Dynamic behaviour of Li batteries in hydrogen fuel cell power trains

A Li ion polymer battery pack for road vehicles (48 V, 20 Ah) was tested by charging/discharging tests at different current values, in order to evaluate its performance in comparison with a conventional Pb acid battery pack. The comparative analysis was also performed integrating the two storage systems in a hydrogen fuel cell power train for moped applications. The propulsion system comprised a fuel cell generator based on a 2.5 kW polymeric electrolyte membrane (PEM) stack, fuelled with compressed hydrogen, an electric drive of 1.8 kW as nominal power, of the same typology of that installed on commercial electric scooters (brushless electric machine and controlled bidirectional inverter). The power train was characterized making use of a test bench able to simulate the vehicle behaviour and road characteristics on driving cycles with different acceleration/deceleration rates and lengths. The power flows between fuel cell system, electric energy storage system and electric drive during the different cycles were analyzed, evidencing the effect of high battery currents on the vehicle driving range. The use of Li batteries in the fuel cell power train, adopting a range extender configuration, determined a hydrogen consumption lower than the correspondent Pb battery/fuel cell hybrid vehicle, with a major flexibility in the power management.     

Investigation of a hydrogen-assisted combustion system for a light-duty diesel vehicle

Two sets of experiments were conducted to investigate the effects of adding gaseous hydrogen to the intake of compression–ignition (CI) engines fueled with 20% bio-derived/80% petroleum-derived diesel fuel (B20). A 1.3 L, 53 kW CI engine coupled to an eddy-current engine dynamometer was tested first. Data were collected on engine operating parameters, fuel consumption, concentration of total oxides of nitrogen (NO_x) in the exhaust, and exhaust temperature. Eight steady-state operating points were tested with hydrogen flow rates equivalent to 0%, 5%, and 10% of the total fuel energy. In a second set of experiments, the stock gasoline engine of a 2005 Chevrolet Equinox was replaced with a 1.3 L, 66 kW CI engine, and urban drive cycles were run on a chassis dynamometer. The drive cycles were repeated with 0%, 5% and 10% of the fuel energy coming from the fumigated hydrogen. In both experiments, the addition of hydrogen did not result in discernable differences in engine efficiency. In the vehicle testing, there were no noticeable differences in drivability. There were modest reductions in NO_x emissions and increases in exhaust temperature with hydrogen addition. This investigation demonstrates that fumigating relatively small amounts of hydrogen into the intake of a modern diesel engine results in only modest changes in combustion efficiency and emissions with no detrimental effects on vehicle performance or drivability. This strategy can be used to partially offset the use of petroleum-based fuels in light-duty transportation vehicles.     

Dynamic response and long-term stability of a small direct methanol fuel cell stack

This study examines the operating characteristics and durability of a small direct methanol fuel cell (DMFC) stack (volume: 39.6 cm³). To investigate the operating characteristics in a real multi-user operating mode, various load cycles (such as gradual acceleration and deceleration), two operating modes (current mode or voltage mode) and four interrupted operating methods (load on-off, load-methanol on-off, load-air on-off, and load-methanol-air on-off) are used. The durability of the DMFC stack is examined at a constant voltage of 2.4 V (0.4 V per cell) by using the load-methanol-air on-off mode for more than 2000 h. In these tests, the DMFC stack exhibits a rapid, stable and dynamic response regardless of the load cycle and operating mode, though the stack performance and response behaviour vary with the interrupted operating modes. Among the operating modes, the air-interruption modes exhibit better stability and higher performance. Moreover, the load-methanol-air on-off mode provides the stack with good durability and a high performance in a long-term test of 2045 h.     

Combustion characteristics of a charcoal slurry in a direct injection diesel engine and the impact on the injection system performance

