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Records with Subject: Energy Management
601. LAPSE:2023.21886
Determinants of the Forward Premium in the Nord Pool Electricity Market
March 23, 2023 (v1)
Subject: Energy Management
Keywords: electricity, forward premium, futures, quantile regression
Nord Pool is the leading power market in Europe. It has been documented that the forward contracts traded in this market exhibit a significant forward premium, which could be a sign of market inefficiency. Efficient power markets are important, especially when there is a goal to increase the share of the power mix stemming from renewable energy sources. We therefore contribute to the understanding of this topic by examining how the forward premium in the Nord Pool market depend on several economic and physical conditions. We utilise two methods: ordinary least squares and quantile regression. The results show that the reservoir level and the basis (the difference between the forward and spot price) have a significant impact on the forward premium. The realised volatility of futures prices and the implied volatility of the stock market have strong effects on both the conditional lower and upper tails of the forward premium. We also find that, as the market has matured, the forward premi... [more]
602. LAPSE:2023.21870
Comparative Study on Optimization Solvers for Implementation of a Two-Stage Economic Dispatch Strategy in a Microgrid Energy Management System
March 23, 2023 (v1)
Subject: Energy Management
Keywords: economic dispatch (ED), energy storage systems (ESSs), microgrid energy management system (MEMS), microgrids (MGs), modeling package, optimization solver
A microgrid energy management system (MEMS) optimally schedules the operation of dispatchable distributed energy resources to minimize the operation costs of microgrids (MGs) via an economic dispatch (ED). Actual ED implementation in the MEMS relies on an optimization software package called an optimization solver. This paper presents a comparative study of optimization solvers to investigate their suitability for ED implementation in the MEMS. Four optimization solvers, including commercial as well as open-source-based ones, were compared in terms of their computational capability and optimization results for ED. Two-stage scheduling was applied for the ED strategy, whereby a mixed-integer programming problem was solved to yield the optimal operation schedule of battery-based energy storage systems. In the first stage, the optimal schedule is identified one day before the operating day; in the second stage, the optimal schedule is updated every 5 min during actual operation to compens... [more]
603. LAPSE:2023.21852
Review of Trends and Targets of Complex Systems for Power System Optimization
March 23, 2023 (v1)
Subject: Energy Management
Keywords: electric vehicles, energy management, Energy Storage, load control, microgrids, optimal power flow, optimization methods
Optimization systems (OSs) allow operators of electrical power systems (PS) to optimally operate PSs and to also create optimal PS development plans. The inclusion of OSs in the PS is a big trend nowadays, and the demand for PS optimization tools and PS-OSs experts is growing. The aim of this review is to define the current dynamics and trends in PS optimization research and to present several papers that clearly and comprehensively describe PS OSs with characteristics corresponding to the identified current main trends in this research area. The current dynamics and trends of the research area were defined on the basis of the results of an analysis of the database of 255 PS-OS-presenting papers published from December 2015 to July 2019. Eleven main characteristics of the current PS OSs were identified. The results of the statistical analyses give four characteristics of PS OSs which are currently the most frequently presented in research papers: OSs for minimizing the price of electri... [more]
604. LAPSE:2023.21832
Optimal Control of Multiple Microgrids and Buildings by an Aggregator
March 23, 2023 (v1)
Subject: Energy Management
Keywords: aggregator, energy management system, interconnected buildings, multi-level, Optimization, renewable resources, smart grid
The electrical grid has been changing in the last decade due to the presence of renewables, distributed generation, storage systems, microgrids, and electric vehicles. The introduction of new legislation and actors in the smart grid’s system opens new challenges for the activities of companies, and for the development of new energy management systems, models, and methods. A new optimization-based bi-level architecture is proposed for an aggregator of consumers in the balancing market, in which incentives for local users (i.e., microgrids, buildings) are considered, as well as flexibility and a fair assignment in reducing the overall load. At the lower level, consumers try to follow the aggregator’s reference values and perform demand response programs to contain their costs and satisfy demands. The approach is applied to a real case study.
