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Records Added in December 2019
Records added in December 2019
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Showing records 176 to 200 of 423. [First] Page: 4 5 6 7 8 9 10 11 12 Last
Modeling and Analysis of a DC Electrical System and Controllers for Implementation of a Grid-Interactive Building
Youngjin Kim
December 10, 2019 (v1)
Keywords: commercial building, grid frequency regulation (GFR), maximum voltage, minimum state-of-charge, plug-in electric vehicles (PEVs), rooftop photovoltaic (PV) systems
As the penetration of photovoltaic (PV) systems on building rooftops increases, the accumulated effect of the rooftop PV power outputs on electric network operation is no longer negligible. Energy storage resources (ESRs) have been used to smooth PV power outputs, particularly when building load becomes low. In commercial buildings, the batteries of plug-in electric vehicles (PEVs) can be regarded as distributed ESRs. This paper proposes a DC electrical system in a commercial building that enables PEVs to compensate for rooftop PV power fluctuation and participate in tracking signals for grid frequency regulation (GFR). The proposed building system and associated controllers are modeled considering steady-state and dynamic operations of the PV system and PEV batteries. Simulation case studies are conducted to demonstrate the performance of the proposed building system under various conditions, determined by such factors as the maximum voltage, minimum state-of-charge, and desired charg... [more]
A High-Frequency Isolated Online Uninterruptible Power Supply (UPS) System with Small Battery Bank for Low Power Applications
Muhammad Aamir, Wajahat Ullah Tareen, Kafeel Ahmed Kalwar, Mudasir Ahmed Memon, Saad Mekhilef
December 10, 2019 (v1)
Keywords: boost converter, high-frequency isolation, power factor correction, single-stage AC-DC converter, uninterruptible power supply (UPS)
Uninterruptible power supplies (UPSs) are widely used to deliver reliable and high quality power to critical loads under all grid conditions. This paper proposes a high-frequency isolated online UPS system for low power applications. The proposed UPS consists of a single-stage AC-DC converter, boost DC-DC converter, and an inverter. The single-stage AC-DC converter provides galvanic isolation, input power factor correction, and continuous conduction of both input and output current. The low battery bank voltage is stepped up to high dc-link voltage by employing a high voltage gain boost converter, thus allows the reduction of battery bank to only 24 V parallel connected batteries. Operating batteries in parallel improves the battery performance and resolves the issues related to conventional battery banks that arrange the batteries in series combination. The inverter provides regulated output voltage to the load. A new cascaded slide mode (SM) and proportional-resonant (PR) control for... [more]
Coordinated Control and Fault Protection Investigation of a Renewable Energy Integration Facility with Solar PVs and a Micro-Turbine
Jiefeng Hu
December 10, 2019 (v1)
Keywords: coordinated control, distributed generations, fault protection, Renewable and Sustainable Energy
In this paper, a renewable energy integration facility (REIF) with photovoltaic (PV) distributed generation resources for micro-grid applications is studied. In grid-tied operation, the PV system together with the grid supply the power to the local loads while the surplus energy is fed back to the grid. In stand-alone mode, a gas micro-turbine is operated as a master to establish the common AC bus voltage to which the PV inverters can synchronize The experimental results demonstrate the stable operation of the REIF under various generation and load conditions. The power quality can meet the IEEE Standard 1547. Furthermore, the responses of the REIF under different fault conditions are investigated. Relevant protection mechanisms are then developed, providing insights into the fault protection for the future grid.
