Application

PV cells can be part of a building, duplicating other building materials, and can have a wide range of application as DG ranging from residential and commercial users to remote power consumers (structures in school, homes, community facilities, and commercial buildings). The greatest potential for PV modules is as green power because they do not emit pollutants or CO₂. However, they are a poor fit as a peaking power application source, since the unit outputs are not easy to control. PV systems produce better power during daylight periods of maximum available solar radiation and require battery storage for backup. They are not a good fit as premium power due to the unpredictable nature of power from solar cells.

Cost Implications

Manufacturers continue to reduce the cost of installation while increasing efficiency as new technology is developed for manufacturing materials and other operational and management costs.

Modeling

PV systems need to be developed and verified to optimize the output of the system at the design stage for maximum energy production and peak-sharing applications. Three models of a PV-equivalent circuit are shown in Figure 9.2. The equivalent circuit consists of a diode and source, which are in parallel. A simplified model has the following V-I equations:

(9.1)

(9.2)

where I_p is the photon current, I_d is the diode current, I_s is the diode ideal factor, K is the Boltzmann constant, T is the absolute temperature, e is the charge of an electron, and I_sc is the solar insulation.

The open-circuit voltage, V_oc, of the PV is given as

(9.3)

At 25°C, Equation 9.2 becomes

(9.4)

Modified Equivalent Circuit

The modified equivalent circuit (Figure 9.3) accounts for a real solar cell with external contacts, and voltage loss (drop) is accounted for through leakage currents and resistances. Using the V–I and Kirchoff's law

(9.5)

(9.6)

(9.7)

Also consider a simpler way (parallel connection):

for parallel resistance

(9.8)

and for series connection

(9.9)

(9.10)

(9.11)

Example 1

Combine PV to series and parallel resistances R_s and R_p, respectively (Figure 9.4). The generalized PV equivalent circuit for both series and parallel resistances will be:

(9.12)

(9.13)

(9.14)

(9.15)

Note that

(9.16)

To obtain from cell to module, we use

(9.17)

where n is the number of cell modules.

PV Systems

A PV system can be connected to a grid (utility system), can stand alone, or can be integrated.

• A PV system connected to a grid sends DC power to a power condition unit converter, which converts DC to AC power.
• A stand-alone PV system off the grid is equipped with battery storage and a generator for backup power.
• An integrated PV system is directly coupled to its loads without battery or major power-conducting equipment.

Different types of loads affect the PV system, as shown from the performance characteristics of the V–I curves.

V–I Characteristics

PV systems connected to different loads exhibit different V–I characteristics, as seen in Figure 9.5. For a simple resistive load

(9.18)

(9.19)

To achieve R_max, we can use a maximum power tracker, which keeps a PV system operating at its highest efficiency point at all times.

Example 2

Consider a solar panel rated 20 W at 1.0 V. Determine:

1. how many of these panels are needed to supply 1 A of current at 120 V
2. how should they be connected
3. value of the necessary load resistance
4. total power that can be obtained from this array of solar cells

Solution:

1. Since each panel produces 12 V, to get 120 V, the number of panels required in series is
   
2. The current rating of each panel can be found from the panel's power and voltage ratings, hence
   

   Thus, each path of panels connected in a series will provide 2 A. Therefore,

   

   Hence, five parallel paths each having twelve panels in a series are required to form an array to meet the power requirement.

3. The value of the required load resistance is found as:
   

   The total power that can be obtained from the solar array is

   

Future Challenge of Solar Energy

The major challenge to solar energy is the cost of equipment and devices. The full cost of installation of a solar energy system is still three to six times as high as the installed cost of conventional nonrenewable generation. The cost of a PV cell module is expressed as the cost per peak watt output at standard insolation. Standard insolation (energy from sunlight on a flat surface perpendicular to the sun's rays) is defined as 1 kW per square meter. The key to developing solar-PV electricity generation is to reduce the cost of PV cells by increasing the production volume of cells so that the benefits of mass production can be realized.

