Remote locations or sites where there is no power supply are motivated by a continuous need for energy to make provisions for energy-storage devices such as rechargeable batteries and lamps—for the same reason that we make provision for a flask when out on a cold day. The human need for energy is extensive and continuous, hence energy is an important subject in a technology-driven world. That is why much attention is directed toward energy production. Energy may not always be available when and where needed and at the required quantity, making energy storage an important component of energy studies [1].
10.2 FORMS OF ENERGY
Energy exists either naturally or in a transformed form as heat, sound, light, kinetic, potential, gravitational, thermonuclear, magnetic, electric, chemical, and nuclear. These can all be categorized broadly as electrical energy, mechanical energy, chemical energy, thermal energy, and electrochemical energy. Today, interconversion of energy from one form to another is not only possible but is being improved upon by the day through continuous research and development efforts all around the world.
10.3 ENERGY STORAGE SYSTEMS
Energy storage is any means employed to store energy and ensure energy security in the future. Some energy storage technologies include:
flywheel energy storage system
pumped hydro energy storage system
battery storage systems
supercapacitor or ultracapacitor energy storage system
solar thermal energy storage system
compressed air energy storage system
superconducting magnetic energy storage system
fuel cell energy storage system
The storage systems are discussed as follows:
(a) Flywheel Energy Storage System
A flywheel (Figure 10.1) [4] is a rotating mechanical device used to store rotational energy. Flywheels have a significant moment of inertia, and thus resist changes in rotational speed. The amount of energy stored in a flywheel is proportional to the square of its rotational speed. Energy is transferred to a flywheel by applying torque to it, thereby increasing its rotational speed and hence its stored energy. Conversely, flywheels release stored energy by applying torque to a mechanical load, thereby decreasing their rotational speed.
where Ek is the kinetic energy, ω is the angular velocity, and I is the moment of inertia of the mass.
The moment of inertia of a solid cylinder is
(10.2)
where m denotes the mass and r denotes the radius.
The amount of energy that can safely be stored in the rotor depends on the point at which the rotor will warp or shatter. The hoop stress on the rotor is a major consideration in the design of a flywheel energy storage system.
(10.3)
where σt is the tensile stress on the rim of the cylinder, ρ is the density of the cylinder, r is the radius of the cylinder, and ω is the angular velocity of the cylinder.
Applications of Flywheel Energy Storage
A flywheel is capable of providing continuous energy when the main energy source is disconnected. They are also used to store energy over time and then release it at a rate beyond the rate of the main source. Finally, they are used for controlling the orientation of the mechanical system.
To control the orientation of mechanical systems, the angular momentum of a flywheel is transferred to a load when energy is transferred to and from the flywheel.
Advantages of Flywheel Energy Storage
One advantage of flywheel storage is that a flywheel cannot be affected by climate change; it can operate at a wide range of temperatures. Flywheel has indefinite working life span unlike lithium ion polymer batteries which operates for limited period. Flywheels are also less damaging to the environment because they is widely made of inert or benign materials, without a negative effect on the environment.
Disadvantages of Flywheel Energy Storage
One limit to the flywheel system is the tensile of the material used to build the rotor. A stronger disc will make it spin faster and store more energy. When the tensile strength of flywheel is exceeded the flywheel will shatter, releasing all of its stored energy once. Hence, it requires strong containment vessels as a safety precaution which increases total mass of the device.
Additional limitations for some flywheel types are energy storage time and energy loss.
Environmental Implications of Flywheel Energy Storage
Flywheels are potentially very environmentally friendly and efficient. In addition, they can be built with harmless materials and without hazardous chemicals. Energy efficiency is important in an energy system where there is still a deficit of renewable-energy sources. Flywheels are green and do not require cooling or ventilation like conventional battery systems, nor do they pose the same environmental hazards as batteries.
Flywheel Energy Storage Costs
Compared to batteries, flywheels generally have a high initial expense, but lower installation and maintenance costs.
(b) Pumped Hydro Energy Storage System
Hydro pump storage techniques (Figure 10.2 [8]) are mainly used for load balancing in a power system. These systems store energy by pumping water uphill to a reservoir at a higher elevation from a reservoir at the lower elevation.
