Modeling and Simulations of Demand Response in Sweden

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Modeling and Simulations of

Demand Response in Sweden

DANIEL A. BRODÉN

Licentiate Thesis

Stockholm, Sweden 2017

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TRITA-EE 2017:148 ISSN 1653-5146

ISBN 978-91-7729-574-7

KTH School of Electrical Engineering Department of Electric Power & Energy Systems SE-100 44 Stockholm SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av teknologie licentiatexamen i elektro- och systemteknik fredagen den 10 November 2017 klockan 10.30 i sal F3, Kungliga Tekniska högskolan, Lindstedtsvägen 26, Stockholm.

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Abstract

Electric power systems are undergoing a paradigm shift where an increas-ing number of variable renewable energy resources such as wind and solar power are being introduced to all levels of existing power grids. At the same time consumers are gaining a more active role where self energy production and home automation solutions are no longer uncommon. This challenges traditional power systems which were designed to serve as a centralized top-down solution for providing electricity to consumers. Demand response has risen as a promising solution to cope with some of the challenges that this shift is creating.

In this thesis, control and scheduling studies using demand response, and consumer load models adapted to environments similar to Sweden are pro-posed and evaluated. The studies use model predictive control approaches for the purpose of providing ancillary and financial services to electricity market actors using thermal flexibility from detached houses. The approaches are evaluated on use-cases using data from Sweden for the purpose of reducing power imbalances of a balance responsible player and congestion management for a system operator. Simulations show promising results for reducing power imbalances by up to 30% and managing daily congestion of 4-19 MW using demand response. Moreover, a consumer load model of an office building is proposed using a gray-box modeling approach combining physical under-standing of buildings with empirical data.

Furthermore, the proposed consumer load model along with a similar model for detached houses are packaged and made freely available as MAT-LAB applications for other researchers and stakeholders working with demand response. The applications allow the user to generate synthetic electricity load profiles for heterogeneous populations of detached houses and office buildings down to 1-min resolution.

The aim of this thesis has been to summarize and discuss the main high-lights of the included articles. The interested reader is encouraged to inves-tigate further details in the second part of the thesis as they provide a more comprehensive account of the studies and models proposed.

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Sammanfattning

Elkraftsystemet genomgår ett paradigmskifte där större andelar förnybara energikällor med varierande produktion så som vind- och solkraft integreras till de olika spänningsnivåerna. Samtidigt börjar konsumenterna ta på sig en mer aktiv roll där hushåll som producerar sin egen el eller som använder sig av smart styrning i hemmet inte längre är ovanligt. Detta utmanar det traditio-nella tankesättet om kraftsystem med centraliserad produktion och toppstyrd överföring till konsument. Förbrukarflexibilitet är en lovande lösning till de utmaningar som paradigmskiftet orsakar.

I denna avhandling presenteras studier för styrning av förbrukarflexibilitet och tillhörande modeller som anpassats efter svenska förhållanden. Studier-na använder sig av en modellprediktiv styrningsapproach i syfte att hantera obalanser med hjälp av förbrukarflexibilitet från värmesystem i småhus. Fall-studier har genomförts med data från Sverige i syfte att minimera obalanser av en balansansvarig aktör samt att hantera nätbelastningar av en elnätsä-gare. Simuleringar visar lovande resultat på minimering av obalanser upp till 30% och hanteringar av dagliga överbelastningar mellan 4-19 MW med hjälp av förbrukarflexibilitet. Dessutom presenteras en modell för kontorshus som använder sig utav en gray box approach där fysiska byggnadsegenskaper och empirisk data kombinerats.

I övrigt har den presenterade modellen tillsammans med en liknande mo-dell för småhus packeterats och gjorts fritt tillgängligt som MATLAB appli-kationer för forskare och andra intressenter inom området. Användaren kan generera syntetiska lastprofiler för heterogena populationer av småhus och kontorshus ner till minutupplösning.

Målet med denna avhandling har varit att summera och diskutera de hu-vudsakliga höjdpunkterna av de bifogade artiklarna. Den intresserade läsaren uppmanas att läsa den andra delen av avhandlingen för en mer fördjupad beskrivning av de utförda studierna och de presenterade modellerna.

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Acknowledgements

First and foremost I would like to thank my family for their loving support throughout this educational journey. Thank you to my parents Sherrie and Lars and to my two brothers Cyrus and Arman. You have encouraged me during difficult times and kept my feet on the ground during others.

In regards to the compilation of this thesis I would like to acknowledge Dr. Claes Sandels and Mikel Armendariz with whom I have closely collaborated. A lot of the work presented here is the fruit of our shared discussions.

I would like to thank my supervisor Professor Lars Nordström for pro-viding me with educational opportunities and continuous feedback. You have been a great manager throughout these years! I would like to thank Asso-ciate Professor Joakim Lilliesköld with whom I have been involved in teaching. Your genuine care for students and other people has not gone unnoticed! I would also like to thank the administrators Annica Johannesson and Elvan Helander for the many happy discussions we have had. You have brightened up the days at our department!

Last but not least, I would also like to thank current and former colleagues who have made my stay pleasant at KTH during the last few years: Ma-tus Korman, Margus Välja, Davood Babazadeh, Moustafa Chenine, Nicholas Honeth, Liv Gingnell, Fabian Hohn, Tin Rabuzin, Dan Pettersson, Eleni Nylén, Brigitt Högberg and many others. Best of luck to you all!

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List of Articles and Reports

1

Included

Article 1: D. Brodén, C. Sandels, L. Nordström, Assessment of Congestion

Man-agement Potential in Distribution Networks using Demand-Response and Battery Energy Storage, Conference on Innovative Smart Grid Technologies North Amer-ica, sponsored by IEEE Power & Energy Society, Washington D.C., United States, 2015, pp. 1-10

Article 2: C. Sandels, D. Brodén, J. Widén, L. Nordström, E. Andersson,

Mod-eling Office Building Consumer Load with a Combined Physical and Behavioral Approach: Simulation and Validation, Applied Energy, Volume 162, 15 January 2016, pp. 472-485

Article 32: D. Brodén, K. Paridari, L. Nordström, MATLAB Applications

to Generate Synthetic Electricity Load Profiles of Office Buildings and Detached Houses, Accepted to Conference on Innovative Smart Grid Technologies Asia, spon-sored by IEEE Power & Energy Society, Auckland, New Zealand, 2017, pp. 1-6

Article 4: D. Brodén, M. Armendariz, L. Nordström, Anticipating Overrides

of Schedulable Space Heating Systems in Detached Houses for Demand Response, Submitted to Journal of Electric Power System Research, 2017, pp. 1-9

Not included

Article 5: M. Armendariz, D. Brodén, N. Honeth, L. Nordström, A Method

to Identify Exposed Nodes in Low Voltage Distribution Grids with High PV Pen-etration, IEEE Power and Energy Society General Meeting, Denver CO., United States, 2015, pp. 1-5

1_{Sorted in ascending order by date of publication/submission} 2_{Subject to minor revisions}

