Texas Space Grant Consortium

Space Solar Power

Ground-Based Energy Storage

Texas Tech University

12/10/97

EE 4334 / ME 4370

Jerry Dinkins

Kerry Lee

Sam Mahserjian

Bryon Pinkoski

Instructor: Dr. D.L.Vines

Advisors: Dr. M. Parten

J. Jones

Abstract

The purpose of this project was to design a system to store energy transmitted via microwave from a space solar satellite system. The RF energy will be received by a large, ground-based rectenna. This rectenna system converts the microwave energy being sent by the satellite system into electricity. The storage system should be able to collect energy for one hour every six hours (tentatively), and disperse it onto the utility grid as needed.

This project involved the evaluation of nine different energy storage systems according to a set of criteria determined by the Texas Space Grant Consortium. Of the nine systems, three systems met the established criteria: Ultra-capacitors, Flywheels, and Superconducting Magnetic Energy Storage. In the continuation of this project, the selected systems will be modeled to demonstrate their effectiveness as an energy storage system.

Introduction

Currently, energy sources in the electric utility industry are oil, coal, natural gas, nuclear, and hydroelectric. These sources are either at their peak production, environmentally unsafe, or are available only for a finite amount of time. A new source of energy for the future has to be environmentally safe, non-depletable, and cost competitive with current sources.

Interest in alternative fuels greatly increased during the oil crisis in the early '70s. During that time, the federal government formed the Department of Energy (DOE) in order to respond to the increasing demand for reliable energy. The purpose of the DOE was to seek viable alternative energy sources. Some of the energy solutions proposed include hydroelectric plants, nuclear power, and solar power satellites. The DOE has suggested that an immediate solution to the energy crises is conservation. Conservation was easily accomplished due to the increasing price of oil, which in turn directly affected the public.

Clearly, conservation was not the final answer; it was just a temporary fix to an ever-increasing problem. Nearly every river in the United States is used by the hydroelectric industry, which is why it is at its peak production. Yet the need for energy is continuing to rise, thus another solution is needed. Nuclear power is efficient, but its by-products are neither environmentally friendly nor popular with the public. Billions of dollars have been spent on the study of fusion energy, with no foreseeable breakthroughs in the near future. A 1979 study of solar power satellites suggested that they were feasible and could be paid for by selling the energy at the current rates. Unfortunately, this energy source lost its funding during the early '80s. Recently, NASA performed a 'fresh look' study on the solar space power (SSP) system concept. This study shows that SSP's were more cost effective and feasible now than in the late '70s due to the decreased cost of producing more efficient photovoltaic cells. Various facilities that are necessary for production of the SSP system are already in use for industrial purposes.

Currently, there are several entities working on the SSP system concept. One of these is the Texas Space Grant Consortium (TSGC), which is an organization that funds the preliminary design of projects that NASA is considering. The TSGC works with universities in Texas to accomplish its goals. Several different universities are accomplishing the TSGC SSP effort; each is assigned to perform preliminary design and analysis of a major system element. Texas Tech University was assigned to work on the energy storage aspect of the complete SSP system.

The Texas Tech group is to design an energy storage system that periodically receives power and constantly distributes power on the electric utility grid.

Objective

The objective of this project was to investigate and identify all practical approaches for storing large quantities of energy, and then choose the best solution(s) based on a set criterion.

Assumptions*
  1. The rectenna will be providing 400MW of DC current to the storage unit one hour out of every six hours.
  2. Charging and discharging will need to occur simultaneously.
  3. All energy storage devices will be scaled for evaluation based on 1MW output.

* These assumptions were necessary due to the dynamic nature of the requirements given by TSGC. That is, the requirements have changed several times over the course of this project.

Solution Criteria

The selected solution(s) should have the following characteristics in order to be practical to build.