The paper presents the research results pertaining to the renewable biomass charcoal-diesel slurries and their use as alternative fuels for combustion in diesel generating plants. The utilization of charcoal slurry fuel aims to reduce diesel oil consumption and would decrease fossil green house emissions into the atmosphere. The paper investigates the formulation, emulsification, sprays, combustion, injection system operation, and subsequent wear with charcoal-diesel slurries. In the research, cedar wood chips were used for the production of charcoal to be emulsified with diesel oil. The slurry’s viscosity of 27 cP achieved the target (<100 cP) and gave prospects of good spray atomization and while maintaining a high calorific value. Thermal analysis studies found that cedar wood will oxidize about 75% of its original mass by 450 °C. Charcoal slurry displayed a high vaporization rate of 75% by wt. at 300 °C. Engine investigations showed that the top combustion pressure at 1200 rpm and 100% load (7.8 brake mean effective pressure (bmep)) was 79 bar for diesel fuel and 78 bar for the charcoal slurry fuel. From the injection and heat release history was found an ignition delay of 1.7 ms for diesel that increased to 2.1 ms for the slurry fuel. A higher net heat release for charcoal slurry was observed, up to 180 J/crank angle degrees (CAD) compared with the diesel at 145 J/CAD The maximum combustion temperature reached 2300 K for diesel and 2330 K for slurry. The heat fluxes for both fuels have similar values and trends during the entire cycle showing the good compatibility of charcoal slurry with a diesel type combustion and low soot radiation. The exhaust temperatures were about 40-50 °C higher for charcoal slurry at 19° before top dead center (BTDC) injection timing. The engine’s bsfc increased as expected due to the lower heating value of the slurry fuel. The smoke Bosch no. was lower for the slurry fuel at any load, and is believed that the oxygen from the charcoal had a beneficial effect. The measured emissions of slurry fuel were better at 13° BTDC than those of diesel fuel with the original engine settings and the remaining 6-10% oxygen content in the charcoal is thought to have a paramount role in helping the diffusion type combustion and diminishing the particulate matter formation. As the load was increased, the amount of time it took to notice a decline in engine efficiency decreased. This was due to the injector sticking open which was seen by a sharp increase in the exhaust temperature. The internal flow into the injector had the tendency to form deposits on the injector’s seat that were critical to the functionality of the injector. In order to alleviate this problem, a reduced charcoal particle size together with a new injector design were produced resulting in stable engine efficiency at 50% load for a period of 90 min without injector sticking. Even with improvements, the needle’s seat into the injector body showed an accelerated wear 4-8 times faster than that in normal operation with diesel fuel and this cannot be sustained for long operational cycles. The investigations have proven that the new charcoal-diesel slurry can produce adequate sprays and burn with very good results in a direct injection diesel engine. The critical aspect of operation is the internal flow into the injector with the tendency to form deposits and wear in the injector.     

An experimental study of a PEM fuel cell power train for urban bus application

An experimental study was carried out on a fuel cell propulsion system for minibus application with the aim to investigate the main issues of energy management within the system in dynamic conditions. The fuel cell system (FCS), based on a 20 kW PEM stack, was integrated into the power train comprising DC–DC converter, Pb batteries as energy storage systems and asynchronous electric drive of 30 kW. As reference vehicle a minibus for public transportation in historical centres was adopted. A preliminary experimental analysis was conducted on the FCS connected to a resistive load through a DC–DC converter, in order to verify the stack dynamic performance varying its power acceleration from 0.5 kW s⁻¹ to about 4 kW s⁻¹. The experiments on the power train were conducted on a test bench able to simulate the vehicle parameters and road characteristics on specific driving cycles, in particular the European R40 cycle was adopted as reference. The “soft hybrid” configuration, which permitted the utilization of a minimum size energy storage system and implied the use of FCS mainly in dynamic operation, was compared with the “hard hybrid” solution, characterized by FCS operation at limited power in stationary conditions. Different control strategies of power flows between fuel cells, electric energy storage system and electric drive were adopted in order to verify the two above hybrid approaches during the vehicle mission, in terms of efficiencies of individual components and of the overall power train.     

Performance improvement of diesel autothermal reformer by applying ultrasonic injector for effective fuel delivery

Technology for the reforming of heavy hydrocarbons, such as diesel, to supply hydrogen for fuel cell applications is very attractive and challenging due to its delicate control requirements. The slow reforming kinetics of aromatics contained in diesel, sulfur poisoning, and severe carbon deposition make it difficult to obtain long-term performance with high reforming efficiency. In addition, diesel has a critical mixing problem due to its high boiling point, which results in a fluctuation of reforming efficiency. An ultrasonic injector (UI) have been devised for effective diesel delivery. The UI can atomize diesel into droplets (∼40 μm) by using a piezoelectric transducer and consumes much less power than a heating-type vapourizer. In addition, reforming efficiencies increase by as much as 20% compared with a non-UI reformer under the same operation conditions. Therefore, it appears that effective fuel delivery is linked to the reforming kinetics on the catalyst surface. A 100-W_e, self-sustaining, diesel autothermal reformer using the UI is designed. In addition, the deactivation process of the catalyst, by carbon deposition, is investigated in detail.     

