Economics of Electricity Supply

Abstract

This chapter provides an introduction to the economic concepts related to the electricity sector. It introduces the key concepts related to the electricity supply industry (such as load duration curve, capacity factor, and load diversity) and provides simple decision-making tools such as merit order dispatch, levelised costs and screening curves that are used in the industry.

Appendices

Annex 10.1: Levelisation Factor for a Uniform Annual Escalating Series

Assume that

• A is the annual cost in the first year,

• a is the escalation rate per year,

• n is the number of years used in the analysis,

• i is the discount rate,

• P is the present worth of the cost series,

• U is the annual levelised cost.

As the cost increases every year at the rate ‘a’, the cost changes from one year to the other as follows: A, A(1 + a), A(1 + a)2,…, A(1 + a)n − 1 

The present value of this cost series is given by

$$ \begin{gathered} P = {\frac{A}{(1 + i)}} + {\frac{A(1 + a)}{{(1 + i)^{2} }}} + {\frac{{A(1 + a)^{2} }}{{(1 + i)^{3} }}} + \cdots + {\frac{{A(1 + a)^{n - 1} }}{{(1 + i)^{n} }}} \hfill \\ \,\,\,\, = \,A\left[ {{\frac{1}{(1 + i)}} + {\frac{(1 + a)}{{(1 + i)^{2} }}} + {\frac{{(1 + a)^{2} }}{{(1 + i)^{3} }}} + \cdots + {\frac{{(1 + a)^{n - 1} }}{{(1 + i)^{n} }}}} \right] \hfill \\ \hfill \\ \end{gathered} $$

(10.13)

Multiplying Eq. 10.13 by (1 + i) results in

$$ \begin{gathered} P(1 + i) = A\left[ {1 + {\frac{(1 + a)}{(1 + i)}} + {\frac{{(1 + a)^{2} }}{{(1 + i)^{2} }}} + \cdots + {\frac{{(1 + a)^{n - 1} }}{{(1 + i)^{n - 1} }}}} \right] \hfill \\ \hfill \\ \end{gathered} $$

(10.14)

Multiplying Eq. 10.13 by (1 + a) results in

$$ \begin{gathered} P(1 + a) = A\left[ {{\frac{(1 + a)}{(1 + i)}} + {\frac{{(1 + a)^{2} }}{{(1 + i)^{2} }}} + \cdots + {\frac{{(1 + a)^{n} }}{{(1 + i)^{n} }}}} \right] \hfill \\ \hfill \\ \end{gathered} $$

(10.15)

Subtracting Eq. 10.15 from 10.14 gives rise to the following:

$$ P(i - a) = A\left[ {1 - \left( {{\frac{{(1 + a)^{n} }}{{(1 + i)^{n} }}}} \right)} \right] $$

(10.16)

Therefore, the present worth of this annual series is

$$ P = {\frac{{A\left[ {\left( {1 - {\frac{{(1 +a)^{n} }}{{(1 + i)^{n} }}}} \right)} \right]}}{(i - a)}} = A \times \left( {{\text{Present}}\;{\text{value}}\;{\text{function}}} \right) $$

(10.17)

where present value function is

$$\text{ \text{PVF}} = {\frac{{A\left[ {1 - \left( {{\frac{{(1 + a)^{n} }}{{(1 + i)^{n} }}}} \right)} \right]}}{(i - a)}} $$

The annual series U that would yield the same present value as above is given by

$$ U = {\frac{{\left[ {1 - \left( {{\frac{{(1 + a)^{n} }}{{(1 + i)^{n} }}}} \right)} \right]}}{(i - a)}}\left[ {{\frac{{i(1 + i)^{n} }}{{(1 + i)^{n} - 1}}}} \right] = \text {PVF} \times \text{CRF} $$

(10.18)

where

$$ \hbox{CRF} = \left[ {{\frac{{i(1 + i)^{n} }}{{(1 + i)^{n} - 1}}}} \right] $$

(10.19)

Note that the levelising factor is reduced to unity when there is no escalation (i.e. a = 0).

For the example in Fig. 10.4, a is 5%, i is 10% and n is 20 years. Using these data in Eq. 10.18 gives, U = 1.423.

For further details on these topics, see Stoll (1989) and Masters (2004).

Annex 10.2: A Brief Description of the WASP-IV Model

The WASP model developed by the International Atomic Energy Agency (IAEA) is a widely used tool that has become the standard approach to electricity investment planning around the world (Hertzmark 2007). The current version, WASP-IV, finds the optimal expansion plan for a power generating system subject to constraints specified by the user. The programme minimises the discounted costs of electricity generation, which fundamentally comprise capital investment, fuel cost, operation and maintenance cost, and cost of energy-not-served (ENS)⁴ (International Atomic Energy Agency (IAEA) 1998). The demand for electricity is exogenously given and using a detailed information of available resources, technological options (candidate plants and committed plants) and the constraints on the environment, operation and other practical considerations (such as implementation issues), the model provides the capacity to be added in the future and the cost of achieving such a capacity addition.

To find optimal plan for electricity capacity expansion, WASP-IV programme evaluates all possible sets of power plants to be added during the planning horizon while fulfilling all constraints. Basically, the evaluation for optimal plan is based on the minimisation of cost function (International Atomic Energy Agency (IAEA) 1984), which comprises of: depreciable capital investment costs (covering equipment, site installation costs, salvage value of investment costs), non-depreciable capital investment costs (covering fuel inventory, initial stock of spare parts etc.), fuel costs, non-fuel operation and maintenance costs and cost of the energy-not-served. Overall, the structure of WASP-IV programme can be presented in Fig. 10.7.

Fig. 10.7

Overall structure of WASP-IV

The model works well for an integrated, traditional system but the reform process in the electricity industry has brought a disintegrated system in many countries. The model is less suitable for such reformed markets.