Hasil untuk "Distribution or transmission of electric power"

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DOAJ Open Access 2026
Large Language Models for Detecting Cyberattacks on Smart Grid Protective Relays

Ahmad Mohammad Saber, Saeed Jafari, Zhengmao Ouyang et al.

This paper presents a large language model (LLM)–based framework that adapts and fine-tunes compact LLMs for detecting cyberattacks on transformer current differential relays (TCDRs), which can otherwise cause false tripping of critical power transformers. The core idea is to textualize multivariate time-series current measurements from TCDRs, across phases and input/output sides, into structured natural-language prompts that are then processed by compact, locally deployable LLMs. Using this representation, we fine-tune DistilBERT, GPT-2, and DistilBERT+LoRA to distinguish cyberattacks from genuine fault-induced disturbances while preserving relay dependability. The proposed framework is evaluated against a broad set of state-of-the-art machine learning and deep learning baselines under nominal conditions, complex cyberattack scenarios, and measurement noise. Our results show that LLM-based detectors achieve competitive or superior cyberattack detection performance, with DistilBERT detecting up to 97.62% of attacks while maintaining perfect fault detection accuracy. Additional evaluations demonstrate robustness to prompt formulation variations, resilience under combined time-synchronization and false-data injection attacks, and stable performance under realistic measurement noise levels. The attention mechanisms of LLMs further enable intrinsic interpretability by highlighting the most influential time–phase regions of relay measurements. These results demonstrate that compact LLMs provide a practical, interpretable, and robust solution for enhancing cyberattack detection in modern digital substations. We provide the full dataset used in this study for reproducibility.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2025
The Optimal Operation Strategy of an Energy Community Aggregator for Heterogeneous Distributed Flexible Resources

Xinyi Yang, Tao Chen, Yuanshi Zhang et al.

The widespread integration of renewable energy into the grid emphasizes the issues of power system uncertainty and insufficient flexibility. Heterogeneous flexible distributed resources can address the above challenges by interacting with distribution networks. This paper proposes a multi-timescale optimal operation strategy for an energy community that aggregates multiple distributed resources. Based on flexibility indicators including the degree of load variation and task laxity, a tri-level structure involving distribution system operators (DSOs), aggregators, and the home energy management system (HEMS) is developed. The aggregator serves as mediator between customers and DSOs, gathering the end user’s flexibility through the rescheduling of household appliances to leverage both upward and downward energy adjustments. According to different scenarios and application requirements, a multi-time-scale rolling optimal dispatch model is proposed. The day-ahead dispatch is combined with the Model Predictive Control (MPC) method to achieve fine-grained rolling adjustment of the power dispatch instructions of distributed resources with different time scales. Finally, a simulation experiment example is constructed to verify the effectiveness of the proposed method. The simulation results demonstrate that the economic benefits of end users and aggregators are improved with more grid-friendly load curves.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2024
A cooperative control strategy for balancing SoC and power sharing in multiple energy storage unit within DC microgrids

Jianlin Li, Honghao You

Abstract This paper proposes a distributed cooperative control scheme for multiple energy storage unit (ESU) in DC microgrids to achieve the control objectives of SoC balancing, power sharing, and bus voltage recovery. In the primary control part, the proposed scheme constructs a control function between the SoC values of each ESU and the droop coefficients to dynamically adjust the droop coefficients. Through a communication network, information is exchanged with neighbouring ESUs to achieve SoC convergence. In the secondary control part, by exchanging power information with neighbouring ESUs, precise power distribution is achieved. Additionally, the proposed scheme maintains bus voltage stability. Finally, a DC microgrid simulation model and experimental platform were developed, demonstrating the feasibility and plug‐and‐play capability of the proposed control strategy through both simulation and experimental case tests.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2024
Series arc‐fault diagnosis using convolutional neural network via generalized S‐transform and power spectral density