Types of Wind Turbines

Wind turbines come in two basic types:

• horizontal-axis wind turbines (HAWTs), which have blades that rotate at about a horizontal axis parallel to the wind
• vertical-axis wind turbines (VAWTs), which have blades that rotates at about a vertical axis

Modeling of Wind Power

The mathematical model for wind power stems from aerodynamic power, given in

(9.20)

where P is the air density, R is the radius of the circular area swept by turbine blade, in meters, v is the actual wind speed, and C_p is the turbine-power coefficient, which represents the power conversion efficiency of a wind turbine.

Tip speed ratio of the machine's blades to wind speed is

(9.21)

where ω =  rotor rotational speed in radians/second  is the rotor rotational speed in radians/second and C_p is maximum at λ_optimal.

The wind-turbine system uses induction generators that are independent of torque variation while speed varies between 1 to 2 percent.

Impact of Tower Height on Wind Power

A taller tower is expected to provide higher-speed winds to the turbine. Surface winds can also easily be affected by the irregularities or roughness of the earth's surface or forests/buildings. This is given as

(9.22)

where v is the wind speed at height H, v₀ is the reference speed at reference height H₀, and α is the friction coefficient.

In the United States,

(9.23)

whereas in Europe

(9.24)

Example 3

If the average wind speed on an open plain is known to be 6 m/s at 10 m height, determine the wind speed at 50 m height if the roughness coefficient α is 0.15.

Solution:

We know that

Thus

Emission-Control Technologies for Wind Power

Wind turbines produce no emissions. As a green-power application, the efficiency of wind turbines is superb, since they do not emit CO₂ or pollutants. However, wind power has an obvious disadvantage. Because its output cannot be controlled, it is mostly suited for peaking applications, producing power only when there is sufficient wind. Wind power cannot serve as premium power because of its unpredictability. Moreover, it is unsuitable for CHP applications. Despite these drawbacks, windmills remain a subject of continuing research, with the principal focus on:

• lowering the minimum wind speed of operation
• developing voltage regulators to improve the turbine's ability to recharge its batteries while simultaneously producing electricity

Wind turbines are a relatively inexpensive way to produce electricity compared with PV, which is the most competitive green power to date.

Example 4

Determine the amount of power that is present in a 10 m/s wind striking a windmill whose blades have a radius of 5m.

Solution:

The area swept by the turbine blade is

Power present in wind is

If the turbine-power coefficient C_p is 0.2, then the amount that will be converted to usable electric power is

Advantages and Disadvantages of Biomass Power

Biomass power is viable only when a sufficient quantity of bioproducts is available and a conversion process is done. Truly continuous applications are likely for biomass systems, and it appears to be a good fit for CHP applications. Since the output of these units cannot be controlled, they are not suitable for peaking applications. Biomass power is not a premium power due to the limited availability of bioproducts. It is also not an ideal green power due to the emission of CO₂ and other pollutants. Several research efforts are under way to improve the quality of biomass power and reduce its environmental impacts.

The form of energy input is very inexpensive. However, the efficiency of biomass power is low (typically less than 20 percent), and is a relatively expensive way to produce electricity compared with PV. Several advances in technology are being used to reduce CO₂ emissions and improve the green-power nature of biomass fuels. The success of biomass energy depends on the continuity of fuel supplies.

Hydroelectric Plant Size

Hydropower plants range in size from small systems for a home or village to large projects producing electricity for utilities. The size of a hydroelectric power plant can also be categorized in terms of its power-generating capacity and the overall head of the system.

1. Power-generating capacity

   Facilities range in size from large power plants that supply many consumers with electricity to small and micro plants that individuals operate for their own energy needs or to sell power to utilities. Although definitions vary, the US Department of Energy has defined the various categories of hydropower plants as follows:

   • Large hydropower facilities have a capacity of more than 30 MW.
   • Small hydropower facilities have a capacity of 100 kW to 30 MW.
   • Micro-hydropower plants have a capacity of up to 100 kW and may be designed for producing electricity for a home, farm, ranch, or village.

   Once we have the flow rate and the head figures, we can roughly estimate the potential power available in kW with the following formula:

   (9.25)

where Q is the discharge, m³/sec, H is the net head, η is the system efficiency,  and γ is the specific weight of water, kN/m³.