Analyzing the Impacts of System Parameters on MPC-Based Frequency Control for a Stand-Alone Microgrid
Thai-Thanh Nguyen, Hyeong-Jun Yoo, Hak-Man Kim
December 10, 2019 (v1)
Keywords: Model Predictive Control, secondary frequency control, stand-alone microgrid, system parameter uncertainties
Model predictive control (MPC) has been widely studied for regulating frequency in stand-alone microgrids (MGs), owing to the advantages of MPC such as fast response and robustness against the parameter uncertainties. Understanding the impacts of system parameters on the control performance of MPC could be useful for the designing process of the controller to achieve better performance. This study analyzes the impact of system parameters on the control performance of MPC for frequency regulation in a stand-alone MG. The typical stand-alone MG, which consists of a diesel engine generator, an energy storage system (ESS), a wind turbine generator, and a load, is considered in this study. The diesel engine generator is in charge of primary frequency control whereas the ESS is responsible for secondary frequency control. The stand-alone MG is linearized to obtain the dynamic model that is used for designing MPC-based secondary frequency control. The robustness of MPC against the variation o... [more]
Optimal Energy Management Strategy for a Plug-in Hybrid Electric Vehicle Based on Road Grade Information
Yonggang Liu, Jie Li, Ming Ye, Datong Qin, Yi Zhang, Zhenzhen Lei
December 10, 2019 (v1)
Keywords: energy management strategy, plug-in hybrid electric vehicles, road grade, state of charge
Energy management strategies (EMSs) are critical for the improvement of fuel economy of plug-in hybrid electric vehicles (PHEVs). However, conventional EMSs hardly consider the influence of uphill terrain on the fuel economy and battery life, leaving vehicles with insufficient battery power for continuous uphill terrains. Hence, in this study, an optimal control strategy for a PHEV based on the road grade information is proposed. The target state of charge (SOC) is estimated based on the road grade information as well as the predicted driving cycle on uphill road obtained from the GPS/GIS system. Furthermore, the trajectory of the SOC is preplanned to ensure sufficient electricity for the uphill terrain in the charge depleting (CD) and charge sustaining (CS) modes. The genetic algorithm is applied to optimize the parameters of the control strategy to maintain the SOC of battery in the CD mode. The pre-charge mode is designed to charge the battery in the CS mode from a reasonable distan... [more]
Robust Operation of Energy Storage System with Uncertain Load Profiles
Jangkyum Kim, Yohwan Choi, Seunghyoung Ryu, Hongseok Kim
December 10, 2019 (v1)
Keywords: battery wear-out cost, energy storage system (ESS), load uncertainty, peak load control, robust optimization
In this paper, we propose novel techniques to reduce total cost and peak load of factories from a customer point of view. We control energy storage system (ESS) to minimize the total electricity bill under the Korea commercial and industrial (KCI) tariff, which both considers peak load and time of use (ToU). Under the KCI tariff, the average peak load, which is the maximum among all average power consumptions measured every 15 min for the past 12 months, determines the monthly base cost, and thus peak load control is extremely critical. We aim to leverage ESS for both peak load reduction based on load prediction as well as energy arbitrage exploiting ToU. However, load prediction inevitably has uncertainty, which makes ESS operation challenging with KCI tariff. To tackle it, we apply robust optimization to minimize risk in a real environment. Our approach significantly reduces the peak load by 49.9% and the total cost by 10.8% compared to the case that does not consider load uncertaint... [more]
Effects of Syngas Cooling and Biomass Filter Medium on Tar Removal
Sunil Thapa, Prakashbhai R. Bhoi, Ajay Kumar, Raymond L. Huhnke
December 10, 2019 (v1)
Keywords: Biomass, dry filter, gasification, syngas cleaning, tar
Biomass gasification is a proven technology; however, one of the major obstacles in using product syngas for electric power generation and biofuels is the removal of tar. The purpose of this research was to develop and evaluate effectiveness of tar removal methods by cooling the syngas and using wood shavings as filtering media. The performance of the wood shavings filter equipped with an oil bubbler and heat exchanger as cooling systems was tested using tar-laden syngas generated from a 20-kW downdraft gasifier. The tar reduction efficiencies of wood shavings filter, wood shavings filter with heat exchanger, and wood shavings filter with oil bubbler were 10%, 61%, and 97%, respectively.