Possible Solutions Considered
  1. Electrolysis/fuel cell array
  2. Ultra-capacitors
  3. Flywheels
  4. Hydroelectric Energy Storage
  5. Thermal Energy Storage
  6. Batteries
  7. Compressed Air Energy Storage
  8. Superconducting Magnetic Energy Storage (SMES)
  9. Magnetic Levitation (Maglev)

Storage Device Evaluation
  1. Electrolysis/fuel cell arrays

The electrolysis/fuel cell possibility has several good attributes. This energy storage system is comprised of two main sub-systems, an electrolysis device and a fuel cell array. Electrolysis is a process by which electrical energy is used to obtain hydrogen and oxygen from water. The oxygen could be sold or discarded due to the fact that it's highly flammable. On the other hand, the hydrogen would be stored for later use with the fuel cell array. The fuel cell process is the exact opposite of the electrolysis process; it produces water and electricity from hydrogen and oxygen. A block diagram of this system is shown below.

Figure 1: Electrolysis/Fuel Cell-Block Diagram

The electrolysis/fuel cell system would have a long life span due to the fact that it doesn't have many moving parts. This solution would also be environmentally safe; it only produces water, electricity, hydrogen, and oxygen. Some disadvantages of this system are that hydrogen and oxygen (in their pure form) are highly flammable and that the electrochemical materials involved are expensive.

2. Ultra-capacitors

Ultra-capacitors store electrical energy by accumulating and separating unlike charges. To discharge an ultra-capacitor, a load is applied between the two terminals so that a charge can flow through it. These devices, are steady state, have no moving parts, and have a very long life. They also have the potential for a high energy density (~4-20kWh/m3). A typical ultra-capacitor system is shown below.

Figure 2: Typical Ultra-Capacitor System

To charge the ultra-capacitors, the switch on the left would be closed and the switch on the right would be open. Reversing this process would discharge the capacitors. The capacitors would discharge according to the demand of the load.

The ultra-capacitor system has the potential to be the best system using size considerations. Ultra-capacitors are currently available with energy densities of 4,000 Wh/m3. Theoretically, these capacitors can have energy densities of around 20,000 Wh/m3 using advanced materials. Such a system for the 400MW requirement would only require a volume of 20,000m3, or ~(27x27x27) m. Also, this system would have an incredible lifetime (>100,000 cycles), or >68 years. Unfortunately, the ultra-capacitor concept is relatively new and expensive. Further research and development must be performed in order to perfect viable manufacturing processes for the advanced materials involved (dielectrics & aerogels).

3. Flywheels

A flywheel consists of a ring spinning on magnetic bearings in a vacuum. The housing enclosing the flywheel must have a strength great enough to withstand a failure, should one occur.

The factor that limits the energy storage capability of a flywheel, is the tensile strength of the material and it's density. A high tensile strength and low density material increases the energy storage capabilities. Currently, the material being used to make flywheels is Kevlar. The main reason kevlar is being used is because when it fails it turns into fiber dust instead of shrapnel.

Kevlar has a current maximum tensile strength of about 4.8 GPa and a density of about 1800 kg / m^3. A flywheel cannot be spun up to its maximum rotational speed, the speed at which the centripetal forces exceed the maximum tensile strength causing failure. The recommended maximum speed a flywheel should be rotated at is 70% of maximum rotational speed. This means it will only store about 50% of the maximum energy possible, since energy storage varies as the square of the rotational speed. Using the previously discussed properties of kevlar and the lower rotational speed yields an energy storage potential of about 181 Wh/kg.

Flywheels are efficient energy storage devices due to the lack of touching parts and the vacuum in which the flywheel is spinning. The lifetime of flywheels is estimated to be about 40 years. Flywheels also have high energy densities, which means that less material is required to build an energy storage facility, as opposed to a low energy density option.

A big disadvantage of using flywheels is the fact that they constitute a new technology that has not been widely implemented. The current prototypes are sized on the order of 10 kWh, which means tens of thousands would be needed for this large-scale energy storage system. With such a large array of devices, large maintenance costs may be a problem.

The current price for building flywheels is estimated at $500/kWh with projected future costs as low as $100/kWh.

The flywheel is a viable solution because it meets all of the selection criteria. This solution will be further analyzed, and an attempt will be made to model it on a small scale to prove its feasibility.

  1. Hydroelectric Energy Storage:

The hydroelectric energy storage system consists of a large water reservoir, electric motors, pumps, a dam, turbines, and generators. The electric motors use the energy supplied from the rectenna to turn the pumps. The pumps will be located in a lower reservoir and will pump water to a higher reservoir. As energy is needed, the water from the high reservoir will be released to flow through turbines creating the momentum needed to turn the generators and produce AC. The figure below shows the cycle with just one pump and one turbine.

