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Physics of the power grid

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Introduction

The electricity market in the United States makes up 7 percent of the gross domestic product (GDP) and plays a crucial role in the functioning of the economy and the society. Various energy generation technologies get used for energy generation throughout the world namely fossil fuels (such as coal, natural gas, and oil), nuclear power and renewable sources of energy (such as wind, solar, hydropower, geothermal and biomass). This paper describes the generation and distribution of electricity in America from a wind power source. Once the electricity is generated, it is distributed through a system of power lines to residential, industrial as well as commercial consumers. The electricity produced operates under pressure (known as voltage) that can get varied depending on whether the electricity gets transported over long distances or gets used in residences and industrial or commercial centers. The electric current is either direct current (DC) or alternating current (AC). The figure below shows the sequence of generation and distribution of electricity.

nversion

The main elements of a wind turbine system include the turbine rotor and blades, generator, gearbox, a yaw mechanism, a power electronic converter system, a transformer and possible power electronics. The main components of a wind power system are shown in the figure 2 below.

ure 2: The main elements of a wind turbine system (Source: Grigsby, 28-2)

The mechanical power of a wind turbine gets converted into electrical energy by an alternating current (AC) generator or a direct current (DC) generator. The AC generator is either a synchronous machine or an induction machine; the latter is widely employed in the wind power industry. The electrical machine functions on the principle of action and reaction of electromagnetic induction. The resulting electromechanical energy conversion is reversible.

The electric power generation entails the transformation of the fluctuating wind energy into mechanical energy, which then gets converted into electrical power through the generator, and transferred into the grid through a transformer and transmission lines. The kinetic power from the wind gets captured by wind turbines through aerodynamically designed blades and converts it to rotating mechanical power. The number of blades is usually three and the rotational speed decreases with the increase of the radius of the blade.  The rotational speed for megawatt range wind turbines will be 10-15 rpm. The weight-efficient approach of transforming the low-speed, high-torque power for electrical energy is to use a gearbox and a generator with standard speed. The mechanical power gets transmitted shaft directly or through a gearbox to the generator shaft from the turbine, depending on the number of poles of the generator. If the generator has a small number of poles say four poles, a gear box commonly gets used to connect the turbine low-speed shaft and the high-speed generator shaft. If the generator with a high number of poles gets used, the gearbox may not be necessary. The generator converts mechanical power to electrical energy that gets fed into a grid through possibly a power electronic converter and a transformer that contains circuit breakers and electricity meters. The power transformer gets located close to the wind turbine to eliminate high currents flowing in long low-voltage cables. Power electronic converters get used so as to allow the wind turbine generator to work at variable speed to produce the maximum power and include operation benefits. The benefits include reactive power and power factor control, minimized mechanical stresses of the drive-train system, and improved grid fault ride-through capability. The connection of wind turbines to the network system can occur at low voltage, medium voltage, high voltage and also at extremely high voltage system because the transmittable power of an electricity system usually raises with increasing the voltage level (Blaabjerg, Frede, and Zhe Chen, 4). All the turbines in a modern wind turbine system have their transformer so as to raise the voltage from the voltage level of the wind turbines (400 or 690V) to the medium voltage. The yaw mechanism rotates the plane of the rotor of the wind turbine so that it is perpendicular to the wind direction so as to extract the maximum power from wind. The yaw controller regulates the yaw mechanism to turn the rotor plane of the wind turbine to be in the direction of the prevailing wind so as to produce the maximum power. When several wind turbine generators get connected to form a wind power plant, the control system of each wind turbine generator gets coordinated by a wind plant central control system through a Supervisory Control and Data Acquisition (SCADA) system.

Generators usually produce 60 cycle/second (Hertz or Hz) alternating current (AC) electricity with voltages between 12 and 30 thousand volts (kV). The frequency of all generating units on a system must be precisely synchronized. Generating units have automatic voltage regulators that control the unit’s voltage output and speed governors that adjust power output according to the changing system conditions.