2. System overall head

   Hydroelectric sites are broadly categorized as low- or high-head sites. Low head typically refers to a change in elevation of less than 10 feet (3 m). A vertical drop of less than 2 feet (0.61 m) will probably make a hydroelectric system unfeasible. A high flow rate can compensate for low head, but a larger and costlier turbine will be necessary.

   Environmental and climatic factors as well as human activities in the watershed determine the amount and characteristics of stream flow on a day-to-day and seasonal basis. A storage reservoir can control flow but unless a dam already exists, building one can greatly increase cost and legal complications.

Problems Related to Hydropower

The following are some of the problems related to hydropower development:

• Unused rivers with good potentials are often far away from cities or in a low-population areas.
• Since water is highly essential to life, projects of this nature often generate disputes.
• The use of rivers or streams for hydropower often competes with recreational uses and environmental concerns.
• Displacement of wildlife is usually a fallout of hydropower projects.
• Flooding and submerged lands can become a problem if the project is not properly designed and managed.
• Siltation of the dam over time often limits the useful life of the dam reservoirs.

Example 5

During the design stage of a small hydropower station, the following data were collected for the site:

• average water flow rate = 23,000 tons/s
• net height of proposed impoundment = 75 m

If the combined efficiency of the water conveyor system from dam to turbine, turbine system, and generator is estimated at 0.77, estimate the capacity of the system. Let g = 9.82 m/s².

Solution:

Operation of Fuel Cells

Although fuel cells use different types of fuels, they operate using the same basic principle. A fuel cell consists of two electrodes: an anode and a cathode, separated by an electrolyte, as seen in Figure 9.9. Through the hydrogen catalyst, atoms split into a proton H + and an electron, and the proton passes through the electrolyte to the positive cathode. A DC current results. Using a converter, we can easily generate an AC current. The combined hydrogen and oxygen at the cathode produce water and heat.

Details on the differences between fuel cells are based on materials and manufacturing costs, operating temperature, efficiency, and power-to-volume (weight) ratio. Additional models of fuel cells and their distinguishing features are available in the literature.

The topology of a fuel cell is defined as a stack that consists of the part of the fuel cell that holds the electrodes and the electrolytic material. Hydrogen is extracted from gasoline, propane, and natural gas refineries to operate commercial fuel cells. Emissions from fuel cells are very low, so they have minimal environmental impacts. Their high efficiency leads to lower fuel costs and minimal maintenance due to a lack of moving parts. They have virtually no pollutant emissions, and CO₂ is rather low. Fuel cells are a good fit for green power and premium power. In addition, they provide a moderately high thermal-quantity output and hence are ideal for CHP applications. However, they perform poorly as peaking power due to extremely high capital cost. Developmental research work to refine the effectiveness of fuel cells is receiving greater attention.

Fuel cell efficiency ranges from 40 to 80 percent. Two of the most commonly used fuel cell types are PAFCs, which operate at relatively high temperature and use an external water-cooling system to cool the stack and PEM cells, which operate at a lower temperature than most of the other fuel cells and contain no chemicals such as liquid acids or molten bases that would cause concerns about the materials of construction.

Power and Energy Relationships

(9.26)

(9.27)

The energy of chemical input and output, i.e., of H₂, O₂, and H₂O, is defined as a chemical energy given as enthalpy, Helmholtz function, or Gibbs free energy. Fuel-cell energy can also be expressed in terms of calorific value. However, Gibbs free energy (G_f) is the preferred measure of fuel-cell energy, defined as the energy to do external work, neglecting any work done by changes in pressure or volume. Gibbs energy represents the external work involved in moving electrons around an external circuit.

G_f energy is used to represent the zero-energy point, and a change in G_f is given by

(9.28)

Consider 2H₂ + O₂ →2H₂O, which is equivalent to the following (after chemical interaction) as

(9.29)

where the new product is one mole of H₂O. Reactants are 1 mole of H₂ and 1/2 mole of O₂, which gives a balance of energy

(9.30)

i.e.,

(9.31)

However, the G_f of the function is not constant. It changes with temperature and the state of the liquid or gas.