When the demand for electricity is low, pumped hydro storage facilities store energy by pumping water from a lower reservoir to an upper reservoir. During periods of high electrical demand, the water is released back to the lower reservoir and turns a turbine, generating electricity. This principle is the same as a hydroelectric station. The water is released through the penstock to the blades of a turbine, which is connected to a generator to produce electricity. This type of technique has an overall efficiency of 75 to 85 percent.
Model and Formulas of Pumped Hydro Energy Storage
(10.4)
where Q is the low in cubic meter second , n is the revolution per second , Vstroke is the swept volume in cubic meters [m3], ηvol is the volumetric efficiency.
where P is the power in watts (Nm/s), n is the revs per second, Vstroke is the swept volume in m3, Δp is the pressure difference over pump in N/m2, and ηmechhydr is the mechanical/hydraulic efficiency.
Advantages of Pumped Hydro Energy Storage
Among the advantages of the hydro pump are that it can be used to store energy through pumped storage, the generation of electricity to meet demand can easily be adjusted, fuel is not burned so there is minimal pollution, water to run the power plant is provided free by nature, and with tidal power it can produce energy for up to ten hours a day.
Disadvantages of Pumped Hydro Energy Storage
It is important to mention that the hydro pump has disadvantages, including the large reservoirs required for the operation of hydroelectric power stations, which result in submersion of extensive areas upstream of dams, destroying biologically rich and productive lowland and riverine valley forests, marshlands, and grasslands. The loss of land is often exacerbated by habitat fragmentation of surrounding areas caused by the reservoir.
Size of Pumped Hydro Energy Storage Plants
Data on the five largest operational pumped-storage plants are shown in Table 10.1.
A battery is a device that converts chemical energy into electrical energy. This is done by means of an electrochemical oxidation-reduction reaction of its active materials. This process involves the transfer of electrons from one material to another through an electric circuit. An oxidation-reduction reaction is defined as a reaction in which electrons are transferred. Oxidation means loss of electrons. Reduction is the process of accepting electrons.
The basic electrochemical unit is the “cell.” A battery of any number of cells is used depending on the desired output voltage. In modern usage, a battery may refer to just one cell or a group of cells.
Types of Batteries
There are two types of batteries:
primary batteries
secondary or storage batteries
Primary batteries can provide only one continuous or intermittent discharge. Bringing together individual chemical components and assembling the battery in a charged state forms a primary battery. In the process of discharge these components are irreversibly changed. Electrical energy is obtained from chemical energy. Primary batteries cannot be recharged; they are used as a source of DC power for everyday items such as flashlights and transistor radios.
A secondary or storage battery is made of several chemical and elemental materials. These materials change during charging and discharging and this change is reversible. After the battery has discharged, it is brought back to a charged state by causing the current to flow back through the battery in the opposite direction. The electrodes are thus returned to approximately their original state.
Secondary batteries are used as a source of DC power when the battery is the main source of power and many discharge and charge cycles are required, such as in electrical vehicles, mine locomotives, or submarines, or when standby power is required, such as in telephone exchanges and emergency lighting. They are often used to supply large, time-repetitive power requirements such as car and airplane batteries. They are also used for load leveling of an electric power supply network.
Disposable batteries are intended to be used once and rechargeable batteries can be used multiple time. Batteries come in multiple sizes ranging from the small-size batteries used in wristwatches to large batteries used for power system applications such as backup power for data centers.
Batteries are made up of cells. A cell is composed of a positive pole and a negative pole immersed in a chemical medium where an exchange of charged particles takes place when the two poles are bridged through a load, e.g., a bulb. This exchange of charged particles is referred to as electric current flow. Various kinds of batteries available are shown in Figure 10.3.
Figure 10.3 Different kinds of batteries. (a) Dry cell. (b) Automotive battery. (c) Deep-cycle battery. (d) Bank of deep-cycle batteries.
Batteries in Series and Parallel Construction
Cells or batteries may be connected in a series or in parallel, shown in Figure 10.4. When connected in a series, the potential differences between the poles is the summation of the individual battery potential differences. Thus, if n batteries are connected in a series, the overall potential difference between the terminals is given by
If the potential difference of each of the batteries is equal,
(10.6)
For n batteries of equal potential difference connected in parallel, the overall potential difference is the potential difference across any one of the batteries, that is
(10.7)
Note that it is unconventional to connect batteries of different potential differences together in parallel. If this is done, the battery with the lower potential difference drains down the battery with the higher potential until an equilibrium potential Ve is reached.