605. LAPSE:2023.21716
Weather Risk Management in Energy Sector: The Polish Case
March 22, 2023 (v1)
Subject: Energy Management
Keywords: energy sector, Poland, weather derivatives, weather risk, weather risk management
The energy sector is perceived as one of the most exposed sectors to the consequences of weather risk both directly (damages of its infrastructure) and indirectly (frictions to the energy supply−demand balance). The main aim of this paper is to provide an insight into the impact of weather risk on economic activity of companies operating in the energy sector in Poland. The empirical objective is to examine whether energy companies: (i) identify their relevant weather risk exposures; (ii) evaluate the impact of weather risk in the cost-revenues dimension; and (iii) implement weather risk management tools, in this case—weather derivatives. In a methodical context, this study relies on a unique research approach and derives from works that examine companies’ risk disclosures in annual reports, by applying textual content analysis. The results indicate that Polish energy companies recognize the impact of weather risk on their performance, also in the cost-revenues dimension. However, altho... [more]
606. LAPSE:2023.21694
Optimal Coordination of Overcurrent Relays in Microgrids Considering a Non-Standard Characteristic
March 22, 2023 (v1)
Subject: Energy Management
Keywords: distributed generation, distribution networks, microgrids, overcurrent relay coordination, power system protection
The optimal coordination of overcurrent relays (OCRs) has recently become a major challenge owing to the ever-increasing participation of distributed generation (DG) and the multi-looped structure of modern distribution networks (DNs). Furthermore, the changeable operational topologies of microgrids has increased the complexity and computational burden to obtain the optimal settings of OCRs. In this context, classical approaches to OCR coordination might no longer be sufficient to provide a reliable performance of microgrids both in the islanded and grid-connected operational modes. This paper proposes a novel approach for optimal coordination of directional OCRs in microgrids. This approach consists of considering the upper limit of the plug setting multiplier (PSM) as a variable instead of a fixed parameter as usually done in traditional approaches for OCRs coordination. A genetic algorithm (GA) was implemented to optimize the limits of the maximum PSM for the OCRs coordination. Seve... [more]
607. LAPSE:2023.21692
Automated Negotiation for Peer-to-Peer Electricity Trading in Local Energy Markets
March 22, 2023 (v1)
Subject: Energy Management
Keywords: automated negotiation, bilateral energy negotiations, local electricity markets, local energy markets, multi-agent systems, P2P electricity trading
Reliable access to electricity is still a challenge in many developing countries. Indeed, rural areas in sub-Saharan Africa and developing countries such as India still encounter frequent power outages. Local energy markets (LEMs) have emerged as a low-cost solution enabling prosumers with power supply systems such as solar PV to sell their surplus of energy to other members of the local community. This paper proposes a one-to-one automated negotiation framework for peer-to-peer (P2P) local trading of electricity. Our framework uses an autonomous agent model to capture the preferences of both an electricity seller (consumer) and buyer (small local generator or prosumer), in terms of price and electricity quantities to be traded in different periods throughout a day. We develop a bilateral negotiation framework based on the well-known Rubinstein alternating offers protocol, in which the quantity of electricity and the price for different periods are aggregated into daily packages and ne... [more]
608. LAPSE:2023.21689
Ancillary Services Market Design in Distribution Networks: Review and Identification of Barriers
March 22, 2023 (v1)
Subject: Energy Management
Keywords: ancillary services, distributed generation, distribution grid, electricity markets, fault contribution, harmonics mitigation, inertia response, primary frequency response, renewable energy resources, voltage regulation
The high proliferation of converter-dominated Distributed Renewable Energy Sources (DRESs) at the distribution grid level has gradually replaced the conventional synchronous generators (SGs) of the transmission system, resulting in emerging stability and security challenges. The inherent characteristics of the SGs are currently used for providing ancillary services (ASs), following the instructions of the Transmission System Operator, while the DRESs are obliged to offer specific system support functions, without being remunerated for these functions, but only for the energy they inject. This changing environment has prompted the integration of energy storage systems as a solution for transfusing new characteristics and elaborating their business in the electricity markets, while the smart grid infrastructure and the upcoming microgrid architectures contribute to the transformation of the distribution grid. This review investigates the existing ASs in transmission system with the respe... [more]