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viii LIST OF ARTICLES AND REPORTS

Article 6: G. Ryckebusch, D. Brodén, E. Lidström, L, Nordström, Analysis

of Demand-Response Participation Strategies for Congestion Management in an Island Distribution Network, 23rd International Conference on Electricity Distri-bution, Lyon, France, 2015, pp. 1-5

Article 7: V. Gliniewicz, G. Ryckebusch and D. Brodén, Economic Impact

As-sessment of using Congestion Management Methods to Enable Increased Wind Power Integration on Gotland, Sweden, 15th Wind Integration Workshop, Vienna, Austria, 2016, pp. 1-8

Article 8: B. Romain, D. Brodén, Economic Simulations of the Participation

of Virtual Power Plants on the Swiss Balancing Market, Conference on Innovative Smart Grid Technologies Europe, sponsored by IEEE Power & Energy Society, Ljubljana, Slovenia, 2016, pp. 1-6

Article 9: M. Armendariz, D. Babazadeh, D. Brodén, L. Nordström, Strategies

to Improve the Voltage Quality in Active Low-Voltage Distribution Networks using DSO’s assets, IET Generation, Transmission & Distribution, vol. 11, no. 1, 2017, pp. 73-81

Report 1: M. Stifter, R. Kamphuis, M. Galus, M. Renting, A. Rijneveld, R.

Tar-gosz, S. Widergren, L. Nordström, D. Brodén, T. Esterl, S. Kaser, P. Koponen, S. Galsworthy, W. Friedl, S. Doolla, Roles and Potentials of Flexible Consumers and Prosumers : Demand Flexibility in Households and Buildings, International Energy Agency DSM Task 17 Phase 3, 2016, pp. 1-84

Report 2: T. Esterl, S. Kaser, M. Stifter, R. Kamphuis, M. Galus, M. Renting, A.

Rijneveld, R. Targosz, S. Widergren, L. Nordström, D. Brodén, S. Galsworthy, Valuation Analysis of Residential Demand Side Flexibility : Analysis of Business Cases and Existing Valuation Frameworks, International Energy Agency DSM Task 17 Phase 3, 2016, pp. 1-96

Tar-gosz, S. Widergren, L. Nordström, D. Brodén, T. Esterl, S. Galsworthy, P. Kopo-nen, S. Doolla, Pilot Studies and Best Practices : Demand Flexibility in Households and Buildings, International Energy Agency DSM Task 17 Phase 3, 2016, pp. 1-72

Tar-gosz, S. Widergren, L. Nordström, D. Brodén, T. Esterl, S. Kaser, S. Galsworthy, S. Doolla, Conclusions and Recommendations: Demand Flexibility in Households and Buildings, International Energy Agency DSM Task 17 Phase 3, 2016, pp. 1-37

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Notes about the Author’s Contributions

The main authoring and concepts are due to Daniel A. Brodén for articles 1, 3, and 4. In article 2 and 5 contributions were made to the data analytical sections. In article 6, 7 and 8, contributions were made to the overall research concept. In article 9 contributions were made to the problem formulation section. In reports 1-4 contributions were made to the sections on the Swedish perspective on demand flexibility.

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List of Abbreviations and

Acronyms

3

AC Alternating Current ANN Artifical Neural Networks DC Direct Current

e.g. For example

HVAC Heating Ventilation and Air Conditioning MPC Model Predictive Control

MPS Model Predictive Scheduling RC Resistance Capacitance RMSE Root Mean Square Error i.e. That is

3_{Sorted in alphabetical order}

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List of Figures, Tables and

Equations

4

Figures

1.1 The basic structure of a power grid [1] . . . 4

1.2 Land-ocean temperature index, 1880 to present, with base period 1951-1980 [2] . . . 5

1.3 Battery storage price trend [3] . . . 6

1.4 Solar panel price trend [4] . . . 7

1.5 Illustration of common applications of demand response with (a) peak clipping (b) valley filling and (c) load shifting [5] . . . 7

1.6 Illustration of the island of Gotland and its power grid [6] . . . 9

2.1 Basic working principle of MPC scheme [7] . . . 12

2.2 A schematic diagram of the R-C model of a building [8] . . . 14

2.3 A graphical representation of a simple neural network [9] . . . 15

3.1 Assumed demand-response setup for model predictive scheduling of the electric space heating system in detached houses . . . 18

3.2 Conceptual overview of an ancillary service toolbox used for congestion management [10] . . . 19

4_{Sorted by order of appearance in thesis}

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3.3 Diagram showing the functioning, interrelationship, and data require-ments of the simulation modules used by the office building consumer load model [11] . . . 22 4.1 Boxplots showing simulation results on the number and duration of

schedule overrides, and the daily power imbalances during 90 consec-utive days when demand response participants have been scheduled . . 30 4.2 Sensitivity analysis on the changes of the total number and duration of

schedule overrides and the total power imbalances between MPS case 2 and 1 as a function of sigma . . . 31 4.3 Simulation results of indoor temperature of demand response

partici-pants for the different seasonal scenarios . . . 33 4.4 Simulation results of tank temperature of demand response participants

for the different seasonal scenarios . . . 33 4.5 Statistical comparison between measured and simulated appliance and

ventilation load in office building floor on validation data set 1 during months without cooling (September-May) . . . 34 4.6 Statistical comparison between measured and simulated load in office

building floor on validation data set 2 . . . 35 4.7 Generated output load from office load electricity application for a

spe-cific set of configurations . . . 37 4.8 Generated output load from house load electricity application for a

spe-cific set of configurations . . . 37

Tables

3.1 Configurable model parameters and variable correspondence to [11] for MATLAB application: Office load electricity . . . 26 3.2 Configurable model parameters and variable correspondence to [12] for

MATLAB application: House load electricity . . . 27 4.1 Simulation results of congestions managed and number of required

de-mand response participants for the different seasonal scenarios . . . 32

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4.2 Summarizing statistics for validation data sets 1 (for cold months) and

2 for office building loads. Note that the RMSE is expressed in kW. . . 35

Equations

3.1 Congestion condition for a one-bus system . . . 19

3.2 Transition probabilities of non-homogeneous Markov chains from state i to j . . . 21

3.3 Total power consumption by appliances on office building floor . . . 22

3.4 Total power consumption by lighting usage in office building floor . . . . 23

3.5 Total occupied office room area on office building floor . . . 23

3.6 Total power consumption by computer usage on office building floor . . 23

3.7 Total power consumption by server usage on office building floor . . . . 23

3.8 Total power consumption of unknown/minor appliance usage on office building floor . . . 23

3.9 Total power consumption of appliance usage in common areas on office building floor . . . 23

3.10 Indoor temperature change on office building floor . . . 24

3.11 Heat gain from solar radiation on office building floor . . . 24

3.12 Heat pump power consumption on office building floor . . . 24

3.13 Heat gain from appliance usage on office building floor . . . 24

3.14 Heat losses (or gains) on office building floor due to temperature ex-change with the outdoor environment . . . 24

3.15 Transmission and ventilation losses on office building floor . . . 24

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Background and Summary of

Articles 1-4

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Chapter 1

Introduction

In this chapter a brief overview of electric power systems is first presented with examples from Sweden and North America. It is followed by a section on some of the current and future challenges in power systems as perceived today. The follow-ing section presents demand response as a potential solution to these challenges, including a brief description of demand response initiatives in Sweden. Finally, research and other forms of contributions of this thesis are summarized.

