Analytic perspectives on efficiency

In the last post I set out a rough framework for organising various aspects of energy efficiency that impact on the energy costs of the energy that we use. Accessing any energy source requires the use of energy; and only a portion of the overall energy that we use goes directly to the specific service that we desire, such as moving goods or people from one place to another. In some situations—for example, many heating applications—almost all of the supplied energy is converted to directly useful forms, but all energy conversions entail energy costs of some magnitude (by “costs” I mean expenditures specifically of energy, not the financial costs associated with that energy—although in most circumstances we can also attribute a financial cost to these energy expenditures). The energy costs of energy use have fundamentally important economic implications, both at the micro and macro scale: the higher the costs, the greater the extent of the physical infrastructure involved in production of primary energy sources, conversion of these to fuels and electricity and delivery of final services. As a general rule, the greater the extent of the infrastructure, the larger and more complex are the institutional arrangements required to manage energy supply. These costs, and especially how they vary between energy sources and conversion technologies (and how they vary over time for particular sources and technologies) have critical implications for how we understand the nature, historical course and future prospects of present societies. In this post, I’ll explore the costs of energy use in more depth by looking at what I’m calling the analytic view of efficiency, in both its engineering and economic guises.

the engineering perspective

As a performance measure for some process, energy conversion efficiency tells us about the relationship between energy inputs and what we regard as the useful outputs of the process, in energy terms. This output is typically in the form of work (electricity is included here), heat or light. This doesn’t exhaust the possibilities though—in the case of fuel production e.g. from petroleum or biomass, the output in which we’re interested, from an efficiency perspective, is the chemical energy associated with the fuel, expressed in terms of the fuel’s nominal heating value.

The efficiency, often designated by the Greek letter η, is the output energy quantity divided by the input energy quantity:


Provided the input and output are expressed in the same units (in the SI system, joules), the efficiency is dimensionless and is typically expressed as a percentage. Efficiency calculations can also be based on the rate of energy input and ouput, that is, with reference to a system’s input and output power.

In order to interpret any energy conversion efficiency value, we need to know about the system with which it’s associated. An expression of efficiency is always relative to the system boundaries that we set. So, for instance, if we are considering the efficiency of an automobile, we need to nominate the specific energy input(s) and output(s) that are of interest to us. In this case, as we’re almost certainly dealing with an internal combustion engine (in which heat is transferred to the engine by burning fuel directly in the expansion chamber of the engine itself) the energy input is relatively straightforward: typically we would consider the chemical energy associated with the fuel, based on the nominal heating value (but note carefully: the efficiency value we calculate depends on whether we use the higher or lower heating value). The energy output is not so straightforward. We’re almost certainly interested in the mechanical work done by the car’s engine, but where we measure this affects the result. For most car owners and users—i.e. the person paying for the fuel—it’s likely to be the work done in moving the vehicle itself that’s of principal interest (though this is a subject to which we’ll apply more critical scrutiny shortly). For engineers involved in the design of the engine itself, it may be the work measured at the engine’s output shaft that’s of interest, perhaps prior to the vehicle’s transmission, and before any of the shaft work is used to drive auxiliary devices such as air conditioning systems, which in most vehicles account for a substantial proportion of the overall energy use when they’re operating. The calculated efficiency will also vary with the conditions under which the vehicle is used—we’ll get a different result for the vehicle’s typical driving cycle i.e. over the course of a real-world trip involving varied terrain and speed compared with laboratory conditions with the engine operating at fixed speed and under constant load. To make adequate sense of a quoted energy conversion efficiency value, we need to know all of the associated conditions and system boundaries.

To illustrate how boundary changes affect energy conversion efficiency on the input side, we can consider the case of thermal electricity generation, as employed in a coal-fired or nuclear power plant. The power generation cycle used in such plants is closed rather than open, as is the case for automobile engines (and for that matter, for the vast majority of our mechanised transport, including trucks, trains, ships and aircraft). This means that the working fluid via which the heat (thermal energy) input is converted to a work (mechanical energy) output doesn’t come into direct contact with the heat source. The working fluid and the heat source are connected thermally by a heat exchanger, but there is no exchange of matter between the two. In such situations, we could take as the energy input for calculating efficiency either the output from the heat exchanger (the quantity of thermal energy delivered to the working fluid) or the fuel input to the combustion system (the quantity of chemical energy delivered to the combustion chamber). In the latter case, the calculated energy conversion efficiency for the power plant would be reduced by the efficiency of the boiler system (the combustion system and heat exchanger).

