Voltage Limits Research Articles

Optimized Dual-Layer Distributed Energy Storage Configuration for Voltage Over-Limit Zoning Governance in Distribution Networks

In this study, an optimized dual-layer configuration model is proposed to address voltages that exceed their limits following substantial integration of photovoltaic systems into distribution networks. Initially, the model involved segmenting the distribution network’s voltage zones based on distributed photovoltaic governance resources, thereby elucidating the characteristics and governance requisites for voltages across distinct regions. Subsequently, a governance model for voltage limit exceedances, grounded in optimizing energy storage configurations, was formulated to mitigate photovoltaic power fluctuations by deploying energy storage systems. This model coordinates the reactive power output of photovoltaic installations with the active power consumption of energy storage systems, thereby augmenting voltage autonomy in the power grid. This study leveraged Karush–Kuhn–Tucker (KKT) conditions and the Big-M method to transform the dual-layer model into a single-layer linear model, thereby enhancing solution efficiency and precision. Finally, a simulation was carried out to demonstrate that the strategy proposed from this research not only achieves commendable economic efficiency, but also significantly improves the regional voltage effect by 28.7% compared to the optical storage capacity optimization model.

Application of Static Synchronous Compensator for Improvement of Power System Transient Stability

Transient stability is the power system’s ability to maintain synchronism when exposed to severe disturbances such as loss of generation, rapid load changes, transmission lines tripping, switching operations and faults. Transient instability causes cascading outages, system collapse and economical losses. This study employed static synchronous compensator (STATCOM) for power system transient stability improvement. The system’s steady state and transient responses were respectively modelled with Newton-Raphson power flow and modified-Euler linearized swing equations. A balanced three-phased short circuit fault was introduced on selected buses for transient stability analysis. The steady state and transient responses of the system were simulated with and without STATCOM. The critical fault clearing time (CFCT) was obtained from the generators’ swing curves. The IEEE 9-bus and 14-bus power networks were used as test cases. The voltage magnitudes of all buses in both networks fell within the specified 0.95 to 1.1 p.u. voltage limit with and without compensation. The total active line loss on IEEE 9-bus and 14-bus networks which were 4.641 and 13.514 MW without compensation reduced to 4.600 and 13.014 MW, respectively with STATCOM’s application. The total reactive line losses of both networks which were 92.160 and 31.393 MVAr without compensation decreased to 90.160 and 30.693 MVAr, respectively with STATCOM’ utilization. The CFCT for fault on bus 8 of the IEEE 9-bus system without compensation were 0.2100 and 0.2700 s for generators 2 and 3, respectively. The system’s stability was, however, extended beyond 0.2700 s due to compensation from STATCOM. In the case of IEEE 14-bus system, the CFCT for fault on bus 6 was 0.36364 s for generators 2, 3, 4 and 5, respectively without compensation. The STATCOM inclusion, however, enhanced the system’s stability beyond 0.36366 s where all the four had lost synchronism. This work established that the use of STATCOM on the considered networks appropriately extended the CFCT such that the stability of the systems was not lost in the event of fault application via robust compensation of reactive power.

Transient Stability Improvement on Power Network using Static Synchronous Compensator: A Case of The Nigerian 330 KV Electricity Grid

This study deals with power system transient stability, enhanced via a static synchronous compensator (STATCOM). The system’s steady state and transient responses were modelled with Newton-Raphson-based power flow and modified Euler-based swing equation, respectively. Simulations were performed with and without STATCOM, considering the Nigerian 34-bus power grid. A balanced three-phase fault was used for the transient stability analysis. The voltage magnitudes of Katampe (0.9373), Kaduna (0.9209), Kano (0.9381), Jos (0.8295), and Gombe (0.7795) in the grid violated the statutory voltage limit of 0.95 to 1.05 p.u. before compensation and were improved to 0.9650, 0.9550, 0.9789, 0.9630, and 0.9550 p.u., respectively after STATCOM was applied. The system’s total real line losses before and after compensation were 57.887 and 55.623 MW, respectively. Fault application on bus 20 (Akangba T.S) caused loss of synchronism on generator 14 when the critical fault clearing time (CFCT) exceeded 0.019 s while generators 2 to 13 experienced marginal stability. The STATCOM application restored stability beyond the CFCT of 0.019 s due to compensation provided by the device. Fault introduction on bus 22 drove Egbin, the largest system’s generator corresponding to generator 7 on the swing curve into marginal stability along with generators 3 to 6 and 8 to 14 while generator 2 lost synchronism beyond a fault CFCT of 0.0130 s. However, the STATCOM application restored the system’s stability. STATCOM aided the transient stability improvement of the Nigerian 34-bus power network for effective operation.

