3.4 Discussion
4.1.1 Technical efficiency limit
There are innumerable types and variations of machines that transform energy to more useful forms and there is no unique way to classify and categorise these technologies. The device classification is the same as the one presented in chapter 3 (Table 3.2)
In the literature the term “technical efficiency limit” (TEL) is used to refer to an array of meanings. In economic assessments of energy efficiency, it refers to the efficiency level that would be achieved without market distortions [133], while in techno-economic assessments, it often refers to the efficiency of the best available technologies [132]. In this study, the technical efficiency limit of each device is defined as the steady-state conversion efficiency that can be achieved while taking into consideration unavoidable energy losses, but ignoring economic considerations. The estimated TEL considers factors such as the properties of materials, unavoidable friction losses and non-ideal thermodynamic cycles. Economic factors and manufacturing constraints are ignored because these aspects are contingent to the present techno-economic situation and are subject to change. Examples of these trends include, the evolution of the minimum feature size that can be economically manufactured [285]
in electronic components and the increase in thermal properties of materials [286] in jet engines.
As is often the case in engineering design, there are trade offs between performance param-eters, therefore increases in energy efficiency can be accompanied by decreases in other parameters such as power density (kW/m3or kW/kg). When defining the TEL, it is important to ensure only options that affect these other parameters marginally, this is particularly important for the transport sector where power density is crucial.
The efficiency limit is estimated only for conversion devices that share the same limitations and function. In particular, the distinction between SI and CI engines is irrelevant for the estimation of the efficiency limit because distinction is only existent due to contingent economic and technological conditions, SI engines are used because they can deliver work with a high power density, low cost and respect emission regulations, while sacrificing efficiency compared to CI engines. However, when estimating the efficiency limit, a device that produces shaft work from chemical energy with a high power density is all that is required and the distinction between SI and CI becomes redundant. The efficiency limit is not estimated for device categories that produce thermal energy directly, the electric heater and burner, because their energy conversion efficiency is already of unity and cannot increase. Therefore, the TEL is estimated for six conversion device categories: Reciprocating Engine, Jet Engine, Boiler, Electric Motor, Cooler, and Light devices. The limit is estimated stochastically to avoid any overconfidence in the results. This approach has already been followed in the literature, for example by Martin et. al [114], Yan et al. [287], and Baker et. al [288]. Since there is no agreed methodology in the literature to estimate the TEL, two methods are presented below and either one or the other is applied to each conversion device.
Method A –Parametric model: a physical model ( f ) of the conversion device is developed to relate the conversion efficiency (η) to a limited number of key performance parameters (for example α and β ).
η = f (α , β ) (4.1)
The optimal value of each parameter (α∗, β∗) is estimated after a thorough literature review taking into account only unavoidable physical limitations to the optimal value of the parameter.
For example, when considering the maximum combustion temperature in a gas turbine, the limiting factor is the activation of endothermic dissociation reactions rather than the melting temperature of current materials. In most cases, there are a range of opinions and values found in the literature, therefore to minimise the consequences of subjective judgement, the optimal parameters are defined as a uniform probability distribution which encompasses the values found in the literature. Such that
α∗∼Uniform(αmin∗ , αmax∗ ) (4.2) β∗∼Uniform(βmin∗ , βmax∗ ) (4.3)
Using a stochastic approach enables a more explicit assessment of the uncertainty associated with the results and helps mitigate overconfidence in the results. The parameters are then fed into the physical model to obtain a probability distribution of the Technical Efficiency Limit as seen in equation 4.4
ηT EL= f (α∗, β∗) (4.4)
Method B –Loss reduction method: the main loss mechanisms for the conversion device are defined and characterised. Then, the magnitude of each loss mechanism (l) in the current best available technology is quantified by means of a literature review. The reduction potential of each loss mechanisms (∆L) is then estimated by relating it to a specific advance in the conversion device technology. The TEL (ηT EL) is then calculated using equation 4.5
ηT EL= ηBAT+
∑
l
Ll∆Ll (4.5)
where Ll is the share of the input lost due to a specific loss mechanism l. The quantification of the reduction potential refers to the reduction that could be achieved by the best possible technical solution, disregarding economic considerations. For example, the reduction poten-tial of iron losses in electric motors should take into account the use of amorphous metals, despite their currently high cost. The loss reduction potentials are estimated as a uniform probability distribution that represents different values found in the literature and the degree of uncertainty of each reduction potential, such that
∆L ∼ Uniform (∆Lmin, ∆Lmax) (4.6)
They are then combined to obtain the technical efficiency limit of the device which is itself a probability distribution.
The parametric model methodology (Method A) is preferred and, whenever possible, this method is used. However, for some devices, physical modelling is prohibitively complex due to a large number of design parameters or due to the presence of important complex interactions that require computationally intensive models (such as computational fluid dynamics or finite element analysis). For these cases, the loss reduction methodology is employed as an alternative physical basis for the technical efficiency limit. A summary of the methodology and the steps taken to model each conversion device is shown in the flowchart in Figure 4.1.
Find energy/exergy loss breakdown of device at current best available technology
Build physical model : η = f(a,b) where a and b are technical parameters
Does the literature provide reliable estimates of maximum practical values attainable by
each parameter?
Run model and calculate the device's efficiency limit
Fig. 4.1 Flow chart showing the decisions and steps taken to determine the technical efficiency limits following both methodologies.
To reduce the number of parameters studied and the complexity of the models, efficiency at steady state and rated power operation is modelled by default. This simplification is acceptable for most conversion devices either because they operate mostly at constant load, or because their performance degrades only marginally for variable load. One important exception is for reciprocating engines used in light duty vehicles, where the highly variable load and the strong correlation of efficiency with load conditions, means that the average efficiency varies significantly from the constant load efficiency [289]. Therefore, for road transport, both the current efficiencies and the TEL are estimated for engines operating over a typical drive cycle.
Methods A and B were used on roughly the same number of devices: gas turbines (including Jet Engines), boilers, and coolers were analysed using method A; reciprocating engines, electric motors, and light devices were analysed with method B. Section 4.2 provides a full analysis of each conversion device including all relevant references and a description of the models used.