Tag Archives: Modelling

Diffusion of energy innovations in a social network

Nick McCullen and colleagues have a new paper out in SIAM Journal on Applied Dynamical Systems entitled ‘Multiparameter Models of Innovation Diffusion on Complex Networks‘. There’s a nice press release summarizing the paper on the SIAM website, and the first few lines of the abstract get right to the point:

A model, applicable to a range of innovation diffusion applications with a strong peer-to-peer component, is developed and studied, along with methods for its investigation and analysis. A particular application is to individual households deciding whether to install an energy efficiency measure in their home. The model represents these individuals as nodes on a network, each with a variable representing their current state of adoption of the innovation. The motivation to adopt is composed of three terms, representing personal preference, an average of each individual’s network neighbors’ states, and a system average, which is a measure of the current social trend.

As the paper notes, many energy innovations are invisible to outside observers. If my neighbour installs loft insulation, I won’t know this even if I go into his or her house since I try not to make a habit of rooting around in my friends’ lofts. The proposed model therefore assumes that the benefits of this technology are only communicated by conversations between peers, which probabilistically might touch upon the installed innovation. From there, it’s basically a formalized model of Rogers’ Diffusion of Innovation theory.

Nick points out in the press release that one of the challenges of validating this kind of model is getting appropriate data. One approach would be to use telecommunications data, as in this paper. But this kind of data is so ‘big’ that one might potentially lose out on important local features and so I wonder if there isn’t scope for a more detailed study of a single neighbourhood.

My doctoral research focused on domestic photovoltaics. While the diffusion of this innovation wasn’t the main area of interest, clearly photovoltaics are a highly visible energy innovation, as might be an obviously electric vehicle parked out front, in contrast to a more hidden technology like insulation.

Can you guess that this is an electric car? Source: Darrenm540 at Wikimedia Commons.

If this was parked in front of your neighbour’s house, would you know it was an electric car? Source: Darrenm540 at Wikimedia Commons.

This suggests that McCullen et al’s model could be modified to include a separate term for visible innovations and by using a fine-grained data set, one could test the relative strengths of the invisible social signal and the visible proximity signal. In fact there are two possible variants of this approach. In one, the physical observation of an energy innovation would increase the likelihood of adoption independently of the social network mechanism. But in a subtle variant, the visible observation mechanism might play an important role in prompting a conversation on the social network. For example, ‘I saw an loft insulation truck earlier today. Which reminds me, didn’t you guys get insulation installed last year?’ This latter mechanism is sort of covered already by the ‘system average’ term in Nick’s model, but it would be interesting to make this mechanism more explicit even if the γ term of the model has relatively little impact on adoption (see below).

Figure 4(a) from McCullen et al (2013). Note that uptake varies primarily as a function of β, the weight on social network messages (versus personal beliefs or general social norms)

New paper: Activity-based modelling of urban energy demands

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I’m not sure how this slipped between the cracks, but we had a new paper published recently in the Journal of Industrial Ecology. The main idea is that you can use detailed patterns of individual activities (e.g. working, shopping, resting at home) as produced by transport models to estimate the stationary energy demands for heat and power at high spatial and temporal resolutions. The paper presents a basic proof of concept but there is lots of room for improvement here.

Urban metabolism is an important technique for understanding the relationship between cities and the wider environment. Such analyses are typically performed at the scale of the whole city using annual average data, a feature that is driven largely by restrictions in data availability. However, in order to assess the resource implications of policy interventions and to design and operate efficient urban infrastructures such as energy systems, greater spatial and temporal resolutions are required in the underlying resource demand data. As this information is rarely available, we propose that these demand profiles might be simulated using activity-based modeling. This is a microsimulation approach that calculates the activity schedules of individuals within the city and then converts this information into resource demands. The method is demonstrated by simulating electricity and natural gas demands in London and by examining how these nontransport energy demands might change in response to a shift in commuting patterns, for example, in response to a congestion charge or similar policy. The article concludes by discussing the strengths and weaknesses of the approach, as well as highlighting future research directions. Key challenges include the simulation of in-home activities, assessing the transferability of the complex data sets and models supporting such analyses, and determining which aspects of urban metabolism would benefit most from this technique.