Triggering cationic/anionic hybrid redox stabilizes high-temperature Li-rich cathodes materials via three-in-one strategy

Efficiently advancing lithium-ion batteries toward high energy density entails overcoming challenges in Li-rich layered oxides, including severe voltage and capacity fading, irreversible oxygen escape and compromised thermal robustness due to the uncontrollable oxygen anionic redox (OAR). Herein, a three-in-one modification strategy, aim at strengthening the reversibility of OAR and structural integrity of MnO6 octahedron, is rationally introduced on Li1.2Mn0.53Ni0.20Co0.07O2 cathode through a universal H3BO3-treatment. Through the introduction of oxygen vacancies and gradient B-doping, the energy level of unhybridized O 2p states is decreased to narrow the band energy gap with transition metal (TM) band, which triggers cationic/anionic hybrid redox at high voltage, thereby stabilizing the peroxo-like (O2)n- species and hindering irreversible oxygen escape, while the lithium borate nano-coating serves to mitigate side reactions, particularly during charging at elevated temperatures. As a result, the modulated cathode exhibits notable capacity retention of 96.3 % after 500 cycles at 1 C with limited voltage fading rate (1.73 mV per cycle) and even stable cyclic performance at high temperature (60 °C). This approach provides an effective and straightforward method to tackle the voltage decay and capacity fading of high-energy Li-rich layered cathode materials.

Fabrication of high voltage and energy dense supercapacitor with Manilkara zapota seeds derived porous activated carbon in acidic electrolyte

Achieving a high working potential window beyond the water electrolysis limit (> 1.23 V) has always been a big challenge in the fabrication of aqueous supercapacitors (SCs). Since energy density has quadratic dependence on voltage, broadening of cell voltage can remarkably increase the energy density of the capacitor. Unfortunately, most of the aqueous electrochemical capacitors operated in strongly acidic or alkaline electrolytes show poor energy densities owing to their narrow operating voltage limit. To obtain a high voltage range of aqueous symmetric carbon/carbon capacitors and achieve high energy density, the chemistry of electrode materials and the electrochemical kinetics of electrolytes play a critical role. Hence, in the present work, we explore a porous activated carbon produced from the seeds of Manilkara zapota (ACMZ-700) in combination with sulfuric acid electrolyte to obtain an encouraging electrochemical stable working voltage window. Thus, the resulting symmetric SC effectively exhibited an enlarged cell voltage of 1.5 V in an acidic medium. Importantly, due to the positive role of oxygenated surface functional groups of the ACMZ-700 active material, the fabricated symmetric cell delivered an attractive specific capacitance of 334 F g−1 @ 1 A/g. As a result of high capacitance and broader working voltage, the symmetric device delivered an excellent energy density of 26 Wh kg−1 at a power density of 748 W kg−1 and held excellent cycling stability over 10,000 charge/discharge cycles.

Optimal allocation of solar PV and wind energy power for radial distribution system using spider monkey optimization

The integration of renewable energy sources, relatable as Solar Photovoltaic (PV) and Wind Power, into the radial distribution system has gained significant attention due to their eco-friendly and sustainable attributes. This article presents a narrative advent for achieving the finest share of Solar PV and Wind force power through a radial distribution system using the innovative Spider Monkey Optimization (SMO) algorithm. Multi-objective function for the minimization of distribution loss and voltage deviation with the constraints of power balance equation and boundary limits of voltage and power is considered. The Spider Monkey Optimization algorithm, stimulated via the community activities of spider monkeys, be employed to effectively search for the finest allotment of Solar PV and Wind Energy Power within the distribution network. The SMO algorithm exhibits robustness in handling non-linear and multi-dimensional optimization problems, making it suitable for this complex task. To authorize the usefulness and efficiency of the planned approach, it is functional to standard 33-bus radial division coordination. Comparative analyses of optimization techniques are reported and SMO reduces the losses to 104 KW and the voltage deviation is minimized to 0.0458 pu. The valuable perception is that incorporating Solar PV and Wind Energy sources into radial distribution systems improves the quality.

