## The Grid

Power Efficiency Guide

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The final element in the electricity supply 'jig-saw' is transmission and distribution. In the electricity supply industry transmission and distribution are viewed as quite separate activities. In the industry, when they talk of transmission, the bulk transfer of electrical power from several power stations to towns and cities is being considered. Typically, power transmission is between one or more power plants and several substations near populated areas. The transmission system allows distant energy sources (such as hydroelectric power plants) to be connected to consumers in population centres, thus allowing the exploitation of low-grade fuel resources that would otherwise be too costly to transport to generating facilities. Electricity distribution, on the other hand, describes the delivery of electricity from the substation to the consumers.

A power transmission system is sometimes referred to colloquially as a 'grid'; however, for reasons of flexibility and economy, the network is not a rigid grid in the mathematical sense. Redundant paths and lines are provided so that power can be routed from any power plant to any load centre, through a variety of routes, based on the economics of the transmission path and the cost of power. Much analysis is done by transmission companies to determine the maximum reliable capacity of each line, which, due to system stability considerations, may be less than the physical or thermal limit of the line.

Owing to the large amount of power involved, transmission at the level of the grid normally takes place at high voltage (275 kV or above in the UK). This means that a transformer park exists at all power stations to raise the generated voltage, which is typically at about 25-30 kV, up to the local grid level, i.e., about ten-fold. This process adds, through ohmic losses in the transformer windings and core losses in its magnetic stack, possibly a further 1% to generation losses. However, transformation to high voltage is essential to avoid much higher losses in the cables of the grid system. This is easily explained by recalling that the magnitude of conductor loss [12] in a wire is proportional to the resistance of the wire and to the square of the current through it. If the grid is required to carry a power (P watts), which is largely equal to the transmission voltage (V) multiplied by the transmission current (I), then by increasing V ten-fold the current can be reduced by a factor of ten for the same power and hence the cable losses by a factor of one hundred. This is a very considerable saving on wires which could be hundreds of miles long.

In calculating the power loss in very long electrical cables it is easy for the unwary engineer to under-estimate its magnitude, because of a phenomenon called 'skin effect'. It is, therefore, sensible to take a short detour here to explain this phenomenon because it is important to some of the transmission issues that will be addressed later. Suppliers of electrical materials are required to perform rigorous testing programmes on their products, to provide users with accurate values for the physical constants of the materials purchased. Examples of these constants are thermal conductivity, specific heat, electrical conductivity, electrical resistivity, permittivity, permeability, etc. The tendency of a material to resist the flow of electron current is represented by its electrical resistivity (ohm-m), or its reciprocal, electrical conductivity (siemen/m). The resistance of a conducting wire in ohms (Q) is then given by resistivity times length divided by cross-sectional area [12], provided the current flow is unvarying (DC). For example a DC cable, comprising two 156 mile long lengths of 5 cm diameter hard aluminium wire, for which the resistivity is 2.86 x 10-8 ohm -m, has a resistance of almost 1.2 Q. This is a very low resistance. Even so, a DC current of 100 A in this cable would generate 12 kW of loss in the form of heat.