609. LAPSE:2023.21673
Vortex-Induced Vibration Characteristics of a PTC Cylinder with a Free Surface Effect
March 22, 2023 (v1)
Subject: Energy Management
Keywords: energy harvesting, free surface, PTC, VIV
The experimental study of vortex induced vibration needs to be carried out in water tunnel, but in previous associated simulation work, the water tunnel was treated as an infinite flow field in the depth direction with the effect of the free surface neglected. In the paper, the dynamic characteristics and physical mechanisms of a passive turbulence control (PTC) cylinder in a flow field with a free surface is studied, and the combined technique of a volume of fluid (VOF) method and vortex-induced vibration (VIV) was realized. In the range of Reynolds number studied in this paper (3.5 × 104 ≤ Re ≤ 7.0 × 104), the dynamic parameters (lift and drag coefficients), vortex structures, VIV response (amplitude and frequency ratios), and energy harvesting characteristics of a PTC cylinder under different flow conditions were obtained. The study found that: (1) the shear layer was made more unstable behind the cylinder by the free surface, which made it quicker to reach periodic stability, and t... [more]
610. LAPSE:2023.21672
Combined Control of DFIG-Based Wind Turbine and Battery Energy Storage System for Frequency Response in Microgrids
March 22, 2023 (v1)
Subject: Energy Management
Keywords: battery energy storage system (BESS), battery management, doubly fed induction generator (DFIG), droop control, frequency control
This paper presents a novel methodology for frequency control of a microgrid through doubly fed induction generator (DFIG) employing battery energy storage system (BESS) and droop control. The proposed microgrid frequency control is the result of the active power injection from the droop control implemented in the grid side converter (GSC) of the DFIG, and the BESS implemented in the DC link of the back-to-back converter also in the DFIG. This methodology guarantees the battery system charge during operation of the connected DFIG in the network, and the frequency control in microgrid operation after an intentional disturbance. In order for the DFIG to provide frequency support to the microgrid, the best-performing droop gain value is selected. Afterwards its performance is evaluated individually and together with the power injected by the battery. The power used for both battery charging and frequency support is managed and processed by the GSC without affecting the normal operation of... [more]
611. LAPSE:2023.21651
Method for Estimating Harmonic Parameters Based on Measurement Data without Phase Angle
March 22, 2023 (v1)
Subject: Energy Management
Keywords: harmonic parameter, harmonic responsibility, monitoring data without phase angle, parameter estimation, power quality
The excessive use of power electronics makes power quality problems in power grids increasingly prominent. The estimation of the harmonic parameters of harmonic sources in the power grid and the division of harmonic responsibilities are of great significance for the evaluation of power quality. At present, methods for estimating harmonic parameters and harmonic responsibilities need to provide the amplitude and phase information of the current and voltage of the point of common coupling (PCC). However, in practical engineering applications, the general power quality monitor only provides the amplitude information of the voltage and current of the measured point and the phase difference information between them. Missing phase information invalidates existing methods. Based on the partial least squares regression method, the present work proposes a method for estimating harmonic parameters in the case of monitoring data without phase. This method only needs to measure the amplitude infor... [more]
612. LAPSE:2023.21641
Strategic-Agent Equilibria in the Operation of Natural Gas and Power Markets
March 22, 2023 (v1)
Subject: Energy Management
Keywords: electricity market, equilibrium analysis, natural-gas market
We consider strategic gas/power producers and strategic gas/power consumers operating in both gas and power markets. We build a flexible multi-period complementarity model to characterize day-ahead equilibria in those markets. This model is an equilibrium program with equilibrium constraints that characterizes the market behavior of all market agents. Using a realistic case study, we analyze equilibria under perfect and oligopolistic competition. We also analyze equilibria under different levels of information disclosure regarding market outcomes. We study as well equilibria under different ownership schemes: no hybrid agent, some hybrid agents, and only hybrid agents. Finally, we derive policy recommendations for the regulators of both the gas and the power markets.