The total wind power, Pw, available to the wind turbine gets given by the equation below:

 

Where is the density of air in kg/m3

A is the swept area in m2

V is the wind speed in m/s

The maximum wind power that can get harnessed by a wind turbine is 59.3 percent (that is known as the Betz coefficient) of the total wind power (Zobaa, Ahmed F., and Ramesh C. Bansal, 70). The electrical output power (Pe) from a wind turbine is given by the equation below;

 

Where Cop is the overall power coefficient of the wind turbine which is the product of the mechanical efficiency (electrical efficiency (and the aerodynamic efficiency (Betz coefficient)

Transmission of alternating current (AC)

Transmission lines get connected to each other in huge interconnected grids that move power from sources to loads that sometimes get located in different states. Transmission lines that form these grids produce electric and magnetic fields as a result of their operation by conducting electric power from its source to the end user. The transmission lines get designed to conduct large amounts of electricity over long distances. The electric current gets transmitted in high voltages so as to overcome the electrical resistance of the transmission line conductors. Transmission lines in the United States normally get rated at standard voltages of 69, 115, 138, 230, 345, 500 and 765 kV (McKetta Jr, John, 435). The AC electricity changes polarity at the frequency of 60 cycles per second (60 Hz) in the United States.

The AC electricity gets generated and transmitted in three phases requiring three separate conductors. At any instant, each step is the one-third cycle (or 1200) before or behind the other two phases (conductors) of the transmission line. The AC transmission has a benefit in that it changes the electrical voltage in the conductors through the use of transformers. Electric power generated at a power plant gets increased from the generator voltage (typically 30kV) to the transmission line voltage (115kV or higher). Where the transmission line ends, the voltage gets reduced to a lower voltage (less than 69kV) for local distribution of the electricity to the end user. This changing of voltage during transmission from the generator to the end-user minimizes the losses of power. The transmission of electricity at high voltage minimizes the fraction of energy lost to resistance. For a given amount of power, a higher voltage reduces the current and hence the resistive losses in the conductor. For instance, raising the voltage by a factor of 10 minimizes the current and hence the I2R losses by a factor of 100 as long as the same-sized conductors get used in both cases (Fogarty, Tom, and Robert Lamb, 112 – 174). This factor makes AC electricity to be superior to DC electricity since it allows for a small number of large centralized generating plants with their inherent economies of scale to operate a wide area through long-distance transmission lines. The transmission of AC electricity over long distances is highly favorablewhen wind power source gets used to generate electricity since wind farms cannot get situated near populous cities.

In the US the average line loss is 7 percent of generated electricity, although actual losses between two points vary with the amount of electrical energy passing through the transmission lines, their design characteristics, the environmental conditions and the distance covered.

Distribution systems

Distribution is the power system function that delivers electric power to end-consumers who include homes, industries, and businesses. It consists of poles, wires, transformers, and control equipment that function at a primary voltage (between 110 – 125 volts in the US). Distribution systems get designed to operate safely and to be following codes and standards that aim at enforcing safe design practices. Distribution systems vary in voltages, grounding configurations, the number of conductors, etc.

In the United States, the widely used system is the utility multi-grounded neutral system that aims at sharing the load current between earth and a conductor (Sutherland, Peter, 148). The phase conductors get mounted on insulators on the top of poles. The neutral conductor gets mounted on insulators on the side of the pole. At distances of about every 0.4 km a ground gets used. The ground comprises of a grounding rod with ground resistance of 25 ohms (Ω) or less. It gets connected by means of a wire running up the pole.

Many of domestic utilities get fed with the familiar center-tapped 120/240 V single-phase transformer. The electrical safety in the residence revolves around two primary concerns that are electrical shock from contact with energized conductors and electrical fires caused by short circuits.

 

Domestic wiring system

The home gets connected to electricity from the local utility company through the service head, from where it flows through the electric company’s meter to the service panel. The main service panel distributes power throughout the house through individual circuits. The individual circuits contain breakers or fuses that safeguard them.


References

Blaabjerg, Frede, and Zhe Chen. "Power electronics for modern wind turbines." Synthesis Lectures on Power Electronics 1.1 (2005): 1-68.

Fogarty, Tom, and Robert Lamb. Investing in the renewable power market: how to profit from energy transformation. Vol. 614. John Wiley & Sons, (2012): p. 112 – 174

Grigsby, L. L.: Power Systems, Third Edition: CRC Press, (2016): P. 28-2

Koester, Eric. Green entrepreneur handbook: the guide to building and growing a green and clean business. CRC Press, (2016): p. 137 – 139

McKetta Jr, John J. Encyclopedia of Chemical Processing and Design: Volume 1-Abrasives to Acrylonitrile. CRC Press, (1976): 435

Sutherland, Peter E. Principles of Electrical Safety. John Wiley & Sons, (2014): p. 148

Zobaa, Ahmed F., and Ramesh C. Bansal eds. Handbook of renewable energy technology: Singapore: World Scientific, (2011): p. 70

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Prof. Richard Brixton

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