Eran Salfati_THESIS - IIS Windows Server

BEN-GURION UNIVERSITY OF THE NEGEV

FACULTY OF ENGINEERING SCIENCES

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Demand-Side Management in Smart Grid Using Game Theory

THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS

FOR THE M.Sc DEGREE

By: Eran Salfati

02/2014

ii

BEN-GURION UNIVERSITY OF THE NEGEV

FACULTY OF ENGINEERING SCIENCES

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

Demand-Side Management in Smart Grid Using Game Theory

THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS

FOR THE M.Sc DEGREE

By: Eran Salfati

Supervised by: Prof. Raul Rabinovici

Author: Date:

Supervisor: Date:

Chairman of Graduate Studies Committee: Date:

02/2014

iii

Abstract

Smart grid describes an electrical power system which characterized by the use of

communication and information technology. By utilizing modern information technologies,

the Smart Grid is capable of delivering power in more efficient ways and responding to

wide ranging conditions and events. One of the main issues in the Smart Grid research is

to encourage the consumer to use energy efficiently. For example, the electric utility can

use real-time pricing to convince some users to reduce their power demand, so that the

total demand profile full of peaks can be shaped to a smoothed demand profile. The

mechanism to control the electric power consumption is called Demand-Side Management

(DSM).

On this work we propose a novel model for DSM which we call Asynchronous

Consumption Mode (ACM). The model principles are borrowed from networks

communication method and using Game Theory algorithm to characterize the consumers

and make a fair energy allocation between them.

The motivation to use game theory in our model is based on three reasons. First, Game

Theory is a strategic analysis of situations involving a number of factors (Players) aspires

for different purposes. Through game theory, we can find an optimal solution to situations

of conflict and cooperation, under the assumption that the involved players act in their

best interest. Even though all players are selfish, by seeking to optimize their individual

objective they end up optimizing a global objective. Second, recently, distributed

approaches, where the decisions are made locally and directly by the end consumer, have

taken more relevance. In this scenario, Game Theory provides a framework to evaluate and

design active side management policies, since it naturally models interactions in

distributed decision making processes. Finally, such model cannot be implemented unless

intelligent pricing schemes are used to provide incentives for the subscribers to follow

them. Game theory provides a natural framework for developing pricing mechanisms to

solve various problems in networks, such as fair allocation of resources among users.

iv

Acknowledgements

First and Foremost, I would like to convey my sincere thanks and gratitude to my

advisor Prof. Raul Rabinovici for his patience, guidance and critical input throughout the

entire thesis. For his believe and support along the way, without him this work would not

have reached the end.

I would like to thank my sister Liat Nakar for her assistance on issues related to the

application of computer science and game theory algorithms.

I also would like to thank to my friends Guy Zaidner and Shahar Levy for many hours

of shared thinking, professional assistance and support.

I would like to thank Dr. Ahuva Mu’alem for her professional advice regarding fair

division methods.

Last but not least, I would like to extend my thanks to my wife Bat-El and my lovely

sons Arbel and Eliya for their support that made this thesis possible.

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Acronyms

ABR Available Bit Rate

ACM Asynchronous Consumption Mode

ACR Available Consumption Rate

AMI Advanced Metering Infrastructure

ATM Asynchronous Transfer Mode

BR Best Response

CBR Constant Bit Rate

CBR Constant Bit Rate

CCR Constant Consumption Rate

CPP Critical Peak Pricing

DLC Direct Load Control

DR Demand Response

DSM Demand-Side Management

ECS Energy Consumption Scheduling

ED Equitable Division

EMS Energy Management Systems

ICT Information and Communication Technology

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ILP Integer Linear Programming