613. LAPSE:2023.21571
A New Method for Peer-to-Peer Energy Exchange in Distribution Grids
March 22, 2023 (v1)
Subject: Energy Management
Keywords: distribution system, microgrids, Nash equilibrium, peer-to-peer energy exchange, power optimization
In this paper, distribution-level peer-to-peer energy exchange is proposed that allows increased matching between load and generation nodes. Contributions of the proposed improved matching system between the local load and generation nodes aim at making efficient use of unused power generation, reducing the cost of electrical energy for consumers, and assisting utility companies by reducing transmission line congestion. The proposed system for matching the load and generation nodes consists of a financial layer and technical layer. In the financial layer, nodes with an excess of energy provide a price to sell energy, while the nodes needing energy bid on a price to purchase energy. A market-clearing mechanism using pool clearing is applied to determine a final price for peer-to-peer exchange. The technical layer determines the connection of energy transfer between the generation and load nodes while considering the distance, power flow constraints, and specified time windows. The propo... [more]
614. LAPSE:2023.21517
Fault Ride-Through Power Electronic Topologies for Hybrid Energy Storage Systems
March 22, 2023 (v1)
Subject: Energy Management
Keywords: buck-boost converter, energy storage system, fault ride-through capability, hybrid
This work presents a fault ride-through control scheme for a non-isolated power topology used in a hybrid energy storage system designed for DC microgrids. The hybrid system is formed by a lithium-ion battery bank and a supercapacitor module, both coordinated to achieve a high-energy and high-power combined storage system. This hybrid system is connected to a DC bus that manages the power flow of the microgrid. The power topology under consideration is based on the buck-boost bidirectional converter, and it is controlled through a bespoke modulation scheme to obtain low losses at nominal operation. The operation of the proposed control scheme during a DC bus short-circuit failure is shown, as well as a modification to the standard control to achieve fault ride-through capability once the fault is over. The proposed control provides a protection to the energy storage systems and the converter itself during the DC bus short-circuit fault. The operation of the converter is developed theor... [more]
615. LAPSE:2023.21479
A Novel Ensemble Algorithm for Solar Power Forecasting Based on Kernel Density Estimation
March 22, 2023 (v1)
Subject: Energy Management
Keywords: distributed generation, ensemble methods, forecasting, kernel density estimation, smart grids, solar PV
A novel ensemble algorithm based on kernel density estimation (KDE) is proposed to forecast distributed generation (DG) from renewable energy sources (RES). The proposed method relies solely on publicly available historical input variables (e.g., meteorological forecasts) and the corresponding local output (e.g., recorded power generation). Given a new case (with forecasted meteorological variables), the resulting power generation is forecasted. This is performed by calculating a KDE-based similarity index to determine a set of most similar cases from the historical dataset. Then, the outputs of the most similar cases are used to calculate an ensemble prediction. The method is tested using historical weather forecasts and recorded generation of a PV installation in Portugal. Despite only being given averaged data as input, the algorithm is shown to be capable of predicting uncertainties associated with high frequency weather variations, outperforming deterministic predictions based on... [more]
616. LAPSE:2023.21458
An Assessment of the Condition of Distribution Network Equipment Based on Large Data Fuzzy Decision-Making
March 22, 2023 (v1)
Subject: Energy Management
Keywords: condition assessment, distribution network equipment, fuzzy iteration, multi information source
As one of the most important components of power grid, a distribution network is the most vulnerable part in the face of various uncertainties, and influences the stability and economy of a power system. In this paper, the operational information, hardware information and human factors were considered, and a state evaluation model of multi-source information fusion was established. Based on big data fuzzy iteration method and a weighted expert library, a weighted distribution of multi-source information was obtained, and an equipment condition assessment was carried out reasonably. Taking the distribution transformer as an example, the assessment showed that fusion of multi-source information presented in this paper is more comprehensive, and has the ability to reflect the state of equipment. The method proposed in this paper can accurately judge the running state of distribution equipment based on all kinds of information, and provides a reference for the follow-up power marketing for... [more]
617. LAPSE:2023.21404
Asymmetrical Three-Level Inverter SiC-Based Topology for High Performance Shunt Active Power Filter
March 22, 2023 (v1)
Subject: Energy Management
Keywords: active damping, active filter, converter circuit, efficiency, harmonics, multilevel converters, power quality, Silicon Carbide (SiC), voltage source converter, wide bandgap devices