Figure 3: Hydroelectric Energy Storage Block Diagram

The hydroelectric energy storage has an overall efficiency of about 73% based on typical component efficiencies and pipe losses. The amount of energy the elevated water can store is dependent upon the height to which the water is pumped. The graph below shows the amount of water needed at a given height to produce 1MW for 6 hours.

Figure 4: Hydroelectric Size Requirements

From the graph it can be seen that nearly 20,000,000 gallons of water are required at a height of 30m. Clearly, this is a disadvantage. Hydroelectric power will require a large amount of land area, and will alter the local environment due to the need to impound a large volume of water.

One big advantage of hydroelectric energy storage is that extracting the power is current technology and has been used for the past 60 - 70 years. The current cost for building a hydroelectric energy storage system is $2500 - $3000 per kW that is produced.

5. Thermal Energy Storage

Thermal storage, in this sense, directly heats the water by concentrating microwaves that are supplied from the satellite, and storing the resulting hot water for later use. The diagram below depicts this system.

Figure 5: Thermal Energy Storage Block Diagram

As this system was defined, it was found that a reconfiguration of the rectenna would be necessary. This thermal storage will not be useful due to the current rectenna specifications, as the conversion losses from electrical to thermal and back again to electrical are too great for this option to be viable.

6. Batteries

The battery energy storage system (BESS) constitutes a pure form of storage technology, which stores electricity as electrochemical potential energy. A typical BESS plant provides round trip efficiencies ranging from 74 to 76 percent and allows for extremely fast discharge times, on the order of five milliseconds. The battery energy storage system is environmentally attractive because the emissions are virtually zero, and recycling of old cell material can be done at current battery recycling stations.

One potential problem with the BESS is its relatively short lifetime. The flooded lead-acid battery has been replaced with a new technology giving a longer lifetime. These new lead-acid batteries are Valve Regulated Lead Acid batteries, such as the Horizon Battery Model No. H12N95. The VRLA battery has a lifetime of 900 cycles, the cycle life being a measure of how many cycles the battery will complete before it needs to be replaced, at 100% depth of depletion (DOD). For this application, using four full cycles per day, 1460 cycles per year would be required. Although the batteries would not be cycled to 100% DOD, the lifetime for this application would still reach a maximum of only one year. Replacing these batteries every year, at a cost of approximately $1.6 million, is not considered economical. Thusly, this large continuous cost is the primary reason for eliminating the BESS as a viable alternative.

One other possible problem with the BESS is the time it takes to charge the battery. For this application, we have assumed, one hour is allowed to store the energy. With current battery technology, the time it takes to charge a battery to 100% is about three hours. These batteries can achieve a 90% charge in approximately 30 minutes. In the near future, charging times could be decreased with some of the newer battery technologies currently being developed. Some of the new battery materials include nickel cadmium, nickel metal hydride, and lead acid. The lifetime of these new batteries should be more than doubled and the cost halved.

Further, the Horizon Battery Model No. H12N95 and its statistics, used in the previous calculations have a nominal energy of 1.14 kWhr. The cost of each battery is three hundred dollars. This gives a total cost of the battery array to be 1.6 million dollars. Even if the cycle life of lead acid batteries were doubled in the near future, these reoccurring costs would still make battery energy storage a non-competitive energy source.

7. Compressed Air Energy Storage

Compressed Air Energy Storage (CAES) plants are gas turbine plants with a compressor and a separate turbine, as shown in the figure below. Each turbine is linked to a motor/generator through a clutch. With a CAES system, the energy received from the rectenna is used to run the compressor. The compressed air is then stored in a tank that, if available, could be a huge underground cavern.

When energy is needed, air from the tank is released, expanded, and sent through the turbine. The shaft of the turbine then turns a generator and the energy produced is transferred to the utility grid.

