Structure of Generation, Transmission and Distribution

Chapter 1 established the two facts that force a power system into existence: primary energy is where geology put it, and electrical energy cannot be stored on the way. This chapter turns those facts into a physical arrangement — what is built, at what voltage, and why the answer is the same in every country that has electrified.

In the first decades of the industry the answer was different. Demand was small, confined to lighting and a little heating, and a generating plant of a few hundred kilowatts sat inside the district it served. As demand grew that arrangement became untenable for reasons that are all economic. A large boiler and turbine are far more efficient than a small one; a station built at the pithead or the dam site avoids hauling fuel; and a single large machine serving many districts runs closer to full load, because the peaks of separate districts do not coincide. Every one of these arguments pushes the generating plant away from the consumer, and once it has moved, the energy has to be brought back.

What brings it back is a network of conductors, and it is conventional and useful to divide that network in two. Transmission carries bulk power over long distances between a small number of large nodes. Distribution spreads it from those nodes over a service area to a very large number of small consumers. The two have different economics, different topologies and different design rules, and they are separated in this book as they are separated in practice. The whole assembly — the conveyance of electric power from the generating station to the consumer's premises — is the electric supply system.

Four characteristics are shared by every power system regardless of size. It is three-phase and operates at essentially constant voltage. Generation and transmission plant is three-phase throughout, and industrial load is invariably three-phase; single-phase residential and commercial loads are distributed as evenly as possible among the three phases so that the system remains balanced, which is what permits the per-phase analysis of Chapter 3. Electricity is generated by synchronous machines, driven by prime movers that convert fossil, nuclear or hydraulic energy into mechanical energy. And the transmission network is not one system but several subsystems at different voltages, joined by transformers.

Trace a kilowatt-hour from the turbine shaft to a lamp filament and it passes through five distinct stages, each at its own voltage and each separated from the next by a transformer.

Generating station. Three-phase alternators operating in parallel produce power at 11 kV, occasionally 6.6 kV on older or smaller machines and up to 21 kV on very large ones. A step-up transformer raises this to the transmission voltage, which is chosen according to the length of the line and the power to be sent — 66, 132, 220, 400 or 765 kV.

Primary transmission. The high-voltage line runs by three-phase, three-wire overhead construction to the outskirts of the load centre. This is the stage the whole of Parts 2 and 3 is about.

Secondary transmission. At a receiving station on the edge of the city the voltage is stepped down to 33 kV, and power is distributed at that level to substations placed at strategic points within the city. The line is still three-phase, three-wire.

Primary distribution. At each substation the voltage falls to 11 kV, again three-phase and three-wire, and these lines run along the main roads. Consumers with a demand above roughly 50 kW are supplied at 11 kV and provide their own substation; it is cheaper for the utility, and it puts the transformer losses on the consumer's side of the meter.

Secondary distribution. Distribution substations — pole-mounted or ground-mounted transformers, sited every few hundred metres — step 11 kV down to a three-phase, four-wire 400 V system. Between any two lines the voltage is 400 V; between any line and the neutral it is \(400/\sqrt3 = 230\) V. Single-phase lighting and domestic loads connect between a line and the neutral, and three-phase loads across the three lines directly.

All the transformers in the ladder exist to serve one result, and it is worth deriving carefully because everything about the geography of a power system follows from it.

Suppose a power \(P\) is to be delivered over a three-phase, three-wire line of length \(l\) at line voltage \(V\) and power factor \(\cos\phi\). Let the conductor have resistivity \(\rho\) and cross-sectional area \(a\), and let the total permissible line loss be \(W\), which we hold fixed — that is the honest comparison, since a line that loses more is not delivering the same service. The line current follows from Chapter 1 and the three-phase relation of Chapter 3:

The factor of 3 for the three conductors has cancelled against the \(3\) hidden in \(I^2\). Solve for the area the loss budget permits, then multiply by the three conductors and by the length to obtain the quantity that is actually bought:

Two consequences deserve to be drawn out. The first is quantitative: raising a line from 132 kV to 400 kV reduces the conductor requirement to \((132/400)^2 = 10.9\%\) of its former value, a saving so large that it pays for the transformers, the taller towers, the longer insulator strings and the bigger switchgear several times over. Example 1 works the numbers.

The second is that \(\cos\phi\) appears in exactly the same way as \(V\). A line operated at 0.7 power factor needs \((1/0.7)^2 = 2.04\) times the conductor of the same line at unity — which is the capital-cost half of the argument that Chapter 1 made on running cost alone. Reactive compensation and high transmission voltage are two forms of the same economy.