Power quality conditioner systems, such as shunt active power filters (SAPFs), are typically required to have low power losses, high-power density, and to produce no electromagnetic interference to other devices connected to the grid. At the present, power converters with such a features are built using multilevel topologies based on pure silicon semiconductors. However, recently new semiconductors that offer massive reduction of power losses such as silicon carbide (SiC) MOSFETs have been introduced into the power electronics field. In the near future, the applications that demand the highest performance will be powered by multilevel converters based on SiC. In this paper a highly efficient three-level (3L) topology based entirely on silicon carbide (SiC) semiconductors for a SAPF is presented and analyzed in great detail. Furthermore, the proposed topology is compared with other full SiC-based conventional topologies: two level (2L), three-level T-type (3L-TNPC), and three-level neut... [more]
618. LAPSE:2023.21403
Minimization of Power Losses through Optimal Battery Placement in a Distributed Network with High Penetration of Photovoltaics
March 22, 2023 (v1)
Subject: Energy Management
Keywords: battery energy storage system, distribution network, renewable energy sources
The problems associated with the deployment of intermittent, unpredictable and uncontrollable solar photovoltaics (PV) can be feasibly solved with battery energy storage systems (BESS), particularly in terms of optimizing the available capacity, increasing reliability and reducing system losses. Consequently, the degree of importance of BESS increases in proportion to the level of PV penetration. Nevertheless, the respective high cost of BESS imposes a huge concern and the need to establish a techno-economic solution. In this paper, we investigate the system losses and power quality issues associated with the high deployment of PV in a grid network and hence formulate BESS capacity optimization and placement methodology based on a genetic algorithm. The concept of the proposed methodology has been tested and validated on a standard IEEE 33 bus system. A brief stepwise analysis is presented to demonstrate the effectiveness and robustness of the proposed methodology in reducing the incre... [more]
619. LAPSE:2023.21352
Overview of Human Walking Induced Energy Harvesting Technologies and Its Possibility for Walking Robotics
March 22, 2023 (v1)
Subject: Energy Management
Keywords: accumulator, biomedical mechanics, energy harvesting, Energy Storage, exoskeleton, gait, hydraulic system
This study is mainly to provide an overview of human walking induced energy harvest. Focusing on the proportion of all energy sources provided by daily activity, the available human walking induced energy is divided with respect to the generation principle. The extensive research on harvesting energy results from body vibration, inertial element, and foot press to convert into electricity is overviewed. Over the past decades, various smart materials have been employed to achieve energy conversion. Generators based on electromagnetic induction or the triboelectric effect were developed and integrated. Small captured power and low overall efficiency are criticized. The concept of human walking energy harvest is extended into the wearable walking robotics using other mediums, such as fluid, to transmit power instead of electricity. By comparison, it is indicated that less energy conversion links are involved in energy regeneration of such applications and expected to guarantee less loss a... [more]
620. LAPSE:2023.21338
Comparative Study of Piezoelectric Vortex-Induced Vibration-Based Energy Harvesters with Multi-Stability Characteristics
March 22, 2023 (v1)
Subject: Energy Management
Keywords: broadband synchronization region, buckling, multi-stability, piezoelectric energy harvesting, vortex-induced vibration
This work reports a comparative study on piezoelectric energy harvesting from vortex-induced vibration (VIV) with multi-stability characteristics by introducing the nonlinear magnetic forces. A lumped-parameter model for the piezoelectric cantilever-cylinder structure is considered for the sake of qualitative investigation. Firstly, the buckling displacement of harvester in monostable and bistable configurations is evaluated by virtue of a static analysis. Then, the coupled frequency and damping of the harvester varying with the electrical load resistance are determined for different values of the spacing distance between magnets. Subsequently, the dynamic behaviors and generated voltage of the harvester in two configurations are elaborately investigated, showing that varying the spacing distance is followed by a shift of lock-in region which is significant for performance optimization according to ambient wind conditions. In addition, the results show the harvester in monostable confi... [more]
621. LAPSE:2023.21325
Review of Voltage and Reactive Power Control Algorithms in Electrical Distribution Networks
March 22, 2023 (v1)
Subject: Energy Management
Keywords: artificial intelligence (heuristic) methods, capacitor batteries, distributed power generation, distribution power grids, photovoltaic converters, reactive power, renewable energy resources, smart grids, transformers, voltage stability
The traditional unidirectional, passive distribution power grids are rapidly developing into bidirectional, interactive, multi-coordinated smart grids that cover distributed power generation along with advanced information communications and electronic power technologies. To better integrate the use of renewable energy resources into the grid, to improve the voltage stability of distribution grids, to improve the grid protection and to reduce harmonics, one needs to select and control devices with adjustable reactive power (capacitor batteries, transformers, and reactors) and provide certain solutions so that the photovoltaic (PV) converters maintain due to voltage. Conventional compensation methods are no longer appropriate, thus developing measures are necessary that would ensure local reactive and harmonic compensation in case an energy quality problem happens in the low voltage distribution grid. Compared to the centralized methods, artificial intelligence (heuristic) methods are a... [more]
