The Physics of Energy, page 168
Efficiency of Hydrogen Energy Systems To determine the efficiency of a hydrogen-based energy system, all the steps in the hydrogen production and storage processes must be included. If the hydrogen used is produced from electrical energy through electrolysis, then the overall efficiency depends upon:
ηconversion: the efficiency for conversion of the original energy source to electricity, including transmission losses from the source to the electrolysis plant;
ηelectrolysis: the efficiency of the electrolysis process;
ηstorage: efficiencies associated with infrastructure (recovery and compression of the H, distribution, transport, and storage);
ηengine: the efficiency of the fuel cell or engine that converts the hydrogen into useful energy.
The product of all these efficiencies,
(37.18)
must be compared with the efficiency of alternatives. For example, one could compare the overall efficiency of an automobile run on a hydrogen fuel cell using compressed hydrogen produced by electrolysis to a plug-in electric vehicle with a chemical battery storage system. The large number of steps in the hydrogen process make it difficult for hydrogen-based systems such as this to compete in efficiency. The principal advantage of the hydrogen fuel cell vehicle compared to a battery-powered plug-in is the substantial difference in energy density, allowing for a much greater range for a vehicle with limited mass devoted to the energy system. If an efficient and inexpensive reversible hydrogen fuel cell is developed in the future, then many of the additional efficiency constraints of the hydrogen-based system would be mitigated.
37.3.4 Combustible Storage
While most combustible fuels, such as fossil fuels, are derived from natural sources, these fuels are also in a sense energy storage devices. Indeed, as discussed in §26, the energy in hydrocarbons and related biological materials is essentially stored solar energy, captured by the process of photosynthesis. By manipulating biological and chemical systems it is possible to transform energy from other forms into the chemical energy of combustible molecules, and to use this as a form of energy storage. As a simple example, consider using solar or wind energy to produce methanol through electrolysis – essentially by running a methanol fuel cell backwards. This converts a natural source of energy to a chemically stored form that can be released through combustion as well as through a fuel cell. Much of the material in previous chapters on combustion-based power plants and fossil fuels applies to artificially produced combustible materials as well as to natural energy sources. As discussed in the previous section, the tradeoff between extracting energy from a given fuel through combustion or through a fuel cell is that the energy extracted from combustion is limited by the 2nd Law, while fuel cells require substantial area and material for high power production.
37.4Other Energy Storage Systems
37.4.1 Flywheels
Pumped hydro stores energy in the form of mechanical potential energy. Energy can also be stored in mechanical kinetic energy. One simple way of using kinetic energy for storage employs a flywheel. Flywheels are often used to provide energy at a continuous rate when the source is intermittent. Flywheels have also been proposed for energy storage in hybrid automobiles.
Figure 37.8 A modern flywheel, with magnetic bearings and vacuum pump to minimize frictional losses (Credit: Slim Films)
Flywheels: Basic Principles Flywheels store energy in the rotational kinetic energy of a massive spinning object. The physics of a flywheel is quite simple (see Example 2.4). The rotational kinetic energy of an object is given by
(37.19)
where ω is angular velocity and the moment of inertia of the object is
(37.20)
For example, for a solid disk of mass M and radius R, the moment of inertia is .
Frictional losses are an important concern for flywheel energy storage. A poorly engineered flywheel will rapidly lose energy to friction at the point of contact between the rotating hub and its support structure. Energy is also lost to air resistance if the flywheel is rotating in air at atmospheric pressure. Modern flywheels use magnetic bearings to minimize friction of the axle, and incorporate a vacuum pump to minimize air resistance.
Flywheels are simple mechanical devices that can be extremely robust, and relatively efficient. Current designs are made of strong carbon-composite material, can be used for – cycles without breakdown, and can have a round-trip storage efficiency of up to 85–90% The energy density of advanced flywheel designs can be comparable to the best battery technologies (up to 500 kJ/kg), although the energy densities of commercially available flywheels are typically an order of magnitude lower. The instantaneous power can be very high for flywheels. Thus, flywheels are of particular use in applications where short power bursts are needed, such as for testing circuit breakers. Flywheels are often used for short-term load leveling and uninterruptible power supplies. Due to their high reliability, long lifetime, and minimal maintenance requirements, flywheels are used for space applications.
Flywheels in Automobiles Flywheels have been explored for possible use in automobile energy storage. The principle of a hybrid automobile engine is to divide the power source into two components. The first component is an efficient but relatively small fossil fuel powered engine, such as an engine based on the Atkinson cycle as discussed in §11. The small internal combustion engine is complemented by an additional power source used for rapid acceleration; generally the additional power source gets its energy from regenerative braking. A flywheel has several advantages as a temporary storage system for kinetic energy from regenerative braking. The transformation of motional kinetic energy into a flywheel’s rotational kinetic energy and back requires only a mechanical coupling. With one efficient transformation needed for storage and another for recovery, flywheel round-trip storage efficiency can easily be engineered in the range ––0.8 and can be above 0.8 for precision-engineered systems. Battery storage, in contrast, requires more steps – the vehicle’s kinetic energy must be transformed into electrical energy using a generator, then stored in the battery, recovered, and transformed again into kinetic energy using a motor. Even if each stage in this process were 80% efficient, the overall round-trip storage efficiency can be below 50% (). Compared to batteries, flywheels are not only more efficient, but can have higher power density and survive many more cycles than any existing battery technology.