1.1 Electric Power Systems in Brief

Electric power systems as we know them today had their beginings in the late 19th century. Early examples are the Godalming Power Station in England or the Pearl Street Station in New York City, which powered lamps for a small set of customers [13, 14]. Electric power systems are frequently referred to as the "power grid" or simply the "grid" and are characterized by a supply and demand chain which consists of generating units on the supply side and conductive cables transporting the electricity over short or long distances to the demand-side. The standard of transporting electricity has been through Alternating Current (AC) which requires maintaining a system frequency of 50 Hz in Europe and 60 Hz in North America. Combining high-voltage with AC allows lower currents to flow through the cables compared to using Direct Current (DC). This minimizes power losses and the need for using thicker cables, leading to reductions in infrastructure costs. The grid is commonly segmented into a transmission and distribution level. The delimitation and terminology may vary between countries but the voltage level is usually the main delimiting factor. In Sweden, the transmission level (stamnät in Swedish) consists of voltage levels greater than 220 kV (considered high-voltage). The dis-tribution level consists of all voltage levels below 220 kV. Medium- and low-voltage levels are typically considered to be 30-220 kV and 0.23-30 kV, respectively

(re-gionnät and lokalnät in Swedish) [15]. There is typically high voltage close to the

generating plants from where it is incrementally stepped-down downstream of the 3

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4 CHAPTER 1. INTRODUCTION

grid to a suitable level to be used by electric appliances (typically 230 V). In Figure 1.1 a diagram of the basic structure of a power grid is presented. Voltage levels and grid classification may vary between countries but the basic principle of the system are similar. Components of a power system include supply, load, conduc-tors, capaciconduc-tors, reacconduc-tors, power electronic devices, protection devices, supervisory control and data acquisition systems, and others. In Sweden, the transmission grid consists of 15,000 km of power lines, 160 substations and switching stations and 16 connections to other countries [16]. The power grid is arguably the most critical infrastructure in developed countries.

Figure 1.1: The basic structure of a power grid [1]

1.2 Current and Future Challenges

Ever since the industrial revolution took off in the 18th century, fossil fuels have been the main source of electricity generation worldwide. In the mid-20th century scientists reached a consensus that global mean temperatures are rising and that it is extremely likely that greenhouse gas emissions are the cause of it. An example of temperature anomalies can be observed in Figure 1.2. A series of international initiatives and agreements have been made in order to reduce greenhouse gas emis-sions. Two notable agreements are the Kyoto Protocol [17] from 1992 and the Paris agreement from 2016 [18].

In the European Union, climate strategies and targets have been set for hori-zon 2020, 2030 and 2050 [19]. A result of these targets is the integration of more renewable energy resources to existing grids, many of which have variable gen-eration, such as solar or wind power. Traditionally, the instantaneous frequency of the power grid has been maintained by regulating the production according to changes in the power consumption. Variable renewable generation does not offer the same regulation capacities as conventional power plants. Therefore, if left unman-aged, imbalances in the power system are expected to increase. Additionally, the power grid is currently undergoing a paradigm shift where the traditional

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central-1.3. DEMAND RESPONSE 5

Figure 1.2: Land-ocean temperature index, 1880 to present, with base period 1951-1980 [2]

ized power production and distribution approach is being challenged by distributed energy resources at the medium and lower-voltage levels. One of the explanations for this is the decrease in cost of energy storage technology and solar panels. Fig-ures 1.3 and 1.4 illustrate an example of the price trends of these technologies in time.

In the midst of these changes the roles and responsibilities of electricity market actors are being challenged. An example is system operators which are increasingly facing power quality challenges in their low-voltage networks due to bi-directional power flows caused by producing consumers [20] (or commonly referred to as pro-sumers).

1.3 Demand Response

A potential solution to cope with current and future challenges is to make use of demand response. The Federal Energy Regulatory Commission of the United States define demand response as "Changes in electric usage by demand-side re-sources from their normal consumption patterns in response to changes in the price of electricity over time, or to incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopar-dized" [21]. This definition is used throughout this thesis. Demand response and demand-side management are often used interchangeably in literature. Controlling or scheduling the load either directly or indirectly offers capabilities for ancillary services to the grid such as congestion management, voltage regulation, frequency

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Figure 1.3: Battery storage price trend [3]

regulation and others. Furthermore, demand response also has the potential to offer financial services to electricity market actors such as minimizing the imbal-ance costs of a balimbal-ance responsible player. Figure 1.5 illustrates an example of three common applications of demand response. Thus, demand flexibility presents promising potential to counteract imbalances caused by the integration of variable renewable generation.

Demand response implies having flexible consumers that are willing to change their consumption patterns; this is sometimes referred to as demand flexibility. The demand flexibility is very much time- and space-dependent, meaning that consumers may be more or less flexible depending on the time of the day and their geographical location. Demand flexibility is also very much dependent on the type of demand-side segment and resources that are providing the response. In this thesis the scope has been delimited to detached houses and office buildings. The appliances in the buildings that have been considered for demand response are electric space heating, domestic hot water tanks, and Heating Ventilation and Air Conditioning (HVAC) systems. These are common appliances in the residential and commercial consumer segments, in particular in Sweden where there are over 600,000 detached houses using electricity as their primary heating systems [22]. The advantage of considering heating systems for providing flexibility over white

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1.4. DEMAND RESPONSE IN SWEDEN 7

Figure 1.4: Solar panel price trend [4]

Figure 1.5: Illustration of common applications of demand response with (a) peak clipping (b) valley filling and (c) load shifting [5]

goods (such as refrigerators, washing machines, and others) is their high power consumption relative to the other appliances. Furthermore, the thermal inertia of a building provides excellent capabilities to use space heating appliances for demand response with little or no noticeable impact on the indoor temperature for building occupants.