Performance and cost of automotive fuel cell systems with ultra-low platinum loadings

An automotive polymer-electrolyte fuel cell (PEFC) system with ultra-low platinum loading (0.15 mg-Pt cm⁻²) has been analyzed to determine the relationship between its design-point efficiency and the system efficiency at part loads, efficiency over drive cycles, stack and system costs, and heat rejection. The membrane electrode assemblies in the reference PEFC stack use nanostructured, thin-film ternary catalysts supported on organic whiskers and a modified perfluorosulfonic acid membrane. The analyses show that the stack Pt content can be reduced by 50% and the projected high-volume manufacturing cost by >45% for the stack and by 25% for the system, if the design-point system efficiency is lowered from 50% to 40%. The resulting penalties in performance are a <1% reduction in the system peak efficiency; a 2-4% decrease in the system efficiency on the urban, highway, and LA92 drive cycles; and a 6.3% decrease in the fuel economy of the modeled hybrid fuel-cell vehicle on the combined cycle used by EPA for emission and fuel economy certification. The stack heat load, however, increases by 50% at full power (80 kW_e) but by only 23% at the continuous power (61.5 kW_e) needed to propel the vehicle on a 6.5% grade at 55 mph. The reduced platinum and system cost advantages of further lowering the design-point efficiency from 40% to 35% are marginal. The analyses indicate that thermal management in the lower efficiency systems is very challenging and that the radiator becomes bulky if the stack temperature cannot be allowed to increase to 90-95 °C under driving conditions where heat rejection is difficult.     

Temperature optimisation of a diesel engine using exhaust gas heat recovery and thermal energy storage (diesel engine with thermal energy storage)

Modern automotive diesel engines are so energy efficient that they are heating up slowly and tend to run rather cold at subzero temperatures. The problem is especially severe in mail delivery operations where the average speed is low and the drive cycle includes plenty of idling. The problem is typically solved by adding a diesel fuelled additional engine heater which is used for the preheating of the engine during cold start and additional heating of the engine if the coolant temperature falls below a thermostat set point during the drive cycle. However, this additional heater may drastically increase the total fuel consumption and exhaust gas emissions of the vehicle. In this study the additional heater was replaced by a combination of exhaust gas heat recovery system and latent heat accumulator for thermal energy storage. The system was evaluated on a laboratory dynamometer using a simulated drive cycle and in field testing in the city of Oulu (65°N), Finland in February 2009.     

Voltage balancing: Long-term experience with the 250 V supercapacitor module of the hybrid fuel cell vehicle HY-LIGHT

On the occasion of the “Challenge Bibendum” 2004 in Shanghai, the hybrid fuel cell—supercapacitor vehicle HY-LIGHT, a joint project of Conception et Développement Michelin and the Paul Scherrer Institut, was presented to the public. The drive train of this vehicle comprises a 30 kW polymer electrolyte fuel cell (PEFC) and a 250 V supercapacitor (SC) module for energy recuperation and boost power during short acceleration and start-up processes. The supercapacitor module was deliberately constructed without continuous voltage balancing units. The performance of the supercapacitor module was monitored over the 2 years of operation particularly with respect to voltage balancing of the large number of SC cells connected in series. During the investigated period of 19 months and about 7000 km driving, the voltage imbalance within the supercapacitor module proved negligible. The maximum deviation between best and worst SC was always below 120 mV and the capacitor with the highest voltage never exceeded the nominal voltage by more than 40 mV.     