So why are flywheels not already the technology of choice for short-term energy storage in hybrid automobiles? While prototypes have been built (Example 37.4), and some engineers argue that flywheel technology offers substantial advantages and has only been held back by industrial inertia, flywheels raise some safety issues if they are used in automobiles. One important issue is that when a flywheel fails – due either to material failure or damage to the system – it can rapidly disintegrate, sending fragments of metal in all directions at velocities above that of a bullet (Problem 37.17). Use of flywheels in passenger automobiles would require safety systems to protect the driver and passengers from flywheel disintegration in case of an accident.
Flywheel Energy Storage
Flywheels store rotational kinetic energy. The effective energy densities of flywheels are of the same order as batteries. Flywheel power densities, however, are higher than any other conventional energy storage system except for supercapacitors, which have much lower effective energy density. Flywheels also have very high instantaneous power, high round-trip storage efficiency, and great longevity – of order 105–107 cycles. Safety issues and gyroscopic effects have so far prevented widespread adoption of flywheels for mobile energy storage.
Another issue for flywheels concerns gyroscopic effects. A rapidly rotating flywheel has a significant amount of angular momentum about a specific axis. Any rotation of a vehicle containing a flywheel that changes the orientation of the flywheel’s angular momentum axis requires an additional torque, according to eq. (2.43). For turns in the plane of the car’s motion, the required torque can be minimized by a vertical flywheel axis, but other common maneuvers can lead to unexpected effects on the car’s behavior – if, for example, the car tilts forward, the flywheel’s angular momentum must tilt with it, requiring a torque that is produced when the car’s center of gravity shifts to one side, adversely affecting its stability (see Example 37.4). Although the torque required to change the flywheel angular momentum is generally small compared to the torque generated by shifting a substantial part of the weight of the car from the wheels on one side to the other, this effect can be large enough to influence the car’s handling and safety. This effect has been dealt with in some existing designs by including two counter-rotating flywheels and ensuring that their angular velocities are equal in magnitude and opposite in direction, thereby canceling all gyroscopic effects.
Example 37.4 Flywheels in Automobiles and Gyroscopic Effects
Prototype automobiles have been constructed that use flywheels for temporary energy storage. In 1997, for example, Rosen Motors successfully road tested a gas turbine powered car that used a 55 000 rpm flywheel for regenerative energy storage and to supplement acceleration. The car, however, was never brought to market.
Gyroscopic effects can affect the handling of a car with flywheel energy storage. Consider a typical passengercar with mass 1800 kg, height 1.4 m, and width 1.6 m. Suppose that this car is traveling at 100 km/h and that its (single) flywheel – a solid disk of mass 5 kg and radius 0.25 m – is spinning at its maximum angular velocity s−1. The flywheel has angular momentum kg m2/s and energy 2.64 MJ. (For this and other calculations in this box, see Problem 37.18.) The energy stored in the flywheel is several times the vehicle’s kinetic energy, and would be enough to keep the car running at 100 km/h for about 4 minutes.
A torque must act on the automobile if it turns in any way that causes the flywheel angular momentum to change. To avoid changing the flywheel angular momentum every time the car turns left or right in the horizontal plane, the flywheel axis can be aligned vertically. If the car tilts forward to descend a hill, however, the direction of the flywheel’s angular momentum is forced to change. The initial torque from the gravitational force as the front wheels enter the hill is along an axis pointing out the left-hand side of the car. In response to this torque, the angular momentum axis of the flywheel shifts in the direction of the torque axis through eq. (2.43), giving the car a tendency to roll onto its left side (looking along the direction of motion) as it tips down the hill. This effect, in which a rapidly rotating object responds counterintuitively to a torque by rotating to align the axis of rotation towards the torque axis, is known as gyroscopic behavior, and can also be seen, for example, when a rapidly rotating bicycle wheel is tilted and appears to rotate around an axis perpendicular to the torque axis.
Suppose, for example, that the car tilts forward by 10° over a distance of 10 meters to descend a hill. For the car to tilt with the hill, the angular momentum must acquire a component kg m2/s in a time of order 0.36 s, requiring a further torque Nm along the car’s direction of motion, in addition to the original torque mentioned above produced from the difference in pressure between the front and back wheels as the car enters the hill. As shown in the figure, the required torque to shift the flywheel angular momentum vector forward is provided by the weight of the car shifting onto its left side. A simple estimate indicates that a roughly 6% increase/decrease in the weight on the left/right side of the car (looking along the direction of motion) would supply the necessary torque. This is a significant effect, comparable to the imbalance caused by a sidewind blowing at a speed of tens of kilometers per hour, and increasing the likelihood of the car’s rolling during a turn if it is simultaneously increasing or decreasing its forward angle of inclination.