Battery Internal Resistance
Secondary cells possess internal resistance, and there is usually some voltage drop across this internal resistance. The practical approach to reducing the battery internal resistance is to increase the size of the cell plates. The limitation to this approach is overall battery weight and cost. Hence an optimal plate size is selected and the plates are connected in parallel, which amounts to connecting resistance in parallel with the overall effect of reduced internal resistance.
Example 1
Five batteries, each with potential difference 5 V and internal resistance 0.8Ω are connected in
series
parallel
with a load resistance of 10Ω. Calculate the current flowing through the load in each case.
Solution:
For a series connection of batteries
with total internal resistance
total resistance in the circuit
and current flowing through the load
For a parallel connection
with current flowing through the load
If the load resistance were connected in series with the parallel connection of batteries, then the overall circuit resistance is
Hence current flowing through the load
Example 2
A battery with terminal voltage 12.5 V and internal resistance 1.2Ω is charged with a 96 V DC source. If a charging current of 3.5A is desired, calculate:
size of the series resistance to be connected
how much energy is expended in charging up the battery if it is charged up in eight hours
charging cost if a unit of electricity is $0.15
Solution:
Net charging voltage = (96−12.5) = 83.5 V
Energy expended for charging
Energy cost
Battery Capacity and Specifications
The capacity of a battery is the product of the current in amperes and the time during which it can supply power until the voltage falls to a particular value Vo, usually specified by the battery manufacturer. Usually, Vo is 1.8 V/cell. Battery capacity is measured in ampere-hours (AH). Batteries are usually specified in terms of capacity and terminal voltage. Thus, a battery rated as 200AH, 12 V can supply 200A continuously for one hour, 100A continuously for two hours, 50A continuously for four hours, and so on.
Battery Efficiency
Battery efficiency is defined as the ratio of the discharge AH to the charging AH:
(10.8)
Battery State of Charge and Depth of Charge
State of charge (SOC) and depth of charge (DOC) are variables that can describe a battery's charge condition. The main difference is that the SOC describes the percentage of remaining charge relative to the nominal capacity, while the DOC represents that relative to the actual capacity under a specific discharge current. These two variables can be obtained by calculating the charge consumed and the battery capacity:
(10.9)
(10.10)
where Qe, C, and CI are charges consumed by load, battery nominal capacity, and actual capacity under discharge current, respectively.
Depth of Discharge
Depth of discharge (DOD) is the percentage of a storage device's useful capacity that has been depleted. For instance, a 90 percent DOD implies that 10 percent of the battery's energy remains.
Self-Discharge Time
Self-discharge is the time required for a fully charged, non-interconnected battery to reach a DOD. The relationship between self-discharge time and DOD is rarely linear so self-discharge times must be measured and compared at a uniform DOD.
Cycle Life
A battery's cycle life is the number of consecutive charge/discharge cycles a storage installation can undergo while maintaining the installation's other specifications within certain limited ranges. Cycle-life specifications are made against a chosen DOD depending on the application of the battery. Cycle life is a measure of how long the battery will last before it needs to be replaced.
Battery-Specific Power
Specific power, in units of power per mass, is perhaps the most important parameter measuring electrical energy storage requirements for hybrid electric vehicles. Because hybrids normally depend on the electrical energy stored onboard to provide the power for accelerations and hill climbs, the higher the power for less mass the better. Hence, high-specific-power batteries are critical to the success of hybrid electric vehicles.
Battery-Specific Costs
Battery-specific costs refers to the cost per unit of energy (kWh) of battery and are related to the economic viability of the battery. Because lead-acid batteries have been around the longest and are the most fully developed battery technology, they have the lowest specific cost at around $125/kWh currently with projections to decrease to $75 with bipolar batteries. Currently, nickel–cadmium and nickel–metal hydride batteries are four to five times more expensive than lead-acid batteries.
Battery Model
In recent years, much of the development of electric energy storage systems have focused on battery storage devices. Presently, a wide range of batteries is commercially available with others in design stages. The most commercially developed type is the lead-acid battery. The first commercially available battery was the flooded lead-acid. However, the valve-regulated lead-acid (VRLA) battery, which is the latest commercially available option, requires low maintenance, is spill and leak proof, and is relatively compact. The development of battery performance models has been under active investigation. Of particular interest here is the kinetic battery model, which consists of three parts:
capacity model
voltage model
lifetime model
The capacity model assumes a first-order chemical rate process; the voltage model is based on the adaptation of the battery energy storage test model in combination with capacity estimates from the capacity part of the model; and the lifetime model initially uses the assumption that the number of cycles a battery can tolerate is a function only of the depth of discharge of the cycles, with each cycle starting with a fully charged battery.
