The power of percent

Which statistic would you use if you were writing the newspaper headline for the following media release: "Tassie’s death rate of deaths arising from transport-related injuries was 13 per 100,000 people, or 50% higher than the national average”? (Martain, 2007). The rate “13 per 100,000” sounds very small whereas “50% higher” sounds quite large. Most people are aware of the tendency to choose between reporting data as actual numbers or using percents in order to gain attention. Looking at examples like this one can help students develop a critical quantitative literacy viewpoint when dealing with “authentic contexts” (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2013a, p. 37, 67). The importance of the distinction between reporting information in raw numbers or percents is not explicitly mentioned in the Australian Curriculum: Mathematics (ACARA, 2013b, p. 42). Although the document specifically mentions making “connections between equivalent fractions, decimals and percentages” [ACMNA131] in Year 6, there is no mention of the fundamental relationship between percent and the raw numbers represented in a part-whole fashion. Such understanding, however, is fundamental to the problem solving that is the focus of the curriculum in Years 6 to 9. The purpose of this article is to raise awareness of the opportunities to distinguish between the use of raw numbers and percents when comparisons are being made in contexts other than the media. It begins with the authors’ experiences in the classroom, which motivated a search in the literature, followed by a suggestion for a follow-up activity.

Maximum loadability achievement in SWER networks using optimal sizing and locating of batteries

This paper presents an optimisation algorithm to maximize the loadability of single wire earth return (SWER) by minimizing the cost of batteries and regulators considering the voltage constraints and thermal limits. This algorithm, that finds the optimum location of batteries and regulators, uses hybrid discrete particle swarm optimization and mutation (DPSO + Mutation). The simulation results on realistic highly loaded SWER network show the effectiveness of using battery to improve the loadability of SWER network in a cost-effective way. In this case, while only 61% of peak load can be supplied without violating the constraints by existing network, the loadability of the network is increased to peak load by utilizing two battery sites which are located optimally. That is, in a SWER system like the studied one, each installed kVA of batteries, optimally located, supports a loadability increase as 2 kVA.

Effectiveness of reactive power capability of photo voltaic inverters to maintain voltage profile in a residential distribution feeder

Large penetration of rooftop PVs has resulted in unacceptable voltage profile in many residential distribution feeders. Limiting real power injection from PVs to alleviate over voltage problem is not feasible due to loss of green power and hence corresponding revenue loss. Reactive capability of the PV inverter can be a solution to address over voltage and voltage dip problems to some extent. This paper proposes an algorithm to utilize reactive capability of PV inverters and investigate their effectiveness for voltage improvement based on R/X ratio of the feeder. The length and loading level of the feeder for a particular R/X ratio to have acceptable voltage profile is also investigated. This can be useful for suburban design and residential distribution planning. Furthermore, coordination among different PVs using residential smart meters via a substation based controller is also proposed.

Effectiveness of reactive power capability of photo voltaic inverters to maintain acceptable voltage profile in a residential distribution system

Integration of rooftop PVs and increasing peak demand in the residential distribution networks has resulted in unacceptable voltage profile. Curtailing PV generation to alleviate overvoltage problem and making regular network investment to cater peak demand is not always feasible. Reactive capability of the PV inverter can be a solution to address voltage dip and over voltage problems to some extent. This paper proposes an algorithm to utilize reactive capability of PV inverters and investigate their effectiveness on feeder length and R/X ratio of the line. Feeder loading level for a particular R/X ratio to have acceptable voltage profile is also investigated. Furthermore, the need of appropriate feeder distances and R/X ratio for acceptable voltage profile, which can be useful for suburban design and distribution planning, is explored.