1.4 Demand Response in Sweden

Demand response in Sweden is not new and has been around for quite some time, particularly at the industrial load segment. For example, large consumers such as paper mill factories have been part of a strategic reserve ensuring enough available capacity for the power system through load shedding in case of scarcity situations [23]. More recently focus has been directed towards residential demand response as residential consumers has the potential to provide great demand flexibility when aggregated and synchronized. A notable pilot project that has investigated feasi-bility and potential from the residential load segment is the Smart Grid Gotland project [6]. The project was conducted between the years 2012-2016 on Sweden’s

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largest island, Gotland. Two to three of the suprojects focused on potential and feasibility of residential demand response. The potential was evaluated through simulations to assess how residential demand could be used to integrate more wind power on the island beyond its current hosting capacity. Electric space heating sys-tems and boilers for domestic hot water in detached houses were considered as the flexible appliances providing demand flexibility within a predefined comfort interval for the house occupants. Simulation results showed technical feasibility to manage daily congestion of at least 5 MW through the control of heating systems of approx-imately 10% of the detached houses on the island. Articles 1, 6 and 7 present results associated with the work performed within this subproject. Furthermore, the more practical aspects of potential and feasibility of residential demand response were evaluated in the market test and installation subprojects. Heating appliances of approximately 260 detached houses were equipped with control systems to enable day-ahead scheduling. The appliances were scheduled based on a reinforced market price such to minimize the cost for the consumer while maintaining comfort require-ments. The market test and installation subprojects showed successful scheduling of the appliances in houses and led to many insights into the challenge of installing and incentivizing demand response participation at scale. As expected, the results did not lead to any major savings for the participants in part due to low market prices during the test period. More details about the studies conducted with influ-ences of the Smart Grid Gotland project can be found in [24, 25]. An illustration of Gotland and its power grid is presented in Figure 1.6.

Similar pilot projects to the one on Gotland have been recently conducted in Sweden. Another example is the Stockholm Royal Seaport project where white appliances in apartment buildings were equipped with control systems to further evaluate demand response. Details about demand response in the Stockholm Royal Seaport project can be found in [26, 27].

There are of course many other demand response initiatives that have taken place in Sweden, both of theoretical and practical nature. In Reports 1-4 further details about some of these initiatives are provided under the sections presenting the Swedish perspective.

1.5 Research Contributions

The research contributions of this thesis are as follows: First, a Model Predictive Scheduling (MPS) approach is proposed which provides potential for ancillary and financial services to electricity market actors by utilizing load while anticipating scheduling overrides of demand response participants. The approach is evaluated for the use-case of a balance responsible player based on Nordic market conditions using data from Sweden. Secondly, an ancillary service toolbox concept is proposed, which provides potential for congestion management in distribution grids using demand response from heating systems in detached houses and battery energy storage. The toolbox is evaluated for a use-case on Gotland, Sweden. Further contributions

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1.6. OTHER CONTRIBUTIONS 9

Figure 1.6: Illustration of the island of Gotland and its power grid [6]

include an office building consumer load model, which uses a combined physical and behavioral approach. The consumer load model is especially well suited for the integration of simulations using demand response where model parameters can be easily configured to consider heterogeneous populations of flexible consumers.

1.6 Other Contributions

Other contributions of this thesis include the development and free availability of consumer load models for office buildings and detached houses as MATLAB appli-cations [28, 29]. The models have been packaged into graphical user interfaces that allow generation of synthetic electricity load profiles down to 1-min resolution for aggregation of heterogeneous buildings. The applications can be used for educa-tional and research purposes such as simulations of power systems, evaluation of classification and clustering algorithms for load segmentation, and others. Further contributions which have not been included in this thesis are International Energy Agency Reports 1-4 where Swedish initiatives and perspective on demand response have been described.

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Chapter 2

Related Work

In this chapter, related work in control and scheduling studies using demand re-sponse and modeling are presented. Brief descriptions are given on studies where demand response has been used to fulfill specific control objectives for electricity market players using model predictive approaches. Furthermore, common types of demand response modeling approaches found in literature are also described. The chapter is concluded by describing the contribution of this thesis in relation to related work.

2.1 Control and Scheduling Studies using Demand

Response

The control and scheduling of demand response for the purpose of providing ancil-lary services or financial services to electricity market players has been the subject of many research papers. Papers [30, 31, 32] are a few examples of this. A popular approach is to use MPC (also refered to as receding horizon control). MPC is a feedback control technique where a constrained optimization problem is repeatedly solved at each time step over a moving time horizon. The control input for the first time step is implemented and the optimization is solved for the next time step with newly acquired information [33]. An illustration of the MPC principle is presented in Figure 2.1.

In [30], an MPC scheme for demand response is proposed and evaluated using controllable electric water heaters on the Swiss day-ahead and intraday markets. The control objective is to minimize the total costs of a balance group using flexibil-ity of demand response participants. Economic results are presented and compared as well as a sensitivity analysis on load parameters, duty cycles and others. Simu-lations show that there is potential to reduce balance group costs, but the authors conclude that such a scheme is not profitable using the current price regime in Switzerland. In [31] an MPC scheme is proposed for domestic freezers with the objective of providing real-time frequency control. The control is demonstrated by

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12 CHAPTER 2. RELATED WORK

Figure 2.1: Basic working principle of MPC scheme [7]

following set-point trajectories communicated by an aggregator. Simulation results are presented for a base line and a load frequency control scenario showing promis-ing control capabilities for providpromis-ing frequency control. In [32] an MPC strategy is applied on an experimental flexible office building in Denmark to investigate the potential for active load management. The results demonstrate the function-ality of such a control strategy in realistic conditions. One of the reasons MPC is such a widely used approach is its ability to control current conditions while ac-counting for future uncertainties. This is particularly interesting when predicting thermal flexibility, which among others, is affected by changes due to occupancy and weather patterns. Furthermore, many studies focus on the savings potential for flexible consumers. In [34], an MPC-based appliance scheduling scheme is proposed for non-thermal and thermal appliances in buildings. The control objective is to minimize the electricity cost for the consumers through the building’s energy man-agement system. Simulations are performed for three different price schemes for different seasons in Chicago, United States, showing notable cost savings for con-sumers using time-varying pricing. In [35], a particle swarm optimization algorithm is proposed to minimize the electricity cost for consumers. The costs are minimized by shifting the loads of the consumers while maintaining their preferences. Simula-tions were performed for residential, commercial and industrial consumers showing notable cost reductions for industrial consumers in particular. What differentiates these studies beyond the control objective is the modeling approach of demand flexibility. The use-cases simulated also vary in geographical locations, which affect the results for the potential of demand response. This is especially true for space heating systems where the power consumption is strongly dependent on the outdoor climate and occupancy patterns in the building.

While many demand response studies have been performed for various geo-graphical locations, few have been performed for the conditions and environment of Sweden — an environment characterized by a temperate and cool climate with a high percentage of detached houses and electric heating appliances [22].

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2.2. MODELING DEMAND RESPONSE 13

2.2 Modeling Demand Response

There are many different approaches to model demand response, many of which have already been studied and proposed in literature. The purpose of the study most often determines which approach is most suitable. In studies of demand response in electricity markets it is common to model the demand flexibility as aggregated price sensitive demand, also refered to as price elasticity of demand — a measure commonly used in the field of economics. Papers [36, 37, 38] are a few of many examples of studies using price elasticity. In [36], a bottom-up model is proposed to estimate the flexibility of white appliances for a group of 500 households under three different pricing schemes. The flexibility is assumed to be provided by deferring the load cycles of the appliances, which is evaluated for different delay options. The results show elasticity matrices of the residential group for the different price schemes and delay options. These results can be used to model the elasticity in demand when white appliances in residential houses are assumed to provide the flexibility. One of the advantages of using a bottom-up modeling approach for the price elasticity is that it takes into account the realistic variability between the flexibility of individual consumers. A possible disadvantage is the complexity of the models compared to a top-down approach. The complexity can become cumbersome as the level of modeling depth increases. In the case of white goods, e.g., a dishwasher, one could model each energy phase, i.e., the pre-wash, heating, main pre-wash, drying, etc, and consider one or more of the phases as independently deferrable.