Adjustment of electrodes potential window in an asymmetric carbon/MnO2 supercapacitor

The electrodes mass ratio of MnO₂/activated carbon supercapacitors has been varied in order to monitor its influence on the potential window of both electrodes and consequently to optimize the operating voltage. It appeared that the theoretical mass ratio (R = 2), calculated considering an equivalent charge passed across both electrodes, is underestimated. It was demonstrated that R values of 2.5-3 are better adapted for this system; the extreme potential reached for each electrode is close to the stability limits of the electrolyte and active material, allowing a maximum voltage to be reached. During galvanostatic cycling up to 2 V, the best performance was obtained with R = 2.5. The specific capacitance increased from 100 to 113 F g⁻¹ during the first 2000 cycles, then decayed up to 6000 cycles and finally stabilized at 100 F g⁻¹. SEM images of the manganese based electrode after various numbers of thousands cycles exhibited dramatic morphological modifications. The later are suspected to be due to Mn(IV) oxidation and dissolution at high potential values. Hence, the evolution of specific capacitance during cycling of the asymmetric capacitor is ascribed to structural changes at the positive electrode.     

Effect of driving cycle on the performance of PEM fuel cell and microstructure of membrane electrode assembly

Driving cycle effect on proton exchange membrane fuel cell (PEMFC) performance and microstructure of membrane electrode assembly (MEA) is simulated to predict the lifetime of PEMFC. The single cell performance after different simulated cycles (100, 150 and 200 cycles) was evaluated by I–V curves. Electro-chemical impedance spectroscopy (EIS) was used to characterize the electro-chemical properties of fuel cell and the active surface area was characterized by cyclic voltammetry (CV). It was found that after 100, 150 and 200 cycles the electro-chemical surface area (ESA) for electro-chemical reaction decreased about 13.6%, 15.4% and 38.9%, respectively, and the performance of PEMFC declined about 0.1 V at 500 mA cm⁻² after 200 driving cycles. Impedance analysis and equivalent circuit showed that ohmic and charge transfer resistance respectively increased from 2.06 to 2.13, 2.215, 2.435 Ω cm² and from 0.7 to 0.905, 1.26, 1.915 Ω cm² after three kinds of driving cycles, and they all increased with increasing driving cycles, which may be one reason for the decline of PEMFC performance. Besides, scanning electron microscopy (SEM) result revealed that the thickness of catalyst layer after cycle test was weakening much more than the fresh one.     

Biodiesel fuel in diesel micro-turbine engines: Modelling and experimental evaluation

Many performance and emission tests have been carried out in reciprocating diesel engines that use biodiesel fuel over the past years and very few in gas turbine engines. This work aims at assessing the thermal performance and emissions at full and partial loads of a 30 kW diesel micro-turbine engine fed with diesel, biodiesel and their blends as fuel. A cycle simulation was performed using the Gate Cycle GE Enter software to evaluate the thermal performance of the 30 kW micro-turbine engine. Performance and emission tests were carried out on a 30 kW diesel micro-turbine engine installed in the NEST laboratories of the Federal University of Itajubá, and the performance results were compared with those of the simulation. There was a good agreement between the simulations and the experimental results from the full load down to about 50% of the load for diesel, biodiesel and their blends. The biodiesel and its blends used as fuel in micro-turbines led to no significant changes in the engine performance and behaviour compared to diesel fuel. The exhaust emissions were evaluated for pure biodiesel and its blends and conventional diesel. The results revealed that the use of biodiesel resulted in a slightly higher CO, lower NO_x and no SO₂ emissions.     

Steam reforming of commercial ultra-low sulphur diesel

Two main routes for small-scale diesel steam reforming exist: low-temperature pre-reforming followed by well-established methane steam reforming on the one hand and direct steam reforming on the other hand. Tests with commercial catalysts and commercially obtained diesel fuels are presented for both processes. The fuels contained up to 6.5 ppmw sulphur and up to 4.5 vol.% of biomass-derived fatty acid methyl ester (FAME). Pre-reforming sulphur-free diesel at around 475 °C has been tested with a commercial nickel catalyst for 118 h without observing catalyst deactivation, at steam-to-carbon ratios as low as 2.6. Direct steam reforming at temperatures up to 800 °C has been tested with a commercial precious metal catalyst for a total of 1190 h with two catalyst batches at steam-to-carbon ratios as low as 2.5. Deactivation was neither observed with lower steam-to-carbon ratios nor for increasing sulphur concentration. The importance of good fuel evaporation and mixing for correct testing of catalysts is illustrated. Diesel containing biodiesel components resulted in poor spray quality, hence poor mixing and evaporation upstream, eventually causing decreasing catalyst performance. The feasibility of direct high temperature steam reforming of commercial low-sulphur diesel has been demonstrated.     