Penghe Zhang, Yiwei Qin

Abstract It is difficult to identify an arc fault accurately when the loads on the user side are more complicated, which hinders the development of low‐voltage monitoring and pre‐warning inspection. This study acquired a series of arc‐fault signals according to IEC 62606. The main time‐frequency features were strengthened with high efficiency by applying the generalized S‐transform to them with a bi‐Gaussian window. Further, the power spectrum density determination allowed for the detection of imperceptible high‐frequency harmonic energy reflections, thus increasing the rate of arc‐fault diagnosis and making it suitable for arc‐fault monitoring of non‐linear loads. The final samples were trained and classified using a 2D convolutional neural network and the overall accuracy of identification was observed to be 98.13%, which involved various domestic loads, thus providing a reference for follow‐up arc‐fault monitoring and inspection research.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2024
Intelligent energy management scheme‐based coordinated control for reducing peak load in grid‐connected photovoltaic‐powered electric vehicle charging stations

Mohammad Amir, Zaheeruddin, Ahteshamul Haque et al.

Abstract Solar‐based Distributed Generation (DG) powered Electric Vehicles (EVs) charging stations are widely adopted nowadays in the power system networks. In this process, the distribution grid faces various challenges caused by intermittent solar irradiance, peak EVs load, while controlling the state of charge (SoC) of batteries during dis(charging) phenomena. In this paper, an intelligent energy management scheme (IEMS)‐based coordinated control for photovoltaic (PV)‐based EVs charging stations is proposed. The proposed IEMS optimizes the PV generation and grid power utilization for EV charging stations (EVCS) by analysing real‐time meteorological and load demand data. The coordinated control of EMS provides power flow between PV generation, distribution grid, and EVs battery storage in a manner which results in the reduction of peak power demand by a factor of two. Further, the adaptive neuro‐based fuzzy control approach includes forecasting solar‐based electricity generation and EVs loads demand predictions to optimize IEMS according to the Indian power scenario. The proposed IEMS optimally utilizes the buffer batteries system for reducing the peak electricity demand with low system losses and reducing the impact of EVs charging load on distribution grid. The results are analysed using the digital simulation model and validated with real‐time hardware‐in‐loop experimental setup.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2024
Optimal harmonic resonance monitoring in electrical network considering area of harmonic pollution and system uncertainty

Sina Shakeri, Mohammad Hossein Rezaeian Koochi, Saeid Esmaeili

Abstract This paper proposes an optimization approach for allocating power quality monitors (PQMs) aiming to monitor all harmonic resonance conditions while taking power system uncertainties into account. The placement approach utilizes the frequency scan response for calculating impedances over a range of frequencies and consequently determining harmonic resonance conditions. Thereby, it is capable of building binary matrices, which include harmonic resonance conditions. Also, by utilizing the union operator at binary matrices, power system uncertainties such as photovoltaic generation and load level can be considered in the allocation method. The placement approach is expressed as a linear problem that determines the best locations of PQMs and their optimal number so that they monitor all harmonic resonance conditions. Besides, by considering the area of harmonic pollution of non‐linear loads in the proposed method, owners of electrical networks can find a solution with fewer PQMs to monitor harmonic resonance orders inside a particular area of the network. The performance of the presented approach is demonstrated using the 15‐node distribution network and a real electrical network, as well as a real large electrical network in Iran. Results show that the proposed method suggests fewer PQMs to monitor harmonic resonance conditions compared to previous methods.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2024
Electrical insulator defect detection with incomplete annotations and imbalanced samples

Fengqian Pang, Chunyue Lei, Jingsheng Zeng

Abstract Insulators are one of the key components in high‐voltage power systems that prevent transmission lines from grounding. Since they are exposed to different kinds of harsh environments and climates, periodic inspection is indispensable for the safety and high quality of power grid. Nowadays, unmanned aerial vehicle (UAV) inspection is more widely used, facilitating incorporation of convolutional neural network‐based detectors in the insulator detection task. However, these methods are generally based on the assumption that the image samples are balanced among different categories and possess completely ideal annotations. The problem of sample imbalance or incomplete annotation is rarely investigated in depth for insulator defect detection. Here, insulator defect detection with imbalanced data and incomplete annotations is focused on. The proposed framework, named Pi‐index, introduces positive unlabelled (PU) learning to solve the problem of incomplete annotation and designs a novel index the class prior, which is a key parameter in PU learning. Moreover, focal loss is integrated in our framework to alleviate the effect of sample imbalance. Experiment results demonstrate that the proposed framework achieves better performance than the baseline methods in situations of sample imbalance and missing annotation.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2024
Triple‐indexed passive islanding detection strategy for grid‐connected distributed generation networks using an extended Kalman filter