Output feedback optimal control with contraints

In Chapters 1 through 9 of the book (with the exception of a brief discussion on observers and integral action in Section 5.5 of Chapter 5) we considered constrained optimal control problems for systems without uncertainty, that is, with no unmodelled dynamics or disturbances, and where the full state was available for measurement. More realistically, however, it is necessary to consider control problems for systems with uncertainty. This chapter addresses some of the issues that arise in this situation. As in Chapter 9, we adopt a stochastic description of uncertainty, which associates probability distributions to the uncertain elements, that is, disturbances and initial conditions. (See Section 12.6 for references to alternative approaches to model uncertainty.) When incomplete state information exists, a popular observer-based control strategy in the presence of stochastic disturbances is to use the certainty equivalence [CE] principle, introduced in Section 5.5 of Chapter 5 for deterministic systems. In the stochastic framework, CE consists of estimating the state and then using these estimates as if they were the true state in the control law that results if the problem were formulated as a deterministic problem (that is, without uncertainty). This strategy is motivated by the unconstrained problem with a quadratic objective function, for which CE is indeed the optimal solution (˚Astr¨om 1970, Bertsekas 1976). One of the aims of this chapter is to explore the issues that arise from the use of CE in RHC in the presence of constraints. We then turn to the obvious question about the optimality of the CE principle. We show that CE is, indeed, not optimal in general. We also analyse the possibility of obtaining truly optimal solutions for single input linear systems with input constraints and uncertainty related to output feedback and stochastic disturbances.We first find the optimal solution for the case of horizon N = 1, and then we indicate the complications that arise in the case of horizon N = 2. Our conclusion is that, for the case of linear constrained systems, the extra effort involved in the optimal feedback policy is probably not justified in practice. Indeed, we show by example that CE can give near optimal performance. We thus advocate this approach in real applications.

On optimal control of constrained linear systems with imperfect state information and stochastic disturbances

We address the problem of finite horizon optimal control of discrete-time linear systems with input constraints and uncertainty. The uncertainty for the problem analysed is related to incomplete state information (output feedback) and stochastic disturbances. We analyse the complexities associated with finding optimal solutions. We also consider two suboptimal strategies that could be employed for larger optimization horizons.

An assessment of the geographical scale of recurrent gene flow in wild populations of two species of Mekong River carps (Henicorhynchus spp.)

The Mekong is the most productive river fishery in the world, and such as, the Mekong River Basin (MRB) is very important to very large human populations across the region as a source of revenue (through fishing and marketing of aquatic resources products) and as the major source for local animal protein. Threats to biodiversity in the MRB, either to the fishery sector itself or to other sectors are a major concern, even though currently, fisheries across this region are still very productive. If not managed properly however, fish population declines will cause significant economic impact and affect livelihoods of local people and will have a major impact on food security and nutrition. Biodiversity declines will undoubtedly affect food security, income and socio-economic status of people in the MRB that depend on aquatic resources. This is an indicator of unsustainable development and hence should be avoided. Genetic diversity (biodiversity) that can be measured using techniques based on DNA markers; refers to variation within and among populations within the same species or reproductive units. In a population, new genetic variation is generated by sexual recombination contributed by individuals with mutations in genes and chromosomes. Over time, populations of a species that are not reproducing together will diverge as differential impacts of selection and genetic drift change their genetic attributes. For mud carp (Henicorhynchus spp.), understanding the status of breeding units in the MRB will be important for their long term persistence, sustainability and for implementing effective management strategies. Earlier analysis of stock structure in two economically important mud carp species (Henicorhynchus siamensis and H. lobatus) in the MRB completed with mtDNA markers identified a number of populations of both species where gene flow had apparently been interrupted or reduced but applying these data directly to management unit identification is potentially compromised because information was only available about female dispersal patterns. The current study aimed to address this problem and to fully assess the extent of current gene flow (nDNA) and reproductive exchange among selected wild populations of two species of carp (Henicorhynchus spp.) of high economic importance in the MRB using combined mtDNA and nDNA markers. In combination, the data can be used to define effective management units for each species. In general, nDNA diversity for H. lobatus (with average allelic richness (A) 7.56 and average heterozygosity (Ho) 0.61) was very similar to that identified for H. siamensis (A = 6.81 and Ho = 0.75). Both mud carp species show significant but low FST estimates among populations as a result of lower genetic diversity among sampled populations compared with genetic diversity within populations that may potentially mask any 'real' population structure. Overall, population genetic structure patterns from mtDNA and nDNA in both Henicorhynchus species were largely congruent. Different population structures however, were identified for the two Henicorhynchus species across the same geographical area. Apparent co-similarity in morphology and co-distribution of these two relatively closely related species does not apparently imply parallel evolutionary histories. Differences in each species population structure likely reflect historical drainage rearrangement of the Mekong River. The data indicate that H. siamensis is likely to have occupied the Mekong system for much longer than has H. lobatus in the past. Two divergent stocks were identified for H. lobatus in the MRB below the Khone Falls while a single stock had been evident in the earlier mtDNA study. This suggests that the two Henicorhynchus species may possess different life history traits and that different patterns of gene flow has likely influenced modern genetic structure in these close congeners. In combination, results of the earlier mtDNA and the current study have implications for effective management of both Henicorhynchus species across the MRB. Currently, both species are essentially treated as a single management unit in this region. This strategy may be appropriate for H. lobatus as a single stock was evident in the main stream of the MRB, but may not be appropriate for H. siamensis as more than a single stock was identified across the same range for this species. Management strategies should consider this difference to conserve overall biodiversity (local discrete populations) and this will include maintaining natural habitat and migration pathways, provision of fish sanctuaries (refuges) and may also require close monitoring of any stock declines, a signal that may require effective recovery strategies.

