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The Internet of Things, source of data and of uncertainty
The idea of resorting to the connected objects is justied by the fact that these objects are being increasingly ubiquitous in the society. In particular, if we consider a single house, the smart thermostat is starting to be wide-spread: 4.9M devices were sold in 2015 according to IoT Analytics (70% of them in North America), representing a 123% growth from Q4/2014 to Q4/2015. The market is still emerging, but the multiplicity of companies proposing smart thermostats or connected weather stations (in France, Sowee, Netatmo, Qivivo, Hector, Atlantic, Schneider Electrics,Ween,…) shows the potential of such products.
Regarding the specic case of individual housing, the connected objects form an ecosystem dening the so-called Smart Home. As represented in Figure 1.4, these objects can be grouped into six categories. The smart grid category encompasses the smart meters, which give access to the overall energy consumption of the building every few minutes. Dedicated meters might also measure specically the local production of renewable energy or the consumption of an electric vehicle charging station. Then, the class of objects related to the thermal comfort covers the smart thermostats and the connected weather stations. These items usually monitor the indoor temperature and indoor air quality. Compared to the former programmable thermostat, the « smart » thermostat aims at reliably save energy through new features, such as smartphone user interfaces, energy-use feedback, occupancy sensing, fault detection, demand response or control of multiple zones [PWM16]. The white goods, i.e. the large domestic electrical goods such as a refrigerator or a washing machine, form the third category. These appliances are starting to get connected, with applications such as distance control or energy monitoring. We include also a potentially smart electric hot water tank (see an investigation in [Bee16]) in this category. The fourth category involves the items that enable the home automation: wireless door or window contacts, smart light bulbs, etc. The security appliances include indoor security cameras or even connected locks. Some connected cameras are for instance able to handle face recognition and send notications accordingly. Finally, the most widely spread connected object is simply the smartphone, which may serve as an interface between the user and other connected appliances.
Following this brief description of the ecosystem of the connected objects, the key assumption of the thesis is that an energy utility may use the information brought by these objects in order to improve the observation of the thermal behaviour of the building and perform a model identication. Starting with the heating loads, the smart meter gives at least an upper bound of this contribution. Moreover, connected electrical appliances may help lower this bound. This is further detailed in Chapter 7. Should the utility decide to provide the client with a connected weather station, they would then have access to a measurement – not the measurement – of the outdoor temperature, and similarly for the indoor temperature. Note that the connected weather stations do not measure the received solar radiation, which is therefore completely unobserved a priori. Finally, the devices in relation to the automation or the security may give information about the number of occupants in the building, and thereby about the metabolic heat gains. However, this seems very tentative at this time (see Chapter 7).
Hence, from an energy utility perspective, it seems reasonable to assume that only the total load curve is accurately measured, that the solar radiation and the metabolic gains are not measured at all, whereas the heating load curve as well as the outdoor and indoor temperatures are measured with some degree of uncertainty. This results in the simplied input-output represention of a building model in Figure 1.3. The constraints that arise in practice alter thus considerably the conditions of application of the standard building identication algorithms. Therefore, tackling these challenges raises a set of new questions for the building identication. What information do the connected objects bring in order to help mitigating the practical constraints? How to model these information mathematically? How can one adapt the identication procedure such that it accounts for some level of uncertainty of the inputs of the system? Can we perform an accurate identication from a reduced set of cheap connected sensors, despite their inherent uncertainty? What sensors are key to a good estimation? The purpose of the thesis is to address such questions. The next section describes the outline of the document and the main contributions to solving the issues raised in this introduction.
Outline of the document and contributions
As a preamble, the structure of the building model and the data that support the numerical experiments throughout the dierent chapters are presented in Chapter 2. Consistently with the chosen data-driven approach, this model is a low-order R3C2 equivalent electrical network, made of three resistors and two capacitors. From a mathematical point of view, the corresponding modelling framework is that of state-space models in closed loop. We emphasize the fact that our purpose in this thesis is not to nd the best representation of a building, but instead to show how to adapt the identication procedure depending on some practical constraints. Hence, the algorithms suggested in the following chapters could easily be adapted to some renements of the R3C2 model. Subsequently to this introductory chapter, the contributions of the thesis are two-fold.
First of all, Part I of the document assumes that every input and output of the R3C2 network is accurately measured, and looks into the algorithmic side of the identication process. Indeed, although many estimation algorithms are suggested in the literature, it is not clear whether the model should be identied in open loop, or within a control loop, the latter case corresponding to the real exploitation of buildings (see Figure 1.2). Hence, Chapter 3 gives some statistical and empirical arguments supporting the claim that an open-loop building model may be identied from on-site measurements and with a maximum likelihood estimator, even if the R3C2 system actually operates in closed loop. This result enables us not to model the feedback loop in general, which simplies the problems studied in the second part of the thesis. We choose then a maximum likelihood identication procedure of the open-loop R3C2 network, with the Expectation-Maximization (EM) algorithm.