The capacity model is given by:
(10.11)
where qmax, 0 is the maximum capacity (at infinitesimal current), k is the rate constant, and C is the ratio of available charge capacity to total capacity.
The voltage model is given by
(10.12)
where Eo is the fully charged/discharged internal battery voltage (after the initial transient); A is the parameter reflecting the initial linear variation of internal battery voltage with state of charge (A is reckoned as positive during charging and negative during discharging); C is the parameter reflecting the decrease/increase of battery voltage when battery is progressively discharged/charged; D is a parameter reflecting the decrease/increase of battery voltage when the battery is progressively discharged/charged, and is normally approximately equal to the maximum capacity; and X is the normalized maximum capacity at the given current.
The normalized maximum capacity X in charging is defined in terms of the charge in the battery by:
(10.13)
While in discharging it is
(10.14)
The voltage model reflects the observation that terminal voltage depends on:
state of the battery (charging or discharging)
state of charge of the battery
internal resistance of the battery
magnitude of the charging and discharging current
Lifetime Model
The lifetime model uses a double exponential curve fit of data to characterize cycle failures versus cycle depth. The equation used is of the form
(10.15)
where CF is the cycle of failure, a1 is the fitting constant, and R is the range of cycle (fractional depth of discharge normalized using qmax, 0).
Benefits of Battery Storage
Storage batteries have many advantages, depending on the type of batteries. For example, low-internal-resistance batteries (around 0.001ohm) can rapidly deliver high initial currents, which can be used for starting large devices such as car engines. Another benefit is the ability to recharge batteries; it is convenient for users to have energy stored in a battery later use but also be able to recharge the battery multiple times. Rechargeable batteries are also beneficial for the environment—rechargeable batteries will decrease the millions of batteries used and discarded every year and save the environment from the chemical products used in batteries.
Environmental Concerns
One of the main environmental concerns is the toxic metals and hazardous chemicals used in batteries. Many countries are now recycling or using proper disposal to prevent dangerous elements such as lead, mercury, and cadmium from penetrating the environment.
Costs of Battery Storage
The costs of battery storage depend on the types of batteries, as shown in Table 10.2.
Battery storage is used as a complement to renewable-energy sources (such as solar PV) to provide power when renewable energy is not available. For example, in a solar power system maintenance-free batteries store solar energy to be used as needed. Grid power systems are another area of renewable energy where batteries are used to store energy for peak hours, especially at night.
A system configuration for a solar PV battery storage system is shown in Figure 10.5. It includes a maximum power tracker, battery subsystem, power-conditioning system, switchgear, and structural/mechanical system for transmission of power. The PV array consists of fixed PV modules that use large-area, solid-state semiconductor devices to convert ultraviolet rays from the sun into DC power. The power-conditioning subsystem includes an inverter system, which converts DC power to AC power, and a step-up transformer, which raises the AC voltage to system-transmission-level voltage. While transmission of power is taking place, the battery storage system is simultaneously being charged up. At sundown or during periods of heavy cloud cover, when solar insolation is drastically reduced and power supply from the system drops below an acceptable threshold, the battery automatically switches on to supply stored DC power, which goes through the same process of conversion to AC, transformation, and transmission. This way, the battery storage system is able to ensure power reliability.
Figure 10.5 Battery storage application in a solar PV system.
Supercapacitors (also known as ultracapacitors), Figure 10.6, are special types of capacitors that can store at least one hundred times more energy per unit volume than an ordinary electrolytic capacitor. They have an advantage over batteries because of a faster and simpler charging process and faster release of stored energy. Thus, they have found application in situations where a short time burst of energy is required. The secret of their high capacitance and energy storage ability is the large size of their plates and the shorter distance between them.
Advantages of Supercapacitor Energy Storage
Supercapacitors have:
an unlimited life cycle, hence can be charged and discharged continuously an unlimited number of times
a simple, fast, and reliable charging system
no problem with overcharge as encountered in batteries
excellent thermal charge and discharge performance
ability to deliver high power to drive high-current load demands because of low resistance
Supercapacitors are, however, limited by high cost and high self-discharge; hence their full energy spectrum is not always available for utilization.