Continuing the calculation in terms of electrical work, we get 2N electrons around the equivalent fuel-cell circuit. N is the Avogadro number, i.e., the charge on one electron.

(9.32)

where F is the Faraday constant or charge on 1 mole of electron.

(9.33)

(9.34)

(9.35)

This equation gives the fundamental emf = reversible open-circuit voltage of the fuel cell.

Supply Characteristics

The energy available from the ocean's surface-wave motion is almost unlimited, but it has proved difficult to capture in any appreciable quantity. Many ingenious systems have been proposed but, except for small installations, very few are generating electricity commercially and most have been thwarted by practical problems.

Some of these proposals are outlined below. Most are still in an experimental phase and many are not scalable into high-capacity systems.

1. Oscillating float systems are one of the simplest and most common solutions. A float is housed inside a cylinder-shaped buoy, which is open at the bottom and moored to the seabed. Inside the cylinder the float moves up and down on the surface of the waves as they pass through the buoys. Various methods have been employed to turn the motion of the float into electrical energy. These include:
   • In hydraulic systems, air is compressed in a pneumatic reservoir above the float during its upward movement on the crests of the waves. After the crests have passed, the air expands and forces the float downward into the following troughs of the waves. A hydraulic system then uses the reciprocating movement of the float to pump water through a water turbine, which drives a rotary electrical generator.
   • In pneumatic systems, air displaced in the cylinder is used to power an air turbine, which drives the generator.
   • Linear generators turn the reciprocating motion of the float directly into electrical power.
   • Instead of generating the electricity on board the buoy, some systems pump the hydraulic fluid ashore to power shore-based generators.
2. Oscillating paddle systems use large paddles moored to the ocean floor to mimic the swaying motion of sea plants in the presence of ocean waves. The paddles are fixed to special hinged joints at the base that use the swaying motion of the paddles to pump water through a turbine generator.
3. Oscillating snake systems use a series of floating cylindrical sections linked by hinged joints. The floating snake is tethered to the seabed and maintains a position head-on into the waves. The wave-induced motion at the hinges is used to pump high-pressure oil through hydraulic motors via smoothing accumulators. The hydraulic motors in turn drive electrical generators to produce the electrical power.
4. Overtopping wave systems use reservoirs filled by wave actions where the collected water is released to drive turbine and generator in same way as hydro power plants does. They focus waves onto a tapered ramp, which causes their amplitude to increase. The crests of the waves overtop the ramp and spill into a low dam. Water from the low dam then flows through hydroelectric turbines back into the sea beneath the floating structure.
5. Lever-based systems have been developed that use long levers mounted onto steel piles or floating platforms. Large floats or buoys are attached to the extremities of the levers, which move up and down with the waves. Movement of the lever arms forces fluid into a central hydraulic accumulator and through to a turbine-generator system. Alternatively, high-pressure water can be pumped ashore to power shore-based generators.
6. Oscillating water columns are formed within large concrete structures built on the shoreline or on rafts. The structure is open at both the top and the bottom. The lower end is submerged in the sea and an air turbine fills the aperture at the top. The rising and falling of the water column inside the structure moves the air column above it, driving the air through the turbine generator. The turbine has movable vanes that rotate to maintain unidirectional rotation when the movement of the air column reverses. Figure 9.10 shows a diagram of an oscillating water-column system.
7. Wave capture systems use a narrowing ramp to funnel waves into an elevated reservoir, as shown in Figure 9.11 [8]. Waves entering the funnel over a wide front are concentrated into a narrowing channel, which causes the amplitude of the waves to increase. The increased wave height coupled with the momentum of the water is sufficient to raise a quantity of water up a ramp and into a reservoir situated above the sea level. Water from the reservoir can then be released through a hydroelectric turbine located below the reservoir to generate electricity.
8. Pressure transducer systems use a submerged, gas-filled tank with rigid sides and base and a flexible, bellows-like top. The gas in the tank compresses and expands in response to pressure changes from the waves passing overhead, causing the top to rise and fall. A lever attached to center of the top drives pistons, which pump pressurized water ashore for driving hydraulic generators.

