This paper investigates the impacts of different current limiting strategies on the transient stability of the Virtual Synchronous Generator (VSG). The power-angle curve of the VSG under different ...operating conditions is theoretically characterized in detail and experimentally verified through tests conducted on hardware-implemented lab-scale VSGs. It is shown that the reference current saturation approaches prioritizing the current vector angle, the d -axis current, and the q -axis current reshape the VSG power-angle curve in different ways. The resulting impacts on the VSG transient stability are comprehensively investigated through time-domain simulation of a battery energy storage system that is operated as a VSG and connected to a medium-voltage Canadian distribution feeder. The transient stability margin of the VSG is evaluated by determining the Critical Clearing Time (CCT) of various fault scenarios. The studies conducted in the PSCAD/EMTDC software environment utilizing a detailed switching model of the VSG indicate that: (i) the current limit of the VSG significantly impacts its power output during and after faults; and (ii) the q -axis priority current limiting strategy provides a larger transient stability margin (CCT) as compared with the current vector angle and d -axis current priority approaches.
This paper deals with the transient stability of a grid-forming converter while embedding a current reference saturation strategy. The novelty of this work consists in investigating the impact of the ...current reference angle on the transient stability. In case of a balanced voltage sag, analytical formulas to estimate the critical clearing angle (CCA) and critical clearing time (CCT) while considering different values of the current reference angle are derived. It is demonstrated that the choice of this angle is constrained by the ability of the power converter to switch back to the voltage control mode. Based on that, its optimal value that enhances the transient stability and allows a switching from the saturated current control mode to the voltage control mode is calculated. Thereafter, the effectiveness of this optimal choice to guarantee the stability in case of a phase shift caused by a line re-closing event is verified. Time-domain simulations and experimental tests validate the correctness of the presented theoretical approaches.
This work analytically establishes a multi-variable energy function for a three-phase grid-following inverter leveraging a unified equivalent-circuit model for its physical- and control-layer ...subsystems. This is a significant contribution to the prior art in which analytical approaches to large-signal stability for inverters have largely been attempted with simplified models. Central to our effort is to cast physical- and control-layer dynamics of each dynamical subsystem as an equivalent circuit consisting of familiar circuit elements adopting a positive-sequence modeling framework. An energy function for the inverter is then constructively synthesized by summing the energy functions across the various subsystems that are readily derived from circuit-theoretic principles. Numerical simulations are presented to validate the equivalent-circuit model of the inverter as well as the efficacy of the synthesized energy function in characterizing large-signal stability following a disturbance.
Microgrids (MGs) with distributed energy resources (DERs) offer multiple advantages in terms of energy efficiency, reliability, and sustainability. However, due to the changes DERs bring to the fault ...currents, ensuring protection for DER-rich distribution grids is more challenging than conventional grids. This paper investigates the implementation of directional overcurrent relays (DOCRs) in MGs, considering the transient stability of the DERs. Given the low inertia of the DERs, the high operating times of DOCRs can potentially impede DERs' stability, even at post-fault. As such, this paper proposes a novel approach using shifted user-defined characteristics of DOCRs that employs two inverse curves to maintain both relay-relay coordination as well as DERs' stability. Then, the critical clearing times of DERs are combined with the coordination constraints to determine DOCR's optimal settings using genetic algorithm. The proposed methodology is evaluated using the modified IEEE 33-bus test system equipped with four synchronous-based DERs. DigSILENT and MATLAB are used to simulate the system, solve the optimization problem, and analyze transient stability. The results indicate the superior performance by the proposed characteristics in comparison with single characteristic to meet both relay coordination and DERs' stability requirements.
•Conflict between computation efficiency and accuracy exists in model-driven method.•Data-driven method is able to correct error of model-driven method.•Error tolerance difference is considered in ...training objection data-driven method.
