1. Lecture 9: Allocation of costs to products
Staff Scientist, Dr. Sc. (Tech.) Timo Laukkanen

2. Allocation of fuels, emissions and costs in a CHP plant
In the case of condensing power plant, district heating plant etc., calculation of the production cost / carbon emissions etc. is relatively straight forward
When electricity and heat are being produced together in a CHP plant, it is not immediately clear how the costs and emissions should be priced
A number of different methods have been developed, based either on thermodynamic or market-based approaches.
Different methods give different results -> important to choose most appropriate methods for a given situation.
Depending on the used methods, different conclusions can be derived on how the plant is optimized or how energy savings investments should be valued

3. Allocation of fuels, emissions and costs in a CHP plant
Energy method
Exergy method
Work method
Alternative energy production method
Method based on fuel consumption ratios of heat and power
Benefit distribution method
Method based on economic value of the products (market-based method)
First residual method

4. Allocation of fuels, emissions and costs in a CHP plant
Energy method
It divides fuels based on the amounts of energy products, i.e. according to the efficiency of the CHP plant.
The fuels can be allocated to electricity (Fe) as follows:
And for heat (Fth):
where E is the electricity production, H is the heat production, and F is the fuels used by the CHP plant.
• The advantage of this method is that it is easy to use.
• The main disadvantage is that it can lead to higher costs for heat than would be the case in a heat-only boiler because of the possible higher efficiency of a heat-only boiler (up to 95%) as compared with up to 90% of a CHP plant.

5. Allocation of fuels, emissions and costs in a CHP plant
Allocate CHP fuel consumption?
• Fe = 30/(30+55)*100 MWh = 35.3 MWh
• Fth = 55/(30+55)*100 MWh = 64.7 MWh
Fuel cost (20 €/MWh) allocation?
• Fe = 30/(30+55)*20 €/MWh = 7.1 €/MWh
• Fth = 55/(30+55)*20 €/MWh = 12.9 €/MWh

6. Allocation of fuels, emissions and costs in a CHP plant
Exergy method
In the exergy method, the allocation of fuels is based on exergy flows of the energy products (electricity and heat).
Exergies can be calculated, when entalpies and entropies are known.
Fuels are allocated to electricity Fe and heat Fth as follows:
Thermal exergy, Hex can be calculated as follows:
This method is rather complicated to use, but it can be considered as the fairest allocation method from a thermodynamic point of view.

7. Allocation of fuels, emissions and costs in a CHP plant
Benefit distribution method
The fuels used in CHP production are allocated to electricity and heat in the proportion of fuel consumption for the alternative energy supply forms.
The fuel consumption of the alternative forms of energy supply, F’e for electrical energy and F’th for thermal energy, can be calculated according to the equations below:
where E is CHP electricity production, ηe the efficiency of condensing power, H is CHP heat production, and ηth the efficiency of heat-only boiler.
The fuel consumption in the CHP plant is then divided as follows:
This method is relatively easy to use and it divides the benefits of CHP production between both electricity and heat.

8. Allocation of fuels, emissions and costs in a CHP plant
Benefit distribution method
Fuel consumption of alternative forms
of energy supply?
• F’e = 30 MWh / 0.36 = 83 MWh
• F’th = 55 MWh / 0.8 = 69 MWh
CHP plant fuel consumption allocation?
• Fe = 83/(83+69)*100 MWh = 55 MWh
• Fth = 69/(83+69)*100 MWh = 45 MWh
Fuel cost (20 €/MWh) allocation?
• Fe = 83/(83+69)*20 €/MWh = 11 €/MWh
• Fth = 69/(83+69)*20 €/MWh = 9 €/MWh

9. Allocation of fuels, emissions and costs in a CHP plant
Comparison of allocation results

10. Allocation of fuels, emissions and costs in a CHP plant
First Residual method
Assume that market price for electricity is 50 €/MWh, and fuel costs 20 €/MWh, alfa= 30/55, Eta= (30+55)/100
Price for heat:
Heatprice= Cfuel*(1+alfa)/Eta -Electricityprice*alfa
Heatprice= 9.1 €/MWh

11. Allocation of fuels, emissions and costs in a CHP plant
First Residual method
The clear benefit of the method is that in industrial CHP the heat costs reflect the electricity market condition
Use heat when electricity is expensive, save heat when electricity is cheap
Example: electricity price is 500 €/MWh, fuel cost is 20 €/MWh
 Heat cost= -236 €/MWh
Example: electricity price is 5 €/MWh, fuel cost is 20 €/MWh
 Heat cost= 33.6 €/MWh
Is it necessary to the heat consuming units to act so flexibly to changes in energy prices?