Technical Challenges and Solutions

Formidable technical challenges are involved in designing practical systems for capturing wave energy.

• Variability of sea conditions: Sea conditions are notoriously variable and the system must be able to cope with a wide range of wave amplitudes and frequencies as well as changes in the directions of currents.
• Matching the generating equipment with the wave characteristics: Mechanisms are required to convert the power of the irregular oscillating mechanical forces induced by the waves into electrical power synchronized with the grid. This could involve some expensive power electronics. Typical rotating machines used for power generation operate at a synchronous speed of 1,200 rpm (20 rps) whereas the frequency of waves driving the generator is likely to be between five and ten cycles/second. A mechanical gearing system is needed to match this 200:1 ratio in operating speeds, possibly combined with special purpose, slow-speed generators, incorporating a large number of pole pairs. One way around these problems is to use hydraulic accumulators either in situ or on shore to smooth out the energy delivery to the generator.

A number of solutions have been proposed to solve these technical challenges.

• Equipment construction: For reasonably sized systems, very high mechanical forces will be involved in converting the wave energy into mechanical energy for driving the electrical generator.
• Housing and mooring the equipment: Substantial housings must be provided to protect the generating equipment from the harsh ocean environment. Holding the installation in place is also particularly difficult in deep water.
• Energy transmission: Low-loss armored and insulated cables or high-pressure pipes must be developed for delivering the electrical or hydraulic energy back to the shore.
• Resistance to storm damage: Storm damage is a major threat. The frequency of occurrence of waves of any particular amplitude follows a Rayleigh distribution similar to that which applies to wind speeds. Though the frequency of serious storms may be rather small, a wave of ten times the average amplitude may be expected once every fifty years. From the power calculation detailed in the next subsection, the wave power is proportional to the square of the wave amplitude. This means that the installation must be designed to withstand forces one hundred times greater than the normal working level. This adds considerably to the costs.

Available Power

The wave power per unit length of the wave front P_L is given by

(9.36)

where ρ is the density of the water (10³ kg/m³), a is the wave amplitude (half of the wave height), g is the gravitational constant (10 m/sec²), λ is the wavelength of the oscillation, and T is the period of the wave.

Example 6

Estimate the power per meter in a wave with amplitude 1.82 m, length 82.15 m, and period 3.5 seconds. Take density of seawater as 1,029 kg/m³ by

Description

Incoming air is compressed to about 3 atm of pressure and sent to a heat exchanger called a recuperate, where hot exhaust gases raise the temperature. The heated steam is mixed with fuel and burned with enough energy to drive the turbine, which subsequently powers the electrical generator. The turbine has only one moving part, which drives the generator at 96,000 rpm on the air bearings and hence does not require lubrication and cuts down on operational/maintenance costs. The generator creates AC current but can be rectified for DC output as needed. It can easily be operated for 60 Hz and reverted to a 50 Hz supply.

Microturbines can also easily be started in parallel for increased power output to 30 to 60 kW.

In general, microturbine emissions are comparable with those of large turbines. Manufacturers base NOx levels on field tests and projections. Emission control to achieve an acceptable standard is focused on combustion design and flame control.

Microturbines are moderately applicable for peaking power but can be used as a stand-alone in limited areas. Their inverter-based generators offer a high premium of power quality. If efficiency degrades as temperature increases, it leads to CO₂ emissions, which further degrade its efficiency. It is a moderate fit for CHP applications.

Further development of microturbines to lower costs due to electronics, power conditioning, and grid connection are concerns. Applications of fuel diversity (low BTU) and digester gas are under development. Microturbine efficiency is up to 30 to 40 percent for non-recuperated units and 20 to 30 percent for recuperated units. The available natural gas pressure level mostly impacts microturbine efficiency. Further work that hybridizes microturbines with fuel cells will facilitate the generation of additional electricity of up to 60 percent efficiency.

There are many models of microturbines produced by a number of manufacturers, e.g., Elliot Group, Ingersoll Rand, Honeywell, and Capstone Turbine Corporation. Microturbines are rated in terms of rated power, fuel input, heat rate, efficiency, emissions (NOx, CO₂), turbine rotation, weight, noise, and size.