One problem with CAES is the inability to respond quickly. The response time is on the order of several minutes. This poor response time can be overcome by combining more than one energy storage system, which can enhance the overall system efficiency and provide more flexibility. Another problem is that for CAES to be cost effective there needs to be an underground cavern available for storage of the air. This indeed is a problem since the storage system needs to be location independent. Also the use of an underground cavern, if available, would disrupt the ecosystem. Any wildlife that found shelter in the cavern would be forced out.

This technology is well established and developed. Several major equipment suppliers provide turbomachinery for CAES units. Westinghouse and GE are two of many manufacturers of gas turbines. These companies manufacture turbines ranging from 1MW to 235MW and ranging in price from .8 million to 47 million.

Figure 6: Compressed Air Energy Storage Block Diagram

8. Superconducting Magnetic Energy Storage (SMES)

The Superconducting Magnetic Energy Storage (SMES) is a way to store electrical energy by circulating a current in a superconducting coil, or inductor. As an ideal inductor no conversion of energy to other energy forms is involved (e.g., mechanical or chemical) and overall efficiency can potentially be very high. Furthermore, as the superconducting coil has no resistance, response to both recharging and discharging is limited only by the switching time of the solid-state components doing the DC/AC conversion.

As an energy storage device, SMES is a relatively simple concept. It stores electric energy in the magnetic field generated by DC current flowing through a coiled wire. If the coil were wound using a conventional wire such as copper, the magnetic energy would be dissipated as heat due to the wire's resistance to the flow of current. When cooled to very low temperatures, the superconducting wire conducts electric current with little or no energy loss enabling it to transmit far more electricity than conventional copper wire of the same size. The energy can be stored in a "persistent" mode, virtually indefinitely, until required.

SMES coils vary in size depending on the energy they are required to store. The superconductor of choice for this application is a niobium-titanium alloy, which needs to be maintained at liquid helium temperatures in order to sustain superconducting properties. High temperature superconductors (HTS), those that operate at liquid nitrogen temperature or above, allow reduced capital and operating costs, but at this time liquid helium temperatures are still needed to prevent quenching of the HTS.

Quenching is the heating of the superconducting material above the temperature of zero resistance. This can either occur to the coil as a whole or in a small point in the coils' material. This can be a planned heating up process for maintenance reasons. Quenching, as an unplanned event, generally affects a small area, at which point all of the charge goes to this small area. The quenched point acts much like a short circuit with much the same result.

The SMES coil, a DC inductor, accumulates direct current from the rectenna and discharges DC through an AC power conditioning system to the utility grid. The power conditioning system (PCS) is required due the necessity of DC-to-AC conversion for the SMES/grid interface. The PCS used would include a standard solid-state DC/AC converter and required control circuitry. In addition to the superconducting coil and the PCS, the only other major elements comprising a SMES plant are the cryogenic refrigerator and systems (including cryostat). A standard switchyard would then connect the SMES/PCS to the utility grid.

9. Magnetic Levitation (Maglev.) The Magnetic Levitation/Cyclotron is a blending of two separate energy storage concepts. The first is that of the flywheel, where a disk or cylinder is accelerated on magnetic bearings. The main problem with this concept is that the outer rim incurs stresses that limit energy storage due to the cohesion properties of the material(just as described with the flywheel). The second concept is that of using magnetic propulsion as way of increasing a particle's kinetic energy. Currently only cyclotrons accelerating atomic size particles have been used. Thus, significant changes would have to be made for this to be used for energy storage on a large scale. Combining these two concepts into something akin to a Maglev car would be a new energy storage concept. The facility would contain a circular track and several "cars" which would be accelerated/decelerated about the track. The track would be placed underground so as to reduce air resistance. The track would consist of a Linear Synchronous Motor propulsion system. Large magnetic fields would be used to draw out the kinetic energy as electrical (Figs. 7 & 8).

Figure 7: Typical Maglev CarFigure 8: Typical Maglev Car Interface
The car itself would consist of propulsion magnets and levitation magnets, both superconducting, as well as a cooling apparatus and an emergency braking system. The rest of the car would be a simple mass used for accelerating as part of the kinetic energy storage. Some of the advantages to this system would be that most of the subsystems have already been used and need only to be integrated into this system. Secondly the acceleration/deceleration methods are both solid state which have no moving parts and therefore have long lifetimes with little wear. There are also some disadvantages to this system. One is the large initial investment, which is considerable due to the required underground structure as well as the superconducting components and large volume of vacuum. The other disadvantage is the damage caused if failure were to occur, as there will be many cars cycling around the same loop. If one car were to fail, even dynamic controls would fail to stop the remaining high velocity cars in time to prevent further collisions and almost total destruction of a large portion of track would be likely.

