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JUMBOS AND THE SQUARE CUBE LAW

The launching of commercial megawatt size wind turbines marks a milestone in wind technology. But these big machines have to prove themselves commercially attractive. The arguments for large machines are: more efficient use of materials; reduced visual impact; savings in foundation costs; savings in electrical connection costs; and savings in operation and maintenance costs. Against large machines is their perceived visual dominance; construction problems with bigger and weightier components; poor road infrastructures in the currently vital markets in the Third World. The key question is, whether manufacturers producing both large and small turbines will be able to push overall plant costs down to the same levels as those who stick with medium size machines only. Wind energy generation costs comprise 75% capital repayments; out of these the wind turbine accounts for 75%, or 60% of total energy cost. Turbine costs increase with weight and, broadly, this increases with the cube of the diameter. But energy output increases roughly as the square of the diameter. Thus the "square cube law" dictates that a point is reached where the returns from larger size diminish or reverse. So far this point has been moving upwards due to advances in technology.

The development of wind turbine technology reached an important milestone in 1994. It was not heralded with any great ceremony but the Dutch firm NedWind quietly started advertising and marketing the first commercial megawatt size wind turbine. The milestone was reached nearly 20 years after early feasibility studies predicted -- almost unanimously -- that the only route to commercially attractive wind energy was via turbines whose output was measured in megawatts, not just kilowatts.

For about ten years, from around 1978 onwards, the goal of producing a commercial large wind turbine was enthusiastically pursued in the United States, Canada Great Britain, Denmark, Sweden, the Netherlands and Germany. That goal was not achieved by any of the machines built and -- usually with hindsight -- the enormous sums pumped into these government funded programmes have been criticised as being a misguided use of public money.

Discussions about why so many doggedly followed the wrong route, or, indeed, if it was the wrong route, have raged ever since. In the UK, criticism has been levelled at the now defunct Central Electricity Generating Board which, quite logically, argued that if wind energy was to make a worthwhile contribution to electricity demand, substantial numbers of turbines would need to be built and it therefore made sense to use large units -- especially as early projections forecast low energy costs from such machines. Similar thinking prevailed elsewhere and was manifested in such projects as the giant two bladed wind turbines built by General Electric and Boeing in the US, the MOD-1 and MOD-2, and in the infamous 3 MW Growian turbine in Germany, finally pulled down after only a few hundred hours of operation, having never worked properly.

The jumbo jet principle

The key problem was, perhaps, that at the time the programmes were initiated, there was a dearth of reliable information on how energy costs might vary with machine size and what evidence there was tended to point in favour of large machines. A "jumbo jet" philosophy also entered into the reasoning. In technologies such as transport, significant savings are realised by building large units. It was reasoned that wind technology would develop along the same route. However, there is a flaw in this argument. Jumbo jets make good economic sense to airlines but the economics of wind energy generated electricity are different.

Airline operating costs stem from a wide range of factors and, as a proportion of the total, capital repayments on the cost of the airline fleet are roughly on a par with its catering costs. Each accounts for about 10% of the total. Wind energy generation costs, on the other hand, comprise 75% capital repayments; and out of these wind turbine costs also account for about 75%, or around 60% of the total energy cost. Wind turbine costs increase with weight and, broadly speaking, this increases with the cube of the diameter. Energy output, on the other hand, increases roughly as the square of the diameter.

Thus a "square cube" law emerges: sooner or later, a point is reached at which the returns from larger sizes diminish or reverse. The size at which this occurs cannot be pin-pointed and will vary depending on advances in methods of production. The interesting point to note, though, is how the "best size" has moved steadily upwards during the past few years.

A second possible reason why the early multi-megawatt machines failed to live up to their promise was simply that they were ahead of their time. Despite the deceptive simplicity of wind energy technology, budgets over-ran and, again with hindsight, many of the machines may have been over-designed. It was also realised that the design process was quite complex, particularly in the controls and the aero-elastic analysis. Despite advances in understanding, two of the machines -- the 100 m 3 MW Growian and the UK's 60 m 3 MW machine at Burgar Hill have suffered blade cracks. Although the 3 MW Burgar Hill turbine is still intact -- and has provided much useful research and development data over the years -- its operation has been curtailed.

While government sponsored research in the European and US tinkered with the dinosaurs, a new strand of technology was being rapidly developed, spawned by the introduction of tax credits for wind plant in California in 1978. Anxious to profit from the incentives as soon as possible, the early pioneers could not afford to wait. They turned to machine sizes that were readily available as well as being reasonably reliable. At that time these machines had ratings of tens of kilowatts and rotor diameters around 15 m. As the Californian wind rush gathered momentum the machines slowly grew in size and reliability also improved as competing manufacturers strove to deliver the most cost-competitive product. Similar encouragement to the industry in Europe accelerated this process. Machine sizes increased steadily during the 1980s and accelerated during the 1990s (fig 2).

The American and European paths, however, are now diverging in their opinion on the best route to follow. In the US, the number of manufacturers is now far fewer than when developments were at their peak in the 1980s; and the remaining manufacturers have concentrated on producing machines around the 300 kW mark. These use standard low cost components and aim to bring prices down by mass production techniques, reinforcing the point that there is no optimum size, but a fairly broad range yielding similar costs. Europe, however, is determinedly pursuing the carrot promised by large machines, with a series of cross-border co-operation projects on large machine R&D. Of the established wind turbine manufacturers now participating in these projects, most have either put a commercial large machine on the market, or are expecting to do so.

To grow or not to grow

The arguments in favour of large machines are the same as they have always been: more efficient use of materials; reduced visual impact due to the reduction in machine numbers; savings in foundation costs; savings in electrical connection costs due to the use of fewer machines; and savings in operation and maintenance costs.

