REFERENCE MANUAL

Electricity

In order to make a current flow through a cable you need to have a voltage difference between the two ends of the cable - just like if you want to make air move through a pipe, you need to have different pressure at the two ends of the pipe.

If you have a large voltage difference, you may move larger amounts of energy through the wire every second, i.e. you may move larger amounts of power (remember that power = energy per unit of time, cf. the page on Energy and Power).

The electricity that comes out of a battery is direct current (DC), i.e. the electrons flow in one direction only. Most electrical grids in the world are alternating current (AC) grids, however.

One reason for using alternating current is that it is fairly cheap to transform the current up and down to different voltages, and when you want to transport the current over longer distances you have much lower energy losses when you use a high voltage. Another reason is that it is difficult and expensive to build circuit breakers (switches) for high DC voltages which do not produce huge sparks.

With an alternating current in the electrical grid, the current changes direction very rapidly, as illustrated on the graph in the side: Ordinary household current in most of the world is 230 Volts alternating current with 50 cycles per second = 50 Hz ("Hertz" named after the German Physicist H.R. Hertz (1857-1894)). The number of cycles per second is also called the frequency of the grid. In America household current is 130 volts with 60 cycles per second (60 Hz).

In a 50 Hz system a full cycle lasts 20 milliseconds (ms), i.e. 0.020 seconds. During that time the voltage actually takes a full cycle between +325 Volts and -325 Volts. The reason why we call this a 230 volt system is that the electrical energy per second (the power) on average is equivalent to what you would get out of a 230 volt DC system.

As you can see in the graph, the voltage has a nice, smooth variation. This type of wave shape is called a sinusoidal curve, because you can derive it from the mathematical formula

voltage = vmax * sin(360 * t * f)

where vmax is the maximum voltage (amplitude), t is the time measured in seconds, and f is the frequency in Hertz, in our case f = 50. 360 is the number of degrees around a circle. (If you prefer measuring angles in radians, then replace 360 by 2*pi).

Since the voltage in an alternating current system keeps oscillating up and down you cannot connect a generator safely to the grid, unless the current from the generator oscillates with exactly the same frequency, and is exactly "in step" with the grid, i.e. that the timing of the voltage cycles from the generator coincides exactly with those of the grid. Being "in step" with the grid is normally called being in phase with the grid.

If the currents are not in phase, there will be a huge power surge which will result in huge sparks, and ultimately damage to the circuit breaker (the switch), and/or the generator. In other words, connecting two live AC lines is a bit like jumping onto a moving seesaw. If you do not have exactly the same speed and direction as the seesaw, both you and the people on the seesaw are likely to get hurt.

The page on Power Quality Issues explains how wind turbines manage to connect safely to the grid.

The power of alternating current (AC) fluctuates. For domestic use for e.g. light bulbs this is not a major problem, since the wire in the light bulb will stay warm for the brief interval while the power drops. Neon lights (and your computer screen) will blink, in fact, but faster than the human eye is able to perceive. For the operation of motors etc. it is useful, however, to have a current with constant power.

It is indeed possible to obtain constant power from an AC system by having three separate power lines with alternating current which run in parallel, and where the current phase is shifted one third of the cycle, i.e. the red curve above is running one third of a cycle behind the blue curve, and the yellow curve is running two thirds of a cycle behind the blue curve.

As we learned before, a full cycle lasts 20 milliseconds (ms) in a 50 Hz grid. Each of the three phases then lag behind the previous one by 20/3 = 6 2/3 ms. Wherever you look along the horizontal axis in the graph above, you will find that the sum of the three voltages is always zero, and that the difference in voltage between any two phases fluctuates as an alternating current. On the next page you will see how we connect a generator to a three phase grid.

On the page on synchronous generators we mention that each of the electromagnets in the stator is connected to its own phase. You may wonder how that can be done, because in a three phase system we usually have only three conductors (wires). The answer is given in the pictures below.

If we call the three phase conductors L1, L2 and L3, then you connect the first magnet to L1 and L2, the second one to L2 and L3, and the third one to L3 and L1. This type of connection is called a delta connection, because you may arrange the conductors in a delta shape (a triangle). There will be a voltage difference between each pair of phases which in itself is an alternating current. The voltage difference between each pair of phases will be larger than the voltage we defined on the previous page, in fact it will always be 1.732 times that voltage (1.732 is the square root of 3).

There is another way you may connect to a three phase grid, however: You may also connect one end of each of the three magnet coils to its own phase, and then connect the other end to a common junction for all three phases. This may look surprising, but consider that the sum of the three phases is always zero, and you'll realise that this is indeed possible.