Energy is the capacity to do work. We make our lives easier by using energy to do work for us. In so doing, the energy is transformed: from natural gas to heat, from coal to electricity, from electricity to light. Any model of the energy system is therefore necessarily a model of the transformation of energy from one form to another.
The 2050 Calculator is such a model. It tracks the energy used by a country from its original sources to its final uses. This note explains how the Calculator keeps track of energy, what the different kinds of energies mean, and the physical principles the Calculator models.
You can read this note either before you have opened the Calculator or after you have looked at it for a bit. If you have never opened the Calculator then you should read the first few sections, at least until you have an idea what a "fuel type" is. Then look at one of the annual summary worksheets in the Calculator (the tabs labelled by years) so that you can make these ideas concrete.
If you have already opened the Calculator then you will likely have a number of questions---among them, I suspect, "why is there a 'gaseous hydrocarbons' fuel type?", and "what's up with bioenergy?" Those questions are answered below but it is nonetheless worth reading the first few sections. Knowing the precise meaning of "fuel type" is helpful to understanding the answers to those two questions.
The rest of this note is structured as follows. First, I describe a simplistic energy system, used in the subsequent sections as an example. The main section explains the entities found in the Calculator. Then there is a short comparison to the usual way of presenting national energy accounts. Finally, there is an explanation of some of the design principles which motivated the workings of the Calculator, and a discussion of the ways in which original Calculator falls short of those design desiderata.
In order to get a feel for the sort of system the Calculator models, it's instructive to consider a very simplistic energy system and to follow one particular flow of energy all the way through that system. The diagram below shows a simplified version of that part of the energy system which involves gas as a fuel for power generation. I shall describe the steps in this system one by one.
Buried under the North Sea are reserves of methane, a source of chemical energy. For this gas to be of any use it first has to be got out from under the North Sea. In the Calculator, extracting gas from under the North Sea is modelled as a transformation of "gas reserves" into "natural gas".
Of course, gas under the North Sea is "natural gas", so there is a sense in which no fundamental transformation has taken place. Nonetheless, for the purposes of the energy system, gas under the North Sea is a very different thing to gas in a pipe. In particular, there are sources of natural gas other than gas reserves (for example, imports) and these must be distinguished to allow proper reporting. In addition, some energy is required to extract the gas (more on this later). So it is important to keep separate the two forms of gas and this is what the Calculator does.
Before being used as a source of energy, gas in the Calculator is first transformed into "gaseous hydrocarbons". That transformation might seem silly as well. After all, natural gas just is a gaseous hydrocarbon, so why not just model its consumption directly?
The reasoning is the same as above. There are sources of methane other than natural gas, such as gas created by the anaerobic digestion of biomass. Methane from recent biogenic sources is just as good, to a user, as methane which came from more distal sources and was buried underground. We need to keep track of these sources but we don't want to add unnecessary complexity to a sectoral model by requiring it to know the difference. I will say more about this later.
The next step in our example more what one would consider a real transformation of energy: The gas is burnt, in power stations, to produce electricity, which is carried to homes by the National Grid. And at this point in the model, something odd appears to happen.
We must account for the use of energy to produce something useful, such as illumination. Now, light is of course a form of energy. However, most national energy statistics make no attempt to quantify the energy produced in the form of light. Instead, they capture only the amount of electricity used by the light bulb. The Calculator does something similar. The final form of energy captured by the Calculator, "lighting and appliances", represents the total energy used in the production of those services, not the energy of those services.
In summary, the diagram above shows the physical reality of one particular energy flow in the UK's energy system. The next few sections explain how this reality is captured in the calculator.
Now, the Calculator is a model, and a model must be precisely specified. Up to now I have described the different kinds of energy in English, but that is insufficiently precise for a computer model. Therefore, the Calculator gives a code to each kind of energy and insists that only energies with codes are allowable as energy kinds.
The codes for the previous example are shown in the figure below.
There is obviously some structure to these codes: they consist of a letter followed by a two-digit number. One might suspect that energies whose codes have the same letter have something in common, and that is correct; but note that this fact is not used in the Calculator. To the Calculator, all codes are opaque; that is to say, meaningless.
A form of energy as the Calculator understands it—that is, a form of energy with a code—is called a fuel type. (Occasionally fuel types are referred to as energy vectors; "vector" in the epidemiological sense of "carrier of something" rather than in the mathematical sense.)