Applications of Supercapacitor Energy Storage
Supercapacitors have found applications in many areas, including:
Providing needed energy storage for firming up a renewable-energy system's output, thereby providing grid stability. This application is very useful, especially in dealing with load frequency control and bus voltage stability issues in microgrids.
Serving as a good energy back-up system for data centers and other sensitive facilities between outage and startup of an uninterruptible power system.
In lifting operations where sharp burst of power is needed, supercapacitors can prove very useful.
Supercapacitor Energy Storage Model
Electromechanical double-layer capacitors (EDLCs) or supercapacitors are electromechanical capacitors that usually have high energy density compared to common capacitors. For the same size as conventional capacitors, EDLCs have a capacitance of several farads, an improvement of about two to three orders of magnitude in capacitance but usually at a lower working voltage. Consequently, EDLCs have very high densities [2]. A typical model is shown in Figure 10.7.
Figure 10.7 Typical equivalent model of an electromechanical double-layer capacitor.
Rs is the series resistance due to the electronic and ionic conductor equivalent ohmic resistance; Rp is the parallel resistance, which is responsible for electrical losses that generate internal heating; and L is the parasitic inductance due to its geometry.
The capacitance is composed of a constant Co and linear voltage dependent part,
(10.16)
where
kv
is a coefficient that depends on technology. The total capacitance at the voltage U is given by
(10.17)
(10.18)
It can be shown that the stored energy is given by
(10.19)
(e) Solar Thermal Electric Storage System
Thermal energy can be stored as sensible heat, as latent heat, or as the heat of a thermochemical reaction. Sensible heat Q is stored in a material of mass m and specific heat
Cp
by raising the temperature of the storage material and is expressed as
(10.20)
The most common heat-storage materials are water, organic oils, rocks, ceramics, and molten salts. Water has the highest specific heat value of 4,190 J/kg°C.
(f) Compressed Air Energy Storage System
Compressed air systems use electric power to run compressors that push air into a tank at very high pressure, and then use the air under pressure in a piston or turbine to generate power on demand. These systems store compressed air in geologic structures such as aquifers or abandoned salt mines or other mines. Generally, compressed air systems have fixed cost that are too high for DG applications. The smallest practical size of such storage is of the order of 10MW power and 100 MWh energy. Compressed air systems have high power and energy density in comparison with pumped hydro.
(g) Superconducting Magnetic Energy Storage
Superconducting magnetic energy storage (SMES) systems store energy in a superconducting magnetic coil immersed in a very cold liquid such as liquid helium, contained in a highly insulated thermal bottle. Superconducting magnetic coils have zero electrical resistance, so electric current being circulated will not diminish over time. The coils themselves are not very large, approximately two feet in diameter and one foot high. Power is stored in an SMES system by circulating a DC electric current in the coil magnetically. It is withdrawn through reversal of the process. A typical SMES unit stores about 250 kWh of energy in a space the size of a large refrigerator weighing approximately 700 pounds. The capacity of an SMES ranges from 0.3 to 3.0MW. Figure 10.8 [7] shows a superconducting magnetic energy storage system that supplies electricity in case of sudden drops in voltage from lightning strikes and other natural phenomenon.
The advantages of SMES are efficiency, robustness, reliability, and noiselessness in operation. Its power conditioning is of the highest quality.
Disadvantages of SMES
The disadvantages of SMES are cooling requirements and high cost of energy per unit, in the range of $2,500 to $3,800/kWh of storage energy. This is twenty times that of lead-acid batteries. Other disadvantages include sensitivity to temperature and very high magnetic field, on the order of 9Tesla or more, which may be a problem for communication equipment. Table 10.3 shows characteristics of energy storage technologies.