If the cable carries a 50 Hz AC signal the above calculation would be erroneous because of the troubling (to students) quantity termed skin effect. So what is skin effect and how do we adjust the calculation to accommodate it? In Sect. 2.4 you will remember that we discovered that electrical energy is stored in electric and magnetic fields. Since power is rate of change of energy, it follows that when we transmit power (move energy) through transmission lines or across space (radio waves) the agency that allows us to do this must be electric and magnetic fields. The transport mechanism takes the form of electromagnetic waves. When AC power is transported through a transmission line, the power is not carried through the interior of the wires, but in the space between the wires as an electromagnetic wave. If transmission system wires could be made perfectly conducting, it would in principle be possible to carry high electrical power along filamentary wires with infinitesimally small cross-sectional area. If their cross-section is tending towards zero in engineering terms (i.e., infinite simally small but not sub-atomic dimensions), it can be concluded that the finite power being transmitted across the grid cannot be propagating in the interior of the wires, otherwise we have the physically impossible scenario of power density tending towards infinity! Again, the important point to reiterate here is that the power is carried through the space between the wires on an electromagnetic wave, and the wave cannot penetrate into the perfectly conducting wires. A perfect conductor is, in fact, a 'perfect mirror' for electromagnetic waves. In this case we can state that the 'skin depth' is zero, and that the current in the wires flows in an infinitesimally thin, 'atomic thickness', surface layer. There are still plenty of 'free electrons' within this 'atomic' layer to accommodate the finite current. In non-perfect conductors such as copper, electromagnetic wave penetration into the interior is possible, but the wave attenuates very rapidly. The skin depth (8 m) for real materials is defined as the distance from the surface at which the penetrating wave has diminished to 1/e of its surface magnitude, where the exponential constant e = 2.718. For aluminium at 50 Hz the skin depth is 17.2 mm. At this frequency skin depth could raise the resistance of the 100 mile long aluminium cable by 50% above the DC value of 1.2 ohms. In practice the suspended grid wires are designed to have a diameter of little more than the skin depth in order to minimise weight, in which case there will not be much difference between the DC and AC resistances of a power line. The line resistance per phase of high voltage grid is typically 0.7 ohms/mile. Given that the line will carry a current of around 300 A we end up with a 'ball-park' figure for the power transmission loss for the grid of 200 kW/mile or 124 kW/km, a statistic that we shall find useful later. In terms of percentage of the power carried, this represents a power loss of 8% per thousand kilometres for a 750 kV line.

The pylon-supported wires of the grid are almost exclusively formed from aluminium laced with a core of steel strengthening strands. Although aluminium is a poorer conductor than, for example, copper it is preferred in this role because it has a much better conductivity to weight ratio making it lighter to support. The steel core, which gives the aluminium wire enough strength to be suspended over long distances, has no electrical effect because of skin depth. There is a limit to how high the voltage can be raised to diminish conductor loss and this is set by air breakdown or corona discharge, particularly in humid or wet conditions. If corona occurs, losses can escalate markedly.

Underground power transmission over long distances is not really an option, unless exceptional circumstances exist, due to its high cost of installation and maintenance (about ten times more costly than overhead cables). It is really only used over short distances, normally in densely populated areas. There is also a significant technical problem in the transmission of AC power with underground or undersea cables. Since they are usually of coaxial construction, this means that they are subject to what the industry describes as high reactive power loss. Very long over ground transmission lines, suffer the same phenomenon. It sounds complicated but all it really means is that in buried cables the current carrying conduc tors (three for three phase transmission) are embedded in an insulating material, which is essential in order to maintain the more closely spaced conductors at a constant separation. This construction results in much higher capacitance per unit length than occurs with pylon supported transmission lines. Capacitance tends to increase with the surface area of the current carrying conductors and to decrease with separation distance, and high capacitance as we have already seen, equates with high electrostatic energy storage, which in turn implies high charge accumulations. The reactive power phenomenon associated with the high capacitance, or high storage capability, of long transmission lines is quite difficult to explain by a gravitational analogy because we cannot include phase effects. Nevertheless we can illustrate the nature of the difficulties that are introduced by the presence of a storage element in a transmission system.