The Calculator treats fuel types in a very formal way. The result of any activity modelled by the Calculator must be a set of energy flows, where each energy flow is to or from a particular fuel type. Fuel types are the fundamental unit of account in the Calculator.
The activities which convert energy from one fuel type to another are also codified. A group of related activities, modelled on a single worksheet, is called sector. Sectors also have codes. The figure below shows the sectors that are used to implement the transformations in the example.
There is something missing from the diagrams I have drawn so far. They show only a part of the story. For example, the production of gas from gas reserves itself consumes gas, but that consumption is not shown above; the production of electricity from gas does not produce as much electrical energy as chemical energy in the gas; the Grid does not transmit to consumers the full amount of electrical energy sent into it.
In other words, there are flows of energy that are present in the physical system but not shown in the previous diagram. The figure below shows the diagram with the missing flows included. I've included example energy flows---these flows have physically reasonable relative sizes but are otherwise invented for the purpose of this example.
Fuel type X.01 captures conversion losses such as energy lost as waste heat in
a power station. Fuel type X.02 captures distribution losses and "own
use". There is a distribution loss in sector XVI.a (which transforms natural
gas into gaseous hydrocarbons) because, in the Calculator, this sector also
models the gas distribution network.
Fuel type I.01 represents energy consumed by industry and is included because,
in the Calculator, energy consumed by the extractive sectors counts as
industrial demand.
The Calculator insists that all flows of energy are captured in the model. It is straightforward to check whether all flows have been captured because it's a physical principle that energy can't come from nowhere or disappear into nothing. The net balance of all energy entering and leaving a sector must be zero: energy is "conserved." We sometimes refer to this idea as the "energy balance principle".1
It turns out that, if nothing else, checking whether or not the energy balance principle holds for each sector is a very good way to find bugs.
Type Code Description
Primary sources Q.02 Oil reserves
Q.03 Gas reserves
Secondary vectors C.02 Oil and petroleum products
C.03 Natural gas
V.01 Electricity (delivered to end user)
V.02 Electricity (supplied to grid)
V.04 Liquid hydrocarbons
V.05 Gaseous hydrocarbons
V.07 Heat transport
Final demands X.01 Conversion losses
X.02 Distribution losses and own use
I.01 Industry
L.01 Lighting & appliances
: Fuels types used in the example, for reference.
Code Description
XV.b Indigenous fossil fuel production
XVI.a Fossil fuel transfers
I.a Power generation
VII.b Electricity grid distribution
X.a Domestic lighting, appliances, and cooking
: Sectors used in the example, for reference.
One way to think about a 2050 Calculator is as a sort of accounting system for energy. Energy is converted from one form to another by the sectors; the point of the rest of the Calculator is to keep track of where the energy comes from and where it goes.
The diagrams in the example above show graphically how energy flows through the real system. But there aren't any circles or arrows in the Excel model: there are just numbers. This section describes the way in which the energy flows are laid out in the Calculator.
The are two kinds of entity in the Calculator (fuel types and sectors) so it is natural to arrange the energy flows in a two-dimensional table, whose rows and columns are indexed by the sectors and the fuel types. That is precisely what is done in the "annual summary" sheets. Here are the full flows from the the example, rewritten as a table in the style of the annual summary sheets:
Energy Q.03 C.03 V.01 V.02 V.05 I.01 L.01 X.01 X.02
XV.b (100) 100 (2) -- (1) 3 -- -- --
XVI.a -- (100) -- -- 99 -- -- -- 1
I.a -- -- -- 38 (98) -- -- 58 2
VII.b -- -- 34 (38) -- -- -- -- 4
X.a -- -- (32) -- -- -- 32 -- --
: Tabular summary of the same energy flows as in the flow diagram. Parentheses indicate negative values. Note that the "natural direction" is left-to-right, in contrast to the annual summary worksheets in the Calculator which flow right-to-left. Rows may not sum exactly to zero due to rounding.
The sum of all flows of energy in each row of the table is necessarily zero. In the Calculator, this sum is computed explicitly to make it clear whether the model is obeying the energy balance principle or not.
The total of a column is not necessarily zero. Typically, the total of a primary
source (or final demand) fuel will be non-zero and will indicate the total
energy produced (or consumed) by that source (or use). For example, in the table
above, the total of L.01 is 32, and indicates that 32 units of energy were
consumed for lighting an appliances.