Detoxification of a Lignocellulosic Waste from a Pulp Mill to Enhance Its Fermentation Prospects
Tamara Llano, Natalia Quijorna, Alberto Coz
December 10, 2019 (v1)
Subject: Biosystems
Keywords: biorefinery, detoxification, Fermentation, inhibitors, spent sulfite liquor, sugars
Detoxification is required for sugar bioconversion and hydrolyzate valorization within the biorefining concept for biofuel or bio-product production. In this work, the spent sulfite liquor, which is the main residue provided from a pulp mill, has been detoxified. Evaporation, overliming, ionic exchange resins, and adsorption with activated carbon or black carbon were considered to separate the sugars from the inhibitors in the lignocellulosic residue. Effectiveness in terms of total and individual inhibitor removals, sugar losses and sugar-to-inhibitor removal ratio was determined. The best results were found using the cation exchange Dowex 50WX2 resin in series with the anion exchange Amberlite IRA-96 resin, which resulted in sugar losses of 24.2% with inhibitor removal of 71.3% of lignosulfonates, 84.8% of phenolics, 82.2% acetic acid, and 100% of furfurals. Apart from exchange resins, the results of evaporation, overliming, adsorption with activated carbon and adsorption with black... [more]
Application of Nanoparticles in Enhanced Oil Recovery: A Critical Review of Recent Progress
Xiaofei Sun, Yanyu Zhang, Guangpeng Chen, Zhiyong Gai
December 10, 2019 (v1)
Subject: Materials
Keywords: chemical flooding, enhanced oil recovery (EOR), gas injection, nanoparticles, review study, thermal methods, water flooding
The injected fluids in secondary processes supplement the natural energy present in the reservoir to displace oil. The recovery efficiency mainly depends on the mechanism of pressure maintenance. However, the injected fluids in tertiary or enhanced oil recovery (EOR) processes interact with the reservoir rock/oil system. Thus, EOR techniques are receiving substantial attention worldwide as the available oil resources are declining. However, some challenges, such as low sweep efficiency, high costs and potential formation damage, still hinder the further application of these EOR technologies. Current studies on nanoparticles are seen as potential solutions to most of the challenges associated with these traditional EOR techniques. This paper provides an overview of the latest studies about the use of nanoparticles to enhance oil recovery and paves the way for researchers who are interested in the integration of these progresses. The first part of this paper addresses studies about the m... [more]
Numerical Investigation of Periodic Fluctuations in Energy Efficiency in Centrifugal Pumps at Different Working Points
Hehui Zhang, Shengxiang Deng, Yingjie Qu
December 10, 2019 (v1)
Keywords: centrifugal pump, Computational Fluid Dynamics, Energy Efficiency, fluctuation
In order to simulate the energy efficiency fluctuation behavior of an industrial centrifugal pump with a six-blade impeller, a full-scale three-dimensional (3D) an unsteady state computational fluid dynamics (CFD) model was used. Five operational points with different flow fluxes were numerically investigated by using the Navier⁻Stokes code with shear-stress transport (SST) k-ω turbulence model. The predicted performance curves agreed well with the test data. A sine function was fitted to the transient calculation results and the results show that the efficiency fluctuates mainly on the blade passing frequency, while the fluctuation level varies with flow rate. Furthermore, high efficiency is not necessarily associated with low fluctuation level. The efficiency fluctuation level is high at part-load points, and becomes relatively low when flow rate exceeds the design value. The effect of change in torque is greater than that of the head lift with respect to fluctuations of efficiency.... [more]
Consideration of Reactor Installation to Mitigate Voltage Rise Caused by the Connection of a Renewable Energy Generator
Yeonho Ok, Jaewon Lee, Jaeho Choi
December 10, 2019 (v1)
Keywords: coordination of protection relay, distribution line, distribution resource, generator, grid connection, power factor, reactor, Renewable and Sustainable Energy, voltage rise
This paper describes the detailed analysis of a reactor application for a power plant to mitigate the voltage rise of a distribution line (DL) caused by the connection of distributed resources (DRs). The maximum capacity of renewable energy generators (REGs) that meets the acceptable voltage rise of a DL and the necessary capacity of the reactor to mitigate that voltage rise according to the different types of REGs are analyzed. The re-coordination of a protection relay and the loss of generation revenue as well as the installation location of a reactor are described. Finally, the ON/OFF conditions of the reactor, such as the magnitudes of the grid voltage and generator voltage, and the duration time of the voltage rise are analyzed. As the voltage rise is mitigated and self-limited in small power plants, it is confirmed that the capacity of the DRs connected to the DL can be increased through a field demonstration.