Through the agency of gravity, as we have seen, water in an elevated reservoir (generator) if released into a descending trough or channel (transmission system) towards a water wheel (load/consumer) at a lower level, will transmit power to the wheel. Some energy in transmission will be lost through frictional losses in the channel and inefficient power collection by the water wheel, but the process is relatively uncomplicated. Let us consider now what happens if a second smaller reservoir exists between the original reservoir and the water wheel. If the low reservoir is initially empty, water will flow down the channel simply transferring potential energy from the upper store to the lower store with no power going to the water wheel. Nevertheless, despite the fact that no power reaches the turbine, fric-tional power loss in the channel continues to occur due to the water rushing to fill the lower water store. It is only once the lower reservoir is full that power gets to the wheel. In electrical terms, with very long transmission lines exhibiting high capacitance (storage capacity), power from the generator is initially used simply to store energy in the grid, resulting in high power loss as current surges into the system. Once energy transfer to the line capacitance is complete (in milliseconds) power will flow steadily to the consumer. This is DC in action. On an AC line the situation is much worse. In terms of the water channel analogy we now have to empty the lower reservoir quickly and completely through an alternative outlet on a regular basis, to get an idea of the problem with long lines and AC transmission. On a very long line the charging current can reach a magnitude that produces excessive ohmic loss in the wires, and the conductors may be raised in temperature to beyond their thermal limit. This means that AC cannot be transmitted across power lines that are more than a few hundred kilometres long, or over long undersea cables, without reactive power compensation. Not surprisingly there is considerable reluctance in the power supply industry to adopt buried or undersea transmission lines, unless there is no alternative. In this case DC becomes the preferred mode of transmission.

The grid itself, as indicated earlier in this section, is a loose interconnection by means of transmission circuits, of multiple power stations and loads (consumers through the agency of substation transformers). This interconnection places stringent frequency and voltage constraints on power suppliers, but this is off-set by versatility of supply, higher operating efficiencies and economies of scale.

The need for frequency and voltage control for grid connected generators can probably best be illustrated by considering a very simple electrical circuit formed from batteries and loads (light bulbs for example). The arrangement is valid insofar as we know that at 50 Hz, wavelength on the grid is so long (~ 6600 km), that branches of the grid (typically 100 km) are sufficiently short in wavelength terms for the voltage and current on the line to be considered to have DC characteristics. 'Power stations' on our elementary 'grid' circuit each have two rechargeable batteries connected through a reversing switch. There are several power stations and several loads (consumers) all interconnected by two copper wire loops, one 'live' and one 'earth'. The power station batteries are connected through a switch such that one (battery A, say) has its positive terminal connected to live with the negative terminal connected to earth, while the other (battery B) is disconnected. When the switch is reversed battery B is connected to the circuit but with the positive and negative terminals swapped over. The bulbs are connected at various positions around the loop with one terminal connected to the live wire and the other to the earth. Provided the reversing switches are synchronised, so that all A batteries are connected to the loop at the same time, power will flow from the batteries to the bulbs, lighting them up, if the batteries are all at the same voltage level. Reversing the switches to connect batteries B to the loop changes nothing electrically provided the switch over is synchronised. In this case the light bulbs will seem to glow uninterrupted. If the reversing switches are all automatically vibrated synchronously at 50 Hz we have essentially what happens on the full scale grid. Clearly it is important that when a new battery pair is to be connected to the circuit, the reversing switch is being vibrated at exactly the same rate as all other switches on the circuit and that it is synchronised so that the positive terminal of battery A is connected to the loop when the loop is positive - and vice versa for battery B. If this does not happen, a high current will flow from the circuit to the battery, possibly causing failure. On the grid, power station failure is unlikely if synchronisation is not achieved, but considerable power loss and instability will result. Our battery circuit also shows us that it is important that all the battery 'stations' supply the same voltage to the loop, otherwise even if synchronised to the loop voltage, a battery pair that is low in voltage will absorb power from the loop - charging up the battery pair. The same is true for the full scale grid, with power flowing from the grid to a power station, if its voltage does not match that of the grid. Finally, in the circuit model if bulbs are removed or added to the system - demand fluctuation - the batteries cope automatically. This is not true of power stations linked to the grid. Demand prediction and control is essential to efficient operation of the system. Synchronisation, voltage control and adjustment to demand, are very important in electrical power systems coupled to the grid, and as we will see, this can present significant difficulties for renewable power sources. For electricity distribution from the grid to cities, towns, factories, hospitals, schools, homes etc., down conversion at substations from 400 to 33 kV, or less, is required. Substation transformer losses add a small but finite contribution to overall transmission and distribution losses.