The conductor-volume argument fixed the loss and asked for the material. Turn the question round: fix the material — more precisely, fix the current density \(J = I/a\), which is what a conductor's thermal rating really constrains — and ask what happens to efficiency and voltage drop as \(V\) rises.

The current \(I\) has cancelled, leaving the loss fraction proportional to \(1/V\). The same cancellation governs the voltage drop. The drop along one conductor is

This is the striking one. At a given current density the absolute drop in volts is the same whatever the line voltage — it depends only on the material, the length and how hard the copper is worked. Expressed as a percentage of the line voltage it therefore falls as \(1/V\). A 5660 V drop is catastrophic on an 11 kV line and negligible on a 400 kV one.

If that were the whole account, transmission would be done at a million volts. It is not, because a second family of costs rises with \(V\) rather than falling. Insulation must be thicker and insulator strings longer; clearances to ground, to steelwork and between phases grow, so the towers grow with them; transformers, circuit breakers, isolators, instrument transformers and surge arresters all become larger and more expensive; and corona sets in, demanding bundled conductors of larger diameter than the loss calculation would justify.

Set the two families against each other. Write the conductor cost, which falls as \(1/V^2\), and the terminal and insulation cost, which rises roughly in proportion to \(V\):

The optimum is where the saving in conductor material from one more kilovolt is exactly offset by the extra cost of insulating it — and, as the last line shows, that balance falls where the terminal equipment costs twice what the conductor does. The curve is flat near its minimum, which is fortunate: it means the standard voltages can be a short list rather than a continuum, and a line need only be built at the nearest standard rung.

For a first estimate before any costing is done, the empirical rule known as Still's formula is used:

At the top of the ladder stands the synchronous alternator, driven by a prime mover that has converted heat, falling water or wind into shaft power. Steam turbines dominate thermal and nuclear stations and turn at 3000 rpm on a 50 Hz system with a two-pole machine; hydro sets turn far more slowly and carry many poles, since the frequency is fixed by \(f = pN/120\) with \(p\) poles and \(N\) in rpm. The machine is the subject of Chapter 26, and its behaviour during a fault is the subject of Chapter 21; here only its terminal voltage concerns us.

If high voltage is so valuable, why generate at a mere 11 kV and pay for a step-up transformer? Because the alternator's insulation problem is far harder than a line's. Its conductors are not suspended in air with metres of clearance but packed into slots in a laminated iron core, separated from earthed steel by a few millimetres of solid insulation, and subject to vibration, thermal cycling and the mechanical forces of a short circuit. The winding voltage a machine can carry is limited by the slot, not by economics, and 11 kV to about 21 kV is what the slot allows. A transformer, by contrast, can be immersed in oil and built to any voltage required — so it is far cheaper to generate low and transform up than to build a machine that generates high.

The differences in this table are what make Part 7 a subject at all. If every machine cost the same to run and started equally quickly, there would be no dispatch problem. Because they do not, Chapter 31 must decide how to share load among the units that are running and Chapter 32 which units to run at all.

Primary transmission is three-phase, three-wire, overhead, and at the highest voltage the system uses. Its conductors are bare aluminium stranded around a steel core (ACSR), suspended from steel lattice towers on strings of porcelain or glass discs, with one or two earth wires strung above them to intercept lightning. Chapter 5 describes the construction; Chapters 6 to 8 compute the inductance and capacitance that the geometry produces.

Secondary transmission at 33 or 66 kV performs the same function on a smaller scale, moving bulk power from the receiving station to substations inside the city. The distinction between primary and secondary is one of role rather than physics: both are three-wire three-phase lines and both are analysed by exactly the same methods in Part 3.

The choice between overhead line and underground cable is decided almost entirely on cost. An underground circuit costs several times its overhead equivalent at distribution voltage and an order of magnitude more at transmission voltage, because the insulation that air provides free must be manufactured, and because a cable fault takes days to locate and repair rather than hours. Against that, cable eliminates the danger of contact with live conductors, removes the visual intrusion of pole lines from crowded streets, and is immune to wind, ice and lightning.