Results

Grading Chart

The chart below a grading system that evaluates each system on how close it was to meeting the set criterion.



Fuel Cell Consumption (ideal)

n = # of equivalents (For H2, n = 2)

F = Faraday = 96,493 Coulombs/equivalent

Vr = Thermodynamic Reversible Voltage = 1.229v

Thus, the maximum work of this system is:

For a 1 megawatt-hour system, the amount of fuel (Hydrogen + Oxygen) needed is:

To convert this to volume, I need the ideal gas law:

Supposing we use tanks that store 1 liter at 3,000 psi (207 atm):

For a 6-hour period of energy production, fuel consumption would be:

Electrolysis Device Requirements (ideal)

The chemical equation for the electrolysis of water is:

From the fuel cell consumption section (previous) we know that 15,151.515 moles of Hydrogen are needed per hour of energy production. Thus for the 6 hour period, 90,909.09 moles of Hydrogen are required.

According to the chemical equation for the electrolysis of water (above), 2 moles of H2 need 2 moles of e-, or 1 mole H needs ½ mole of e-. Thus,

Now, the Faraday equation can be used to determine the amount of charge required. One Faraday is the charge carried by one mole of e-, which equals 96,485.309 C. Thus,

The current (I) needed to produce 6 MW of power is:

I expect high losses (low efficiency) in the electrolysis part of the energy storage system because of the huge amount of current required to produce enough Hydrogen. The energy lost will be in the form of heat.

Present Fuel Cell/Electrolysis Systems

Currently, there are no large-scale fuel cell/electrolysis systems developed for stationary power. However, several companies including Hamilton-Standard and Ballard are producing large-scale fuel cell systems (usually methane based). One such unit is the Hamilton-Standard PC 25, which is rated at 200 kW. The PC 25 statistics are:

The PC 25 is designed for indoor or outdoor use and converts natural gas fuel to alternating-current power.

Hamilton-Standard has a subsidiary, Praxair, which produces trailer-sized electrolysis units. These systems deliver Hydrogen with purity up to 99.999 percent and are sized to produce from 6,000 to 30,000 cubic feet per hour.

If these systems were to be used to produce 1MW an hour for 6 hours, 5 PC 25's would be needed.

This system would also produce a large amount of heated water, specifically:

Hydrogen consumption would be relative to natural gas (CH4) consumption.

In order to meet the requirement of 57,000 ft3 for the fuel cells, at least 2 of the maximum-size electrolysis units (30,000 ft3 per hour) would be needed (or any number of smaller units that could meet the required volume of Hydrogen).

The third significant part of this system would be the compressors that put the Hydrogen in a high-pressure (3,000-psi) state. For a 1MW system with a storage cycle of 6 hours, the compressors would have to be able to compress 57,000 ft3 of gas in 1 hour at 3,000-psi. I believe that this will lower the overall efficiency of the system due to the large numbers involved, and the mechanical nature of compressors. That is, mechanical systems of this size are subject to friction and/or physical wear. The lifetime of the compressors would be far less than that of the fuel cells and electrolysis. They would need regular maintenance and eventual replacement.

Ultra-Capacitor Systems

The capacitance of a standard parallel-plate capacitor can be defined as:

where A is the area of the electrode, d is the plate separation, e0 is the permittivity of free space, and er is the relative permittivity, or dielectric constant, of the dielectric between the plates. A parallel-plate capacitor is represented in the picture below.

The energy stored in a capacitor is:

where V is the potential across the plates. For ultra-capacitors, high energies can be attained through high capacitance. High capacitance is what designates a capacitor as an ultra-capacitor. Usually the high capacitance is achieved with large electrodes (high area). The direct relationship between energy and area (A) is:

For a spacing of d, we can store a maximum potential:

Thus:

Assuming a 28 mm film of polyvinylidene fluoride (PVDF) laminated-polymer dielectric (common for ultra-capacitors), where:

Using these values, the volumetric energy density of a parallel-plate capacitor can be calculated, ignoring the volume of the electrodes for now. That is:

For a PVDF capacitor:

For storage of 6 MW, the volume of the capacitors would be:

or, approximately a 15 m cube.