Reliability Assessment of Power Generation Systems Using Intelligent Search Based on Disparity Theory
Athraa Ali Kadhem, Noor Izzri Abdul Wahab, Ishak Aris, Jasronita Jasni, Ahmed N. Abdalla
December 10, 2019 (v1)
Keywords: disparity theory, Genetic Algorithm, power generation, reliability assessment
The reliability of the generating system adequacy is evaluated based on the ability of the system to satisfy the load demand. In this paper, a novel optimization technique named the disparity evolution genetic algorithm (DEGA) is proposed for reliability assessment of power generation. Disparity evolution is used to enhance the performance of the probability of mutation in a genetic algorithm (GA) by incorporating features from the paradigm into the disparity theory. The DEGA is based on metaheuristic searching for the truncated sampling of state-space for the reliability assessment of power generation system adequacy. Two reliability test systems (IEEE-RTS-79 and (IEEE-RTS-96) are used to demonstrate the effectiveness of the proposed algorithm. The simulation result shows the DEGA can generate a larger variety of the individuals in an early stage of the next population generation. It is also able to estimate the reliability indices accurately.
High Performance Silicon Carbide Power Packaging—Past Trends, Present Practices, and Future Directions
Sayan Seal, Homer Alan Mantooth
December 10, 2019 (v1)
Subject: Materials
Keywords: 3D packaging, high power density, power electronics, wide bandgap, wire bondless
This paper presents a vision for the future of 3D packaging and integration of silicon carbide (SiC) power modules. Several major achievements and novel architectures in SiC modules from the past and present have been highlighted. Having considered these advancements, the major technology barriers preventing SiC power devices from performing to their fullest ability were identified. 3D wire bondless approaches adopted for enhancing the performance of silicon power modules were surveyed, and their merits were assessed to serve as a vision for the future of SiC power packaging. Current efforts pursuing 3D wire bondless SiC power modules were described, and the concept for a novel SiC power module was discussed.
A New Method of Ground Fault Location in 2 × 25 kV Railway Power Supply Systems
Jesús Serrano, Carlos A. Platero, Máximo López-Toledo, Ricardo Granizo
December 10, 2019 (v1)
Keywords: 2 × 25 kV, fault location, ground faults, protection, railways
Owing to the installation of autotransformers at regular intervals along the line, distance protection relays cannot be used with the aim of locating ground faults in 2 × 25 kV railway power supply systems. The reason is that the ratio between impedance and distance to the fault point is not linear in these electrification systems, unlike in 1 × 25 kV power systems. Therefore, the location of ground faults represents a complicated task in 2 × 25 kV railway power supply systems. Various methods have been used to localize the ground fault position in 2 × 25 kV systems. The method described here allows the location of a ground fault to be economically found in an accurate way in real time, using the modules of the circulating currents in different autotransformers when the ground fault occurs. This method first needs to know the subsection and the conductor (catenary or feeder) with the defect, then localizes the ground fault’s position.
Development of a Vibration-Based Electromagnetic Energy Harvester by a Conductive Direct-Write Process
Yao-Yun Feng, Shih-Jui Chen, You-Lin Tu
December 10, 2019 (v1)
Keywords: direct-write, electromagnetic generator, vibrational energy
A conductive direct-write process of multilayered coils for micro electromagnetic generators is proposed. This novel approach of using silver ink to form the conductive structures largely reduces the fabrication complexity, and it provides a faster alternative to the conventional semiconductor methods. Multi-layered coils with insulation were accurately layered on a micromachined cantilevered diaphragm by a dispenser. Coils several layers thick could be used to increase the power output and double coils were separated by a layer of insulation. Six prototypes, all capable of efficient conversion of vibrational energy into electrical energy, were fabricated. The experimental results, which include measurements of the electromotive force and power output, are presented. Prototypes with two coils and thicker conducting layers had less resistance and the power output was much more than that of a single-coil unit. This generator can produce 82 nW of power at a resonance frequency of 275 Hz u... [more]
Numerical Study on the Effect of Lambda Value (Oxygen/Fuel Ratio) on Temperature Distribution and Efficiency of a Flameless Oxyfuel Combustion System
Mersedeh Ghadamgahi, Patrik Ölund, Nils Å. I. Andersson, Pär Jönsson
December 10, 2019 (v1)
Keywords: combustion, computational fluid dynamics (CFD), flameless oxyfuel, lambda value, soaking pit furnace
The flameless oxyfuel combustion technology has been proven to be a promising new method to reduce the fuel consumption and pollutants in industrial applications [...]