The way that we account for activities peripheral to the principal energy conversion process but essential for the overall practical functioning of our energy supply infrastructure also has implications for the energy conversion efficiency. Taking the coal-fired power stations that provide most of our electricity here in Melbourne, Australia as an example, while plant design engineers may be principally interested in the efficiency with which the coal’s chemical energy is converted to electrical energy, the power station owners are interested in all facets of operation including the open-cut coal mine. The power station fuel is mined using massive electrically-powered bucket wheel dredgers. The electricity supply for the dredgers and associated conveyor systems is provided directly from the power station itself, and hence reduces the effective output—the amount of electricity available for sale to paying customers. Just for the record, the national average efficiency for all coal-fired power stations in Australia is around 33 percent. That’s electricity generated, minus that used in the station, divided by the fuel’s higher heating value.  The mine operations appear to be “efficiency reducing”—they reduce the effective energy conversion efficiency of the overall plant. This brings us to the important distinction, when thinking about energy efficiency, between the essential costs of production, and losses due to irreversible processes.

In any energy conversion process, there are, of course, no ultimate losses—just losses of utility to us in terms of what it is we’re trying to achieve. This follows from the first law of thermodynamics, dealt with early on in the inquiry as energy law 1. This is why energy conversion efficiency in what I’m calling the analytic view is also known as first law efficiency (see Table 1 in the previous post). This is the efficiency of converting the energy with which we commence to valuable outputs. While the remainder is in a sense “lost”, this is only from the perspective of whoever it is that decides what counts as a valuable output. All of the energy inputs to a process leave as outputs in one form or another. In the case of automobiles and power stations, it’s respectively the transport work and electricity that typically count as useful. Most of the other 80-odd percent (in the case of automobiles) and 60-odd percent (power stations) of the energy leaves as heat—it increases the temperature of the car’s or the power station’s surrounding environment (and ALL of the energy eventually ends up as heat after we’ve extracted what utility we can from the portion that we deem useful).

It’s common to refer to the thermal energy rejected from a power station in the course of its normal operation as waste heat. The reference to “waste” in this context is often taken to have pejorative connotations—as in “a resource that has been squandered”. As we’ll see shortly, there are circumstances in which this may be reasonable—but this is not due to a failing on the part of the station’s designers or operators per se. Just as work must be done to provide the station’s fuel, heat must be rejected as part of the fundamental operating process for a heat engine. In an earlier post I discussed the ideal Carnot cycle and its associated efficiency—the theoretical maximum efficiency that any thermal power generation (i.e. heat engine) cycle can achieve. While the actual value depends on the specific temperatures involved, the Carnot efficiency based on input and output temperatures associated with a typical power station operating on the steam Rankine cycle (the basic heat engine cycle used for electricity generation, in which the working fluid is water) is in the order of 70 percent. Very roughly, of the 60-odd percent of fuel energy not converted to saleable electricity by real-world power stations, around half of this is lost as a fundamental physical consequence of producing electricity using a heat engine. While some of this is in principal a technological constraint—fuel cells for instance can achieve conversion efficiencies higher than the Carnot efficiency—at present we have no practical way of converting the energy associated with coal to electrical energy other than via heat engines. If we have coal (or oil or natural gas for that matter) and we want electricity on large scale, then we have to wear the associated energy cost. While good design and operating practices can minimise the gap between the theoretical maximum efficiency and the actual conversion efficiency, there are practical limits to what can be achieved, associated for example with the properties of materials and capital cost. In practice, designers and plant owners must contend with a range of design criteria beyond the desire to maximise efficiency, and as such they’re limited by various real-world constraints. The key point to take from this, though, is that most “losses” are a necessary entailment of the activities required to provide output energy in our desired form. To the extent that we value the desired output, there is usually little to be gained by resenting the associated costs! This is not to imply that ongoing design improvements can’t reduce the costs—but we might as well appreciate them as part and parcel of metaphorically “doing business” in the first place.

Irreversible processes—or simply irreversibilities—present  us (and more specifically, design engineers) with a slightly different challenge. These processes relate to the myriad ways in which real physical behaviour departs from the ideal models that we use to think about it in the abstract. Here we’re dealing with effects such as friction losses in mechanical energy conversions, resistive losses in the conductance of electricity and conductive losses of thermal energy due to practical performance limits on insulation. Ideal processes are conceptualised as reversible, or loss-less. What we’re dealing with here is the discrepancy between our models of the world, and how things are in practice. Nonetheless, many of these discrepancies are subject to technical design intervention. We can reduce the size of resistive losses in electrical conductors by approaches such as changing materials, increasing their area, or reducing their length. We can reduce friction with better bearings or lubrication. Drag forces on a vehicle can be reduced by changing the vehicle’s body shape. Turbulent flow losses can be reduced in the exhaust manifolds for internal combustion engines, or at the trailing edge of turbine blades. A great deal of design effort goes into reducing losses due to irreversibilities—for the primary reason that these are to a certain extent (unlike the work required to mine coal for instance) unnecessary losses. They can never be reduced to zero, but they can be minimised, and where the benefit of minimising them further outweighs the costs of doing so, they’re worth pursuing. While friction and its analogues are facts of life, a healthy disdain for them may be a useful part of motivating engineers to reduce their impact on energy conversion efficiency.