TABLE 10.3Characteristics of Energy Storage Technologies [8]
Characteristic
Pumped Hydropower
CAES
Flywheels
Batteries
SMES
Supercapacitors
Thermal
MJ Energy Range
1.8 × 106 − 36 × 106
18 × 104 − 18 × 106
1–1,800
1,800–180,000
1, 800 − 5.4 × 106
1.10
1–100
Power Range MWe
100–1,000
50–1,000
1.10
Lead acid 60–180;
nickel– metal hydride –370;
Li–ion 400–600
10–100
0.1–10
0.1–10
Cycle Overall Efficiency
64–80%
60–70%
∼ 90%
∼ 75%
∼ 95%
∼ 90%
∼ 80 − 90%
Charge/Discharge Time
Hours
Hours
Minutes
Hours
Minutes to hours
Seconds
Hours
Life Cycle
⩾ 10.000
⩾ 10.000
⩽ 10.000
⩽ 20.000
⩾ 10.000
> 10.000
> 10.000
Footprint/Unit Size
Large if above ground
Moderate if under ground
Small
Small
Large
Small
Moderate
Siting Ease
Difficult
Difficult to moderate
N/A
N/A
Unknown
N/A
Easy
Maturity
Mature
Early development
Early development
Lead acid mature, others under development
Early R&D stage, under development
Available
Mature
10.4 COST BENEFITS OF STORAGE
Cost–benefit analysis (CBA) is a tool for analyzing the relation between the costs and benefits of a project and comparing similar projects on the basis of those results. CBA is a formal technique for balancing the benefits that a project produces against the costs of producing that benefit. It may be viewed as an art consisting of a series of techniques for decision-making. CBA is also a systematic, quantitative method of assessing the life-cycle costs and benefits of competing alternative approaches and determining which alternative is best.
The standard criterion for justifying a project is that the benefits exceed the costs over the life cycle of the project. The competing alternative with the greatest net benefit (benefits minus costs) should be selected. In considering a CBA for storage system, it should be noted that:
The cost of energy storage depends on the specific technology involved.
The benefits of energy storage depend on the service it provides and the local energy market or utility electric tariffs.
However, energy storage added to an electric power system at any level is capable of:
improving the grid's operation
reducing overall electricity costs, which is good for all players in the energy sector
improving electric energy reliability
integration of renewable-energy systems such as solar and wind
allowing excess energy to be stored for dispatch at periods of low or zero generation
10.4.1 Battery Energy Storage System Case Study
A battery energy storage system is a mature storage technology that enjoys wide applications in industrial, commercial, and domestic day-to-day needs. An average individual is constantly using at least one battery at any moment in time through a wristwatch, cell phone, wearable device, iPod, computer, or other electronic device that has become part of our daily existence. More energy-intensive applications include electric vehicles and home or commercial energy applications. In recent years, the deployment of battery storage systems within the power grid have received increased attention and implementation. It is important to ascertain the cost benefits of this technology, especially at utility scale, and particularly for renewable-energy penetration. The following cost components are associated with deployment of battery energy storage systems.
Battery costs in large-scale applications, especially at the grid level, are a very substantial fraction of the cost of a storage-deployment project. Batteries for any application may be acquired new or refurbished. Obviously, new costs more than refurbished.
Power electronics inverters for grid connection are in addition to the cost of batteries. The cost of the inverters includes all the wiring for the connections of battery packs and/or modules (for series/parallel connections for desired voltage and current levels) and the inverter's control system (digital signal processor for inverter control) and sensors.
Operation and maintenance costs include periodic and unscheduled maintenance, repair, or replacement of failed or damaged battery packs and maintenance of the power electronic converter. The annual cost, estimated based on a similar system, is divided by the power rating to obtain the dollars per kilowatt per year value. The annual operation and maintenance costs do not include the recharging costs of the batteries as this is application dependent.
Shipping/transportation costs depend on the classification of batteries as either new or used. Utility-scale battery energy storage systems are quite substantial in weight and consequently are a major cost factor.
Hazardous materials or hazardous waste costs may be incurred if used batteries must be transported from a dealer to a refurbishing factory by truck; the driver may be an employee of the refurbishing company, and the variable costs include gasoline and maintenance. The costs of the driver and truck will add only a few cents per kilowatt hour to the fixed cost.
The total system cost for this analysis encompasses the price of batteries, transportation, power electronics, and operation and maintenance. Clearly, the price of batteries depends on the supply, demand, and the price of new batteries.
10.4.2 Battery Energy Storage System Benefits
Electric supply capacity: While sharp permanent increases in demand require utility companies to permanently add capacity, additional capacity is not necessarily the solution to small increases in demand. Because of this, some utility companies rent generation capacity in the wholesale market. Energy storage alternatives can be used in lieu of adding or renting additional capacity. The financial value of the benefit can be estimated by using either of two options (i.e., adding or renting capacity).
Load following: The marginal cost of generation is primarily fuel and maintenance. This cost can be avoided or reduced if energy storage is used instead of generation to provide load-following service. The capacity-related costs (i.e., costs incurred to add generation capacity) depend on the need, which can vary depending on the region and the time of year. Additional generation capacity could be from hydroelectric to combined cycle-generation capacity.