Present Ultra-Capacitor Systems

Currently, I only found one company (PolyStor) that manufactures ultra-capacitors. PolyStor produces Aerogel capacitors (aero-capacitors), which are a type of ultra-capacitors. Aero-capacitors were developed at the Lawrence Livermore National Laboratory. The aero-capacitor uses thin-film carbon aerogel paper as both the positive and negative electrodes. The carbon aerogel electrodes have high surface area and uniform pore-size, which allow increased energy storage in a small size.

PolyStor has developed an AA size (14-mm diameter by 50-mm height) aero-capacitor, the A-14500. The company is currently sampling these and plans to take them into production by the end of 1997. The samples cost $25. Listed below are the specifications for the PolyStor A-14500.

The energy stored in one PolyStor A-14500 is:


Flywheel SystemThe energy stored in a flywheel can be expressed as
  1. where I is the moment of inertia, which is dependent upon the shape, and is the angular speed at which the flywheel is rotating. The further the mass is from the rotating axis the larger I becomes and, thus the larger the energy storage. To save material expenses the best shape to choose is a ring because this will minimize the amount of mass required by keeping all the mass at a large distance from the rotating axis (see figure below).The moment of inertia (I) for a rotating ring is given by
  2. where m is the mass, is the outer radius, and is the inner radius, as shown above. Since the mass contributes more to I when it is further away from the axis of rotation, it would be wise to make this ring as thin as possible, or where goes to , and a conservative approximation of (2) can be written as
  3. We also know that the mass is simply the density of the material multiplied by the volume. This is represented below with the volume of the ring.
  4. Where t is the thickness of the ring as shown in the above figure, and is the density of the material. Now plugging the results of (3) and (4) into (1) we arrive at
  5. This is a good equation to use in order to find the energy of a flywheel that is being tested, but in designing a flywheel a different approach should be taken. In the above equation we can continue increasing the rotational speed to our hearts content, however the material will only be able to withstand a finite amount of centrifugal force before it is ripped apart. The maximum stress of a material can be equated proportionally to the rotational speed with the following equation (Seely and Ensign 1952)
  6. Where is the tensile strength of the flywheel material. The tensile strengths of most materials are known and can be found in material property books. If the tensile strength is known then (6) can be solved for, which is the maximum speed at which a flywheel can be spun without failure.
  7. Now equation (6) can be plugged into (1) while substituting for I with equation (3) and we find
  8. It is important to note that the flywheel will not be spun up to its maximum speed since failure is likely to occur. Through experiments a recommendation for rotating speed is to not exceed more than 70% of maximum. It can be seen from equation (6) that the maximum energy storage is dependent upon the square of the rotational speed. Therefore, the actual energy storage will only be about 50% of the maximum.
  9. Using this equation to find the energy density for a kevlar flywheel disk with and a density of 1800 we arrive at (10)

Hydroelectric System The energy that water can store is based on it's physical properties and the height at which it is stored. The basic equation is the equation for potential energy.(1) The weight of water mg can be expressed as(2) Where is the specific density of water and V is the volume. Now plugging (2) into (1) we get

