Expected electricity costs for the US Mod 2 windmill

Robert Lowe presents here an analysis of the expected cost of electricity production from the US Mod 2 windmil l , using accounting criteria currently recommended for energy technologies in the UK. The results show that if expected cost targets are met, the Mod 2 design wil l be a highly economic means of generating electricity.

The US ERDA/NASA wind electricity programme has gone through three phases, Mod 0, Mod 1 and Mod 2. Further phases are planned but are not dealt with here. The Mod 0 machines, of which several were built, are fairly expensive 200 kW prototypes designed to give operational and manufacturing experience with large wind generators. They generated electricity at a cost of 30-50c/kWh, based on typical US utility accounting practices.

The Mod 1 machine, the first of which is now operating at Boone, North Carolina, is basically a larger version of the Mod 0 machines. It consists of a 61 m diameter variable pitch rotor with a synchronous 2 MW generator. The

Table 1. Breakdown of electricity cost for the Mod 2 windmill (%).

Item Share of cost

Blades/hub/pitch change mechanism/controls 24

Gearbox/generator/shafts/ bearings 22

Tower access 11 Nacelle/yaw drive/yaw bearings 11

Foundation/site preparation 9 Assembly and checkout 8 Other (spares/equipment/ plant) 4

Transport 2 Operation and maintenance 9

100

Table 2. Costs of electricity (p/kWh).

Mean wind First Mod 2 lOOth Mod 2 speed (mph)

12 4.5 (9.8) 1.8 (3.9) 14 3.3 (7.3) 1.3 (2.8) 16 2.8 (6.1) 1.05 (2.3) 18 2.4 (5.2) 1.0 (2.2)

Note. The figures in parenthesis are the costs in c/kWh. These costs were converted to p/kWh using an exchange rate of $2.2 = £1.

Mod 1 machines are expected to generate at between 10 and 25c/kWh.

Finally, the Mod 2 machine, the first of which was planned to be operational by the middle of the year, is a much more sophisticated, lighter machine than the Mod 1. It consists of a 91 m diameter rotor with blade tip control and a 2.5 MW synchronous generator. The design life of the machine is 30 years. The first unit is expected to generate at between 6 and 10c/kWh. The production of large numbers of Mod 2 machines is being contemplated and this is expected to reduce costs further, by over a factor of two.

The details of these machines are taken from Robbins and Thomas) The costs of electricity (COE) presented by Robbins and Thomas are calculated according to the formula:

(c + r) /E,

where c = capital cost x fixed charge rate,

r = operation and maintenance costs,

E = annual energy production.

The fixed charge rate used by Robbins and Thomas is 18%. They also give the breakdown of cost of electricity from the Mod 2 design shown in Table 1.

Fuel saved

At this stage I ought to say something about the value of wind generated electricity. The wind is not a dependable source of electricity and to a first approximation does not reduce the requirement for conventional generating plant in a given system, unless installed with storage. Detailed study shows that the cost of the plant mix required to back up wind electricity is less than the cost of the optimum plant mix without wind generators, and this should be taken into account in assessing the

value of wind electricity. However, ignoring this effect, the value of wind generated electricity can be taken as the value of the fuel which would be saved if the generators were built and operated with the present mix of conventional generating plant. In the UK, for wind power programmes of the order of a few GW, the fuel saved would mainly be coal, which currently costs 1.1- 1.2p/kWh of electricity sent out (coal at £25/tonne, 25 GJ/tonne). This gives us a rough measure against which to assess the estimates of cost of electricity from the Mod 2.

Discount rate

Robbins and Thomas 2 give a graph for the cost of electricity from Mod 2. I have converted the figures to p/kWh, and these are shown in Table 2.

According to these figures the Mod 2 in volume production is likely to be economic on sites with mean wind speeds (measured at the standard 10 m) of 16 mph or more.

However, the figures in Table 2 are worked out on the basis of an 18% capital charge rate, which is equivalent to a discount rate of about 17.9%. The discount rate currently recommended for the energy industries in the UK is 5% 3 and in addition the UK Department of Energy publicly expects fuel prices to double or treble by the year 2000. 4

The capital charge rate based on a 5% discount rate and depreciating over 30 years is about 6.5%, instead of 18%.

Table 3. Cost of electricity from Mod 2 windmill, using modified discount rate (p/kWh).

Mean wind First Mod 2 lOOth Mod 2 speed (mph)

12 1.9 0.74 14 1.4 0.53 16 1.2 0.44 18 1.0 0.42

Table 4. Breakaven value of electricity from Mod 2, assuming real fuel price increase (p/kWh).