Similarity solutions for flow and heat transfer of non-Newtonian fluid over a stretching surface

Similarity solutions are carried out for flow of power law non-Newtonian fluid film on unsteady stretching surface subjected to constant heat flux. Free convection heat transfer induces thermal boundary layer within a semi-infinite layer of Boussinesq fluid. The nonlinear coupled partial differential equations (PDE) governing the flow and the boundary conditions are converted to a system of ordinary differential equations (ODE) using two-parameter groups. This technique reduces the number of independent variables by two, and finally the obtained ordinary differential equations are solved numerically for the temperature and velocity using the shooting method. The thermal and velocity boundary layers are studied by the means of Prandtl number and non-Newtonian power index plotted in curves.

Power buffer with model predictive control for stability of vehicular power systems with constant power loads

Electrification of vehicular systems has gained increased momentum in recent years with particular attention to constant power loads (CPLs). Since a CPL potentially threatens system stability, stability analysis of hybrid electric vehicle with CPLs becomes necessary. A new power buffer configuration with battery is introduced to mitigate the effect of instability caused by CPLs. Model predictive control (MPC) is applied to regulate the power buffer to decouple source and load dynamics. Moreover, MPC provides an optimal tradeoff between modification of load impedance, variation of dc-link voltage and battery current ripples. This is particularly important during transients or starting of system faults, since battery response is not very fast. Optimal tradeoff becomes even more significant when considering low-cost power buffer without battery. This paper analyzes system models for both voltage swell and voltage dip faults. Furthermore, a dual mode MPC algorithm is implemented in real time offering improved stability. A comprehensive set of experimental results is included to verify the efficacy of the proposed power buffer.

Optimal Bayesian experimental design for models with intractable likelihoods using indirect inference applied to biological process models

This paper addresses the problem of determining optimal designs for biological process models with intractable likelihoods, with the goal of parameter inference. The Bayesian approach is to choose a design that maximises the mean of a utility, and the utility is a function of the posterior distribution. Therefore, its estimation requires likelihood evaluations. However, many problems in experimental design involve models with intractable likelihoods, that is, likelihoods that are neither analytic nor can be computed in a reasonable amount of time. We propose a novel solution using indirect inference (II), a well established method in the literature, and the Markov chain Monte Carlo (MCMC) algorithm of Müller et al. (2004). Indirect inference employs an auxiliary model with a tractable likelihood in conjunction with the generative model, the assumed true model of interest, which has an intractable likelihood. Our approach is to estimate a map between the parameters of the generative and auxiliary models, using simulations from the generative model. An II posterior distribution is formed to expedite utility estimation. We also present a modification to the utility that allows the Müller algorithm to sample from a substantially sharpened utility surface, with little computational effort. Unlike competing methods, the II approach can handle complex design problems for models with intractable likelihoods on a continuous design space, with possible extension to many observations. The methodology is demonstrated using two stochastic models; a simple tractable death process used to validate the approach, and a motivating stochastic model for the population evolution of macroparasites.

Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation

We examine the effect of a kinetic undercooling condition on the evolution of a free boundary in Hele--Shaw flow, in both bubble and channel geometries. We present analytical and numerical evidence that the bubble boundary is unstable and may develop one or more corners in finite time, for both expansion and contraction cases. This loss of regularity is interesting because it occurs regardless of whether the less viscous fluid is displacing the more viscous fluid, or vice versa. We show that small contracting bubbles are described to leading order by a well-studied geometric flow rule. Exact solutions to this asymptotic problem continue past the corner formation until the bubble contracts to a point as a slit in the limit. Lastly, we consider the evolving boundary with kinetic undercooling in a Saffman--Taylor channel geometry. The boundary may either form corners in finite time, or evolve to a single long finger travelling at constant speed, depending on the strength of kinetic undercooling. We demonstrate these two different behaviours numerically. For the travelling finger, we present results of a numerical solution method similar to that used to demonstrate the selection of discrete fingers by surface tension. With kinetic undercooling, a continuum of corner-free travelling fingers exists for any finger width above a critical value, which goes to zero as the kinetic undercooling vanishes. We have not been able to compute the discrete family of analytic solutions, predicted by previous asymptotic analysis, because the numerical scheme cannot distinguish between solutions characterised by analytic fingers and those which are corner-free but non-analytic.

CFD simulations of flow and heat transfer through the porous interface of a metal foam heat exchanger

This paper offers numerical modelling of a waste heat recovery system. A thin layer of metal foam is attached to a cold plate to absorb heat from hot gases leaving the system. The heat transferred from the exhaust gas is then transferred to a cold liquid flowing in a secondary loop. Two different foam PPI (Pores Per Inch) values are examined over a range of fluid velocities. Numerical results are then compared to both experimental data and theoretical results available in the literature. Challenges in getting the simulation results to match those of the experiments are addressed and discussed in detail. In particular, interface boundary conditions specified between a porous layer and a fluid layer are investigated. While physically one expects much lower fluid velocity in the pores compared to that of free flow, capturing this sharp gradient at the interface can add to the difficulties of numerical simulation. The existing models in the literature are modified by considering the pressure gradient inside and outside the foam. Comparisons against the numerical modelling are presented. Finally, based on experimentally-validated numerical results, thermo-hydraulic performance of foam heat exchangers as waste heat recovery units is discussed with the main goal of reducing the excess pressure drop and maximising the amount of heat that can be recovered from the hot gas stream.

A review of modern computational algorithms for Bayesian optimal design

Bayesian experimental design is a fast growing area of research with many real-world applications. As computational power has increased over the years, so has the development of simulation-based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, facilitating more complex design problems to be solved. The Bayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the Bayesian optimal design. We also discuss other computational strategies for further research in Bayesian optimal design.

An analysis on the possibility of using capacitors of a three-level capacitor clamped inverter as power smoothing elements for wind power systems

This paper presents a new direct integration scheme for supercapacitors that are used to mitigate short term power fluctuations in wind power systems. The idea is to replace ordinary capacitors of a 3-level flying capacitor inverter by supercapacitors and operate them under variable voltage conditions. This approach eliminates the need of interfacing dc-dc converters for supercapacitor integration and thus considerably improves the overall efficiency. However, the major problem of this unique system is the change of supercapacitor voltages. An analysis on the effects of these voltage variations are presented. A space vector modulation method, built from the scratch, is proposed to generate undistorted current even in the presence of dynamic changes in supercapacitor voltages. A supercapacitor voltage equalisation algorithm is also proposed. Furthermore, resistive behavior of supercapacitors at high frequencies and the need for a low pass filter are highlighted. Simulation results are presented to verify the efficacy of the proposed system in suppressing short term wind power fluctuations.

A Battery Energy Storage interface for wind power systems with the use of grid side inverter

This paper presents a novel concept of Energy Storage System (ESS) interfacing with the grid side inverter in wind energy conversion systems. The inverter system used here is formed by cascading a 2-level inverter and a three level inverter through a coupling transformer. The constituent inverters are named as the “main inverter” and the “auxiliary inverter” respectively. The main inverter is connected with the rectified output of the wind generator while the auxiliary inverter is attached to a Battery Energy Storage System (BESS). The BESS ensures constant power dispatch to the grid irrespective of change in wind condition. Furthermore, this unique combination of BESS and inverter eliminates the need of additional dc-dc converters. Novel modulation and control techniques are proposed to address the problem of non-integer, dynamically-changing dc-link voltage ratio, which is due to random wind changes. Strategies used to handle auxiliary inverter dc-link voltage imbalances and controllers used to charge batteries at different rates are explained in detail. Simulation results are presented to verify the efficacy of the proposed modulation and control techniques in suppressing random wind power fluctuations.