IT Information Technology

LAN Local Area Network

NE Nash Equilibrium

NIST National Institute of Standards and Technology

PAR Peak to Average Ratio

PD Proportional Division

QOS Quality Of Service

RTP Real Time Pricing

SCADA Supervisory Control And Data Acquisition

STM Synchronous Transfer Mode

TOU Time Of Use

UBR Unspecified Bit Rate

UCR Unspecified Consumption Rate

UD Utilitarian Division

VBR Variable Bit Rate

VCG Vickrey-Clarke-Groves

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Contents

1111 IntroductionIntroductionIntroductionIntroduction .................................................................................................................................................................................................................................................................................................................................................................................................... 1111

1.1 The Fundamental Problem................................................................................. 1

1.2 Introduction to Smart Grid ................................................................................ 2

1.3 Research Topics on Smart Grid ......................................................................... 7

1.4 Demand-Side Management (DSM) ..................................................................... 9

1.5 The Motivation of Using Game Theory ........................................................... 14

1.6 Thesis Objectives .............................................................................................. 15

1.7 Thesis Organization .......................................................................................... 15

1.8 Conclusions ....................................................................................................... 15

2222 Game Theory as a Tool for DemandGame Theory as a Tool for DemandGame Theory as a Tool for DemandGame Theory as a Tool for Demand----Side ManagementSide ManagementSide ManagementSide Management ........................................................................................................................ 16161616

2.1 Introduction ...................................................................................................... 16

2.2 A Problem Representation Using Game Theory .............................................. 17

2.3 Nash Equilibrium ............................................................................................. 18

2.4 Mechanism Design ............................................................................................ 19

2.5 Fair Division ..................................................................................................... 21

2.6 Conclusions ....................................................................................................... 25

3333 Related WorksRelated WorksRelated WorksRelated Works ............................................................................................................................................................................................................................................................................................................................................................................ 26262626

3.1 Introduction ...................................................................................................... 26

3.2 Demand-Side Management Based on Scheduling ............................................. 26

3.3 Real Time Demand-Side Management ............................................................. 30

3.4 Open Issues on Related Works ......................................................................... 32

3.5 Conclusions ....................................................................................................... 34

4444 Demand Side Management Control System ModelDemand Side Management Control System ModelDemand Side Management Control System ModelDemand Side Management Control System Model .................................................................................................................................................... 35353535

4.1 Introduction ...................................................................................................... 35

4.2 System Goals .................................................................................................... 36

4.3 System Model ................................................................................................... 37

4.4 Control Loop Description ................................................................................. 38

4.5 Asynchronous Consumption Mode (ACM) ....................................................... 39

4.6 Consumer Characterization .............................................................................. 40

4.7 Fair Division Algorithm ................................................................................... 42

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4.8 Price Profile ...................................................................................................... 46

4.9 Energy Consumption Controller (ECC) ........................................................... 47

4.10 Conclusions ....................................................................................................... 48

5555 Performance DemonstrationPerformance DemonstrationPerformance DemonstrationPerformance Demonstration ............................................................................................................................................................................................................................................................................................ 49494949

5.1 Introduction ...................................................................................................... 49

5.2 Experimental Setup .......................................................................................... 50

5.3 Simulation Results ............................................................................................ 51

5.4 Interpretation of the results.............................................................................. 62

5.5 Conclusions ....................................................................................................... 63

6666 SummarySummarySummarySummary ............................................................................................................................................................................................................................................................................................................................................................................................................ 64646464

6.1 Conclusions ....................................................................................................... 64

6.2 Thesis Presentations ......................................................................................... 64

6.3 Thesis Contributions ........................................................................................ 65

6.4 Future Directions ............................................................................................. 66

7777 BibliographyBibliographyBibliographyBibliography ........................................................................................................................................................................................................................................................................................................................................................................................ 67676767

1

1 Introduction

1.1 The Fundamental Problem

The initial research question of this thesis describes a system with several consumers

connected to a single limited energy source as describes in Figure 1. All consumers need a

certain amount of energy from the total capacity of the source, but the total demand of all

consumers together, exceeds the supply capacity of the shared source. The basic questions

are how to manage the shared resource fairly and how to do it using tools borrowed from

game theory.