Distribution network risk assessment with distributed generation impact based on non-sequential Monte Carlo method

At present, the development of renewable energy distributed generation is fast, and the distribution network is facing significant challenges. Unlike traditional fossil fuels, new energy generation is characterized by significant volatility caused by uncertain factors like environmental and meteorological conditions. This paper presents a risk assessment index system that utilizes the non-sequential Monte Carlo method to tackle the given issue. The system comprises two assessments: voltage limit risk and reliability index assessment. Through the application of the Monte Carlo method, a comparative analysis of the results with alternative calculation approaches is conducted. Subsequently, these findings are utilized to evaluate the effectiveness of two commonly employed protection strategies.

Aging Behavior of Polyethylene and Ceramics-Coated Separators under the Simulated Lithium-Ion Battery Service Compression and Temperature Field

In this paper, a device was set up, which could simulate the separator environment in the battery to track the influence of compression, temperature, and the electrolyte on the structure and electrochemical performance of separators. A commercial polyethylene separator and alumina- or boehmite-coated separators were selected, and the high-temperature cyclic compression was carried out in a mixed solvent environment with a ratio of vinyl carbonate and diethyl carbonate of 1:1. Compared with that compressed for 50 cycles under room temperature, the compression at 60 °C resulted in pore structure deterioration in the polyethylene separator. The oxidative voltage limit was reduced to 3.6 V, and after 200 charge and discharge cycles, the capacity was reduced by more than 50%. For the coated separator, the presence of a coating layer exhibited some protective effects, and the microporous structure in the base membrane was preserved. The oxidative voltage limit was above 4.2 V. However, as a result of the compression, the coating particles were still inserted into the pore structure, leading to a decrease in porosity and a decrease in discharge capacity, especially at a rate of 4 C. Compared with that coated with alumina particles, the interface resistance for the separator coated with boehmite particles was minimally affected, and the electrochemical performance after cyclic compression under 60 °C was better, exhibiting higher application ability.

A cleaner lignin-induced 3D porous MXenes hybrid electrode with enlarged voltage and high capacitance retention

Conventional supercapacitors face narrow voltage and an inevitable reduction in capacitance retention during operation, significantly preventing its further commercial application. So, biomass-derived composite materials have attracted intensive attention, especially for pseudocapacitive supercapacitors. Herein, a high-end utilization strategy of lignin to induce a 3D porous layered MXenes/graphene oxide hybrid electrode (LGM2-80) and homologous gel electrolytes with low interface resistance for lignin-derived supercapacitors is demonstrated by a simple hydrothermal method. A more uniform distribution and smaller nanospheres ≈<10 nm of lignin prevent the restacking and increase the interlayer spacing of graphene oxide, also play an adhesive role between graphene oxide and MXene, guaranteeing the maximization of the pseudocapacitance effect between lignin and MXene. Consequently, the LGM2-80 electrode showed a wide operating potential (−0.7∼1.0 V), breaking through the bottleneck of MXene-derived devices with limited working voltage (typically≤0.6 V). Furthermore, the lignin-derived symmetric quasi-solid-state supercapacitor (LGM2-80//lignin gel//LGM2-80) possesses an excellent capacitance retention rate of 149 % at 5,000 cycles, which is far exceeding the current reported supercapacitors. This innovative use of lignin opens up new perspectives for ultra-voltage and ultra-high capacitance retention of advanced supercapacitors.

Assessing the Nationwide Benefits of Vehicle–Grid Integration during Distribution Network Planning and Power System Dispatching

The diffusion of electric vehicles is fundamental for transport sector decarbonization. However, a major concern about electric vehicles is their compatibility with power grids. Adopting a whole-power-system approach, this work presents a comprehensive analysis of the impacts and benefits of electric vehicles’ diffusion on a national power system, i.e., Italy. Demand and flexibility profiles are estimated with a detailed review of the literature on the topic, allowing us to put forward reliable charging profiles and the resulting flexibility, compatible with the Italian regulatory framework. Distribution network planning and power system dispatching are handled with dedicated models, while the uncertainty associated with EV charging behavior is managed with a Monte Carlo approach. The novelty of this study is considering a nationwide context, considering both transmission and distribution systems, and proposing a set of policies suitable for enabling flexibility provision. The results show that the power and energy demand created by the spread of EVs will have localized impacts on power and voltage limits of the distribution network, while the consequences for transmission grids and dispatching will be negligible. In 2030 scenarios, smart charging reduces grid elements’ violations (−23%, −100%), dispatching costs (−43%), and RES curtailment (−50%).