Fuel types representing real fuels do sum to zero in the Calculator, as the Calculator does not "carry over" an energy balance from one year to the next.2
In the final part of this note I want to explain the relationship between the tabulation described above and the arrangement that is usually used to present a country's national energy accounts. Before doing so, however, there are two oddities that the reader might be puzzling over. The first concerns the hierarchical nature of fuels; the second is about the meaning of "primary source" and "final demand". I shall take these in order.
The Calculator has no sense of "similarity" of fuel types. To the model, the difference between "natural gas" and "electricity" is no greater and no less than the difference between "electricity (delivered to grid)" and "electricity (delivered to consumer)".
However, looking at the complete list of fuel types (at the end of this Appendix), you will see a number of fuel types that appear not only to be similar but even to overlap. For example, "coal and fossil waste" is presumably a subcategory of "solid hydrocarbons"; "natural gas" is definitely a subcategory of "gaseous hydrocarbons." What is going on?
The first thing to note is that there is naturally a hierarchy of fuels. Lignite, for example, is a kind of coal, which is a kind of solid hydrocarbon, which in turn is a kind chemical energy. However, I do not know of a usable method of managing hierarchies of categories in Excel.3 We got around this problem in the original Calculator simply by not explicitly representing the hierarchical relationship, which is why apparently overlapping fuel types coexist. Perhaps it's more correct to say that we ignored the problem.
But why did we bother having these overlapping types at all? Why have the "higher level categories", such as natural gas? After all, actual, real fuels are always of a particular type, such as lignite. Why not just record these in the Calculator and ignore the general kinds?
The answer is that it helped to simplify the sectoral models. Consider transport, for example. Cars typically use specific kinds of liquid fuel: either petrol or diesel. But the technologies which use these fuels (variations on the internal combustion engine) are for all intents and purposes identical. Yes, there are engineering design differences, but the efficiency is about the same, as are the emissions for a given energy consumption. So there's no need to model both these kinds of technology in the calculator. Since there's no need, we shouldn't do so; it would only introduce unnecessary complications.
Indeed, for the purposes of the transport sector, even liquid biofuels count as the same kind of energy and the technology which uses them is the same technology. There's no point in distinguishing biofuel powered cars from petrol or diesel powered ones. We don't need to maintain tables of efficiencies and emissions intensities for all three; we just assume there's one kind of car which uses "liquid hydrocarbons" as a fuel.
On the other hand, energy is produced in these different forms and there are usually constraints on the production of different forms, not to mention that users of the model typically like to know how much comes from each. For example, some liquid hydrocarbons are, in fact, petroleum based whereas others are biogenic. There are limits on biogenic fuels chosen by the user; the balance must come in the end from oil reserves.
All of this goes some way to explaining why there are some sectors (such as
XVI.a, "Fossil fuel transfers"), which don't seem to implement a particular
transformation or use of energy, but instead recategorise energy from a
more specific form to a more general one.
If there is a general principle, it might be this: in the model, energy is produced in the most specific form appropriate and consumed in the most general form possible. It would be nice if the model could do the recategorisation automatically, as required, but it doesn't.
I have alluded briefly to the different nature of "primary source" and "final demand" fuel types: they represent the point where the model stops tracking the nature of the energy. The value of the "lighting & appliances" fuel type, say, refers to the total energy consumed by this sector, rather than the energy in light.
For certain sectors this difference is starker. It is hard even to say what energy one should count in measuring "transport". Kinetic energy of the car, perhaps? Yet the car eventually stops. An initially promising approach is to measure final demand in terms of the theoretically minimum energy required to achieve the observed service demand. (The difference between the energy entering the sector and the minimum required would be captured in an "inefficiency" fuel type.) But even that doesn't work for transport: the energy theoretically required to transport something from A to B can be made as close to zero as you like (ignoring friction in the mechanism of the car) simply by going slowly enough.
The choice of where to stop tracking energy flows is somewhat arbitrary. Stopping too soon introduces challenges of interpretation. In the current calculator, the "final demand for lighting" is the energy consumed by lights, not the "service demand" (which would presumably be the energy of light emitted). Suppose that lighting demand decreases in some pathway. It's not possible to tell, from the output of the Calculator, whether lighting demand is decreasing because the demand for illumination is lower, or because lights are becoming more efficient. But we have to stop somewhere, at least if we want to quantify service demand in some way, lest the entire Calculator simply become a method of converting nuclear energy into heat.
