Projected Costs of Generating Electricity - OECD Nuclear Energy ...

Appendix 7
Allocating the Costs and Emissions
of CHP Plants to the Produced Electricity and Heat
The appendix introduces a theoretical approach to cost and emission allocation for a combined heat and
power plant. This method was not used to estimate electricity generation costs of the CHP plants
considered in the study (Chapter 5) but may be considered in future studies dedicated to dual product
plants.
Endoreversible thermodynamics improves the insight in the behaviour of the efficiency for the
conversion of heat into work. A new relation is derived which relates such an endoreversible efficiency
to the efficiency of a real engine. The behaviour of this relation has been compared to existing ones,
e.g. efficiency relations of Curzon-Ahlborn and Carnot. Further the behaviour of the efficiency of real
engines is modelled as a function of upper and lower temperatures. The relations concerned are used to
allocate costs and emissions of combined heat and power (CHP) plants to electricicty and heat produced.
1. Law of conservation of energy, which reads:
Σ Q i + W = 0
where Q i represent the heat flow per unit of time at temperature T i and W is work flow per unit of time
over one complete cycle of an engine.
App.
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2. Law of increase of entropy, which reads:
∇ S ≥ 0 where S i = Q i /T i
Carnot engine
From these laws a Carnot engine can be defined (Figure A7.1), which has the following characteristics:
1. It possesses a high temperature heat reservoir (T 1 ) and a low temperature heat reservoir (T 4 ).
2. A work cycle of two adiabatic and two isothermal paths which form a closed cycle and which is completed
in a reversible way. This means that:
∇ S = 0 or Q 1 /T 1 –Q 4 /T 4 = 0 (1)
in which Q 1 is the heat flow from the high temperature heat reservoir to the engine and Q 4 the heat flow
from the engine to the low temperature heat reservoir.
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