Keirstead, J., & Sivakumar, A. (2012). Using Activity-Based Modeling to Simulate Urban Resource Demands at High Spatial and Temporal Resolutions Journal of Industrial Ecology, 16 (6), 889-900 DOI: 10.1111/j.1530-9290.2012.00486.x

Urban Energy Systems: Techniques

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This post is part of a four-part series giving an overview of our recently published book Urban Energy Systems: An Integrated Approach. Parts I and II can be read here.

Part III: Techniques

Part III is titled Analysing Urban Energy Systems. The goal here is to introduce specific modelling and analytical techniques for urban energy systems, with an emphasis on optimization models which are helpful for planning new system designs.

Modelling urban energy systems

Nilay Shah opens the section with a brief chapter on the variety of modelling approaches that might be used to analyse urban energy use. One could focus on energy supply or demand, the environmental impacts, or narrow cost objectives. However a recent review shows that there is a growing interest in integrated modelling approaches that combine the strengths of different techniques in order to give a broader view of urban energy systems at all stages of development. To this end, we developed the SynCity hierarchical modelling framework which is illustrated below. It incorporates four models that respectively cover the design of energy efficient land-use plans, the simulation of citizen activities within an existing city, the design of efficient integrated energy systems to meet carbon reduction goals, and the operation of energy systems to maximize the benefits for system operators or households. The remaining chapters then explore some of these models in detail.

Overview of SynCity modelling platform

Optimization and systems integration

Nouri Samsatli and Mark Jennings discuss the role of optimization models in planning urban energy systems. Such models are usually described as being ‘normative’, i.e. they show the world the way it should be and not necessarily the way it is. However when designing a new urban energy system, this is usually a good thing as you want to design a system, for example, that meets a given level of performance but for a minimum cost.

The chapter gives the detailed formulation of a mixed integer linear programming model called TURN (Technologies and Urban Resource Networks). The model allows multiple energy system technologies and fuels to be evaluated simultaneously, choosing the number of technologies, their locations, and operating rates, and other parameters so that a given pattern of energy service demands are met.

An example TURN for an urban energy system using biomass. Boxes represent conversion processes, circles resources.

Two example applications of the modelling framework are shown. The first investigates the optimal use of bioenergy resources within a proposed eco-town development, selecting a wood-chip based district heating solution with storage that illustrates the benefits of an integrated assessment framework. The second case study considers the optimal timing of retrofit investment decisions over a ten-year period and takes into account the different preferences of owner-occupiers versus private or public landlords.

Ecologically-inspired UES models

The objective of an optimization model like the TURN model is typically to minimize the total system cost subject to some constraints. However an alternative perspective would be to minimize environmental impact. In her chapter, Nicole Papaioannou develops such a model using a range of environmental impact measures. The case study she presents looks at the energy requirements of a typical urban area and investigates how the optimal energy system configuration will vary depending on whether one’s priority is to minimize global warming potential, local air pollution, or resource consumption. A second analysis uses scenarios instead of an optimization model to describe the energy system options and then applies three different environmental impact assessment methods: life cycle analysis, material flow analysis, and ecological footprinting.

Activity-based modelling

Energy demands are described by economists as a ‘derived demand’; in other words, people don’t consume energy for its own sake but only do so in order to achieve other goals, like travelling from A to B or keeping one’s house warm. [link][Aruna Sivakumar] therefore presents activity-based modelling as a way of explicitly describing what people are doing within the city and using this information to then infer energy demands. It is a very powerful technique that allows complex, and more realistic, urban behaviour to be captured. The figure below, for example, shows how a change in work patterns might create an opportunity for a longer shopping period, leading to a ‘cold start’ of the vehicle’s engine and worse environmental performance.

If you got off work early, you might spend a longer time shopping which could have an impact on vehicle emissions.