There are, however, downsides. Perhaps most importantly, large diameters could mean that machines are more dominant in certain landscapes, especially in crowded Europe, incurring the wrath of so-called protectors of the countryside. But this apart, technical and economic barriers also loom:

¥ construction problems are likely to arise with bigger and weightier components, chiefly with blades

¥ the "square cube law," as discussed, will begin to bite around 45 m diameter -- generators, gearboxes and cranes for megawatt machines all cost more than double those for 500 kW designs

¥ and in the Third World, particularly in India and China, it appears that smaller machines, in the 200-300 kW range, are often better suited to markets where road infrastructure is still underdeveloped and large cranes are in short supply.

Moreover, sites capable of hosting only, say, 500-1000 kW of wind plant will do better to install several 300 kW machines as these will provide smoother output and less mains disturbances on start-up and shutdown than one or two large machines. Manufacturers who opt for big turbines therefore risk losing out in some markets unless they sell both large and small units. The key question is, will manufacturers with two production lines be able to push overall plant costs down to the same levels as manufacturers who stick with the medium size machines only?

It is important to note that it is size that matters -- not rated power, which can vary within wide limits at a given rotor swept area. With the new generation of prototypes (table), rated power mainly ranges from 750 kW-1.5 MW, while size is relatively static at between 50-60 m for rotor diameter and around 60 m for hub height. It is the size of components for megawatt machines -- and the extra cost this puts on transport and installation -- which tends to erode the economic advantage of building fewer machines for a given size of wind plant (fig 1).

Extending the boundaries

The rapid development of wind technology during the 1980s spawned a second generation of large turbines towards the end of the decade. Those behind these machines thought the technology was better understood and that a "quantum jump" could be made. Five turbines were built in Europe, the 2 MW Elsam unit in Denmark, the Howden 1 MW in the UK, the Spanish/German AWEC-60/WKA 60 (all with three blades), the Italian Gamma 1.5 MW and the 1 MW Newecs 45 in Holland (each with two blades). With hindsight, again, the leap was too great and this batch were again experimental and still too far in advance of the market.

Nonetheless, a thorough analysis by the European Commission (EC) still showed good prospects for the larger sizes. Based on these findings, a comprehensive programme of research and development of large machines was launched. Unlike the earlier government sponsored initiatives, this current programme is evolutionary rather than revolutionary in its philosophy. Apart from the Aeolus II/WTS -- which has origins in the very first generation of large turbines -- the programme builds on the success of tried and tested wind turbines in the 300-500 kW range, rather than blindly leap frogging vital stages of development.

Once again the EC is playing a leading role, supporting machines under programmes run by the Directorate General for Science Research and Technology, DG XII, and the Directorate for Energy, DGXVII. DG XII supports the WEGA II machines, as part of the Joule programme, while DG XVII's Thermie programme, for demonstration and dissemination of new energy technology, supports those not part of WEGA. Outputs range from 750 kW to 1.5 MW, overlapping commercial developments at the lower end. In a fruitful partnership between industry, national governments and the EC, the aim is to nudge the commercial size range upward and bring costs down further. Evidence of the success of this approach can be seen in NedWind and Nordex who are already marketing their machines.

Furthermore, comparisons between a wide range of design philosophies will be enabled by an EC programme of measurements, carried out by Elsam Projekt in Denmark, which includes all the large machines in WEGA II and Thermie. The aim of the programme is to standardise measurements and presentation of results and so facilitate inter-machine comparisons. Nearly all the machines in the programme build on the success of smaller versions and results from this exercise, which should start to become available later this year, are awaited with considerable interest. The Commission has also set up a grouping of 14 major European utilities with an interest in renewable energies, EURE, which will assist in the identification of wind projects for support and promote exchanges of information.

The future

This new generation of large machines differs markedly from earlier prototypes. Substantial savings in weight have been made throughout the group. Blade set weights of the current range of machines weigh, typically, half the weight of their predecessors (fig 3). These blade weight savings have enabled further savings to be made in the nacelle assembly and towers. Despite this, there are no signs of a move towards uniformity of design concept. Most of the manufacturers have retained their particular preferences, although a few have changed; HMZ WindMaster of Belgium and the Netherlands, for example, has switched from three blades to two, probably to secure important weight (cost) savings, which are around 20%. There has, however, been a move towards two-speed operation, as this yields valuable extra energy.

Confirmation that large machines are not suited to all sites has emerged during the past year, with at least two manufacturers (Enercon and Tacke in Germany) producing 300 kW designs aimed at markets in the developing world, where wind speeds are often lower and ease of transportation is vital. There are likely, therefore, to be two strands of development, for big machines and for medium scale units. Both will be commercial, but aimed at different markets.

Whether the large machines will carry on growing will depend on the continued existence of market incentives. If these are cut back, this would harm manufacturers developing larger sizes, who need steady production runs to recoup their development costs to a greater extent than those who have decided to stick to a single product and market the smaller (300 kW) sizes only. If incentives continue the next question is whether the preferred size will settle at rotor diameters around 50 metres, 60 metres, 80 metres, or simply continue upwards. Cost comparisons between current commercial wind turbines and the new generation of 50 m megawatt machines, show the balance appears to tilt in favour of the larger machines (fig 1). But how large can they go? Only Germany and Sweden, alone among the early pioneers, have persevered with multi-megawatt development. Building on the experience gained with earlier, unsuccessful machines, they are progressing with a "first generation twice removed" multi-megawatt concept -- two sister 3 MW machines named Nasüden II and Aeolus II in Sweden and Germany, respectively.

Whatever the route chosen to find the optimum turbine size, the "square cube law" will make its presence felt eventually. Meantime, though, other considerations, such as ease of construction and transport, may inhibit development. The crystal ball may be cloudy, but further cost reductions seem assured.

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