Nauman Ali Larik, Mengshi Li, Qinghua Wu

Abstract Islanding detection is a challenging issue in modern grid‐connected distributed generation networks (GCDGN). Generally, islanding detection has two categories local and remote, local schemes can be categorized into active, passive, and hybrid schemes. This article proposes a triple‐indexed passive islanding detection (TIPID) scheme using an extended Kalman filter (EKF). Initially, the EKF algorithm is applied on voltage signal at the point of the common coupling to estimate the desired fundamental and non‐fundamental features. The first index, known as the cumulative voltage logarithmic index, is computed by taking the natural logarithm of the fundamental voltage features to detect any variations in the GCDGN. The second index, known as the voltage differentiation index (VDI), is calculated from the fundamental voltage features, while the third index, known as the odd‐order harmonic distortion index (OOHDI), is obtained from the non‐fundamental odd‐order harmonics of the PCC voltage. Then, the VDI and OOHDI are compared to pre‐defined threshold to detect/distinguish islanding events. The proposed TIPID method is validated through extensive simulations on the IEEE 13‐bus test bed via MATLAB/Simulink 2022b. Results show that under both balanced/unbalanced load & generation, the proposed TIPID approach detects islanding occurrences with reduced non‐detection zone (NDZ) in less than 5 ms.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2024
Investigating the characteristics of internal discharge shock waves in gas‐insulated switchgear under varied gap configurations

Chenglong Jia, Peng Haochu, Wenbin Zhao et al.

Abstract Gas‐insulated switchgears (GIS) are crucial components of high‐voltage power transmission and distribution systems. Internal discharges within GIS have garnered significant attention in the field of power engineering. This study investigates the characteristics of internal discharge shock waves in GIS under an air pressure of 0.3 MPa and three different discharge gap conditions: 1, 1.5, and 2 mm. High‐speed shadowing techniques are used to analyse the propagation speed, morphology, and post‐wave parameters. The study findings reveal that although the characteristics of internal discharge shock waves in GIS noticeably change with the gap size, they also exhibit a consistent trend: as the gap size increases, the initial shock wave accelerates, intensifying the discharge. Simultaneously, the rate of attenuation rises, with the shock wave becoming weaker after ≈30 µs. Furthermore, the post‐wave parameters follow a similar pattern, with an increase in gap size leading to higher parameter values but also a faster decay rate. The parameters decay more rapidly between 10 and 20 µs, slow down between 20 and 30 µs, and ultimately stabilize after around 30 µs. The results of this study hold significant theoretical and practical implications for the monitoring, diagnosis, and prevention of internal discharges in GIS.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2024
Robust higher order sliding mode control of grid‐forming converters with LCL filter in weak grid scenarios for fast frequency support

Tuhin S. Das, Udaya D. Annakkage, Dharshana Muthumuni et al.

Abstract This paper presents a nonlinear higher‐order sliding mode control (HO‐SMC) designed for a droop control‐based grid‐forming converter. In weak grid scenarios, where the rate of change of frequency is notably high, achieving a rapid frequency response becomes imperative. The stable operation of a grid‐forming converter using droop control, coupled with classical vector control that employs cascaded voltage and current loops (multiloop) with PI controllers, faces limitations when higher droop coefficients are applied. This constraint on the application of classical vector control in weak grid conditions necessitates alternative solutions. Operating as a grid‐forming converter, the grid‐connected converter with an LCL filter represents a second‐order system. HO‐SMC mitigates the switching challenges associated with conventional SMC by integrating robust feedback linearized control. A graphical method is proposed for designing the switching gain using Lyapunov's direct method to counteract the impact of a matched disturbance. The study demonstrates that the implementation of HO‐SMC in the grid‐forming converter enhances fast frequency response by increasing the gain margin of the power frequency (P--f) loop. Finally, it is illustrated that the proposed control method also improves the transient response of the converter.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2023
PowerSAS.m—An Open-Source Power System Simulation Toolbox Based on Semi-Analytical Solution Technologies

Jianzhe Liu, Rui Yao, Feng Qiu et al.