In the field of system identification, statistical methods and empirical data are used to construct mathematical models of dynamical systems. Models are com-monly classified into three categories: white-, gray-, and black-box models. White-box models are typically models which are proposed based on undisputed physical principles or laws. A commonly proposed white-box model for modeling ther-mal flexibility in buildings is the lumped capacitance model (or R-C model). The parameters of an R-C model have clear physical meanings and are analogous to components in electric circuits, such as the resistance and the capacitance, where the connecting nodes represent temperatures. Figure 2.2 depicts an R-C model and its correspondence to the physical properties of a building.

One of the advantages with R-C models of this type is that there is physical understanding of the temperature change in the building. Additionally, the param-eters of the models can be easily modified to account for changes in the indoor environment. One of the drawbacks is that the parameters are not easily identi-fiable and rely on the need for empirical data. A comprehensive literature review on R-C models for buildings can be found in [9]. On the other hand, a black-box model is a model that is entirely data-driven where there is no knowledge of the physical parameters of the building. A popular example of black-box models for thermal flexibility in buildings is Artificial Neural Networks (ANN). ANN mimics the biological structure of the brain, requiring a set of inputs where the output is generated by a complex network of nodes (or neurons) and hidden layers. A

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Figure 2.2: A schematic diagram of the R-C model of a building [8]

graphical representation of a simple neural network is illustrated in Figure 2.3. There are many papers that have used ANN to predict the thermal flexibility of buildings; papers [39, 40, 41, 42] are a few of many examples found in literature. In [39] Model Predictive Control (MPC) is used to forecast the thermal behavior of a building and control the HVAC system with respect to thermal comfort. A self-adapting model is used based on ANN, where the neural network is first trained using data generated from a detailed building model implemented in an external simulation software. Simulations show promising results for producing the thermal behavior of the building. One of the advantages with black-box approaches such as ANN is that no prior information about the physical properties of the build-ing is needed. This is especially advantageous today where smart meter data is collected often with little or no information about the physical properties of build-ings. The ANN approach can be made adaptive and self-learning unlike physical models, which makes it applicable to a wider range of buildings. One of the disad-vantages with black-box models is that there is no physical understanding of the model. Thus it cannot be characterized by its model parameters. Moreover, a common problem with black-box models such as ANN is the problem of overfitting the model with training data, which leads to poor forecasting performance. How-ever, there exist pruning algorithms such as the "optimal brain surgeon" algorithm, which can be applied to reduce the problem of overfitting [43]. Finally, gray-box models are a combination of white- and black-box models, thus combining physical principles and laws with a data-driven approach. Linear parametric models such as

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2.3. CONTRIBUTIONS IN RELATION TO RELATED WORK 15

Figure 2.3: A graphical representation of a simple neural network [9]

regression or autoregressive-moving-average with exogenous inputs are examples of this. Furthermore, papers [44, 45, 46] are a few of many examples where gray-box models have been proposed and evaluated for thermal building flexibility. In [44] a series of linear parametric models are proposed and compared to predict the ther-mal behavior of an office building in London. These models include Box-Jenkins, autoregressive with external inputs, and output error models. The models are de-veloped using measurement data collected from the building management system of an office. Results show reasonably good predictions for all models with a consid-erable advantage for the Box-Jenkins model. The main advantage of the gray-box modeling approach is that it combines physical understanding of the system with empirical data. A possible disadvantage with some of the linear parametric models proposed is the risk of poor prediction accuracy for nonlinear systems.

2.3 Contributions in Relation to Related Work

As opposed to the demand response studies presented in related work, which have focused on use-cases in Switzerland, Denmark or the United States, the studies presented in this thesis focus exclusively on demand response flexibility for Swedish conditions. Moreover, the studies take on a more practical approach than many other papers by considering Nordic market constraints and by balancing the objec-tives of electricity market players in a manner considered more viable for demand response participation. This is performed by introducing the notion of schedule overrides for demand response participants, which are assumed to occur whenever

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comfort constraints of the house occupants are violated. These studies also con-tribute to new perspectives and approaches for scheduling and utilizing electric load for the purpose of providing ancillary and financial services to electricity market actors. The studies include quantified use-case results for various electricity market actors which could be used to assess demand response potential.

Furthermore, a bottom-up consumer load model for office buildings has been proposed and validated using a gray-box modeling approach. The model differenti-ates itself from other proposed models by combining both physical and behavioral attributes and by being easily configurable for demand response simulations of dif-ferent building types. Few models have considered the behavioral effect on load consumption and provide effective ways of simulating heterogeneous populations of flexible consumers.

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Chapter 3

Materials & Methods

In this chapter, the materials and methods of Article 1-4 are briefly described. First, control and scheduling studies using thermal flexibility from detached houses are presented, followed by a section on the proposed office building consumer load model and its modules. Finally, the MATLAB applications developed to generate synthetic load profiles of office buildings and detached houses are presented.

3.1 Control and Scheduling using Thermal Flexibility from

Houses

Two studies are performed using demand response to (i) reduce daily power imbal-ances for a balance responsible player, and (ii) manage congestion in a distribution grid for a system operator. These studies are briefly described in the following subsections where further details can be found in Articles 1 & 4. The studies have been considerably influenced by the demand response set-up and learning from the Smart Grid Gotland project. Related studies which have not been included here are Articles 6 and 7.

Power Imbalance Reductions for a Balance Responsible Player

A demand response set-up is assumed which consists of the scheduling of individual electric space heating systems in detached houses using a model predictive approach. The set-up is inspired by a market test and installation that was recently conducted in the scope of the Smart Grid Gotland project [6]. A mixed integer quadratic op-timization problem is formulated where the objective is to minimize the deviations between the estimated power consumption from the demand response participants after scheduling and a desired space heating load profile. The optimization problem is formulated into words as

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18 CHAPTER 3. MATERIALS & METHODS

Minimize Schedule changes from the desired space heating load profile Subject to Indoor temperature constraints

Physical constraints

The desired profile is computed based on the specific objective of an electricity market actor and under the assumption of perfect information about the day-ahead states of the space heating systems of the demand response participants during nor-mal operation (i.e., without response). The scheduling is performed by solving the optimization problem while considering the thermal flexibility of the participat-ing houses which is constrained by a maximum and minimum indoor temperature bound. The optimized schedule is assumed to take either one of two states ("ON" or "OFF) with a constant power consumption corresponding to the minimum and maximum capacities of the heater. It is further assumed that schedule overrides occur at each individual demand response participating house whenever comfort requirements of +/-1◦C from a reference temperature of 20◦C are violated. Figure 3.1 illustrates the demand response set-up and process.