The gyroscopic problem can be solved in various ways, either by including counterrotating flywheels or using gimbals, to decouple the direction of the angular momentum from the direction of motion of the car. Such systems, however, increase the complexity and cost of flywheel energy storage. Failure of these systems could subject the vehicle to strong torques. The gyroscopic problem, potential problems with catastrophic flywheel destruction in automobile accidents, and the inertia of the auto industry, have kept flywheels from playing a major role so far in commercial hybrid automobile technologies.
37.4.2 Capacitors
Storing electromagnetic energy effectively is particularly challenging. The simplest direct approach to storing electromagnetic energy is to store it as electrostatic potential energy; most other approaches to electromagnetic energy storage involve conversion to chemical or mechanical form. In §3.1.3 we reviewed the basic physics of energy storage in capacitors. While capacitors cannot store a lot of energy, they can release their stored energy very quickly. In addition, they are relatively light, very durable, do not need to contain exotic or toxic components, and do not heat up during use. Disadvantages of capacitors as energy storage devices, beyond their relatively low energy storage capacity, are that they are intrinsically low-voltage devices, that their voltage drops linearly as they discharge (remember ), and that the stored charge leaks away over relatively short time scales (on the order of hours or days for typical standard capacitors).
Traditional Capacitors Traditional capacitors are based on the plate–dielectric–plate design described in §3.1.3. Energy in a capacitor can be thought of as being stored in the electric field as expressed in eq. (3.20)
(37.21)
While the volumetric energy density of a capacitor that uses air as a dielectric is limited to roughly 40 J/m3, this can be increased significantly by using more sophisticated materials as the dielectric. The storage capacity of a capacitor is increased both by increasing the dielectric constant , since C is proportional to κ, and by using a dielectric material with a higher breakdown voltage than air, since the maximum possible V is proportional to the breakdown voltage. Even with optimal materials, however, the energy density of conventional capacitors is on the order of 400 J/kg, smaller than that of available batteries by a factor of 1000.
While the energy density of capacitors is generally low, the power density can be very high. The internal resistance of a capacitor can be quite small. This allows a large fraction of the charge stored in the capacitor to be released very quickly. For most batteries, on the other hand, the internal resistance is relatively high due to the kinetics of the electrochemical reactions involved. Power densities of electrochemical batteries generally range from ~1 W/kg (rechargeable AA batteries) to ~500 W/kg (peak power of some lead-acid batteries powering automobile starter motors), while conventional capacitors can have power densities of ~5–10 kW/kg or higher. Capacitors are also very robust and reliable due to their simple construction. Thus, capacitors are used in many situations where short high-power energy release is needed. Typical applications include boosters for starter motors and powering electronic devices during short downtimes while batteries are changed.
Super- and Ultracapacitors In recent years, more sophisticated materials and technologies have been used to create supercapacitors and ultracapacitors. These devices combine aspects of electrostatic and electrochemical storage to achieve both relatively high energy density and high power density.
Unlike conventional capacitors, which generally use a solid dielectric, ultracapacitors store electrostatic energy at an interface region between a conducting electrode and an electrolyte. The charge separation distances involved are on the order of 1 nm or less, which enables the capacitance to be quite large. This mechanism is known as double-layer capacitance.
Supercapacitors can also employ electrochemical storage mechanisms involving the electrodes, known as pseudocapacitance. This substantially enhances capacitance without generating excess resistance that would compromise power density.
Different super- and ultracapacitor designs combine these electrostatic and electrochemical mechanisms in different ways to achieve capacitors that can have power densities comparable to conventional capacitors but much higher energy densities (see Figure 37.1). While the terms supercapacitor and ultracapacitor are often used interchangeably, the term ultracapacitor can be used specifically for capacitors where the double-layer electrostatic energy is dominant and supercapacitor can be used to describe capacitors dominated by pseudocapacitance. For supercapacitors with large pseudocapacitance, the voltage–charge relation deviates from the simple linear form of a capacitor and begins to look more like that of a battery. The specifications of an example ultracapacitor are described in Example 37.5. While ultra- and supercapacitors have energy/mass densities that are much higher than conventional capacitors, they are still below batteries by roughly one order of magnitude, so supercapacitors will not be used as primary power sources for laptops or automobiles in the immediate future. In particular, the constraints on electrostatic energy density per unit volume from breakdown field and electrochemical energy density per unit mass from fundamental chemical constraints suggest that supercapacitors will never surpass electrochemical batteries in energy density.
Example 37.5An Ultracapacitor
Recent advances in the understanding of materials at the nanometer scale have made possible the construction of ultracapacitors that have very large capacitance while maintaining small size and weight. Ultracapacitors and supercapacitors combine electrostatic and electrochemical energy storage mechanisms to combine the high powerdensity typical for capacitors with relatively high energy density per unit mass.
A Maxwell Technologies BCAP0310 ultracapacitor, for example, is roughly the same size as an ordinary D-cell battery, has a capacitance of 310 F, and works with voltages up to 2.85 V [295]. This ultracapacitor has a cylindrical shape, roughly mm high and mm in diameter. The internal resistance of the BCAP0310 is mΩ.