Dynamics and observation of the outdoor temperature
First of all, at time-step = 10 minutes and over a span of a few days only, we suppose that the actual outdoor temperature #o evolves according to a one-dimensional random walk. At discrete time t := t, we have #o;t = #o;t1 + « t;where « t is a Gaussian white noise process with constant variance 2 » . This is the simplest dynamic model possible, which assumes that the current value #o;t of the outdoor temperature is in the neighborhood of the past value #o;t1, this neighborhood being characterized by « . In particular, we do not include any periodic component in the model, because such component is already included in the observation To.
The observed outdoor temperature To is a biased version of the hidden state #o, where the bias remains to be specied. In accordance with our dataset (BESTLab experiment), let us consider the case of a temperature sensor close to the building but not necessarily protected from the solar radiations. An example of the corresponding series is given in Figure 5.3. It illustrates in particular the fact that the dierence between the two sensors does not depend on the actual outdoor temperature: high values of the bias may occur even for cold climates. This represents typically the situation where an energy utility has access to the measurements of the end-user’s temperature sensor but does not know its precise location around the building. We suggest to represent the bias as another hidden state, denoted #b, with a random walk behaviour: #b;t = #b;t1 + t; (5.2a) To;t = #o;t + It#b;t + t;
Table of contents :
Introduction en francais
1 Introduction
1.1 The context of building identication
1.2 On the importance of the data
1.3 The Internet of Things, source of data and of uncertainty
1.4 Outline of the document and contributions
List of conference papers
List of patents
I Perfect observation of the building
2 Modelling framework and available data
2.1 A low-order builing model
2.1.1 The choice of a grey-box model
2.1.2 Model description
2.1.3 Linear discrete-time state space representation
2.2 Available data
2.2.1 BESTLab experiment
2.2.2 Simulated data
2.3 Summary
3 Open-loop identication of a building observed in closed loop
3.1 Literature review
3.2 A maximum likelihood estimator
3.3 Asymptotic properties of the maximum likelihood estimator
3.3.1 Data generated in open loop
3.3.2 Data generated in closed loop
3.4 Numerical experiments
3.4.1 Case 1: simulated dataset
3.4.2 Case 2: BESTLab data
3.5 Summary
II Identication under practical constraints
4 Missing observations of the indoor temperature
4.1 A modied closed loop model
4.2 Hybrid Monte Carlo sampling method
4.2.1 Hamiltonian dynamics
4.2.2 MCMC using Hamiltonian dynamics
4.2.3 Practical improvements
4.3 Application to building identication
4.3.1 Principle
4.3.2 Numerical illustration
4.4 Summary
5 Bias reduction of the outdoor temperature
5.1 Motivation
5.2 State space representation
5.2.1 Dynamics and observation of the outdoor temperature
5.2.2 Global model
5.3 Estimation of the parameters
5.3.1 EM for a time-varying linear state-space
5.3.2 EM for a switching linear state-space
5.4 Numerical illustration
5.4.1 Validation procedure
5.4.2 Smoothed outdoor temperature
5.4.3 Estimation of the R3C2 model
5.5 Summary
6 Learning the dynamics of the unobserved solar gains
6.1 Nonlinear modelling
6.1.1 Solar radiation model
6.1.2 Global state-space model
6.2 Rao-Blackwellised particle smoother EM algorithm
6.2.1 Problem formulation
6.2.2 Rao-Blackwellised particle ltering and smoothing
6.2.3 Algorithm
6.3 Numerical illustration
6.3.1 Simulated data
6.3.2 BESTLab data
6.4 Summary
7 Uncertainty on the heating load curve
7.1 Characterization of the connected objects
7.1.1 Typology
7.1.2 Main hypotheses
7.2 Estimation procedure
7.2.1 Notations
7.2.2 Overview of the algorithm
7.2.3 Detailed description
7.3 Stochastic generation of domestic load curves
7.3.1 Domestic building occupancy model
7.3.2 Generation of domestic electric load curves
7.3.3 Validation of the model
7.4 Numerical experiments
7.4.1 Implementation
7.4.2 Analysis of a single experiment
7.4.3 Multiple experiments
7.4.4 BESTLab data
7.5 Summary and discussion
III Conclusion and perspectives
8 Conclusions and perspectives
A Estimation of the solar radiation: kriging model
Bibliography