Earlier I inferred that there may be situations where it is in fact reasonable to think of waste energy in the folk sense of squandering a valuable resource. The basis for this is pretty straightforward: while the waste heat from a power station is of no value for generating electricity (the temperature at which it is rejected is too low—or more precisely, too close to that of the plant’s environment), it may be valuable for other purposes. For example, the temperature may be well-matched to industrial heating requirements, or as is more often the case, to heating living and working spaces. Where this is the case, and where there is a sufficiently large heating demand in appropriate proximity to the power station (often in very cold climates where year-round heating is required), the waste heat from electricity generation can be used to displace other fuel use. Facilities where this occurs are known as co-generation or combined heat and power plants. In such situations, the valuable heating duty can be added to the numerator of the efficiency calculation, substantially increasing the overall efficiency. It’s particularly noteworthy that the increase in efficiency is a consequence of a change in the perception of the value of a waste stream—while appropriate physical infrastructure is required to make use of the thermal energy, it’s a change in thinking about the relationship between a power station and its surrounding environment that leads to the increase.

A related approach to increasing energy conversion efficiency, usually for electricity generation fueled by natural gas, is the use of combined cycle power plants. These couple together a gas turbine (similar to an aviation jet engine, but producing only shaft power rather than a combination of shaft power and the high velocity combustion gas stream that propels the plane) with a steam Rankine cycle. Rather than exhausting the hot combustion stream from the gas turbine directly to the atmosphere, the exhaust gas is fed to a boiler to produce steam, which then drives a steam turbine. Waste heat must be rejected from the steam cycle as previously described, but the overall efficiency when the output of both gas and steam turbines is combined is much higher than for a single cycle—often over 50 percent.

The economic perspective

Energy conversion efficiency has a close parallel in the economic realm where improving the resource use efficiency associated with production of goods and services is a primary aim of most schools of economic thinking, from the conventional (i.e. neo-classical) to the more avant garde (e.g. ecological economics). Improvements in energy conversion efficiency are themselves directly relevant here—where the “good” being supplied is itself an energy product such as electricity, the efficiencies sought by the economist and the engineer are more or less the same thing. The principal point of departure, though, is that in economic terms a product’s value is not simply a function of the energy associated with it (though this hasn’t stopped numerous misguided attempts over many decades to force economic value into just such a mono-dimensional and reductionist view). As such, most economists are not directly motivated by maximising the ratio of energy output to energy input, except where this correlates closely with maximising economic value in monetary terms. What they are interested in is maximising the productivity of resources in general. I don’t want to push the distinction between the engineering and economic views of efficiency too far—in many respects, both are dealing with shared aims relating to the satisfaction of human needs and wants (in fact, in the household I grew up in, an engineer was regarded as “someone who could do for a dollar what anyone else could do for ten”). It’s probably fair to say though that the economic view is more general than the engineering view, in that what counts as relevant input resources and output products is regarded more broadly. In addition to the productivity (and hence the efficiency of use) of all material and energy resources, economists tend to be particularly interested in the productivity of labour and capital. Comparing the approaches to efficiency and productivity in each of these areas will be particularly instructive when we look at rebound effects further down the track.

In preparing the way for that though, one further matter is worth highlighting at this point: as a performance measure, efficiency—from the engineering or economic viewpoint—doesn’t tell us anything about the absolute scale of either inputs or outputs. In fact, if we focus only on efficiency, we can miss altogether what is happening in terms of overall resource use. This is especially noteworthy, given the extent to which efficiency improvements are now pursued in the expectation of reducing either resource use, or the environmental impacts of human activity. I’ll leave the detailed discussion for why this is so important for a later post in this series. For now though, this also sets the context for the next post, where—following on from introductory comments in the last post—I’ll look in detail at the relationship between efficiency, and the associated performance measures of efficacy and effectiveness.

One thought on “Analytic perspectives on efficiency

  1. Pingback: The engineering view of systemic efficiency: available energy | Beyond this Brief Anomaly

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