Equation 5.2 is the formulation for LCOE provided by PCGE. The top row represents the summation of the various costs (apart from ‘O&M’, which stands for operation and maintenance, the notation should be obvious), discounted at a rate r for the year in which they occur. The bottom row expresses the total amount of electricity generated, again, discounting this according to the year in which it was produced.

^ ((Investmentt + О & Mt + Fuelt + Carbonf + Decommissioningf)(l + r) ‘)

[5.2]

(Electricityt (1 + r) )

Computations of the LCOE can be greatly simplified by making a few assumptions, namely, that:

• the investment cost occurs in year zero and includes interest paid on capital (assumed for simplicity to be at the discount rate) during the period ofconstruction

• the discount rate (r) is constant with time

• costs that occur during the operational period (O&M, fuel, carbon and decommissioning) have constant yearly values

• the same amount of electricity is generated every year.

The conceptual scheme represented by these assumptions is shown in Fig. 5.2. Under these conditions it can be shown that

[5.3]

where,

CAP is the capital cost component of the LCOE;

DECOM is the decommissioning cost component of the LCOE, explained further below;

OPER is the operating and maintenance cost per unit of electricity generated;

FUEL and CARBON are the costs of fuel and carbon per unit of electricity generated;

nth is net thermal efficiency of the generating plant (which makes allowance for electricity consumed by the plant);

INVEST is the overnight cost (capital costs plus contingency, per electrical output of the plant calculated as though all the costs were incurred overnight);

Availty is availability, the ratio between the actual output and the theoretical maximum;

c is the length of the construction period (years);

f is the cost of decommissioning as a fraction of the overnight cost;

n is the length of the operational period (years);

I is the normalised financing cost i. e. the multiplier that must be applied to the overnight cost because of the delay (caused by the construction time) in creating the asset;

R is the capital recovery factor;

r is the discount rate; and

8760 is the number of hours in a year.

Total decommissioning costs are assumed to equal a fixed fraction (f) of the overnight cost. These costs are met by paying a constant annual amount (DECOM) into an accumulating decommissioning fund throughout the period of operation. The fund is assumed to earn interest at a rate, i, that is lower than the discount rate. This allows decommissioning management to be treated as an operating cost and answers the argument that the application of discount rates over long periods does not respect the principle of intergenerational equity.2 This approach is equivalent to that used for waste
management and disposal where the costs are included in the price of the fuel. In this case

[5.4]

n x Availty x 8760 (1 + z’)((l + i)n -1)

An advantage of Eq. 5.3 is that it provides a clear demonstration that the LCOE scales linearly with decommissioning, maintenance, fuel and carbon costs. The influence of net thermal efficiency and availability also become apparent. Cost discounting is represented by two terms: the first of which (I) represents financing costs and the other (R) is the capital recovery factor. This can be regarded as the annual payment that must be made, given n and r, to raise a capital sum of unity. When r = 0, R reduces to 1/n, which shows that the practice of amortising the capital cost over the lifetime of the plant, which was common practice until the 1970s, is equivalent to a discount rate of zero, an assumption that greatly favours high capital cost plant.