Figure 3.1: Assumed demand-response setup for model predictive scheduling of the electric space heating system in detached houses

The thermal flexibility is modeled using a consumer load model for detached houses proposed in [12] where select model parameter values have been random-ized to introduce a heterogeneous demand response population. Simulations are performed for a use-case consisting of a balance responsible player looking to min-imize its daily power imbalances through the scheduling of 100 detached houses from its set of consumers. The scheduling is performed in hourly resolution with daily cycles to comply with Nordic market conditions. Hourly weather data from Stockholm, Sweden is used along with synthetically generated behavioral data from a non-homogeneous Markov chain model [12]. The MPS is performed in hourly res-olution while the simulations for the actual response of the consumers are simulated in minute resolution. Two MPS cases and a base case are proposed for compari-son: a base case which is non-predictive and MPS cases which differ in the level of information known about the building properties of the heterogeneous population.

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3.1. CONTROL AND SCHEDULING USING THERMAL FLEXIBILITY

FROM HOUSES 19

For the sake of simplicity no prognosis errors are considered. Furthermore, simula-tions are performed for an individual day and 90 consecutive days during a Swedish winter season, chosen due to the high use of space heating load during this period.

Congestion Management for a System Operator

An ancillary service toolbox is proposed to manage congestion on a radial distri-bution system with power export capabilities to an overlaying power grid. The distribution system is simplified to a one-bus system. Figure 3.2 presents a concep-tual overview of the proposed ancillary service toolbox.

Figure 3.2: Conceptual overview of an ancillary service toolbox used for congestion management [10]

The ancillary service toolbox uses prognosis data for the total generation Pgen

and load Pload to forecast congestions on day- and hour-ahead timescales.

Conges-tions are assumed to occur when

Pgen(t) − Pload(t) > Plimit (3.1)

where Plimit denotes the transmission capacity limit to the overlaying power

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on day-ahead such to maximize power consumption during the hours of congestions while maintaining end-user comfort requirements. The comfort requirements are assumed to be maintained when the indoor temperature is 18-22◦C and the tank temperature 60-100◦C. An hour-ahead cluster of participants is controlled to mini-mize prognosis errors that result from the day-ahead scheduling. Further, a battery energy storage system (abbreviated BESS in Figure 3.2) with a charging capacity of 280 kWh is used to absorb prognosis errors that may remain from the hour-ahead control. Finally, variable renewable generation (abbreviated VG in Figure 3.2) is curtailed in cases where there are prognosis errors which cannot be absorbed by the battery. Electric space heating and domestic hot water appliances in detached houses are assumed to be the resources providing the demand flexibility by relax-ing constraints on indoor and tank temperatures. A consumer load model usrelax-ing a combined physical and behavioral approach (similar to the office building consumer load model) is used from [12] to model the thermal flexibility. The congestion man-agement problem is formulated as a linear optimization problem expressed in words as

Maximize The total power consumption from space heating and domestic hot water

appliances for all demand response participants during hours of expected congestions

Subject to Transmission capacity constraint Load shifting balance constraint Indoor temperature constraint Tank temperature constraint

The ancillary service toolbox concept is applied to a use-case on the island of Gotland in Sweden. The power grid on Gotland has large shares of wind power and export capabilities to the Swedish mainland through two high-voltage DC cables. The distribution network on Gotland is assumed to be regarded as one aggregated generator Pgenand load Ploadin the study. The transmission capacity Plimitto the

mainland is assumed to be limited to 130 MW as specified by the manufacturer [47]. Hourly weather data from Gotland in 2012 and synthetically generated behavior data from a non-homogenous Markov chain model introduced in [12] are used as input to the consumer load model of the detached houses. Furthermore, hourly data from Gotland in 2012 are used for the total generation and load where an offset is applied to provoke hours of congestion of at least 5 MW per day, i.e.,

Plimit(ti) = 135 MW where ti is any hour of the day i = {1, 2, ..., 24}. The offset

for the generation is applied such that it does not exceed more than 5 MW of the maximum theoretical wind power capacity of 195 MW on the island, i.e., 200 MW. The offset for the load is applied such to provoke the congestion hours based on the generation while making sure the load does not drop below the minimum observed load on Gotland for the year 2012. The day- and hour-ahead prognosis errors for the generation and load are assumed to be normally distributed with

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3.2. MODELING OFFICE BUILDING CONSUMER LOAD 21

a standard deviation σ. The standard deviation is determined for day- and hour-ahead prognoses respectively by calculating the normalized Root Mean Square Error (RMSE) after applying a persistence method on the observations of the generation and load data. The persistence method consists of using the current observation as a prognosis for the next hour (for hour-ahead prognosis) or for 24 hours ahead (for day-ahead prognosis) and so forth. The normalized RMSE can thus be computed yielding values used as standard deviations for the day- and hour-ahead prognoses. Furthermore, four simulation scenarios are proposed consisting of three consecutive days in the winter, spring, summer and autumn. The simulation scenarios are selected as such to capture the seasonal effect on thermal flexibility.

3.2 Modeling Office Building Consumer Load

The office building model is constructed based on three modules which have been il-lustrated in Figure 3.3: the occupancy, appliance and HVAC module. By combining the outputs of these modules one can simulate the aggregated power consumption of an office building floor. The modules are briefly described in the following sub-sections. Furthermore, two data sets are used to validate the models; data set (i) consists of data from an office building floor in Sweden and data set (ii) consists of data from a substation in Sweden. Further details can be found in Article 2.

Occupancy Module

The occupancy of building floors is simulated using non-homogeneous Markov chains. Markov chains are stochastic processes where one moves between one state to another with a transition probability that depends on the state one is mov-ing from. Additionally, non-homogeneous Markov chains imply that the transition probabilities between states are time-dependent. For a Markov chain X the tran-sition probability between state i to j at time t is defined as

pij(t) = P r(X(t+1)= j|Xt= i) (3.2)

This is more simply read as the probability of transitioning to state j at time

t + 1 knowing that one is moving from state i at time t. From Equation 3.2 one can

note the fundamental Markov property where the probability of each move is solely dependent on the current state without further memory of past moves. Two states are defined for the occupancy module: i = 1 (or state 1) corresponding to office building room unoccupied, and i = 2 (or state 2) corresponding to office building room occupied. The transition probabilities are sampled from minute resolution occupancy sensor data from an office building floor in Sweden [11].