Improving the specific impulse of Hall thrusters using a wide channel design

This paper proposes increasing the width of the discharge channel to improve the specific impulse of Hall thrusters. In our study, we significantly increased the achievable channel width by optimizing the magnetic circuit topology, and the design freedom of the Hall thruster was improved. A prototype of a wide-channel high-specific-impulse Hall thruster was designed and experimentally verified. The effects of channel width on the discharge process and the characteristics of an aft-loaded magnetic field Hall thruster were investigated. The high-intensity luminous region did not diffuse radially with an increase in the channel width, and the plasma was always concentrated near the channel centerline. A wider channel is more conducive for improving the propellant utilization efficiency, thereby effectively improving the specific impulse of the Hall thruster. By optimizing the discharge channel width, the upper limit of the discharge voltage was increased, and the maximum specific impulse was increased from 3170 to 3794 s, a relative improvement of 20%. The effect of the specific impulse improvement at the same discharge voltage was analyzed and discussed. The results of this study are significant for the design of high-specific-impulse Hall thrusters.

Pentafluorophenyl diethoxy phosphate: An electrolyte additive for high-voltage cathodes of lithium-ion batteries

Increasing the upper limit of the charging voltage in commercial lithium-ion batteries (LIBs) can enable them to have a higher energy density, but during high-voltage charging and discharging, the electrolyte will accelerate the decomposition, and the interfacial adverse reaction among the cathode and electrolyte is serious, which corrodes the cathode active material and consumes excessive electrolyte, and ultimately lead to a shorter service life of lithium-ion batteries. To address this issue, an electrolyte additive with properties suitable for high voltage cathodes, named pentafluorophenyl diethoxy phosphate (FPOP), was synthesized in this work and successfully applied to LiNi0.8Co0.1Mn0.1O2 cathode (NCM-811). Density Functional Theory (DFT) computations reveal that the FPOP additive undergoes preferential oxidation and self-polymerizes on the NCM-811 cathode surface to establishing a safeguarding film at the cathode-electrolyte interface (CEI). This film effectively inhibits detrimental side reactions. The electrochemical performance test data indicated that the retention rate of discharge-specific capacity in batteries was markedly enhanced with 0.1 wt% of FPOP when added to the standard electrolyte. Specifically, after subjecting the batteries to 200 cycles at a current of 0.2C and under voltages ranging from 4.2 V to 4.5 V, the retention of discharge ratio capacity increased by 37.6 %, 39.2 %, 26.9 %, and 37.1 % correspondingly. Morphology characterization and spectroscopic characterization showed that FPOP could not only construct a stable CEI film by oxidation during the first stages of lithium precipitation but also remove HF by strongly binding to the HF in the electrolyte or dissociating H+ and F− from HF, which ultimately enhanced the batteries' capacity to operate effectively at elevated voltage levels. Therefore, incorporating FPOP as an additive in electrolyte presents a cost-efficient approach to achieving elevated energy density.

Emerging trends and prospects in aqueous electrolyte design: Elevating energy density and power density of multivalent metal-ion batteries

Aqueous batteries, using multivalent metallic charge carriers (Zn2+, Mg2+, Ca2+, Al3+), show promise as next-generation electrochemical energy storage due to their adequate energy density, high power density, and cost-effectiveness. The electrolyte, serving as a bridge between the cathode and anode, plays a crucial role in functionality. However, the use of aqueous electrolytes introduces issues such as limited voltage range, slow kinetics of multivalent cations, and side reactions on metal surfaces. Electrolyte engineering has emerged as a key solution to overcome major challenges in multivalent metal-ion batteries. This innovative approach involves optimizing factors such as electrolyte concentration, specific additives, pH management, and manipulating the ligand effect of cation salts. Additionally, incorporating anti-freezing agents is crucial. A systematic review of this domain is crucial for further development and refinement of electrolyte engineering strategies. This review should primarily focus on assessing how these modifications can enhance energy and power densities, broaden the operational range of the batteries (by adjusting water activity and LUMO/HOMO energy levels), improve cation transport (via enhanced ion conductivity, dielectric constant, transference number, and solvation structure), and effectively mitigate detrimental side reactions, such as metal deposition, interphase formation, and hydrogen bonding regulation. The electrolyte design strategies in multivalent metal-ion systems are outlined in terms of their effectiveness in smoothing metal dendrites, managing solvation shells and free water molecules, and minimizing side reactions between the metal surface and electrolyte. The article proposes future innovation directions and development prospects for enhancing electrolyte design engineering in these systems.