Those fuel types which represent energy in a form that doesn't have a counterpart in the real world are called nominal fuel types. In contrast, fuel types which represent energy that one could, in principle, point to, are called real fuel types.4
Nominal fuel types are a consequence of insisting on the energy balance principle. We have to stop tracking the energy flows somewhere, but the energy balance principle mandates that the energy has to come from, or go to, somewhere—so we invent a fuel type to act as the source or the destination. Nominal fuel types therefore represent the initial, "primary", source of energy in the model; and the final destination of all energy.5
The table in the figure shows a traditional presentation of the energy system described in the example above.6
On the face of it, this presentation looks similar in some respects to the tabular view used in the Calculator. There are descriptions of activities down the left hand side, and the columns are labelled by types of energy. However, there are two obvious differences: First, only the real fuel types are shown; and, second, those sectors that are part of the "energy system" are treated specially.
These traditional presentations should be read from top to bottom. The top section shows the production of energy from "primary sources"; the middle section shows the transformation of energy from one real form to another; and the bottom section shows the uses of energy. (The sign convention is somewhat confusing, and I am not convinced about the placement of the subtotals, but the meaning can usually be understood from the context.)
The connection between these two presentations can be made closer by imagining that the "total" column in the traditional view is really a catch-all term for various nominal fuel types. So, for example, in the top section, "total" really refers to a primary source; in the middle section it means either losses or final demand, depending on the nature of the activity; and in the bottom section it means final demand.
In this section I outline some of the design choices we made in developing the Calculator and describe the reasoning behind them. Some of these decisions stem from the nature of the problem, others arise from quite abstract design principles, and some simply from the author's previous experience.
The first rule of modelling that one learns is "divide and conquer". To follow this rule is to decompose the full problem into a number of smaller problems which are (ideally) easier to solve.
In some sense, the application of this rule to energy system modelling is almost trivial. The energy system is naturally made up of individual parts---power stations, light bulbs, cars, and so on---and so that is typically how it is modelled. In the Calculator, we follow this principle by decomposing the energy system into sets of related activities, called sectors, and model each sector on a separate worksheet.
Of course, once the model becomes a collection of smaller models, the question arises of how to re-integrate the component parts. It is necessary to define, for each sub-model, an interface. An interface is an agreement between the submodel and the rest of the model about how the two parts will interact.
The general principle here is that the fewer things there are for the modeller to worry about the better. So the ideal is for different component parts to have the same interface, so far as possible, and for this interface to be as simple as possible. In other words, one should try to abstract the nature of subparts of the model so that they are all examples of the same kind of thing.
This principle is followed in the Calculator in the following way. The model is decomposed into sectors (which are really collections of related activities); all sectors are the same kind of submodel in that they all compute energy flows. These energy flows must be given as increases or decreases of energies of particular fuel types, and the fuel types are universal within the model.7 Under this view, a sector is simply a way of computing a set of energy flows. The interface to each sector is just the set of such flows.
Indeed, it was a design desideratum that the only interaction between sectors should be by way of the energy flows. This principle was for the most part followed. For example, the "last resort" power sector---gas-fired power generation---"decides" how much electricity to generate by producing whatever is required to make up the difference between total consumption and all other forms of generation.8
The principle of abstraction also goes some way toward motivating the introduction of nominal fuel types. With these fuel types, all sectors are the same kind of thing; without those fuel types, the supply sectors would be different entities to the transformation sectors and to the demand sectors.
In a model with only real fuels, the calculation of total demand requires the model to sum the total fuel used by the demand sectors, excluding the other two kinds of sector. With nominal fuel types, the model instead adds up the total flows of all final demand fuel types, regardless of sector. That might not seem like an improvement but it does have the very important implication that adding a new sector is more straightforward. The modeller only needs to specify which fuel types are used; it is not necessary to identify the sector as demand-side, supply-side, or part of the "energy system" somewhere else in the model. Since adding sectors is a more common occurrence than modifying fuel types, this would appear to be a good trade-off.
We introduced nominal fuel types for another reason which is that the author already had some experience with bookkeeping systems. Financial systems and energy systems are similar: they value everything in the system using the same measure (either by money or by energy) and you can't create or destroy that measure overall. Bookkeeping systems---proper ones---universally use "double-entry accounting". All that means is that every credit or debit of money must be matched by a corresponding debit or credit. If you receive money into your bank account, there must be somewhere for it to have come from; if you spend money, there must be somewhere for it to go. One necessarily arrives at nominal accounts.
Another way of looking at this comes from the idea of a conserved quantity. A conserved quantity is a quantity that is guaranteed to be unchanged by the action of the model. Therefore, by checking that it is unchanged, we can test whether the model is working as expected. In the case of the Calculator, that conserved quantity is energy, and the principle of conservation of energy is what we have called the "energy balancing principle". The nominal accounts allow us to define and compute a conserved quantity.