We have been developing our own activity-based modelling platform, known as AMMUA (Agent-based Microsimulation Model of Urban Activities), but as the chapter describes, there are many difficulties in gathering the required data, understanding the behaviour of such complex model systems, and evaluating their performance as a tool for policy analysis. Nevertheless, activity-based modelling is one of the most powerful and unique tools for urban energy systems analysis.

Uncertainty and sensitivity analysis

The final chapter in this section discusses uncertainty and sensitivity analysis. These techniques are not modelling techniques /per se/, but rather general methods that could be applied to any modelling framework in order to assess the impact of uncertainty on the model results. Having formal methods for evaluating uncertainty is important for urban energy systems because of the complexity of such systems: even if we manage to make a nice neat quantitative model of the system, there will still be questions about the choice of values for specific model parameters.

Penetration of domestic energy efficiency measures as part of Newcastle’s overall energy strategy

The chapter illustrates how uncertainty analysis — the description of model output variability given uncertain inputs — can be performed using the R package and Monte Carlo simulation. I also discuss the use of sensitivity analysis — the attribution of model output variability to specific uncertain inputs — as a way of improving the quality of model results and promoting more robust policy conclusions. The methods are applied to a case study from Newcastle-upon-Tyne where we worked with the local council to develop an energy systems strategy to 2050 that clearly illustrated the benefits of prioritising energy efficiency interventions.

These chapters show that no one modelling technique can answer all questions about urban energy systems. Optimization models work well for technical design problems and long-term planning, but simulation models based on citizen activities are valuable for capturing the complexity of urban life and its impact on energy consumption. But even more to the point, computational models are only part of an analyst’s toolkit. Part IV therefore looks at some qualitative lessons that be drawn from experience in urban energy systems around the world.

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How can Newcastle achieve their 2050 carbon target?

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Another new paper out, this time looking at urban carbon reduction strategies. Working with Carlos Calderon at Newcastle University, we investigated how a goal-oriented optimization model could inform urban energy and carbon reduction strategies in contrast to current practice, which relies mainly on ad hoc bottom-up models. In particular we focused on the need for models that could capture spatial dependencies in both energy supply and demand, as well as parameter uncertainty.

The results allow us to offer robust policy advice, such as installing loft insulation and cavity wall insulation over the next ten years, because it is cost- and carbon-effective in almost all future scenarios. Here’s the key figure, with the maximum rates of penetration indicated by the dashed line and the grey areas showing the interquartile range:

Penetration of domestic energy efficiency measures as part of Newcastles overall energy strategy

The abstract:

Local authorities often rely upon urban energy and carbon modelling tools to develop mitigation policies and strategies that will deliver reductions in greenhouse gas emissions. In this paper the UK example of Newcastle-upon-Tyne is used to critique current practice, noting that important features of urban energy systems are often omitted by bottom-up tools including interactions between technologies, spatial disaggregation of demand, and the ability to pursue over-arching policy goals like cost minimization. An alternative optimization-based approach is then described and applied to the Newcastle case, at the scale of both the whole city and the South Heaton district, and using Monte Carlo techniques to address policy uncertainty. The results show that this new method can help policy makers draw more robust policy conclusions, sensitive to spatial variations in energy demand and capturing the interactions between developments in the national energy system and local policy options. Further work should focus on improving our understanding of local building stocks and energy demands so as to better assess the potential of new technologies and policies.

Keirstead, J., & Calderon, C. (2012). Capturing spatial effects, technology interactions, and uncertainty in urban energy and carbon models: Retrofitting newcastle as a case-study Energy Policy DOI: 10.1016/j.enpol.2012.03.058

A review of urban energy system models

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Our review paper on urban energy modelling has just been published in Renewable and Sustainable Energy Reviews. This is a paper that should have been written a few years ago when our urban energy systems work started out, but the extra experience has been helpful in understanding how all the different types of models people use fit together. The paper’s divided into three sections: a review of current practice, an analysis of common problems and challenges, and a discussion of future opportunities for improved practice. I’ve been touring this paper for a few months now, and the response has been encouraging.