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Figure 3.3: Diagram showing the functioning, interrelationship, and data require-ments of the simulation modules used by the office building consumer load model [11]

Appliance Module

The occupancy patterns generated by the occupancy module are used as input to the appliance module. The appliance usage in each office room is assumed to be split into four categories: (i) lighting, (ii) computers, (iii) servers, and (iv) others. Categories (i)-(iii) have been identified as commonly used appliances in Swedish office buildings [48]. The total power consumption of the appliances is defined as

Papp(t) = Plight(t) + Pcomp(t) + Pserver(t) + Pordo(t) + Pother(t) [W] (3.3)

In category (i), lighting has been assumed to depend on the occupancy level

Nocc, the daylight level L, its limit Llim, and installed lighting capacities Plight,min

and Plight,max as follows

Plight(t) = K(t) · Plight,min· L(t) Llim+ Plight,max· (1 − L(t) Llim), L(t) ≤ Llim Plight,min L(t) > Llim [W] (3.4)

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3.2. MODELING OFFICE BUILDING CONSUMER LOAD 23

where K denotes the total occupied office room area at time t defined as

K(t) = Aof f,occ· Nocc(t) (3.5)

In categories (ii) and (iii) the computer and server usage are defined as

Pcomp(t) = Pcomp,on· Nocc(t) [W] (3.6)

Pserver(t) = Pserver,min· (1 − Nocc(t) Nocc,persons ) + Pserver,max· Nocc(t) Nocc,persons [W] (3.7)

where Pcomp,on is the power rating of a computer, Pserver,min is the standby

power, and Pserver,maxis the maximum power rating of the server. In category (iv)

Pordo denotes unknown appliances or those too small to consider on an individual

level. They are defined as

Pordo(t) = Pordo,on· K(t) [W] (3.8)

where Pordo,on denotes the power rating of the unknown devices. Furthermore

the appliance usage taking place in the non-office room areas is defined as

Pother(t) = Aother· (Pworkhrs(t) + Pbase) t ∈ Ψworkhrs [W] (3.9)

where Aother denotes the common area of the building floor, Pworkhrs(t)

de-notes load that depend on work hour schedules, Pbase denotes constant load that

is independent of time, and Ψworkhrs denotes the set of regular working hours.

HVAC Module

Outputs from both the occupancy and appliance modules are used as input to the HVAC module. The objective of the HVAC module is to maintain the indoor temperature T and air quality level at constant set point values. It is assumed that each office building floor is equipped with a heat pump which supplies the heating or cooling — a common setup in Swedish office buildings [48]. It is further assumed that each building floor is equipped with a variable air volume ventilation system, which regulates the air flow. The indoor temperature change between time step t and t + 1 is defined as

T (t + 1) = T (t) + 1 Cin

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where Cindenotes the thermal inertia of the building floor, Qhp the capacity of

the heat pump to supply heating or cooling, Qsunthe heat gain from solar radiation,

Qint the heat gain from appliance usage and occupancy, and Qlossthe heating and

cooling losses. The heat gain from solar radiation is defined as

Qsun(t) = αred· Asidewindow· Psun(t) [W] (3.11)

where αred denotes the reduction factor (due to possible shading), Asidewindow the

total window area per building side, and Psun the solar radiation power. The

capacity of the heat pump is defined as

Qhp(t) = COP(Tout(t)) · Php(t) t ∈ Ψhvac [W] (3.12)

where COP(Tout) is the Coefficient of Performance (COP) value at specific

outdoor temperature Tout, and Php is the power consumption of the heat pump.

The heat pump is assumed to only operate during a predefined time schedule Ψhvac.

The heat gain from appliance and occupancy usage is defined as

Qint(t) = Pmet· Nocc(t) + Papp(t) [W] (3.13)

where Pmet denotes the heat dissipated by occupants due to metabolism, Nocc

the occupancy level, and Pappthe power consumption due to appliance usage. The

temperature exchange between the indoor and outdoor environment is determined by the transmission and ventilation losses of the building and is defined as

Qloss(t) = (Λtrans+ Λvent) · (T (t) − Tout(t)) [W] (3.14)

where Λtrans denotes the transmission losses, Λvent the ventilation losses, and

Tout the outdoor temperature. The transmission and ventilation losses are further

defined as

Λtrans=PjUj· Aj [W/◦C]

Λvent= Vf loor· ¯Nvent· Cp· (1 − αrc) [W/◦C]

(3.15)

where Uj is the transmission coefficient of each building component j, Aj is the

total area of that component, Vf loor denotes the total volume of the building floor,

¯

Nvent the average air exchange rate, Cp the specific heat capacity of the air, and

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3.3. MATLAB APPLICATION DEVELOPMENT FOR CONSUMER LOAD

MODELS 25

3.3 MATLAB Application Development for Consumer

Load Models

The consumer load models proposed in [11, 12] are made freely available on MAT-LAB central [49] as MATMAT-LAB applications entitled "Office load electricity" and "House load electricity", respectively. The applications generate synthetic elec-tricity load profiles of office buildings and detached houses in minute, quarterly, half-hourly, and hourly resolution up to 365 days. Both applications consist of two panels: one for user configurations and the other for analysis. In the configuration panel the user can specify time resolution, the number of buildings to simulate, the time period, and values of select building model parameters. In the analyze panel the user can analyze the generated load profile in both aggregated or disaggregated form along with other indigenous and exogenous variables such as building occu-pancy, outdoor temperature, solar radiation, and indoor and tank temperatures. The load profile can be further decomposed into individual components assumed by the consumer load models. The applications are developed using the code struc-ture imposed by App Designer, i.e., applications consisting of callback functions, utility functions and properties. Both applications use their own default data set from where weather and behavioral data are sampled. The weather data used in the applications are from Stockholm, Sweden for the year 2015, and the behavioral data are generated from the non-homogeneous Markov chain models in [11, 12].

A series of assumptions are made to generate the load profiles. Tables 3.1 and 3.2 present the configurable model parameters in the applications along with their variable correspondence to articles [11, 12]. The user options are mapped to quantitative ranges in which they are randomized upon selection between the upper and lower boundaries. Furthermore, thermostat control is assumed for the heating and cooling systems with the objective of maintaining a reference temperature at all times. The heating systems are further assumed to either operate at full rated capacity or minimum capacity, thus taking the shape of a step function when activated. Further details about the applications can be found in Article 3.

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Table 3.1: Configurable model parameters and variable correspondence to [11] for MATLAB application: Office load electricity

Model param. User options Quant. values Var. corresp.

Building floors Few 1-3

Average 4-6 Nof f

Many 7-9

Floor size Small 440 sqm

Average 640 sqm Af loor

Large 840 sqm

Occupants/floor Few 5

Average 15 Nocc,persons

Many 25

Thermal inertia Low 1200e3 min 80e3 qtr 40e3 hhr 20e3 hrs

Moderate 3600e3 min Cin

240e3 qtr 120e3 hhr 60e3 hrs High 7200e3 min

480e3 qtr 240e3 hhr 120e3 hrs

Heating/cooling Low 6 kW

capacity Moderate 10 kW Qmax_hp

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3.3. MATLAB APPLICATION DEVELOPMENT FOR CONSUMER LOAD

MODELS 27

Table 3.2: Configurable model parameters and variable correspondence to [12] for MATLAB application: House load electricity

Model param. User options Quant. values Var. corresp.