Enhanced capacitance and rate capability of graphene/polypyrrole composite as electrode material for supercapacitors

Graphene and polypyrrole composite (PPy/GNS) is synthesized via in situ polymerization of pyrrole monomer in the presence of graphene under acid conditions. The structure and morphology of the composite are characterized by X-ray diffraction (XRD), Raman spectroscopy, Fourier transform infrared spectrometer (FTIR), X-rays photoelectron spectroscopy (XPS) and transmission electron microscope (TEM). It is found that a uniform composite is formed with polypyrrole being homogeneously surrounded by graphene nanosheets (GNS). The composite is a promising candidate for supercapacitors to have higher specific capacitance, better rate capability and cycling stability than those of pure polypyrrole. The specific capacitance of PPy/GNS composite based on the three-electrode cell configuration is as high as 482 F g⁻¹ at a current density of 0.5 A g⁻¹. After 1000 cycles, the attenuation of the specific capacitance is less than 5%, indicating that composite has excellent cycling performance.     

Importance of biodiesel as transportation fuel

The scarcity of known petroleum reserves will make renewable energy resources more attractive. The most feasible way to meet this growing demand is by utilizing alternative fuels. Biodiesel is defined as the monoalkyl esters of vegetable oils or animal fats. Biodiesel is the best candidate for diesel fuels in diesel engines. The biggest advantage that biodiesel has over gasoline and petroleum diesel is its environmental friendliness. Biodiesel burns similar to petroleum diesel as it concerns regulated pollutants. On the other hand, biodiesel probably has better efficiency than gasoline. One such fuel for compression-ignition engines that exhibit great potential is biodiesel. Diesel fuel can also be replaced by biodiesel made from vegetable oils. Biodiesel is now mainly being produced from soybean, rapeseed and palm oils. The higher heating values (HHVs) of biodiesels are relatively high. The HHVs of biodiesels (39–41 MJ/kg) are slightly lower than that of gasoline (46 MJ/kg), petrodiesel (43 MJ/kg) or petroleum (42 MJ/kg), but higher than coal (32–37 MJ/kg). Biodiesel has over double the price of petrodiesel. The major economic factor to consider for input costs of biodiesel production is the feedstock, which is about 80% of the total operating cost. The high price of biodiesel is in large part due to the high price of the feedstock. Economic benefits of a biodiesel industry would include value added to the feedstock, an increased number of rural manufacturing jobs, an increased income taxes and investments in plant and equipment. The production and utilization of biodiesel is facilitated firstly through the agricultural policy of subsidizing the cultivation of non-food crops. Secondly, biodiesel is exempt from the oil tax. The European Union accounted for nearly 89% of all biodiesel production worldwide in 2005. By 2010, the United States is expected to become the world's largest single biodiesel market, accounting for roughly 18% of world biodiesel consumption, followed by Germany.     

Design of experiment approach applied to reducing and oxidizing tolerance of anode supported solid oxide fuel cell. Part II: Electrical, electrochemical and microstructural characterization of tape-cast cells

One of the major limitations of the nickel (Ni) - yttria-stabilized zirconia (YSZ) anode support for solid oxide fuel cells (SOFC) is its low capability to withstand transients between reducing and oxidizing atmospheres (“RedOx” cycle), owing to the Ni-to-NiO volume expansion. This work presents results on different anode supports fabricated by tape casting. Three compositions are prepared, as the outcome of a preceding design of experiment approach. The NiO proportion is 40, 50 and 60 wt% of the anode composite.The anode support characteristics like shrinkage during sintering, in-situ conductivity at high temperature, electrochemical performance and tolerance against RedOx cycles have been measured. Performance up to 0.72 W cm⁻² (0.62 V, 800 °C) is recorded for the 60 wt% NiO sample on small cells. The open circuit voltage is maintained within ±5 mV after 10 full RedOx cycles at 800 °C and one at 850 °C. Performances tend to be stabilized after one or multiple RedOx cycles. The microstructural observations show round Ni particles after the first reduction; after a RedOx cycle, the Ni particles include micro-porosities that are stable under humidified reducing atmosphere for more than 300 h.     