The abstract:

Energy use in cities has attracted significant research in recent years. However such a broad topic inevitably results in a number of alternative interpretations of the problem domain and the modelling tools used in its study. This paper seeks to pull together these strands by proposing a theoretical definition of an urban energy system model and then evaluating the state of current practice. Drawing on a review of 219 papers, five key areas of practice were identified technology design, building design, urban climate, systems design, and policy assessment each with distinct and incomplete interpretations of the problem domain. We also highlight a sixth field, land use and transportation modelling, which has direct relevance to the use of energy in cities but has been somewhat overlooked by the literature to date. Despite their diversity, these approaches to urban energy system modelling share four common challenges in understanding model complexity, data quality and uncertainty, model integration, and policy relevance. We then examine the opportunities for improving current practice in urban energy systems modelling, focusing on the potential of sensitivity analysis and cloud computing, data collection and integration techniques, and the use of activity-based modelling as an integrating framework. The results indicate that there is significant potential for urban energy systems modelling to move beyond single disciplinary approaches towards a sophisticated integrated perspective that more fully captures the theoretical intricacy of urban energy systems.

Keirstead, J., Jennings, M., & Sivakumar, A. (2012). A review of urban energy system models: Approaches, challenges and opportunities Renewable and Sustainable Energy Reviews, 16 (6), 3847-3866 DOI: 10.1016/j.rser.2012.02.047

Gaussian process regression with R

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I’m currently working my way through Rasmussen and Williams’s book on Gaussian processes. It’s another one of those topics that seems to crop up a lot these days, particularly around control strategies for energy systems, and thought I should be able to at least perform basic analyses with this method.

While the book is sensibly laid-out and pretty comprehensive in its choice of topics, it is also a very hard read. My linear algebra may be rusty but I’ve heard some mathematicians describe the conventions used in the book as “an affront to notation”. So just be aware that if you try to work through the book, you will need to be patient. It’s not a cookbook that clearly spells out how to do everything step-by-step.

That said, I have now worked through the basics of Gaussian process regression as described in Chapter 2 and I want to share my code with you here. As always, I’m doing this in R and if you search CRAN, you will find a specific package for Gaussian process regression: gptk. The implementation shown below is much slower than the gptk functions, but by doing things manually I hope you will find it easier to understand what’s actually going on. The full code is given below and is available Github. (PS anyone know how to embed only a few lines from a gist?)

Step 1: Generating functions

With a standard univariate statistical distribution, we draw single values. By contrast, a Gaussian process can be thought of as a distribution of functions. So the first thing we need to do is set up some code that enables us to generate these functions. The code at the bottom shows how to do this and hopefully it is pretty self-explanatory. The result is basically the same as Figure 2.2(a) in Rasmussen and Williams, although with a different random seed and plotting settings.

Example of functions from a Gaussian process

Step 2: Fitting the process to noise-free data

Now let’s assume that we have a number of fixed data points. In other words, our Gaussian process is again generating lots of different functions but we know that each draw must pass through some given points. For now, we will assume that these points are perfectly known. In the code, I’ve tried to use variable names that match the notation in the book. In the resulting plot, which corresponds to Figure 2.2(b) in Rasmussen and Williams, we can see the explicit samples from the process, along with the mean function in red, and the constraining data points.

Example of Gaussian process trained on noise-free data

Step 3: Fitting the process to noisy data

The next extension is to assume that the constraining data points are not perfectly known. Instead we assume that they have some amount of normally-distributed noise associated with them. This case is discussed on page 16 of the book, although an explicit plot isn’t shown. The code and resulting plot is shown below; again, we include the individual sampled functions, the mean function, and the data points (this time with error bars to signify 95% confidence intervals).

Example of Gaussian process trained on noisy data

Next steps

Hopefully that will give you a starting point for implementating Gaussian process regression in R. There are several further steps that could be taken now including:

Changing the squared exponential covariance function to include the signal and noise variance parameters, in addition to the length scale shown here.
Speed up the code by using the Cholesky decomposition, as described in Algorithm 2.1 on page 19.
Try to implement the same regression using the gptk package. Sadly the documentation is also quite sparse here, but if you look in the source files at the various demo* files, you should be able to figure out what’s going on.