Thevenin Equivalent Parameters Research Articles

Modeling of direct AC/AC hybrid distribution transformer based on relaxed two port network theory

Traditional distribution transformers have shortcomings such as poor dynamic characteristics and unreasonable voltage compensation. It is difficult for them to meet the demand for power quality with the large-scale integration of new energy into the grid. Hybrid distribution transformers (HDTs) are an important means of addressing these issues. They have good flexibility in voltage regulation and huge development potential. To analyze the operating status and losses of an HDT, this study constructs a simplified equivalent impedance model for an HDT. First, the operating principle, characteristics, and voltage regulation range of a direct AC/AC HDT were analyzed. Second, based on the state–space averaging method, we obtain the HDT single-phase average circuit topology and construct an HDT relaxed two-port network model. Third, considering the operating losses of the transformer, Thevenin equivalent parameters of an HDT were derived. Then, a simplified equivalent impedance model for an HDT and the corresponding control strategies are presented. Finally, we verify the correctness and rationality of the proposed theory by constructing an HDT simulation model.

AC/DC Hybrid Power System Damping Control Based on Estimated Model Predictive Control Considering the Real-Time LCC-HVDC Stability

High Voltage Direct Current (HVDC) can quickly vary its power to stabilize an AC power system when the latter is subject to a disturbance. Typically, linear control is used to design that control strategy. However, due to the uncertainties of the faults and the system model, it is necessary to estimate the linear model of the post-fault power system using real-time measurements. This leads to two main problems: Firstly, after the fault, the HVDC will quickly evolve to steady-state operating conditions and, therefore, result in an unobservable control matrix. Secondly, the HVDC power should not exceed its stable range, which is limited by the post-fault system. To address the above issues, the main novelties are as follows: First, this paper proposes a novel system identification method to handle that case when there is no control input excitation. Second, this paper presents an AC/DC hybrid power system control strategy that fully considers the real-time stability constraints of the HVDC. More specifically, this paper proposes to estimate the system matrix and the control matrix separately. Based on the linearized model of the AC/DC hybrid system, the control matrix is calculated using the sensitivities of the active powers of the generators with respect to those of the HVDC. Then, the system matrix is estimated in real-time using measures of the power angle and frequency. Finally, by processing the local voltage and current measurements, the associated Thevenin equivalent parameters on the system side of the HVDC connecting point are estimated in real-time and the upper bound of the DC power is determined. According to the linearized model and the HVDC power constraints, a control strategy is proposed using the model predictive control method. Simulation results reveal the effectiveness of the proposed strategy.

Communication-less adaptive directional overcurrent protection strategy considering islanded mode detection in active distribution networks

The integration of distributed energy resources (DERs) in electric distribution networks originates the Active Distribution Networks (ADNs). The presence of DERs introduces challenges to conventional protection schemes due to bidirectional power flows and variations in fault current magnitudes; furthermore, the connection and disconnection of DERs result in multiple ADN operating modes (OMs), deteriorating the effective operation of protective relays. Considering the above, this document presents an adaptive protection strategy to address the challenges related to the variable nature of the ADN operation. The main contribution of the proposed approach is accurate islanded mode detection without requiring communication links, enabling fault detection in all ADN operating modes. The protection strategy maintains directional overcurrent relays' coordination using local voltage and current measurements to continuously estimate the Thevenin equivalent, fault currents, and adaptive coefficients.Relay coordination is maintained through tests conducted on a modified IEEE 34-bus feeder, considering several OMs, fault types, and locations. A comparison between the proposed adaptive protection strategy and a conventional overcurrent scheme shows that relay operating time is better in 100% of the analysed cases for the former strategy. On the other hand, the maximum errors in the fault current estimation using the Thevenin equivalent parameters are between 0.05% to 2.6% for all of the analysed operating modes when compared with the true fault current magnitudes. Finally, the adequate results validate the potential of the proposed communication-less protection strategy for modern protective relaying applications.