Area regulation: For the calculation of energy storage benefits of area regulation, the storage benefit will be the same as conventional, generation-based regulation and reflect the prevailing price for the service in dollars per megawatt. Unlike generation used for area regulation, efficient storage can provide 2 kW for each 1 kW of rated output because it can provide for regulation while charging and discharging.
Electric supply reserve capacity: The electric supply reserve capacity benefit is somewhat small because generation-based reserves are inexpensive. The estimate of benefit is based on the price paid for reserves and the number of hours per year during which storage provides reserves.
Voltage support: During outages the voltage-support application power rating may vary from 1MW to 10MW, assuming a distributed deployment to locally serve the voltage support. The required time durations for voltage support may vary from fifteen minutes to one hour considering the time needed for system stabilization and orderly load shedding. For the cost calculations for the voltage-support application, a power rating of 1MW and thirty minutes of discharge duration (500 kWh storage capacity) are usually the basis for analysis.
Transmission support: Energy storage can complement the load-carrying capacity of transmission systems, avoid transmission outages, and defer the need to add transmission capacity (purchase of additional transmission and distribution (T&D) equipment and/or rent to participate in wholesale electric marketplace). The estimated benefit is the cost of the most likely alternative if storage was not deployed. For example, if capacitors are proposed as the standard solution, then the energy storage offset is the cost of capacitors.
Transmission congestion: Transmission congestion occurs when there is insufficient energy to meet the demands of all customers. The power rating for the transmission-congestion-relief application varies from 1MW to 100MW depending on the severity of the congestion. Based on the work in transmission congestion management, 20MW peak power was selected for transmission-congestion relief. The discharge duration for this application may vary from three to six hours based on the peak demand hours as congestion typically occurs in peak demand hours. Therefore, four hours of discharge capability would be reasonable for relieving the congestion, resulting in 80 MWh total energy capacity. Cost of benefit may be computed by comparing these costs with the possible revenue loss due to an outage.
10.4.3 Computation of CBA
In computing a cost–benefit ratio (CBR), the financial value of all costs and benefits must be evaluated. The undiscounted CBR = .
If the concept of time value of money is factored in, CBR may be computed from
(10.21)
where, Ci is the overall cost associated with the ith option, Bi is the overall monetized benefits associated with the ith option, ri is the interest rate attached to the ith option, and n is the time span.
10.4.4 Generalized Procedure for CBA Implementation
The general procedure for performing CBA is as follows:
Determine/define objectives.
Document current process and estimate future requirements.
Make any relevant CBA assumptions (e.g., the discount rate for the benefit stream may be set equal to that of the cost stream for some projects).
Define or break down the decision process into its elements.
Calculate, research, or estimate the cost and benefits associated with each element.
Identify all tangible and intangible costs, benefits, and respective distribution weights.
Aggregate all real costs and benefits based on their priority and social or distributional weights.
Present worth or discount the costs and benefits if necessary.
Compute the CBR.
Rank the “elements” into a hierarchy that reflects the impact of their potential success/failure on the entire process.
Assign weighting values to each element, ranked on their instrument value.
Estimate the likelihood of success or failure of each element.
Compute the risk associated with each element or perform sensitivity analysis.
Evaluate alternatives and make final recommendations.
CBA is significant in assessing the benefits and costs of storage technologies and systems related to the integration of distributed energy resources, such as solar, wind, and microgrids, into the planning and operations of the power system. This helps in evaluation and sizing of the suitable energy storage technology for the microgrid when considering optimal operation.
10.5 CHAPTER SUMMARY
In this chapter, we presented and discussed energy storage. Electric power is generated and consumed in real time. However, to manage certain contingencies, energy storage devices store excess energy during peak energy production. Stored energy may then be released during periods of energy shortage. Different types of storage systems and their characteristics and models were presented. The rationale for studying storage systems is based on the fact that some key renewable-energy resources do not produce energy around the clock. It is therefore important to make provision for periods when energy production is low or unavailable. In addition, storage devices were shown to play other critical roles in microgrids besides backup duties. Different components of storage technologies were given to help distinguish their capabilities and limitations.
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, n is the revolution per second 
, Vstroke is the swept volume in cubic meters [m3], ηvol is the volumetric efficiency.
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