The critical clearing time (CCT) is one of the most important indexes for large-disturbance rotor angle stability margin evaluation. In practice, model-driven methods are usually realized based on simplified models to ease the computational burden, but the accuracy is sacrificed. To solve this problem, a data-driven method is adopted in this paper for fast error correction of a model-driven method, creating an integrated method. Both a reliable accuracy and an acceptable computation speed can be achieved with this integrated method. Meanwhile, involvement of model-driven method helps enhance robustness of the integrated method to training sample insufficiency, measurement error and power system scale. In addition, the data-driven method is further transformed on the basis of a cost-sensitive approach where the error tolerance for different actual CCT values should be differentiated during the training process instead of being treated equally in the common data-driven method. To mitigate the negative effect caused by such transformations, an ensemble learning structure is also constructed. In this paper, an integrated extended equal-area criterion (IEEAC) and an extreme learning machine (ELM) are applied as model-driven and data-driven methods, respectively. A genetic algorithm (GA) is used in the ensemble learning structure construction. Validations show that the proposed integrated method with the transformed data-driven method can improve the CCT prediction accuracy and avoid the polarization of the error distribution.
•This paper proposes a new modified multi-objective evolutionary algorithm.•The proposed framework is simple and does not have complexities.•The proposed approach is applied on Distribution feeder ...reconfiguration (DFR).•The effectiveness of the proposed method is studied based on a typical 33-bus test system.
This paper proposes a multi-objective evolutionary algorithm method for Distribution feeder reconfiguration (DFR) with distributed generators (DG) in a practical system. Considering the low inertia constant of DG units in order to take the transient stability of DGs into account is one of the major issues in power systems. Especially when the penetration of DGs is low, the impacts of them on the distribution system transient stability may be neglected. However, when the penetration of DG increases, the transient stability of them must be taken into account (more DGs, more transient issues). To this end, the DFR problem has been solve by an enhanced Gravitational Search Algorithm (EGSA) to improve the transient stability index and decrease losses and operation cost in a distribution test system with multiple micro-turbines. The effectiveness of the proposed approach is studied based on a typical 33-bus test system. For getting close to the practical condition and considering the detailed dynamic models of the generators and other electric devices in power system, simulation and programming of this approach are done by the DIgSILENT® Power Factory software.
•The impact of both solar PV and wind power plants on the national electricity grid of Lesotho electricity company (LEC) was investigated.•Dynamic impact studies (critical clearing time, voltage, ...frequency and rotor angle stability) and steady state voltage analysis were undertaken.•For the solar PV only scenario, the maximum allowable solar PV capacity was found to be 35 MW.•For the wind only generation scenario, the maximum allowable wind capacity was found to be 50 MW.
Utility-scale integration of solar photovoltaic (PV) and wind farms has gained momentum as countries pursue sustainable power systems. Increased penetration of solar PV and wind alters the operation of power grids as they have different electrical properties from conventional power plants. The paper assesses the dynamic and steady state impacts of intermittent (variable) renewable energy generators (IREGs) on the Lesotho power grid. Maximum allowable penetration of both solar PV and wind generators were determined for Ha-Ramarothole and Letseng sub-stations, respectively. Dynamic impact studies were performed by applying the short circuit fault at the bus bar with the least critical clearing time (CCT) and observing voltage, frequency and rotor angle as the renewable energy capacity was varied. Steady state voltage analysis was performed based on the hourly load of 2018 and generation of both IREGs and Muela Hydropower. Voltage, frequency and rotor angle stability were evaluated against the Grid Code of Lesotho. The impact studies were done using DigSILENT PowerFactory software. Maximum allowable penetrations for solar PV was about 19% at Ramarothole substation while for wind it was found to be 27% at Letseng substation. Simulations revealed that increased penetration of the IREGs led to grid instability. The solar farm penetration of 36 MW connected at 132 kV resulted in grid instability mainly from the rotor angle instability while the wind farm penetration of 52 MW connected at 88 kV resulted from an overvoltage of 1.051 p.u. at the neighboring 33 kV substation of Tlokoeng.