In summary, the principles we have tried to follow are:
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All sectors are equivalent (to the model).
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All fuel types are equivalent (to the model).
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All interactions between sectors are through the energy flows alone.
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All output from the model can be derived from the totals of the energy flows for each fuel type (this principle was not universally followed; see later).
In this final section, I'd like to talk about what improvements one could imagine making to the Calculator; improvements, at least, that one could make to the conceptual framework, without delving into the details of any particular sector. Most of these thoughts are attempts to narrow the gap between the ideal design principles set out above and the reality of the Calculator. Some of that gap stems from the limitations of Excel. But some of it arises because we didn't manage to solve all the conceptual problems that came up. I think it's certainly possible to do better in two areas and perhaps possible to do better in a third, but maybe not in Excel. Those three areas are: (1) Communication between sectors; (2) Output from the model; and (3) Hierarchies of fuel types.
There are a number of places where an apparently ad hoc energy flow
calculation is performed within the annual balance sheets rather than in a
sectoral worksheet. In particular, you will notice that subtotals are calculated
for certain fuel types and used by the heat supply (XVII.a), power generation
(II.a, I.b, I.a), electricity distribution (VII.b), and biomass (V.a
and V.b) sectors, a subtotal is computed. This subtotal is the total energy
flow, of a particular fuel type, from a subset of the sectors. (There is a
similar calculation done for XVI.b, balancing imports, which really should
have been done in its own sectoral worksheet).
What is going on turns out to be straightforward, although it certainly doesn't appear so at first glance. The job of certain sectors is to supply (or demand) an amount of energy that is not fixed by the assumptions, but depends upon what is demanded by the rest of the model. For example, electricity from gas generation is produced in whatever quantity is required to meet the total demand for electricity. So somehow the amount of electricity demanded needs to be passed to that sector. The subtotal adds up all the flows except those from one particular sector.
We should have formalised this calculation. Here is one approach to doing so. For each real fuel type, the modeller would designate a single sector as the "balancing sector" for that fuel type. (The designation might be done in one of the front worksheets.) In the annual summary worksheets, introduce a "Total of fixed flows" row beneath all the sectoral rows. The cells in the "Total of fixed flows" row contain a formula to add up all flows from the rows above except that from the designated sector. Finally, all balancing sectors, which require this total as an input, could obtain it with a common lookup.
The original plan was that all output from the model (at least, that relating to energy flows) would be derived from the total energy flows in each fuel type, without reference to any particular sector. I wanted the model to produce a summary of all total energy flows, by fuel type, and for all output to come from this summary. My reasoning was similar to that which produced nominal fuel types: that sectors wouldn't have to "know" about anything other than their inputs and outputs (which is, really, all they ought to know about) and this would make building the model easier and less error-prone.
There are, I think, two reasons that this plan failed. First, it turned out that we often wanted to know the gross flow through a particular fuel type. As a good example, the Calculator reports total electricity flows "over the grid", although the net balance of electricity at the end of each time period is zero.9 Since the Calculator doesn't carry over energy from one period to the next, net flows (in real fuel types) are always zero. We ended up "looking inside" particular sectors to see their total inputs or outputs.
The second reason is related to the hierarchy problem. We often want to extract quite detailed information from the model---for example, energy lost in conversion by power stations. That kind of detail isn't available if one restricts oneself to broad fuel types, unless the fuel types are subejct to a rich and detailed classification. But in the current approach, where each level of the fuel type hierarchy requires its own fuel type, that would mean lots of very similar fuel types, not to mention multiple "little" sectors to recategorise energy from one to another.
At any rate, a partial solution would be to record, for each fuel type, not just the net flow but the gross flow: that is, the total inflow (or outflow) only. To do so, each sector would specify not just a flow for particular fuel types, but also whether those flows were "production" or "consumption".10 I think this would be a good start, even though a full solution seems to require a solution to the hierarchy problem.
It would be nice to classify fuel types in their natural hierarchies. It's just hard to see how that would be done in Excel. But suppose, for the sake of discussion, that there was a version of the Calculator which could support hierarchies. How might we use that facility?
I think one interesting improvement would be to have the model automatically convert between subtypes and more generic types. If you were writing a sector which consumed a particular fuel, you would specifiy the most general form of that fuel: for example, "gaseous hydrocarbons" for a gas-burning technology. The model would then "look for" any subtype of that fuel, such as "natural gas", if it were needed.
