). The key idea is to reformulate the original frequency divider by modeling the contributions of DFIGs with inertia emulation and external regional power system through Thevenin equivalents. The distributed frequency divider is general and able to estimate local bus frequencies in a distributed manner. Besides, only the knowledge of the rotor speeds of synchronous generator, boundary bus frequencies and terminal bus frequencies of DFIGs as well as the admittance matrix are required to estimate the frequencies at all buses. This is drastically different from existing approaches that require system observability by PMUs to monitor all bus frequencies. Numerical results carried out on the IEEE 39-bus and modified 118-bus power systems with DFIGs demonstrate and effectiveness and robustness of the proposed method.

Shifted frequency‐based electromagnetic transient simulation for AC power systems in symmetrical component domain

Power systems are becoming more and more complicated. Traditional simulation tools such as transient stability programs and electromagnetic transients (EMT) programs are unable to meet the accuracy or efficiency requirements. This paper proposes a shifted frequency-based EMT (SFEMT) simulation in the symmetrical component-domain (abbreviated as SCSFEMT simulation) for the three-phase transmission system. The sequence-decoupled SCSFEMT modeling for the power system components is first presented based on the symmetrical component transformation. Then, the solution procedure of the presented SCSFEMT simulation algorithm is elaborated in detail based on the EMTP-type solution and multi-sequence Thevenin equivalence (MSTE). With the MSTE, the three sequence networks can be decoupled during the whole simulation. Thus, the dimension of the system is greatly reduced. Last, the accuracy and efficiency of the SCSFEMT simulation are validated on the 10-machine 39-bus New England system by comparing it with traditional EMT and SFEMT simulation. Test results show that the SCSFEMT simulation algorithm is much more efficient than traditional SFEMT simulation.

A novel method for online voltage stability assessment based on PMU measurements and Thevenin equivalent

From the power systems security point of view, determining the voltage stability margin is essential for the operation of systems. An inaccurate determination of the maximum loading factor or voltage collapse point in a power system may cause voltage instability and blackout of the system. So, applying a proper method with high accuracy and high speed is vital in analysing voltage stability in power systems. This article presents a novel method based on Thevenin equivalent of power systems to accurately determine load-ability margin using phasor measurement units (PMUs) data. The proposed method is based on the fact that at the voltage collapse point, the characteristic curves of ‘the reactive power at the receiving end’ and ‘the reactive power of the load’ in the weakest bus are tangential to each other. Furthermore, online application of the proposed method requires accurate estimation of the ‘ZIP load model’ and ‘Thevenin equivalent’ of the system. The proposed method is designed to determine the load-ability margin, ZIP load model and Thevenin equivalent of the power system, simultaneously. This characteristic of the method makes it possible to be applied for online voltage stability assessments. To demonstrate the effectiveness of the proposed method, the simulation results for IEEE 14-bus, 39-bus New England and IEEE 300-bus are presented and analysed.

Decentralized data-driven estimation of generator rotor speed and inertia constant based on adaptive unscented Kalman filter

This paper proposes an online decentralized and data-driven method for synchronous generator rotor speed and inertia estimation. First, an analytical relationship between the generator terminal voltage/current phasors and its internal rotor speed is derived using the Thevenin equivalent. The parameters of the latter are obtained via a recursive estimator, which allows us to estimate the generator’s internal rotor speed from voltage/current phasors without the need for any generator information. Second, we reformulate the equivalent swing equation into the Kalman filter form, which enables us to use a priori-estimated internal rotor speed along with measured real and reactive power injections to obtain an estimate of the inertia for each online synchronous generator. This is achieved through an adaptive unscented Kalman filter. We demonstrate that the use of terminal bus frequency to approximate the rotor speed for inertia estimation by existing methods leads to large estimation biases/errors. Numerical simulations carried out on the IEEE 39-bus and Texas 2000-bus systems reveal that our proposed method is consistently more accurate than existing methods. Moreover, our proposed method is insensitive to both the type and location of system disturbances, and it is robust to different levels of measurement noise.