It is a computationally challenging task to analyze the transient stability of large-scale, strongly nonlinear power systems containing induction motors (IMs). Among existing methods for transient ...stability analysis (TSA), time-domain simulation is too time-consuming and only suitable for offline analysis, while direct methods fail to consider the detailed dynamics of IM. To address this challenge, this paper proposes a systematic method to construct Lyapunov functions for power systems containing IMs, and presents a two-stage expanding boundary (TSEB) algorithm to compute the tightest critical value of Lyapunov function. The TSEB algorithm can provide more accurate estimates of domain of attraction (DA) and critical clearing time (CCT). The main novelties include the following three aspects. First, we can construct Lyapunov functions systematically for large-scale power systems containing IMs. Second, we use relative angles as state variables to express a multi-machine power system containing multiple IMs as a Lure -type system. This technique can eliminate the one-dimensional equilibrium manifold and obtain tighter estimates for TSA. Third, by utilizing linear approximation to eliminate the non-convexity, the TSEB algorithm is proposed to calculate the largest critical value of Lyapunov function. The effectiveness of our proposed method is demonstrated on a 20-machine 39- bus system and 35-machine 118- bus system.
•This paper presents the mathematical model of the heterogenous three-machine system, considering the dynamics of the pre-fault, fault-on, and post-fault systems.•Based on the developed model, the ...critical clearing time is derived analytically for transient stability assessment. The method can deal with the nonlinearity between SG’s rotor angle and VSC’s PCC voltage phase.•Decreasing the active current component of VSCs has the potential to increase the maximum active power transmission capacity between the interconnected AC systems, so that the transient stability can be enhanced.•With the help of WAMS, the proposed enhancement control strategy achieves dynamic current modulation based on the angle difference between SGs and the PCC voltage phase of VSCs.•The proposed enhancement control strategy is adaptable to multimachine systems with the concept of COI.
This paper analyzes the transient angle stability mechanism of interconnected AC power systems with voltage source converter (VSC) based generations and presents a stability improvement control strategy for the VSCs. Firstly, the mathematical model of the prototype AC system with both synchronous generator (SG) and VSC is developed, considering the dynamics of the pre-fault, fault-on, and post-fault systems. For the heterogenous three-machine system, the analytical method for the critical clearing time (CCT) is proposed for transient stability assessment. Then, the evolution of the transient stability margin of the AC system is studied, considering the impact of the VSCs. Under the conditions that VSCs can keep synchronism with the grid during the fault, reducing the active current of the VSCs benefits the transient angle stability of SGs. Based on the mechanism analysis, an enhancement control strategy is developed. It achieves active and reactive current modulation of the VSC using the frequency measurements of the critical SGs (CSGs) in the AC system. The proposed method devotes to boosting the electromagnetic power of CSGs during the entire transient process. Finally, time-domain simulations in PSCAD/EMTDC demonstrate the theoretical analysis. The effectiveness and robustness of the enhancement controller are further validated by the time-domain simulations in a 2-area interconnected system with 4 SGs and a modified New England 39-bus test system.
A fault current limiter (FCL) is an economical option to limit the increased fault current levels, which may also improve the rotor angle stability. Previous studies on this topic mainly focused on ...the FCLs with quick recovery and concluded that the FCL improves the rotor angle stability. However, some commercially available FCLs have delayed recovery, which may pose different challenges and need to be studied. This paper studies the impact of a superconducting fault current limiter (SCFCL) with delayed recovery on transient rotor angle stability. This paper first develops an analytical understanding of the stability of a system with SCFCL using the equal area criterion. Later, time-domain simulations are employed to demonstrate the impacts of the SCFCL on the rotor angle stability of a single-machine infinite-bus system. The results show that the SCFCL with delayed recovery leads to rotor angle instability in some cases.
•Identification of the adverse impact of SCFCL with delayed recovery on transient stability.•Transient stability assessment with different SCFCL technologies.•Transient stability assessment with different SCFCL parameters, locations, and fault types.