The capacitance row is the one that has technical rather than commercial consequences. A cable's conductors are separated by a millimetre or two of dielectric instead of several metres of air, so its shunt capacitance per kilometre is one or two orders of magnitude larger. The resulting charging current is drawn whether or not any load is connected, and beyond a few tens of kilometres at transmission voltage it consumes the whole current rating of the cable. That single fact is why long submarine links are built as HVDC (Chapter 38) — a d.c. cable draws no steady charging current at all.

Below 11 kV the design problem changes character. Transmission moves a large power between two points and is judged on efficiency; distribution delivers small powers to very many points and is judged on voltage regulation and on the cost of the copper spread over a service area. Its three kinds of conductor are distinguished by whether load is tapped from them along their length.

The arrangement of the distributors decides the reliability. A radial system, in which each distributor is fed from one end only, is the cheapest and the simplest to protect, but a fault anywhere along it darkens everything beyond the fault, and the voltage drop is worst at the far end. A ring main, fed at two or more points as in the figure, halves the worst-case drop and allows any one section to be isolated without loss of supply — at the cost of more conductor and considerably more complicated protection, since fault current can now arrive from either direction. Chapter 36 returns to that difficulty when directional relays are introduced.

Voltage drop, not loss, is the binding constraint on a distributor, and statutory limits are typically \(\pm6\%\) at the consumer's terminals. Example 5 works out the standard result for a distributor loaded uniformly along its length, which is the model for a street of similar houses.

The ladder of Section 2-2 is an a.c. structure, and it is worth asking why, since on several technical counts direct current is plainly superior.

A d.c. link needs two conductors instead of three. It has no inductance, no capacitance and no phase angle, so there is no reactive voltage drop and no charging current — a d.c. line's regulation is better and a d.c. cable can be any length. There is no skin effect, so the whole cross-section of the conductor carries current instead of a surface layer. For a given insulation level the working voltage is higher, because insulation is stressed by the peak of an a.c. wave and \(V_{\text{peak}}=\sqrt2\,V_{\text{rms}}\); a d.c. line can therefore run at \(\sqrt2\) times the r.m.s. voltage of an a.c. line with the same insulators. Corona loss and radio interference are lower. Dielectric losses in cables vanish. And, decisively for long links, two a.c. systems joined by d.c. need not stay in synchronism with one another — there are no stability limits and no synchronising problems of the kind Part 6 is devoted to.

Against that stands one fact of overwhelming practical weight. Direct voltage cannot be transformed. Power cannot be generated at high d.c. voltage, because commutation in a d.c. machine limits it; it cannot be stepped up for transmission or down for distribution by any device as simple, as cheap and as efficient as a transformer; and d.c. circuit breakers are hard to build, because there is no natural current zero at which to extinguish the arc. A.c., meanwhile, can be generated at high voltage, transformed up and down at will with better than 99% efficiency, and interrupted by a breaker that need only hold off the arc for the few milliseconds until the current passes through zero of its own accord.

Nothing so far requires more than one generating station feeding one set of loads. In practice every station of consequence is tied to every other through the transmission network, and the reasons are the same economic ones that moved the station away from the city in the first place.

Interconnection lets the cheapest plant on the whole system serve the load, rather than the cheapest plant in one district — which is precisely the problem Chapter 31 formulates and solves. It reduces the reserve capacity that must be held idle, since a spare unit shared among many systems covers the loss of any one of them. It smooths the aggregate load, because the peaks of different regions and different industries occur at different times, so the ratio of peak to average demand improves and every unit runs closer to its best efficiency (Chapter 30). And it lets seasonal resources be traded — hydro in the monsoon, thermal in the dry months.

The price is that the network becomes a single dynamical object. Every synchronous machine on it turns in step with every other, locked by the electrical angle across the lines that join them; the frequency is a system-wide variable, and a disturbance at one bus is felt, attenuated but not localised, at every other. A fault must therefore be cleared in a fraction of a second or the machines will lose synchronism and the system will separate — the subject of Chapters 27 to 29. Protection must be selective enough to remove only the faulted element, since tripping more than necessary can propagate a disturbance into a cascade (Chapters 35 to 37). And the frequency must be regulated continuously against a load that never stops changing, which is the automatic generation control of Chapter 33.

Take \(\rho = 2.83\times10^{-8}\ \Omega\,\mathrm{m}\) for aluminium and \(1.72\times10^{-8}\ \Omega\,\mathrm{m}\) for copper unless told otherwise, and assume balanced three-phase, three-wire transmission. State clearly whether a voltage quoted is line-to-line or line-to-neutral before substituting it anywhere.