The Orchard Convention
This convention for the analysis of CHP calculates the fuel burn per unit of heat by comparing electricity generators with different electrical efficiencies to each other to calculate the amount of fuel to allocate to the heat to equalise fuel use per unit of electricity from competing CHPs feeding an electricity network.
The method does not require any assumption about alternative source of heat displacement in the heat sector. It thus allows the heat and electricity sectors to be modelled as separate entities for the different products heat and electricity.
The convention allows simple comparisons between CHP heat and other measures to decarbonise or reduce primary energy use in the heat sector. The model allows easy comparison of the capital costs of insulation of buildings, new boilers, heat from electric or directly driven heat pumps and other heat sources to low CO2 heat supply from CHP/DH.
Calculation of percentage savings for all the different options for the heat sector are then comparable, all relating to a heat and the heat sector, with no electricity sector element in the calculation as can arise for calculations for CHP.
This paper is intended to be read in conjunction with the excel spreadsheet which models the formulas and allows the selection of different parameters to generate the charts.
Symbols in the paper and the equations follow conventions in the EU Cogeneration Directive
2 Symbols used in Excel Spreadsheet and Charts.
| CHPE+H? | CHP Overall Efficiency (CHPE? + CHPH?) |
| CHPEFB | CHP Fuel Burn per unit of Electricity |
| CHPEPES | CHP Primary Energy Savings per unit of electricity |
| CHPE? | CHP Electrical Efficiency |
| CHPHFB | CHP Fuel Burn per unit of Heat |
| CHPHPES | CHP Primary Energy Savings per unit of heat |
| CHPH? | CHP Heat or Thermal Efficiency |
| CO2 | Carbon Dioxide |
| CoP | Coefficient of Performance |
| FB | Fuel Burn (units of fuel per unit of energy (electricity or heat) |
| lossesE | Electrical distribution losses |
| lossesH | Heat distribution losses |
| PES | Primary Energy Savings |
| Ref | Reference Heat or Electricity Source (Power Plant or Boiler) |
| RefEFB | Fuel burn per unit of electricity from reference power plant (=1/ RefE?) |
| RefE? | Efficiency of reference power plant |
| RefHFB | Fuel burn per unit of electricity from reference boiler (= 1/ RefH?) |
| RefH? | Efficiency of reference heat source |
| ? | Efficiency |
3 Calorific Values, Nett and gross, lower and Higher.
The charts use the higher or gross calorific value (CV) of the fuel.
The nett or lower CV assumes that we cannot condense the vapour in exhaust gases.
Condensing this vapour is increasingly common. The result is the reporting of efficiencies of over 100% because due to the lower or nett CV only measuring part of the total energy available in the fuel.
There is a strong case to revert to the original gross CV as the basis for all efficiency calculations as it reflects the maximum potential energy in the fuel it also puts fuels and fuel conversion appliances on a common basis when assessing their comparative performance by measuring efficiency.
4 Principle for determining fuel use per unit of heat for CHP.
We illustrate the results from the algorithm and model in the following chart to illustrate how it works.
We allocate all fuel initially to electricity the purple line. We do not allocate fuel to heat, the green line. This reflects electricity generation where no use is made of its waste heat.
The model then compares power plants with different electrical efficiencies and overall efficiencies for the two different useful products waste heat at a suitable temperature and electricity. We calculate a fuel use for the heat that means in electricity from less efficient electrical generation plant has the same fuel use per unit of electricity as the reference plant.
4.1 Reference power plant.
We select a reference power plant, RefE?, for comparison with other electricity generation plants with their different efficiencies.
The electrical efficiency of a sample reference power plant in Figure 1 is a 50% efficient CCGT rejecting the other 50% of its fuel as heat at 28C from to its cooling towers and 80C from its chimney.
A yellow line rising from the X-axis represents the CCGT. The line cuts the purple curve at two units of fuel the fuel use per unit of electricity. The purple curve charts fuel use for other power plants with either higher or lower efficiencies than the reference plant. We show a range of electrical efficiencies from 0% to 60% on the X-axis.
We show units of fuel use either for electricity or heat on the Y-axis.
4.2 Overall efficiency.
The overall efficiency (CHPE+H?) reflects the sum of the waste heat delivered usefully to the heat sector and useful electricity for the electricity sector.