In handling complex power system simulation tasks, semi-analytical solution (SAS) methods have proven to be numerically robust and computationally efficient. They provide a competitive alternative to traditional numerical approaches. Still, there is inadequate power system simulation software, especially the open-source tools, that implements this technology. This paper introduces PowerSAS.m, an open-source toolbox that closes this gap by providing SAS baseline simulation options for power system steady-state and dynamic simulations. At its core, it implements a novel SAS method and encloses various heuristics and simulation techniques to ensure enhanced computational performance. In case studies, we verify PowerSAS.m in benchmarking comparisons and demonstrate its functionalities in grid analysis scenarios.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2023
A visual faulty feeder detection method for power distribution network based on spatial image generation and deep learning

Wei Guo, Yuntao Shi

Abstract In the case of a single‐phase grounding fault in the distribution network, the transient zero‐sequence current (TZSC) tends to be non‐linear and non‐stationary. The faulty line selection is relatively difficult. The distributed power access further brings many difficulties to faulty line selection. This work proposes a novel method of faulty line selection using spatial image generation and deep learning. At first, the optimal smooth denoising model can be used to smooth the zero‐sequence current for each line, reducing the external environment electromagnetic interference. Then, the treated zero‐sequence current is mapped into the colorful floral hoop image by using symmetrized Hilbert transform pattern (SHTP). The SHTP transforms the one‐dimensional time domain signal into the two‐dimensional space domain image, enhancing invisible information and obtaining more abundant feature information. Finally, the deep features of the SHTP floral hoop image are extracted by means of deep learning method. In order to improve the faulty line selection universality, a mixed sample library containing three different topologies is established, including the 10 kV radial distribution network, IEEE‐13 node model, IEEE‐34 node model and StarSim platform. The comparisons show that the proposed method has a more noticeable visualization effect on fault features, higher classification precision rate, and better anti‐noise performance.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2023
A Partial Discharge Localization Method for AC XLPE Cable Based on Improved GCC Algorithm

Maosen Guo, Jiajie Xu, Yi Zhang et al.

Due to the influence of electromagnetic noise and other factors, existing cable partial discharge location methods cannot accurately locate discharge faults. To handle it, this paper proposes an online localization method for cable partial discharge signals that is suitable for practical engineering applications, based on the double-end localization method. The proposed method uses an improved generalized correlation algorithm to estimate the signal time delay, and takes into account the wave speed uncertainty of the local discharge signal. To improve local localizing accuracy under multiple localizing samples, a trimmed-mean data filtering speed algorithm is employed. Simulation and experimental results demonstrate that the proposed method effectively enhances time delay estimation accuracy and reduces localization error, even under complex electromagnetic noise environment and restricted sampling rates of detection equipment, when compared to traditional time delay estimation localization methods. The positioning accuracy of partial discharge in field experiments reached 97.43%-99.89%, which meets actual engineering requirements.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2022
Capacity sizing of the integrated wind‐solar‐storage system: A nested game approach

Chuan Wang, Wei Wei, Yuguang Xie et al.

