Electromagnetic Machines
Transmission Lines
The power produced or used in an electrical machine can be calculated using the formula P=VI, where P = Power (W, Watts), V = Voltage (V, Volts) and I = Current (I, Amps). Using Ohm’s Law (V=IR) it can also be written as: P=I^2R or P=V^2÷R.
The problem with transmitting electricity over large distances is that throughout the power line, electricity is lost and transferred in heat energy due to the resistance of the wire. In a traditional household the average consumption of energy per day is roughly 18.1kW (18,100W). With a power station generating power and then only transmitting 240V across a long stretch of transmissions wires to a household can have an extreme loss in electrical efficiency (Paris, Zini, Valtorta, Manzoni, & De Franco, 2014).
With a power station producing 240V and transporting that 240V via 500km to a house with a wire of only 0.1Ω of resistance it can result in a loss of voltage of roughly 2.5V. This loss of voltage requires the power plant to produce more energy than will need to be consumed. However with this model the power station only has to power one house. In reality the one power station must power thousands of houses, thus making the voltage output from the station at minimum 11kV (11,000V) and in some stations 3MV (3,000,000,000), however the power that is output from a plant is purely a design choice.
Transmitting 11kV across a wire with a resistance of 0.1Ω will result in a voltage loss of 1,100V. The only way to reduce the voltage loss is to either reduce resistance by changing the wire (to either gold or silver that have very low resistance values) (Lloyd, 1998) or to reduce the current by increasing the voltage. According to the formula V=IR, it can be gathered that when the current is increased the voltage lost will also be increased at the same rate, this is known as a direct relationship. Therefore from this it can be deduced that in order two have the voltage loss lower and the resistance stay constant, the current would have to be altered. They current altercation will be a decrease in current due to the direct relationship between the current and the voltage loss. This decrease in current is achieved from the use of transformers which will be explained later is this website. The reason the factor of resistance isn't changed is due to the fact that the metals that have lower resistances are incredibly expensive and rare.
Tansformers
The two different types of transformers are a step up and a step down transformer. If the windings are not equal this can create a step up/down transformer. The step up or down transformers use different winding ratios to change the voltage being inserted or exerted. The amount of voltage that is change is dependent on the number of coils (BeoWorld Ltd., 2013). Step down transformers converts high voltage and small current power into low voltage high current power. A step up transformer turns low voltage and high current power into high voltage low current power (All About Circuits, 2014). Step up/down transformers can be used in reverse also.
This ability to turn high voltage and low current into low voltage and high current and vice versa, is very convenient when having to transmit electricity across long distances due to the fact that energy/power in transmission lines are converted into heat energy from the wires resistance. Having high voltage and low current power can vastly reduce energy loss via resistance.
The way hydroelectric power stations and all other sources of power production reduce the loss of voltage is by using transformers. A transformer consists of two conductive wire coils wrapped around a single piece of metal (ferromagnetic core). The first coil (the primary winding) is connected to an alternating current (AC) power source. The current then induces a changing magnetic field in the ferromagnetic core. This changing magnetic field induces an alternating current in the secondary winding (T&D Enginerring Magazine, 2014).
Energy Transferance Efficiency
Hydroelectric power is one of the most inexpensive and efficient sources of electrical energy, being able to convert 90% of the available energy into electricity. They are much more efficient compared to the best fossil fuel plants that are only 50% efficient (Davison, 2008). The hydro power stations lose this 10% of efficiency through friction of the turbine, shaft and rotor and by loss of electricity through transmission lines. The friction caused by the shaft, rotor and turbine transfers energy from kinetic into heat, therefore, creating loss of energy and efficiency (U.S. Department of Energy, 2011). The loss of energy via heat and friction cannot be calculated however the loss of energy from transmission wires can be calculated.
Wihtout Transformers:
With Transformers:
From the above equations it is clear that with the transformers active the efficiency is greatly increased. This increase of efficiency comes from the increase of voltage and the loss of the current. This increase in efficiency reinforces that when the current is lower and the voltage is higher, there will be less resistance and, therefore, more power supplied and a higher efficiency.
(National Earth Science Teachers Association, 2012)