Effects of secondary combustion on efficiencies and emission reduction in the diesel engine exhaust heat recovery system

An experimental study on the effects of secondary combustion on efficiencies and emission reduction in the diesel engine exhaust heat recovery system has been undertaken. The co-generation concept is utilized in that the electric power is produced by the generator connected to the diesel engine, and heat is recovered from both combustion exhaust gases and the engine by the fin-and-tube and shell-and-tube heat exchangers, respectively. A specially designed secondary combustor is installed at the engine outlet in order to reburn the unburned fuel from the diesel engine, thereby improving the system’s efficiency as well as reducing air pollution caused by exhaust gases. The main components of the secondary combustor are coiled Nichrome wires heated by the electric current and diesel oxidation catalyst (DOC) housed inside a well insulated stainless steel shell. The performance tests were conducted at four water flow rates of 5, 10, 15 and 20 L/min and five electric power outputs of 3, 5, 7, 9 and 11 kW. The results show that at a water flow of 20 L/min and a power generation of 9 kW, the total efficiency (thermal efficiency plus electric power generation efficiency) of this system reaches a maximum 94.4% which is approximately 15–20% higher than that of the typical diesel engine exhaust heat recovery system. Besides, the use of the secondary combustor and heat exchangers results in 80%, 35% and 90% reduction of carbon monoxide (CO), nitrogen oxide (NO_x) and particulate matter (PM), respectively.     

Effect of temperature on tribological properties of palm biodiesel

Biodiesel, as an alternative fuel is steadily gaining attention to replace petroleum diesel partially or completely. The tribological performance of biodiesel is crucial for its application in automobiles. In the present study, effect of temperature on the tribological performance of palm biodiesel was investigated by using four ball wear machine. Tests were conducted at temperatures 30, 45, 60 and 75 °C, under a normal load of 40 kg for 1 h at speed 1200 rpm. For each temperature, the tribological properties of petroleum diesel (B0) and three biodiesel blends like B10, B20, B50 were investigated and compared. During the wear test, frictional torque was recorded on line. Wear scars in tested ball were investigated by optical microscopy. Results show that friction and wear increase with increasing temperature.     

Synthesis and performance of carbon-coated Li3V2(PO4)3 cathode materials by a low temperature solid-state reaction

The carbon-coated monoclinic Li₃V₂(PO₄)₃ (LVP) cathode materials can be synthesized by a low temperature solid-state reaction route. The influences of different heat treatments on the LVP have been investigated using X-ray diffraction (XRD), scanning electron microscopy (SEM) and electrochemical methods. In the range of 3.0-4.3 V, both LVP/C electrodes present good rate capability and excellent cyclic performance. It is found that the sample (LVP1/C) prepared by the two-step heat treatment with pre-sintering at 350 °C delivers the initial discharge capacity of 99.8 mAh g⁻¹ at 10 C charge-discharge rate and still retains 95.8 mAh g⁻¹ after 300 cycles. For the sample (LVP2/C) synthesized by the one-step heat treatment, 95.9 and 90.0 mAh g⁻¹ are obtained in the 1st and 300th cycles at 10 C rate, respectively. Our results based on the XRD patterns and the SEM images suggest that the good rate capability and cyclic performance may be owing to the pure phases, small particles, large specific surface areas and residual carbon. In the range of 3.0-4.8 V, compared with the LVP2/C, the LVP1/C also exhibits better performance.     

Electrophoretic deposition of nickel oxide electrode for high-rate electrochemical capacitors

Nanostructured nickel hydroxide electrode is fabricated directly by electrophoretic deposition (EPD) method. After annealing at 300 °C for 3 h, nickel hydroxide nanoplatelet converts into nickel oxide. EPD method is useful in depositing nickel hydroxide nanoplatelets from isopropyl alcohol suspension containing iodine and water additives. Hydrogen ions are generated by the reaction between iodine and water and then adsorbed on the nickel hydroxide, resulting in positively charged nickel hydroxide. Positively charged nanoplatelet of high zeta potential is beneficial to EPD and dispersion. An electrode deposited by EPD has better uniformity than one deposited by dip coating. Electrochemical performance of the electrodes is investigated by cyclic voltammetry in 0.5 M KOH. Specific capacitance of the nickel oxide electrode prepared by EPD is higher than that of prepared by dip coating even at a very high rate of 500 mV s⁻¹. In addition, an electrode prepared by EPD also shows excellent cycle-life stability because its specific capacitance decreases only slightly after 5000 charging/discharging cycles.