Optimal Scheduling of Microgrid with Multiple Distributed Resources Using Interval Optimization
Chongxin Huang, Dong Yue, Song Deng, Jun Xie
December 10, 2019 (v1)
Keywords: distributed resources, interval optimization, microgrid, optimal scheduling scheme
In this paper, an optimal day-ahead scheduling problem is studied for a microgrid with multiple distributed resources. For the sake of coping with the prediction uncertainties of renewable energies and loads and taking advantage of the time-of-use price for buying/selling electricity, an interval-based optimization model for maximum profits is developed. To reduce the computational complexity in solving the model, the possibility degree comparison between an interval and a real number is used to convert the interval constraints into the general ones; meanwhile, some slack variables and complementary conditions are introduced to eliminate the absolute-value operation. Unlike the stochastic optimization, the interval optimization only needs the upper-lower bounds of the uncertain variables instead of their probability distribution functions, which is beneficial to the practical application. Furthermore, the possible profit interval and the expected optimal profit can be determined by solving... [more]
Flame Structure and Chemiluminescence Emissions of Inverse Diffusion Flames under Sinusoidally Driven Plasma Discharges
Maria Grazia De Giorgi, Aldebara Sciolti, Stefano Campilongo, Antonio Ficarella
December 10, 2019 (v1)
Subject: Other
Keywords: diffusive methane/air flames, inverse flames, plasma actuator
Reduction of nitric oxides (NOx) in aircraft engines and in gas turbines by lean combustion is of great interest in the design of novel combustion systems. However, the stabilization of the flame under lean conditions is a main issue. In this context, the present work investigates the effects of sinusoidal dielectric barrier discharge (DBD) on a lean inverse diffusive methane/air flame in a Bunsen-type burner under different actuation conditions. The flame appearance was investigated with fixed methane loading (mass flux), but with varying inner airflow rate. High-speed flame imaging was done by using an intensified (charge-coupled device) CCD camera equipped with different optical filters in order to selectively record signals from the chemiluminescent species OH*, CH*, or CO2* to evaluate the flame behavior in presence of plasma actuation. The electrical power consumption was less than 33 W. It was evident that the plasma flame enhancement was significantly influenced by the plasma d... [more]
An Improved LCL Filter Design in Order to Ensure Stability without Damping and Despite Large Grid Impedance Variations
Marwa Ben Said-Romdhane, Mohamed Wissem Naouar, Ilhem Slama Belkhodja, Eric Monmasson
December 10, 2019 (v1)
Keywords: design methodology, grid connected power converter, LCL filter, total harmonic distortion factor (THD), weak grid conditions
With the smart grid revolution, there is a growing interest in the use of power converters associated to LCL filters to interface between the main utility grid and loads or renewable energy sources. LCL filters are commonly used mainly due to their low cost and high filtering performances. To achieve these performances, it is necessary to meticulously pick out the LCL filter parameters, taking into account grid code requirements and grid configuration and/or conditions. Several methodologies for LCL filter design have been presented and discussed in the literature. The main goal of this paper is to propose a simple, robust and systematic design methodology for LCL filter parameter tuning. The considered design methodology is aimed to overcome the shortcomings of classical design methodologies, namely, stable operation under different grid configurations and conditions. Compared to previous works, the proposed design methodology allows the achievement of robust LCL filter design with re... [more]
Improved Electrogeometric Model Suitable for EHV and UHV Transmission Lines Developed through Breakdown Testing for Long Air Gaps
Yeqiang Deng, Yu Wang, Zhijun Li, Min Dai, Xishan Wen, Lei Lan, Yunzhu An, Shenglong E
December 10, 2019 (v1)
Keywords: electrogeometric model, lightning-shielding failure, negative switching surge discharge tests of long air gaps, striking distance, ultra-high-voltage transmission line
As a type of engineering model used for solving lightning-shielding problems, the electrogeometric model has been widely used for assessing lightning-shielding failure in high-voltage and extra-high-voltage transmission lines. However, with the increase of voltage levels in ultra-high-voltage lines and the growth of the air gap, the results previously yielded by the electrogeometric model are no longer consistent with those observed. Therefore, this study corrected the equation for the relationship between lightning current and striking distance, by using data on a negative polarity 50% discharge voltage from the rod-rod gap −20/2500 μs switching impulse test wherein an air gap of up to 10 m was first tested. Subsequently, the return stroke velocity distribution observed by Idone was newly applied. In addition, the correction factor for the ground was corrected in this study. Thus, an improved electrogeometric model for application in EHV and UHV transmission lines is proposed in this... [more]