Broadening the Voltage Window of 3D-Printed MXene Micro-Supercapacitors with a Hybridized Electrolyte.

The burgeoning demand for miniaturized energy storage devices compatible with the miniaturization trend of electronic technologies necessitates advancements in micro-supercapacitors (MSCs) that promise safety, cost efficiency, and high-speed charging capabilities. However, conventional aqueous MSCs face a significant limitation due to their inherently narrow electrochemical potential window, which restricts their operational voltage and energy density compared to their organic and ionic liquid counterparts. In this study, we introduce an innovative aqueous NaCl/H2O/EG hybrid gel electrolyte (comprising common salt (NaCl), H2O, ethylene glycol (EG), and SiO2) for Ti3C2Tx MXene MSCs that substantially widens the voltage window to 1.6 V, a notable improvement over traditional aqueous system. By integrating the hybrid electrolyte with 3D-printed MXene electrodes, we realized MSCs with remarkable areal capacitance (1.51 F cm-2) and energy density (675 µWh cm-2), significantly surpassing existing benchmarks for aqueous MSCs. The strategic formulation of the hybrid electrolyte-a low-concentration NaCl solution with EG-ensures both economic and environmental viability while enabling enhanced electrochemical performance. Furthermore, the MSCs fabricated via 3D printing technology exhibit exceptional flexibility and are suitable for modular device integration, offering a promising avenue for the development of high-performance, sustainable energy storage devices. This advancement not only provides a tangible solution to the challenge of limited voltage windows in aqueous MXene MSCs but also sets a new precedent for the design of next-generation MSCs that align with the needs of an increasingly microdevice-centric world.

Electrical and Electro-Thermal Characteristics of (Carbon Black-Graphite)/LLDPE Composites with PTC Effect.

Electrical properties and electro-thermal behavior were studied in composites with carbon black (CB) or hybrid filler (CB and graphite) and a matrix of linear low-density polyethylene (LLDPE). LLDPE, a (co)polymer with low crystallinity but with high structural regularity, was less studied for Positive Temperature Coefficient (PTC) applications, but it would be of interest due to its higher flexibility as compared to HDPE. Structural characterization by scanning electron microscopy (SEM) confirmed a segregated structure resulted from preparation by solid state powder mixing followed by hot molding. Direct current (DC) conductivity measurements resulted in a percolation threshold of around 8% (w) for CB/LLDPE composites. Increased filler concentrations resulted in increased alternating current (AC) conductivity, electrical permittivity and loss factor. Resistivity-temperature curves indicate the dependence of the temperature at which the maximum of resistivity is reached (Tmax(R)) on the filler concentration, as well as a differentiation in the Tmax(R) from the crystalline transition temperatures determined by DSC. These results suggest that crystallinity is not the only determining factor of the PTC mechanism in this case. This behavior is different from similar high-crystallinity composites, and suggests a specific interaction between the conductive filler and the polymeric matrix. A strong dependence of the PTC effect on filler concentration and an optimal concentration range between 14 and 19% were also found. Graphite has a beneficial effect not only on conductivity, but also on PTC behavior. Temperature vs. time experiments, revealed good temperature self-regulation properties and current and voltage limitation, and irrespective of the applied voltage and composite type, the equilibrium superficial temperature did not exceed 80 °C, while the equilibrium current traversing the sample dropped from 22 mA at 35 V to 5 mA at 150 V, proving the limitation capacities of these materials. The concentration effects revealed in this work could open new perspectives for the compositional control of both the self-limiting and interrupting properties for various low-temperature applications.