Abstract Energy storage (ES) can be a good option to reduce power curtailment and increase the total profits of an integrated energy system. This article addresses the sizing problem for the ES and renewable power plants in the integrated wind‐solar‐storage system (IWSSS). A basic IWSSS model is first constructed to analyze the operation relationship among each part. A nested game model is established to study the capacity sizing problem. The outer layer is a non‐cooperative game among the wind power plant (WPP), the solar power plant (SPP) and the ES. Each of them aims to obtain the maximum revenue which is calculated from the imputation method in the inner cooperative game. This nested game considers both the competitive relationship among three players and the reasonable imputation scheme in the grand system. A nested game algorithm is then proposed to solve this sizing problem and the optimal capacity of each player is found when the Nash equilibrium is achieved. According to the case studies, the optimal capacity ratio of the WPP, the SPP and the ES should be 0.73:0.19:0.08 under the unit transmission line capacity. Results are also conducted to demonstrate the effectiveness of the approach compared with the other two methods.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2022
Fault current compensations in resonant grounded distribution systems to mitigate powerline bushfires using a nonsingular terminal sliding model controller

Tushar Kanti Roy, Md Apel Mahmud

Abstract A fault current compensation technique is proposed in this paper for resonant grounded power distribution systems in bushfire prone areas. Arc suppression devices with residual current compensation inverters are used to compensate fault currents due to single line‐to‐ground faults in order to mitigate powerline bushfires. The main contribution of this paper is the design of a compensation technique for the T‐type residual current compensation inverter using a non‐singular terminal sliding mode control scheme. The main objective of the proposed scheme is to reduce the fault current and bring its value to a level so that it cannot ignite fires. The proposed controller is designed based on the selection of a sliding surface in a way the singularity problem can be avoided and chattering effects in existing sliding mode controllers can be eliminated. The desired current injection through the residual current compensation inverter is ensured by enforcing the control law into the terminal sliding surface where the control law is determined by satisfying the Lyapunov stability criteria. The performance of the non‐singular terminal sliding mode controller is compared with an integral sliding mode controller by considering different values of fault currents where these values are varied by changing fault resistances. Results for simulation in the software and processor‐in‐loop simulations are verified against operational standards which are essential for mitigating powerline bushfires. This work focuses to design a non‐singular terminal sliding mode controller for the residual current compensation inverter which is used in an arc suppression device to compensate both active and reactive components of the fault current and keeps its value below 0.5 A within 2 s after activating the residual current compensation inverter which is a requirement as per the operational standard. This controller is designed based on the selection of a terminal sliding surface while satisfying the condition for avoiding the singularity problem.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2022
Decomposition-Residuals Neural Networks: Hybrid System Identification Applied to Electricity Demand Forecasting

Konstantinos Theodorakos, Oscar Mauricio Agudelo, Marcelo Espinoza et al.

Day-ahead energy forecasting systems struggle to provide accurate demand predictions due to pandemic mitigation measures. Decomposition-Residuals Deep Neural Networks (DR-DNN) are hybrid point-forecasting models that can provide more accurate electricity demand predictions than single models within the COVID-19 era. DR-DNN is a novel two-layer hybrid architecture with: a decomposition and a nonlinear layer. Based on statistical tests, decomposition applies robust signal extraction and filtering of input data into: trend, seasonal and residuals signals. Utilizing calendar information, temporal signals are added: sinusoidal day/night cycles, weekend/weekday, etc. The nonlinear layer learns unknown complex patterns from all those signals, with the usage of well-established deep neural networks. DR-DNN outperformed baselines and state-of-the-art deep neural networks on next-day electricity forecasts within the COVID-19 era (from September 2020 to February 2021), both with fixed and Bayesian optimized hyperparameters. Additionally, model interpretability is improved, by indicating which endogenous or exogenous inputs contribute the most to specific hour-ahead forecasts. Residual signals are very important on the first hour ahead, whereas seasonal patterns on the 24th. Some calendar features also ranked high: whether it is day or night, weekend or weekday and the hour of the day. Temperature was the most important exogenous factor.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2021
Modeling and Performance Evaluation of Grid-Interactive Efficient Buildings (GEB) in a Microgrid Environment