HPPC Test Methodology Using LFP Battery Cell Identification Tests as an Example

The aim of this research was to create an accurate simulation model of a lithium-ion battery cell, which will be used in the design process of the traction battery of a fully electric load-hull-dump vehicle. Discharge characteristics tests were used to estimate the actual cell capacity, and hybrid pulse power characterization (HPPC) tests were used to identify the Thevenin equivalent circuit parameters. A detailed description is provided of the methods used to develop the HPPC test results. Particular emphasis was placed on the applied filtration and optimization techniques as well as the assessment of the quality and the applicability of the acquired measurement data. As a result, a simulation model of the battery cell was created. The article gives the full set of parameter values needed to build a fully functional simulation model. Finally, a charge-depleting cycle test was performed to verify the created simulation model.

Distance protection with fault resistance compensation for lines connected to PV plant

The output power of the inverter-interfaced photovoltaic (PV) plant has the continuous variations due to the properties of PV modules and environmental conditions. These variations fundamentally affect the performance of the conventional distance protection during nonmetallic faults. This paper proposes a positive sequence network-based distance protection scheme for the transmission lines connected to the PV plants. Different from the adaptive mho and quadrilateral characteristics, the proposed scheme is independent of PV plant parameters and fault resistance. In this method, the Thevenin equivalent parameters of the grid seen from the PV plant are calculated. Thevenin equivalent parameters are calculated using prefault current and voltage data at the local terminal, without additional costs related to the requirements of the communication channel. The obtained parameters are used in the fault resistance compensation. Furthermore, by eliminating the fault resistance effect on the relay impedance, the exact fault location is also calculated. Since the fault line impedance formula is derived only from the positive sequence network, the proposed method is applicable to different grid codes. The efficiency of the proposed scheme is evaluated on the Western System Coordinating Council (WSCC) 9-bus and IEEE 30-bus test systems. The obtained simulation results verify the validity of the proposed scheme under various fault and PV plant conditions.

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.

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.

Steady State Voltage Stability Estimation by Using Local Bus Parameters

In this study, an estimation approach based on local bus measurements of voltage, current and phase angle is presented to assess voltage stability at any of the system load bus. For this purpose, Thevenin equivalent circuit parameters of the IEEE 30-bus standard test system are estimated by using local measurements from Bus k which is selected to be evaluated in terms of voltage stability. Estimated Thevenin equivalent circuit parameters are used to calculate critical voltage values and voltage stability margin values of Bus k online for the voltage stability assessment. In conclusion, the voltage stability margin results of the proposed approach are compared with three different Thevenin equivalent based voltage stability estimation approaches. Simulation results show that the proposed approach successfully estimates the voltage stability margins of any load bus in the system. From the perspective of voltage stability, estimated voltage stability margins can be used to assess the loading levels of any load bus, to define critical busses and to make decision for load shedding.

Real-Time LCC-HVDC Maximum Emergency Power Capacity Estimation Based on Local PMUs

The maximum active power that a Line-Commutated-Converter High Voltage Direct Current (LCC-HVDC) can provide instantly, called LCC-HVDC-MC Maximum Emergency Power Capacity, is an important information for determining the emergency control strategy of a power system subject to a large disturbance. However, it is a challenging task to calculate this capacity accurately due to system model uncertainties and contingencies. To address this problem, we propose to estimate this capacity by real-time tracking the Thevenin equivalent (TE) parameters of the AC system based on local PMUs. This new TE estimation method can handle the large disturbances and yield an accurate HVDC-MC while considering various constraints. Specifically, we first investigate the impacts of the TE potential changes on the TE impedance estimation under a large disturbance. To reduce the estimation error caused by the TE potential change, we develop an adaptive current screening process of the current measurements. Moreover, we use the total least square estimation method to further filter out the PMU errors. Finally, we calculate LCC-HVDC maximum emergency power capacity while accounting for the limitations of the control performance, voltage dependent current order limit, the converter capacity, and the AC voltage. The simulations show that the proposed method can accurately track the TE parameters and the real-time LCC-HVDC maximum emergency power capacity following a large disturbance.