  1. For water is 9790 . The total energy that we will be storing at one time is 6MWh, which corresponds to 21,600MJ. Using this figure for E in equation (3) and also the specific density of water, and solving for V we arrive at
  2. This is the equation that was used to plot the graph in the above section on hydroelectric energy storage. From this equation it can be seen that the higher the water is stored the smaller the required volume becomes. A consequence of pumping the water higher is the expense of more pumps, yet if the available land area is small this is the only alternative for this system. Since this system requires large quantities of water and a significant amount of land it does not meet the criteria of location independence, and therefore is not a chosen solution.Actual Hydroelectric Systems Actual hydroelectric systems are generally not an energy storage device, such as discussed above. They usually involve the damming of a river and then extruding the energy already in the motion of the water due to the downward slope. Systems such as these have much the same components as the previous system discussed, except they do not require the pumps to pump the water back to the higher reservoir. Mother Nature provides that system in the form of precipitation at higher elevations. Hydroelectric power has been around for thousands of years. One of the first applications of waterpower was the water wheel. Systems, like those of todays, have been around for over 60 years. The largest and most famous is Hoover Dam which produces over 2000MW of power. The energy storage hydroelectric system will use the pumps in order to consume the tremendous amount of energy, 400MW, being provided from the rectenna. To consume this much power very large pumps are required. The largest pump found is made by Peerless Pump, which is able to consume 3730kW, while pumping 41,150 to a height of 30m, operating at optimum speed. To use the entire 400MW, 108 pumps would be required. As for our standard 1MW plant only two pumps would be needed. The projected cost to build an actual energy storage hydroelectric plant is $2500 to $3000 / produced kW (John J. Brooks). For a 1MW output the cost would be $2.5-3 Million. A plant such as this can be expected to have an efficiency of 73% (John J. Brooks).Compressed Air Energy Storage

With compressed air energy storage, gas is released and spins a turbine in order to produce electricity. For simplicity of calculation, assume that the expansion is adiabatic and the gas ideal. The equation for adiabatic expansion is:

Where (Gamma) is 1.4 for air. Also recall that the work done by an expanding gas is :

This is an integral over volume, but the volume of the tank is fixed. The gas is, however, escaping into the environment, where it will finally take up some volume. Since Equation 1 must be true before and after the expansion to atmospheric pressure, the final volume at 1 atm must be:

Since p changes as the gas is released, an equation is needed for it in Equation 2. Again using Equation 1:

Plugging this into Equation 2 and integrating from Vtank to Vatm (as calculated in Equation 3) gives a total available work of:

At a given pressure, volume, and temperature, the ideal gas law will give the mass of the gas:

where M is the molar weight of the gas in kg, m is the gas total mass. The maximum energy (work) available for a tank with rupture pressure Pr is then:

with units of Joules if Pmax is in N/m2 and Vt is in m3.BESS

Actual Compressed Air Energy Storage

McIntosh Plant

The first and only U.S. CAES unit is a 110 MW, 26-hour unit built in 1991 by Alabama Electric Cooperative Inc (AEC). The plant is located at McIntosh, Ala., and is now owned and operated by AEC. The plant is located above a nine million cubic ft cavern, which is used to store the compressed air. During the summer the plant is used to generate power about 10 hours each weekday. AEC partially recharges the storage cavern each night and fully recharges it each weekend. During other seasons, the plant generates power two or three days a week. Typically, the plant operates in the generating mode about 1700 hours per year. AEC can start the McIntosh plant in about half the time it takes to start up a normal combustion turbine and can load follow at a rate up to 33 percent of nameplate capacity per minute.

Present Applicable Battery Characteristics

Horizon Battery Model No. H12N95 -characteristics-

Voltage: 12 V

Nominal Capacity: 95 Ahr

Total Energy Stored per Battery

(12V)(95Ahr) = 1.14 kWhr

Conclusion
Of the energy storage alternatives evaluated several meet the specified criterion qualifications and others failed. For the systems that remain viable (i.e. the SMES, the ultra-capacitors, and the flywheel) further analysis and the integration of the design into the total system will be considered which will hopefully lead to a single solution.
COMPARISON CHARTS
SMES
Maglev
Cost analysis
-initial
.6-2.4million
54.5million
Efficiency
~95%
~90%
Lifetime
>50 years
>35 years
Environmental Hazards
Large Magnetic Fields
n/a
Safety
Liquid Helium
High Velocity Object
Response Time
-charge
~10ms
minutes
-discharge
as demanded
minutes
Specific Energy [Wh/kg]
6.48
Total Energy Stored [Wh]
6MWh
6MWh
Feasiblility
New Technology
Smaller units exist
Technology exists
for passenger use
Future
Reduced Cost
Increased speeds
Larger Systems
Improved Controls
References

John J. Brooks, John Brooks Hydraulic Equipment Group USBR,

jbrooks-ibr8f7@ibr8gw80.usbr.gov.