Improved Thevenin Equivalent Model of MMC Considering Pre-charge Conditions and DC Side Fault Conditions

The traditional Thevenin equivalent Modular Multilevel Converter (MMC) model has poor versatility for the two working conditions of pre-charging and DC-side faults. In this paper, an improved Thevenin equivalent MMC model considering pre-charge conditions and DC side fault conditions is proposed. The model divides the pre-charging condition into a Controllable charging stage and an Uncontrollable charging stage. The DC-side fault condition is divided into the pre-blocking and post-blocking conditions of the converter. The circuit characteristics are analyzed, and the equivalent model topology is comprehensively improved to make it suitable for full-condition simulation, and a control strategy suitable for the equivalent model is proposed. The detailed model and the proposed improved equivalent model were built in PSCAD/EMTDC for comparison and analysis. The simulation results shows that the improved equivalent model can be applied to various working conditions, and the versatility of the traditional Thevenin equivalent model is improved.

Multi-objective particle swarm optimization and training of datasheet-based load dependent lithium-ion voltage models

In this study, a datasheet-based lithium-ion (Li-ion) battery cell model is built, trained and validated by utilizing Multi-Objective Particle Swarm Optimization (MOPSO). Firstly, in order to determine the most suitable solver among various multi-objective solutions, a first-order (1RC) Thevenin model is adopted. At this stage, a thorough comparison is carried out among the Mean Squared Errors (MSE), Mean Signed (MSD) and Average Deviations (AD) of five study cases, where the proposed solver showed both up to 71%,96% and 54% improvements respectively compared to the previously reported optimal result, and capability to converge over the whole available capacity of the cells. Secondly, the optimal solver selection is followed by a comparative study among various equivalent circuit models (1RC, 2RC and 3RC), which are thoroughly evaluated upon computational time, model complexity and accuracy. Thirdly, the proposed optimized Thevenin Equivalent Circuit Model (ECM) is parameterized and compared to an experiment-based model of a commercial high-power Li-ion cell, for both charge and discharge processes. Outcomes indicate an improved performance of the proposed methodology which is ultimately utilized to train a dataset obtained from the manufacturer and successfully apply it on several unspecified current profiles. As a result, a wide range of accurate voltage-model outputs is acquired from a few input profiles, indicating the overall robustness of the method and rendering it as a strong candidate for non-dynamic loading battery applications.

STATCOM integration into a DFIG-based wind park for reactive power compensation and its impact on wind park high voltage ride-through capability

This paper presents static synchronous compensator (STATCOM) integration into a doubly-fed induction generator (DFIG) based wind park (WP), analyses the impact of STATCOM on the WP high voltage ride-through (HVRT) capability, and proposes a transient function for the STATCOM to improve the WP HVRT capability. An actual WP is adopted as a test system. The STATCOM size is selected considering the grid code requirement for power factor control, and various wind turbine (WT) and medium voltage (MV) feeder outage scenarios. The WP HVRT capability is assessed with electromagnetic transient (EMT) simulations by analyzing the responses to a parametric voltage waveform. The external system is represented by a Thevenin equivalent. The pre-described voltage waveforms are applied to the Thevenin source in order to assess the conformity of the HVRT capability to Hydro-Quebec specifications. The WP simulation model includes all details regarding collector grid and overvoltage protection. The simulation results demonstrate that, STATCOM usage provides a noticeable improvement in HVRT capability of the WP, especially with the proposed transient function.

Hybrid Simulation for Large-Scale AC/DC Power System by Serial Interaction Process

Electromechanical transient (EMT) and transient stability hybrid simulations can make full use of their fast-solving ability and high-precision computing ability to accurately simulate the dynamic characteristics of large-scale AC/DC systems. This paper selects the bus as the hybrid simulation interface bus in the AC system near the DC system, which can effectively improve the simulation accuracy of the AC/DC system interaction. At the interface bus, Norton equivalent and Thevenin equivalent are applied to the EMT simulation side and electromechanical transient simulation side, respectively. The three-phase simulation data and three-sequence component simulation data are extracted respectively, and the serial iteration method is used for hybrid simulation calculation. This paper takes Zhangbei multi terminal AC/DC system as an example, compares the hybrid simulation results with the EMT simulation results, and tries to verify the accuracy and effectiveness of the hybrid simulation method.