Detection and Mitigation of Cyber Attacks on Voltage Stability Monitoring of Smart Grids

This paper investigates the possible cyber-physical attacks on voltage stability monitoring of a power transmission system. By considering a smart adversary that can launch a vector attack based on power flow equations, conventional voltage stability monitoring systems based on voltage stability indexes will fail to detect the instability issue. This can mislead the Power System Operator (PSO) to take inappropriate corrective action. In order to prevent and to combat such a malicious attack, a new indicator for efficient intrusion detection and a novel mitigation algorithm is proposed. This proposed detection algorithm employs the multi-port equivalent circuit of the power system to calculate the Thevenin Equivalent (TE) parameters. These TE parameters are then used to calculate an indicator, which reveals the attack on Phasor Measurement Unit (PMU) data. The proposed mitigation scheme then helps PSO to detect which PMU is under-attack. Furthermore, the amount of injected attack vectors is computed or estimated depending on the number of compromised PMUs. The effectiveness of the proposed techniques is demonstrated via illustrative case studies.

Impact of local PMU‐based equivalent methods on real‐time voltage stability assessment

This study promotes a critical discussion about the phasor measurement unit (PMU)-based equivalent methods in order to investigate the impact of the Thevenin equivalent (TE) parameters on real-time power system voltage stability assessment. Although several articles indicate good performance at impedance magnitude matching theory, they neglect the influence of TE impedance angle and voltage source magnitude, introducing inaccuracies or mathematical inconsistencies in stability evaluation. The former three parameters are highlighted in this study due to being directly used to compute active power margins and indexes, according to the maximum power transfer theorem. The approach identifies the methods’ robustness and weaknesses by the use of generic expressions. The main contribution of this study is presenting equations for directly calculating the parameters that may lead to inconsistent interpretations, particularly when measurement noise is considered. Disregarding these inconsistencies may result in an incorrect determination of the system's critical limit, increasing the risk of voltage instability. The conception of the new formulation relies on network equivalents based on the least-squares method, Tellegen's theorem and adaptive method. Following the simulations carried out in Nordic Test System, and 9, 14 and 39 Bus Test Cases available in MATPOWER, analyses substantiated in the derived expressions are given.

Real time voltage stability prediction of smart grid areas using smart meters data and improved Thevenin estimates

One of the important factors of power delivery disruption is voltage instability. As loads increase, the grid is pushed toward instability and the voltage drops. Once instability is reached, the area will experience a blackout. Many methods exist which can be used to determine grid stability. One popular technique used for estimating the maximum available power as well as grid area stability, without knowing the grid model, uses the concept of the Thevenin equivalent circuit. The maximum power can be used to support demand response methods. In addition, it is possible to use the Thevenin parameters to determine how reactive power compensation affects the maximum power. Existing Thevenin equivalent techniques use aggregate load measurements, which provide poor estimates of the Thevenin equivalent parameters. This affects the accuracy of the available maximum power estimate.The objective of this paper is to take advantage of individual load measurements from smart meters to provide improved estimates of the Thevenin parameters. Additionally, a new real time stability index that alerts utilities when the system approaches instability is proposed.The proposed improved Thevenin estimates and stability index were tested using an IEEE 30 bus power system. The simulation results show that the new estimator is capable of generating better Thevenin parameters estimate than the classical method. The results also show the ability of the proposed stability index in predicting voltage instability ahead of time to give utilities the chance to react properly before a blackout takes place.