Mean wind First Mod 2 lOOth Mod 2 speed (mph)

12 1.3 0.51 14 0.96 0.37 16 0.80 0.30 18 0.69 0.29

E N E R G Y P O L I C Y D e c e m b e r 1 9 8 0 3 4 7

Communications

As 91% of the cost of electricity given in Table 2 is capital charge, the ratio of cost of electricity based on a 5% discount rate to cost of electricity based on an 18% capital charge rate is:

COE (UK) 0.91 x 0.065 _ + 0.09

COE (US) 0.18

= 0.33 + 0.09 = 0.42

The cost of electricity is thus reduced by a factor of 2.4 by changing the discount rate. The result is shown in Table 3.

The implication of the above analysis is that the prototype Mod 2 machine will be economic on good sites, while if the economies of mass production are realised, the UK would be justified in installing Mod 2 machines at sites of below 12 mph mean wind speed.

Real fuel price

The situation changes again if we take into account expected real fuel price increases. A doubling of fuel price by the end of the century is about equivalent to a 4% per year increase. Taken with a 5% discount rate, this is formally equivalent to a 1% discount rate. On this basis the capital charge rate becomes 3.9%. The ratio of costs on these criteria to costs given by Robbins and Thomas-' becomes:

COE (UK) 0.91 x 0.039 - + 0.09

COE (US) 0.18

= 0.20 + 0.09 = 0.29

Strictly, the resulting cost figures are not costs of electricity but the lowest current marginal costs of electricity that the Mod 2 could economically displace assuming that the value of the fuel saved by the windmill increases at 4% per year. These marginal costs are given in Table 4.

Adding incremental costs

All of the above costs exclude the incremental system costs associated with wind plant, eg the costs of grid connection and load dispatching. Estimates of this cost in the U K are given in Energy Paper 21 and shown in Table 5. 6

These sums are for a 46 m diameter, 1 MW basic windmill design. I will assume

Table 5. Incremental costs (£1 000 (1977)).

Item Cost

Aerogenerators on site 1

Incremental cost 256 Incremental cost per machine 256 Total cost per machine (basic 364

price + incremental cost)

2 3 4 5

286 312 336 370 143 104 84 74 251 212 192 182

Note: The figures given in this table lead to double counting the cost of site access. The estimates of total costs are not greatly affected by this inaccuracy.

that between 2 and 5 machines are placed on each site and will inflate the costs by 15% per year to 1980. I will also assume that the incremental cost is independent of machine size. (This is not a bad assumption given the above figures.) The incremental cost per Mod 2 windmill in 1980 is therefore likely to be in the range £110-220 000. Converting these costs to p/kWh gives the results show in Table 6.

Finally, Table 7 shows the sum of costs of electricity for the 100th Mod 2 presented in Tables 3 and 4 and the system costs given in Table 6.

Conclusions

The breakeven value of wind generation from Mod 2 windmills, assuming a production run of at least 100, a 5% discount rate and a 4% per year real fuel price increase is likely to be in the range of 0.3-0.7 p/kWh. If the cost

assumptions are correct, UK Central Electricity Generating Board will be able to justify ordering Mod 2 windmills for sites with mean wind speeds below 12 mph, ie over most of the UK, within

a few years. Robert Lowe

Energy Research Group Open Universi ty

Mi l ton Keynes, UK

This paper appears in the proceedings of the Second British Wind Energy Association Workshop, 1980, published by the Multi-Science Publishing Co, The Old Mill, Dorset Place, London E15 1D J, UK, by whose kind permission it appears here.

l W.H. Robbins and R.L. Thomas, 'Large HAWT development', paper to the Workshop on Economic and Operational Requirements and Status of Large Scale Wind Systems, Monterey, CA, March 1979. 2 Ibid. 3 Energy Technologies for the UK, Energy Paper 39. HMSO, London, 1979. * District Heating Combined with Electricity Generation in the UK, Energy Paper 35, HMSO, London, 1979. s Robbins and Thomas, op cit, Ref 1.

The Prospects for the Generation of Electricity from the Wind in the UK, Energy Paper 21, HMSO, London, 1977.

Table 6. System incremental costs (p/kWh).

Mean wind 5% discount rate, speed (mph) constant fuel price

2 windmills 5 windmills per site per site

12 0.22 0.11 14 0.17 0.09 16 0.14 0.07 18 0.12 0.06

5% discount rate, 4% per year fuel price increase

2 windmills 5 windmills per site per site

0.13 0.06 0.10 0.05 0.08 0.04 0.07 0.03

Table 7. Cost of electricity, including system costs (p/kWh).

Mean wind 5% discount rate, speed (mph) constant fuel price

2 windmills 5 windmills per site per site

12 O.96 0.85 14 0.70 0.62 16 0.58 0.51 18 0.54 O.48

5% discount rate, 4% per year fuel price increase

2 windmills 5 windmills per site per site

0.64 0.57 0.47 0.42 0.38 0.34 0.36 0.32

3 4 8 E N E R G Y P O L I C Y D e c e m b e r 1 9 8 0