622. LAPSE:2023.21309
Distributed Optimization in Low Voltage Distribution Networks via Broadcast Signals †
March 22, 2023 (v1)
Subject: Energy Management
Keywords: active distribution network, broadcast signals, low voltage distribution network, Nash equilibrium, player compatible equilibrium, voltage control
With the development of distributed energy resources, the low voltage distribution network (LVDN) is supposed to be the integrator of small distributed energy sources. This makes the users in LVDNs multifarious, which leads to more complex modeling. Additionally, data acquisition could be tricky due to rising privacy concerns. These impose severe demands on control schemes in LVDNs that the classical centralized control might not be able to fulfill. To tackle this, a model-free control approach with distributed decision-making architecture is proposed in this paper. Employing statistical methods and game theory, individual users in LVDNs achieve local optimum autonomously. Comparing to conventional approaches applied in LVDNs, the proposed approach is able to achieve active control with less communication burden and computational resources. The paper proves the convergence to the Nash Equilibrium (NE) and uses player compatible relations to form the specific equilibrium. A variant of t... [more]
623. LAPSE:2023.21269
Status of Deep Borehole Disposal of High-Level Radioactive Waste in Germany
March 22, 2023 (v1)
Subject: Energy Management
Keywords: deep borehole disposal, Germany, high-level radioactive waste, Site Selection Act
The phase-out of nuclear energy in Germany will take place in 2022. A site for final disposal of high-level radioactive waste (HLRW) has not yet been chosen, but a site selection process was restarted by the Site Selection Act in 2017. This Act was based on a recommendation by a commission which also advised to follow up the development of deep borehole disposal (DBD) as a possible option for final disposal of HLRW. This paper describes briefly the status of DBD in Germany and if this option is to be pursued in Germany. Although DBD has some merits, it can only be a real option if supported by research and development. The technical equipment for larger boreholes of the required size will only be developed if there is funding and a feasibility test. Furthermore, any DBD concept must be detailed further, and some requirements of the Act must be reconsidered. Therefore, the support of DBD will likely remain at a low level if there are no political changes.
624. LAPSE:2023.21219
SmartLVGrid Platform—Convergence of Legacy Low-Voltage Circuits toward the Smart Grid Paradigm
March 21, 2023 (v1)
Subject: Energy Management
Keywords: low-voltage distribution grid automation, smart circuits, smart grid convergence
The current electrical system is transitioning towards a new technological model called the smart grid. The transition duration between the traditional Electric Power System (EPS) and the full smart grid depends on well-designed strategic plans, implementing transition models that are as close to smart grids as possible, based on the processes and technological resources available at the time, but always considering their economic feasibility, without which no solution thrives. In this article, we present a method for convergence of the traditional power distribution grid to the smart grid paradigm by retrofitting the legacy circuits that compose this grid. Our results indicate that the application of such a method, through a distributed system platform with integrated technological resources added to the legacy infrastructure, converts these passive grids into intelligent circuits capable of supporting the implementation of a smart grid with a broad scope of functionalities. Based on... [more]
625. LAPSE:2023.21206
The Concept of Dynamic Hosting Capacity for Distributed Energy Resources: Analytics and Practical Considerations
March 21, 2023 (v1)
Subject: Energy Management
Keywords: and harmonic voltage distortion, distributed energy resources, distributed generation, dynamic hosting capacity, power quality indexes, voltage rise
The hosting capacity approach is presented as a planning, improving, and communication tool for electrical distribution systems operating under specific uncertainties, such as power quality issues, power stabilities, and reliability, among others. In other words, it is an important technique, when renewable sources are present, to answer the amount of power that is possible to supply to the system without trespassing power performance limits. However, the power flow in a distribution system, for instance, can change throughout time due to the penetration of distributed generation, as well as load consumption. Based on the dynamic nature existing in distribution grids nowadays, it is important to highlight that the hosting capacity should not be calculated in a specifically chosen time only, but must be analyzed throughout a period of time. Thus, this paper introduces an extended concept of hosting capacity in relation to an integrated impact of harmonic voltage distortion and voltage r... [more]
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