Study the Flow behind a Semi-Circular Step Cylinder (Laser Doppler Velocimetry (LDV) and Computational Fluid Dynamics (CFD))
S. M. Sayeed-Bin-Asad, Tord Staffan Lundström, Anders Gustav Andersson
December 10, 2019 (v1)
Keywords: computational fluid dynamics (CFD), fish migration, laser doppler velocimetry (LDV), shedding, step cylinder, vortex street
Laser Doppler Velocimetry (LDV) measurements, flow visualizations and unsteady Reynolds-Averaged Navier-Stokes (RANS) Computational Fluid Dynamics (CFD) simulations have been carried out to study the turbulent wake that is formed behind a semi-circular step cylinder at a constant flow rate. The semi-circular cylinder has two diameters, a so-called step cylinder. The results from the LDV measurements indicate that wake length and vortex shedding frequency varies with the cylinder diameter. This implies that a step cylinder can be used to attract fish of different size. By visualizations of the formation of a recirculation region and the well-known von Kármán vortex street behind the cylinder are disclosed. The simulation results predict the wake length and shedding frequency well for the flow behind the large cylinder but fail to capture the dynamics of the flow near the step in diameter to some extent and the flow behind the small cylinder to a larger extent when compared with measurem... [more]
Signal-Based Gas Leakage Detection for Fluid Power Accumulators in Wind Turbines
Jesper Liniger, Nariman Sepehri, Mohsen Soltani, Henrik C. Pedersen
December 10, 2019 (v1)
Keywords: FaultDetectionandIsolation (FDI), fluidpower, leakage, pistonaccumulator, wavelet transform, windturbinepitchsystem
This paper describes the development and application of a signal-based fault detection method for identifying gas leakage in hydraulic accumulators used in wind turbines [...]
Effect of Load Change on the Thevenin Equivalent Impedance of Power System
Tiankui Sun, Zhimin Li, Shuang Rong, Jian Lu, Weixing Li
December 10, 2019 (v1)
Keywords: impedance match theory, load change, power systems, Thevenin equivalent impedance
This paper discusses the effect of load change on the Thevenin equivalent impedance of power systems. In this paper, the Thevenin equivalent impedance influenced by the derivative of active load with respect to reactive load (dP dQ) is analyzed. The Thevenin equivalent impedance forms a closed curve in a complex plane and shrinks to one point when voltage collapses. The magnitude of the Thevenin equivalent impedance at the collapse point is equal to the magnitude of the load impedance. Therefore, the impedance match theory still holds under the effect of the load change. These features are verified on a New England 39-bus system.
Fundamental Analysis of Thermal Overload in Diesel Engines: Hypothesis and Validation
Sangram Kishore Nanda, Boru Jia, Andrew Smallbone, Anthony Paul Roskilly
December 10, 2019 (v1)
Keywords: diesel engine, flame visualisation, thermal overload, validation
‘Thermal Overload’ can be defined as a condition under which design threshold values such as the surface temperature of combustion chamber components is exceeded [...]
Effects of Biogas Substrate Recirculation on Methane Yield and Efficiency of a Liquid-Manure-Based Biogas Plant
Frauke P. C. Müller, Gerd-Christian Maack, Wolfgang Buescher
December 10, 2019 (v1)
Subject: Biosystems
Keywords: biogas, hydraulic retention time (HRT), methane output, organic loading rate (OLR), recirculation
Biogas plants are the most complex systems and are heavily studied in the field of renewable energy. A biogas system is mainly influenced by biological and technical parameters that strongly interact with each other. One recommended practice when operating a biogas plant is the recirculation of the substrate from the second fermenter into the first fermenter, which extends the recirculation amount (RA) and, in turn, the recirculation rate (RR). This technique should be applied to support and secure the biogas process. In this investigation, the RA was varied, starting with the recommended “best practice” of 10.0 m³/d (RR 40%). Every ten days, the RA was reduced in steps of 1.5 m³/d, with 5.5 m³/d (RR 27%) being the final value. The basic question to be addressed concerns to what extent the RR influences the methane yield and thereby influence the efficiency of a manure-based biogas plant in practice. Diverting the “best practice” to a RR of 27% stabilised the fermentation process and l... [more]
Showing records 176 to 200 of 423. [First] Page: 4 5 6 7 8 9 10 11 12 Last
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