There's a question, of course, of how the model should decide which subtype of the fuel it should use and that in turn raises a wider issue. In the model as it stands, there are two kinds of sector: those for which the input and output energy flows are fixed (at least once a particular trajectory is chosen) and those whose activity level, and therefore input and output, varies to match what is going on in the rest of the model. For example, the transport sector is one whose flows are fixed by the trajectory; whereas the import sector varies to balance supply and demand.
In some imaginary, future Calculcator, the designer should specify which kind of sector is which, and the model should report whether the collection of all sectors forms a soluble model; neither underspecified nor overspecified.
The following table lists all the fuel types in the current version of the UK Calculator. (Other versions and other Calculators may well have a different list, as there is nothing fundamental about these.)
Code Description
*Primary Sources*
N.01 Nuclear fission
R.01 Solar
R.02 Wind
R.03 Tidal
R.04 Wave
R.05 Geothermal
R.06 Hydro
R.07 Environmental heat
A.01 Agriculture
W.01 Waste
Y.01 Biomass oversupply (imports)
Y.02 Electricity oversupply (imports)
Y.03 Petroleum products oversupply
Y.04 Coal oversupply (imports)
Y.05 Oil and petroleum products oversupply (imports)
Y.06 Gas oversupply (imports)
Q.01 Coal reserves
Q.02 Oil reserves
Q.03 Gas reserves
Secondary vectors
C.01 Coal and fossil waste
C.02 Oil and petroleum products
C.03 Natural gas
V.01 Electricity (delivered to end user)
V.02 Electricity (supplied to grid)
V.03 Solid hydrocarbons
V.04 Liquid hydrocarbons
V.05 Gaseous hydrocarbons
V.06 Blast furnace gas
V.07 Heat transport
V.08 Edible biomass
V.09 Dry biomass and waste
V.10 Wet biomass and waste
V.15 Gaseous waste
V.11 Domestic solar thermal
V.12 H2
V.13 Energy crops (second generation)
V.14 Energy crops (first generation)
Final demand
X.01 Conversion losses
X.02 Distribution losses and own use
Z.01 Unallocated
T.01 Road transport
T.02 Rail transport
T.03 Domestic aviation
T.04 National navigation
T.05 International aviation
T.06 International shipping
I.01 Industry
H.01 Heating and cooling
L.01 Lighting & appliances
F.01 Food consumption [UNUSED]
: Fuel types used in the Calculator.
Footnotes
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There's a second kind of energy balancing idea in the Calculator. The model is not allowed to "carry over" energy from one year to the next, so the total production of to, say,
C.03in one year must equal the total consumption ofC.03in the same year. This point is discussed later. ↩ -
This is not quite true. The totals of
V.01andV.02, the two electricity fuel types, are not zero, for technical reasons which now seem much less compelling than they did at the time. If you are building a Calculator and would like to fix this, please do so. ↩ -
Hierarchies are difficult in general. I don't think I've seen any system for managing them which has struck me as the "right way". For some discussion see, for example, Trees and Hierarchies in SQL for Smarties by Joe Celko. ↩
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In the Calculator, real fuel types are sometimes called "secondary vectors". Sorry about that. ↩
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Interestingly, it is in the introduction of nominal fuel types that the Calculator starts to look most like an accounting system. Accounting systems track the flow of money from one kind of "account" to another. There are real accounts, representing actual piles of money (or assets), and then there are nominal accounts which are used to hold income and expenses. (There are also "personal" accounts, or liabilities, but they don't seem to exist in the Calculator version of things.) ↩
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See the Digest of UK Energy Statistics for other good examples. The traditional approach is described in International Recommendations for Energy Statistics, http://unstats.un.org/unsd/energy/ires/ ↩
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It it also true that the sectors compute emissions---I am ignoring these here, but note that emissions, too, come in well-defined types such that emissions may be aggregated over all sectors. ↩
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I am sure that there is at least one exception to this principle in the UK Calculator but I have forgotten what it is. ↩
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Which also, in part, explains why the electricity fuel types break the rule that real fuel types should sum to zero. ↩
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It might well be suggested that there's no need for each sector to specify the direction of each flow since that information ought to be encoded in the sign of the energy flow. In other words, one could simply compute $\sum |\text{flow}|/2$. Well, yes, and no. For some reason, I feel that the direction of the flow is something different from its sign. I don't have a coherent reason for this. ↩