An overall efficiency of the CHP (CHPE+H?), of 80%, a typical value for both small and larger CHP[1] is selected for the sample chart.
4.3 Heat efficiency.
We calculate “heat efficiency” for the heat element from the CHP as the overall efficiency minus the electrical efficiency: CHPH? = CHPE+H? – CHPE. Reflecting the useful heat element of the joint products.
4.4 Method to determine fuel use per unit of useful heat.
The model allocates fuel from electricity to heat for electricity generators where their electrical efficiency is lower than the reference power plant, so that the electricity from both plants have the same fuel use per unit of electricity.
Figure 1: Fuel burn per unit of electricity or heat from CHP (Orchard Convention)
The fuel allocation calculation in the “Orchard Method” now works in the following way:
The purple curve reflects the (fuel burn per unit of electricity, calculated as CHPEFB = 1/CHPE?).
The green line zero on the Y-axis, the fuel burn per unit of heat, CHPHFB = 0).
Where the electrical efficiency of the CHP (CHPE?) is higher than the electrical efficiency of the reference power plant (RefE?), the fuel burn for the heat is assumed to be zero, point A on the chart.
The fuel burn for the electricity, where the electrical efficiency of the CHP is equal or higher than the electrical efficiency of the reference power plant, is shown at point B. The blue curve follows the purple curve as we allocate all fuel burn beyond point B and reference efficiency to the electricity sector, reducing the fuel use in that sector from higher efficiency electricity generation.
For CHP with electrical efficiencies smaller than the reference electrical efficiency, the fuel burn for the electricity, to the left of point B, stays at the same value as the fuel burn of the reference power plant shown by the blue horizontal line.
The additional fuel burn per unit of electricity due to its lower efficiency is the difference between the purple and blue line in the chart. We allocate this fuel to the relevant units of heat.
Note the difference between the purple and blue line gets larger as we move away from point B.
Note also the ratio between heat and electricity production of the CHP changes. The increasing difference between the blue and purple lines is allocated to the increasing heat production per unit of electricity.
This is the reason the path of the red line is different from the path of the purple line.
At point C on the chart, the CHP’s electrical efficiency is zero. No heat is being converted to electricity this point thus has the same characteristics as a boiler with the same efficiency as the overall efficiency of the heat and electricity from the CHP.
As the overall efficiency is in this example is set to 80%, point C shows a boiler that is 80% efficient. The fuel burn per unit of heat of such a boiler is 1/80% = 1.25.
The fuel burn for the electricity and heat from CHP can be expressed using the following formulas:
4.5 Formula for calculation of fuel use per unit of heat from CHP.
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for CHPE? > RefE? |
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for CHPE? < RefE? |
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for CHPE? > RefE? |
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for CHPE? < RefE? |
The following figure shows the same chart with different input data: The CHP units still have the same overall efficiency of 80%, but with a different reference power plant that is now 33% efficient (for example, a nuclear, coal or large biomass fired power plant).
Figure 2: Fuel burn per unit of electricity or heat from CHP (different reference power plant)
Note our scale changes on the Y-axis.
The orange vertical line moves to a new point A and B. Point C does not change as it reflects the same overall efficiency for electricity and heat production as Figure 1.
CHPEFB the red curve is now steeper and dropping faster but starting at the same point C.
4.6 Other spreadsheet functions.
The spreadsheet calculates CO2 emissions and primary energy savings from the fuel use per unit of heat that forms the basis of the Orchard Method.
A useful output is the CO2 footprint for the heat when there are different fuel inputs to the CHP.
One result from the model is that it shows significant CO2 savings arising in the when we supply the heat sector with heat from coal fired CHP serving a low temperature district heat there are significant displacements of CO2 compared to heat from gas fired boilers.
A supplementary paper explains how the model accounts for marginal and average losses on electricity and heat networks. It analyses the effects of location in making comparisons between reference remote electricity generation and local CHP. The paper also explains how primary energy savings in the heat sector are calculated where the CHP heat displaces heat from boilers, electric heating, electric heat pumps and other heat sources.
WRH Orchard.
March 2011
[1] Note: The overall efficiency for heat and electricity output for micro CHP engines tends to be similar to that of very large scale CHP. The important factor for optimal use of fuel is as high an electrical efficiency as possible for the same overall efficiency for the two products.