Saifur Rahman, Ashraful Haque, Zejia Jing

A detailed analysis of how Grid-interactive Efficient Buildings (GEB) can participate as active elements in a microgrid through on-site PV electricity generation and energy efficiency applications is presented. A case study using three US Department of Energy (DoE)-developed prototype commercial building models are used. These represent a secondary school, a hospital and a large office building. Simulation results show that when schools, hospitals and office buildings are operated as GEBs, there are always electricity savings, but savings amounts vary depending on levels of HVAC and lighting controls within the limits of customer comfort levels. These comfort level ranges are determined through interactions with building occupants which resulted in <inline-formula> <tex-math notation="LaTeX">$\Delta \text{T}$ </tex-math></inline-formula> of 2-<inline-formula> <tex-math notation="LaTeX">$5^{\circ }\text{F}$ </tex-math></inline-formula> and dimming level range of 20&#x0025; to 50&#x0025;. Savings in the school building are so much higher for two reasons. One, because without GEB application these buildings are operated in a business-as-usual fashion throughout the year, even when the school is not in session. The second reason is &#x2013; being a two-story building the roof area is comparatively much higher than the hospital or the multi-storied office buildings.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2021
Power Distribution System Synchrophasor Measurements With Non-Gaussian Noises: Real-World Data Testing and Analysis

Can Huang, Charanraj Thimmisetty, Xiao Chen et al.

This short paper investigates distribution-level synchrophasor measurement errors with online and offline tests, and mathematically and systematically identifies the actual distribution of the measurement errors through graphical and numerical analysis. It is observed that the measurement errors in both online and offline case studies follow a non-Gaussian distribution, instead of the traditionally assumed Gaussian distribution. It suggests the use of non-Gaussian models, such as Gaussian mixture models, for representing the measurement errors more accurately and realistically. The presented tests and analysis are helpful for the understanding of distribution-level measurement characteristics, and for the modeling and simulation of distribution system applications, such as state estimation.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2021
Two‐stage ANN‐based bidding strategy for a load aggregator using decentralized equivalent rival concept

Mohammad Kiannejad, Mohammad Reza Salehizadeh, Majid Oloomi‐Buygi

Abstract As an intermediator between the wholesale electricity market and retail market, a typical load aggregator submits an optimal bid to the system operator to meet the expected demands of its customers. In this regard, the provision of an effective optimal bidding strategy is very crucial for a load aggregator to increase its profit. Within this context, this paper proposes a two‐stage artificial neural network based adaptive bidding strategy procedure for an LA by revealing, modelling, and predicting the aggregative behaviour of the competitors in an hourly electricity market. To this end, we develop the concept of decentralized equivalent rival whose behaviour in the electricity market reflects the aggregation of behaviours of all individual competitors. Also, an equivalent market which its outcomes are approximately equal to those of the real market is modelled. The equivalent market's participants are the load aggregator and its corresponding DER. The proposed approach is capable enough to consider transmission constraints. The performance of the proposed approach has been examined on an illustrative example and the IEEE 30‐bus test system by considering transmission network constraints. The proposed artificial neural network‐based adaptive bidding strategy has compared with a Q –learning‐based bidding approach and the results are analysed.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations
DOAJ Open Access 2017
Second‐order cone programming relaxation‐based optimal power flow with hybrid VSC‐HVDC transmission and active distribution networks

Tao Ding, Cheng Li, Yongheng Yang et al.

The detailed topology of renewable resource bases may have the impact on the optimal power flow (OPF) of the voltage source converter (VSC)‐based high‐voltage direct current (HVDC) transmission network. To address this issue, this study develops an OPF with the hybrid VSC‐HVDC transmission and active distribution networks to optimally schedule the generation output and voltage regulation of both networks, which leads to a non‐convex programming model. Furthermore, the non‐convex power flow equations are based on the second‐order cone programming (SOCP) relaxation approach. Thus, the proposed model can be relaxed to an SOCP that can be tractably solved. Numerical results on a three‐bus VSC‐HVDC network and the European system verify the effectiveness of the proposed model and suggest that the proposed model can guarantee the voltage magnitudes of both networks within the allowable ranges.

Distribution or transmission of electric power, Production of electric energy or power. Powerplants. Central stations

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