Occupants/house Few 1-3

Average 4-6 βf amily

Many 7-9

Building size Small 50 sqm

Average 100 sqm Af loor & Aroof

Large 200 sqm Thermal inertia Low 12000 min

800 qtr 400 hhr 200 hrs Moderate 6000 min τ 400 qtr 200 hhr 100 hrs High 3000 min 200 qtr 100 hhr 50 hrs

Space heater Low 4 kW

capacity Moderate 6 kW Qmax

heat

High 8 kW

Water tank size Small 150 L

Average 300 L Vtank

Large 600 L

Water tank Low 1.5 kW

boiler capacity Average 3 kW Pboil

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Chapter 4

Results & Discussions

In this chapter results are presented and discussed for the demand response studies, the office load consumer model, and the MATLAB applications proposed.

4.1 Use-Case Results from Demand Response Studies

Power imbalance reductions

Figure 4.1 presents the results for the daily number and duration of schedule over-rides by demand response participants, and the daily power imbalances for the simulation of 90 consecutive days. The results are presented for the base-case and the proposed MPS cases, where MPS case 1 corresponds to the case with more information about the building properties of the demand response population com-pared to case 2. The median and interquartile ranges between the MPS cases are reduced compared to the base-case. In terms of imbalances, one can note a reduc-tion of 5-9% from 7.3 MWh in the interquartile range and 4-6% from 2 MWh in the median. Furthermore one can also note that MPS case 1 outperforms case 2 (as expected) where the number and duration of schedule overrides help explain this difference. In total, power imbalances are reduced by 207-262 MWh from expected imbalances for the different cases corresponding to a power imbalance reduction of up to 30%.

Figure 4.2 presents the performance change between the MPS cases expressed as the difference in absolute values between MPC case 2 and 1. The change is evaluated as a function of the level of heterogeneity of the population. One can observe a considerable increase for all performance metrics as the level of hetero-geneity increases. The results highlight the effect of considering individual building attributes in the prediction.

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30 CHAPTER 4. RESULTS & DISCUSSIONS

Figure 4.1: Boxplots showing simulation results on the number and duration of schedule overrides, and the daily power imbalances during 90 consecutive days when demand response participants have been scheduled

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4.1. USE-CASE RESULTS FROM DEMAND RESPONSE STUDIES 31

Figure 4.2: Sensitivity analysis on the changes of the total number and duration of schedule overrides and the total power imbalances between MPS case 2 and 1 as a function of sigma

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Table 4.1: Simulation results of congestions managed and number of required de-mand response participants for the different seasonal scenarios

Scenario Day Accumulated Managed Day-

Hour-load shifted [MW] congestion hours ahead partic. ahead partic.

Winter 1 5 2 out of 2 1000 100 2 4 1 out of 1 1200 100 3 19 7 out of 7 1300 500 Spring 1 14 5 out of 5 1000 100 2 10 2 out of 2 800 100 3 16 4 out of 4 1600 100 Summer 1 4 1 out of 1 700 100 2 5 1 out of 1 600 100 3 5 1 out of 1 600 200 Autumn 1 5 1 out of 1 900 100 2 17 6 out of 6 800 700 3 5 1 out of 1 800 100

Congestion management

Table 4.1 presents the simulation results for the different seasonal scenarios. There is a total of 4-19 MW of load shifted daily using demand response for the different congestion scenarios, where all congestion events are successfully managed. The number of day-ahead demand response participants ranges between 600-1600 and the hour-ahead participants between 100-700, meaning that less than 10% of the detached houses on Gotland is needed to balance congestion scenarios of at least 5 MW per day. Figures 4.3 and 4.4 present the indoor and tank temperatures of participants where one can observe that the comfort requirements of 18-22◦C are maintained for indoor temperature and 60-100◦C for the tank temperature. One can also observe that temperature rises during congestion hours (as expected) in order to reduce the power exported to the overlaying grid. Moreover, the wind power is curtailed in 3 out of the 4 scenarios ranging from 37 to 286 kW (not shown here).

4.2 Validation of Office Building Consumer Load Model

Figure 4.5 presents a statistical comparison between the measured and simulated appliance and ventilation loads from data set 1 during cold months, i.e., September-May, assumed to be months without cooling operation. From subfigure A) one can observe the appliance load variation for each hour of the day during workdays. One can observe that the simulated consumption follows the patterns of the measured consumption with a rise in load around 6:00-9:00 during morning hours, a steady consumption during work hours, and a decrease around 16:00-19:00 during evening

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4.2. VALIDATION OF OFFICE BUILDING CONSUMER LOAD MODEL 33

Figure 4.3: Simulation results of indoor temperature of demand response partici-pants for the different seasonal scenarios

Figure 4.4: Simulation results of tank temperature of demand response participants for the different seasonal scenarios

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hours. Subfigure B) shows similar results for the ventilation load variation, with the exception of large differences in variation during morning and evening hours. Subfigure C) shows the probability distribution function of the measured and simu-lated load where one can observe similarities in peaks and valleys. Finally, subfigure D) shows the total variation in load between weekday and weekends where one can observe similarities in the median and interquartile range.

Figure 4.5: Statistical comparison between measured and simulated appliance and ventilation load in office building floor on validation data set 1 during months without cooling (September-May)

Figure 4.6 presents a statistical comparison between measured and simulated load from data set 2. From subfigure A) one can observe a strong linear dependency between the simulated and measured load. From subfigure B) similarities in peaks and valleys of the load distribution functions for the simulated and measured load can be observed. From subfigure C) one can observe that the simulated load follows the patterns of the measured data throughout the day without major differences except during some of the morning hours (6:00-9:00) and evening hours (16:00-19:00).

Table 4.2 presents statistical metrics from fitting a linear regression model for the simulated and measured load for each of the two data sets. The metrics include the coefficient of determination R2, RMSE, model slope coefficient value β, and the probability value p-val. Descriptive statistics of the two data sets divided into

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4.2. VALIDATION OF OFFICE BUILDING CONSUMER LOAD MODEL 35

Figure 4.6: Statistical comparison between measured and simulated load in office building floor on validation data set 2

weekend and weekdays are also presented. One can observe high R2 _percentages

and reasonable RMSE values indicating that the linear fit models represent ade-quately the relationship between the measured and simulated load. Furthermore, the descriptive statistics of the load show strong similarities between the simulated and measured loads.

Table 4.2: Summarizing statistics for validation data sets 1 (for cold months) and 2 for office building loads. Note that the RMSE is expressed in kW.

Regression Weekday load [kW] Weekend load [kW]

R2 _{RMSE β p-val} _{Min Mean Std Max} _{Min Mean Std Max}

(Data set 1)

Sim. app. load 0.75 1.91 1.07 6.06 0.75 0.75 0.12 1.82 81% 0.5 0.83 <1e-3

Meas. app. load 0.00 1.89 1.21 5.70 0.00 0.88 0.16 2.28 Sim. vent. load 0.00 0.24 0.22 0.68 0.00 0.00 0.00 0.00

79% 0.1 0.96 <1e-3

Meas. vent. load 0.01 0.24 0.21 0.86 0.02 0.03 0.01 0.48 (Data set 2)

Sim. load 92.1 299.4 160.4 593.1 91.7 142.8 22.0 167.2 89% 51.1 0.89 <1e-3

Modeling and Simulations of Demand Response in Sweden