Distributed Optimization for Reactive Power Sharing and Stability of Inverter-Based Resources Under Voltage Limits

Distributed Optimization for Reactive Power Sharing and Stability of Inverter-Based Resources Under Voltage Limits

Comparative Analysis of the Power Output Capabilities of Grid-Following and Grid-Forming Inverters Considering Static, Dynamic, and Thermal Limitations

This paper investigates the maximum transferable power (MTP) of inverter-based resources (IBRs) and provides the output capability curves (OCCs) of grid-tied grid-following inverters (GFLIs) and grid-forming inverters (GFMIs). To this end, in the first part of the paper, mathematical equations for GFLI static, thermal, and phase-locked loop (PLL)-induced power transfer limits are derived in terms of the grid short-circuit ratio (SCR) and its X/R ratio. Then, considering other operational limitations, such as the IBR AC- and DC-side voltage limits, the OCC of the GFLI is obtained. Additionally, the impact of the reactive current and the reactive control mode on the OCC is further studied, and accordingly, an auxiliary control loop is proposed to maximize the GFLI MTP. In the second part of the paper, a similar approach is employed to derive mathematical equations for GFMI static and thermal limits, and accordingly, the OCC of a GFMI is obtained. The effects of the variation of the voltage set-point of the GFMI on its OCC are then studied, and the superiority of GFMIs compared to GFLIs is shown in terms of the MTP capability. Eventually, several simulation and experimental cases are conducted to validate the obtained equations and OCCs for both grid-following and grid-forming control modes.

Technical/economic/environmental optimal wind generation allocation in power systems

This paper proposes an optimization technique to find the optimal allocation of wind farms (WFs) in a transmission network considering several objectives associated with economic, losses, voltage profile, and environmental impact represented in the reduction of carbon emissions. The problem is solved on the basis of maintaining three constraints which are transmission line power limits, active/reactive power constrain, and bus voltage limits. The particle swarm optimization (PSO) algorithm and Newton-Raphson method for load flow analysis are utilized to solve the optimization problem as a whole. In this context, there are two wind turbines added to the transmission network and a matrix laboratory (MATLAB) has been devised to evaluate their performance with varying capacities at different locations in the system. The proposed approach has been validated on the modified IEEE 14-bus transmission system.

An Angle-Based Virtual Vector Model Predictive Current Control for IPMSM Considering Overmodulation

The conventional model predictive control method suffers from large current and torque harmonics due to the limited voltage vectors. To increase the control performance, in many papers, the methods of extending the predictive control set by adding virtual vectors are proposed. However, constructing virtual vectors will bring extra computational burden for vector optimization. To solve this problem, this paper proposes an angle-based virtual vector model predictive current control (ABVV-MPCC) method for interior permanent magnet synchronous motor (IPMSM). In this method, a hexagonal coordinate system is introduced to define the virtual vectors. After obtaining the composite relationship between the reference voltage vector and the adjacent basic vector, the vector optimization range is reduced from six voltage sectors to one voltage sector. And the optimal voltage vector is directly obtained by searching for the closest candidate voltage vector. After adopting the proposed method, the exhaustive optimization is avoided and the calculation burden is independent from the virtual voltage vectors number. Therefore, virtual voltage vectors number can be set arbitrarily, which greatly reduces current harmonics. Besides, a simple overmodulation dealing method by finding the optimal reachable voltage vector is proposed. And the dynamic performance under overmodulation is increased without adding additional control module.

Optimal Sizing of Fuel Cell and Battery in a Direct-Hybrid for Electric Aircraft

The climate impact of aviation can be reduced using powertrains based on hydrogen fuel cells and batteries. Combining both technologies in a direct-hybrid without a DC/DC converter is a promising approach for light-weight systems. Depending on the power demand, both the fuel cell and battery are used to provide power or only the fuel cell is connected to the powertrain. The system voltage in a direct-hybrid is determined by the fuel cell and battery, but the performance of fuel cells is affected by low-ambient pressure at high altitudes and the battery voltage is affected by state of charge and discharge rate. Taking this into account, the presented work demonstrates how a direct-hybrid system must be designed based on a scaled mission profile of a 40-seater aircraft. The fuel cell and battery are configured and sized according to the power demand in different flight phases while considering voltage limits given by the powertrain. The energy requirement from the fuel cell and the battery is calculated for a flight based on a realistic mission profile and different battery and fuel cell configurations are evaluated. By optimizing the battery and fuel cell size, the energy required from the battery was reduced by 57% and the total weight of the fuel cell and battery was reduced by 11%.