Optimal current calculation for a PMSG based wind energy system integrated into an unbalanced weak grid

Grid connection is an important consideration when it comes to integrating an energy source. A common problem with the existing wind energy conversion systems is that they are often located far from energy consumption centres. Owing to their remote location these systems are sometimes forced to connect with weak distribution networks which are usually designed for small linear loads. When the nature of these loads is changed, the voltage level at the point of common coupling may go above or below the nominal value which may result in power system instability. To improve the voltage variation, this study discusses an optimal current calculation technique based on Thevenin equivalent parameters of an electrical network. The functional capability of the technique is demonstrated with the help of a traditional converter topology utilised as a power conditioning system for a permanent magnet synchronous generator connected to a weak grid. The system in particular monitors a medium voltage distribution line, measures line load impedance and redistributes the currents in a way that provides maximised power transfer into a network with least incurred losses. A real-time controller with built-in data acquisition/field-programmable gate array modules is used for the execution of experimental investigations.

Online Thevenin Equivalent Parameter Identification Method of Large Power Grids Using LU Factorization

Real-time tracking and identification of Thevenin equivalent parameters is crucial for voltage stability online monitoring of large power grids. An online parameter identification method based on wide-area measurements and nodal analysis is proposed in this paper. The node-voltage equation is utilized directly, and the open-circuit voltage is calculated accurately as the Thevenin equivalent voltage of load buses. Moreover, the equivalent parameters can be identified precisely under the generator reactive power over-limit condition. To avoid repetitive Gaussian elimination of the high-dimensional linear system, lower upper factorization and optimized substitution are used to accelerate the open-circuit voltage solution process. The simulation results of multiple test systems demonstrate the accuracy and rapidity of the proposed method.

An Optimal Thévenin Equivalent Estimation Method and its Application to the Voltage Stability Analysis of a Wind Hub

A simplified voltage stability analysis method is to use a static Thevenin equivalent to represent the electrical connection to a load center. Assuming fixed values of the Thevenin voltage and reactance, a power-voltage ( $PV$ ) curve analysis can be performed to find the voltage collapse point and stability margin. This paper proposes a method to compute the static Thevenin equivalent voltage and reactance of a power system using measured data. The method is validated with simulated PMU data and with 24-hour SCADA data at a wind hub on a medium voltage transmission system in the US western system. For the wind hub, the Thevenin equivalent parameters are used to compute the maximum power transfer capability of the wind hub as constrained by voltage stability. Then the method is extended to online application by using short data windows and forgetting factors.

Robust Thevenin Equivalent Parameter Estimation for Voltage Stability Assessment

This letter presents a robust approach to accurate estimation of Thevenin equivalent (TE) parameters using phasor measurement unit (PMU) data for online voltage stability assessment. The TE parameter estimation is formulated as a worst-case robust least squares problem to take PMU uncertainties into account. A second-order cone programming technique is then utilized to solve the problem. Case studies on several IEEE standard networks and a practical power system, along with comparative results, illustrate the effectiveness and robustness of the presented approach.

Fast Analysis Method of Static Voltage Security Based on Thevenin Equivalent

With the large-scale renewable energy incorporation, the system operation fluctuation and randomness are increasing, and the real-time requirement of the static voltage security analysis of power system is more urgent. In order to meet the requirements of real-time, fast Thevenin equivalent parameter is used as the static voltage safety analysis index. The fast N-1 scanning of the static voltage security is achieved by studying the analytic relationship between line outage and Thevenin equivalent parameters, and then instable points of the voltage are found to ensure the system at safe operation level. The advantage of this method is that it can calculate the Thevenin equivalent parameter after disconnection, only using the voltage, phase angle, active power and reactive power of the system before line outage. The validity and correctness of this method are verified by simulation results.

Online Determination of External Network Models Using Synchronized Phasor Data

This paper proposes an online measurement-based method for determining multiport Thevenin equivalent circuit parameters of an external power system. The equivalent circuit is estimated using synchronized voltage and current phasors measured at the boundary nodes and it is intended to work continuously leading to real-time equivalent models of the external system. The measurement errors and noise are taken into account by utilizing extra measurements and applying the least-squares method to find the equivalent model parameters. A method to determine the origin of the disturbances is proposed to detect system changes that can be used for the parameter identification process. The performance of the proposed method has been demonstrated by using the IEEE 118 bus system.