Practical example of such case can be factory operates several facilities through local

generator. The goal of the factory owner would be to maximize the utilization of the

expensive generator.

Figure Figure Figure Figure 1111 – The Fundamental Problem DescriptionThe Fundamental Problem DescriptionThe Fundamental Problem DescriptionThe Fundamental Problem Description

2

1.2 Introduction to Smart Grid

1.2.1 Definition

The ”Smart grid” phrase does not have an absolute definition yet. There are several

basic articles [1] [2] [3] [4] and entities [5] [6] which explain the meaning of the phrase, the

motivation, the goals and the challenges. Generally, Smart grid is a phrase that describes

an electrical power system which characterized by the use of communication and

information technology in the generation, delivery and consumption of electrical energy.

Smart Grid uses two-way flows of electricity and information to create an automated and

distributed advanced energy delivery network.

By utilizing modern information technologies, the Smart Grid is capable of delivering

power in more efficient ways and responding to wide ranging conditions and events. For

example, the electric utility can use real-time pricing to convince some users to reduce

their power demand, so that the total demand profile full of peaks can be shaped to a

smoothed demand profile.

Secure Communication Interface

Electrical Interface

Figure Figure Figure Figure 2222 – NIST Smart Grid FrameworkNIST Smart Grid FrameworkNIST Smart Grid FrameworkNIST Smart Grid Framework

3

The conceptual model of smart grid according to the National Institute of Standards

and Technology (NIST) consists of seven domains [7] namely, Bulk Generation,

Transmission, Distribution, Customers, Operations, Markets and Service Providers. From

the pictorial illustration in Figure 2, it is clear that information flow is vital for the

operation of Smart Gird, connecting the various domains and forming the lifeline of the

grid. It is this 2-way communication that enables the smart grid to be ”SMART” and

dynamic compared to the traditional grid. The traditional electricity grid had information

flow in only one direction from generation to the customer.

1) Bulk GenerationBulk GenerationBulk GenerationBulk Generation – The generation of electricity from a variety of sources both

renewable and non-renewable in bulk quantities used to supply the customers.

2) TransmissionTransmissionTransmissionTransmission – The transmission of the electricity from distributed bulk generation

sources to substations. It takes care of the operational stability of the grid by

balancing the supply and demand.

3) DistributionDistributionDistributionDistribution – A bridge between the transmission and customer domains. The

distribution network connects all the customers to the grid using the smart meter

which forms the information network of the grid.

4) CustomersCustomersCustomersCustomers – The customers has the capability for communication to the utility

company through secure interface for interactions. This can be used to provide

advanced Energy Management Systems (EMS) at the customer end.

5) Service ProviderService ProviderService ProviderService Provider – Support the business process of energy generation, distribution

and customers through billing, customer account management, to providing

assistance in home energy generation.

6) OperationsOperationsOperationsOperations – Responsible for smooth operation of the grid by monitor, analyze and

optimize the grid operations, fault management and grid statistics.

7) MarketsMarketsMarketsMarkets – The financial end of the smart grid. It is responsible for market

management and operations, retailing, trading, ancillary operations etc.

4

1.2.2 The Current Electric Grid Limitations

The key characteristics of the conventional electric energy system includes [8]:

Centralized sources of power generation, Unidirectional flow of energy from the sources to

the customers, Passive participation by the customers, Customer knowledge of electrical

energy usage is limited to a monthly bill, Real-time monitoring and control is mainly

limited to generation and transmission and Lack of flexibility in integrating alternative

sources and efficiently manage new services desired by the users. These conventional

attributes have adequately served the needs of electric utilities and their customers in the

past.

In most cases today, there are no sensors in distribution grids that communicate the

actual voltages delivered to customers, so systems must be operated based on estimates of

losses along the line. Another source of inefficiency arises from the peaked nature of

electricity demand. Generation and transmission capacity is provided to meet peak

demand that occurs infrequently, for example on hot summer afternoons in areas where air

conditioning represents a significant load. Residential consumers generally pay little

attention to how they use electricity because they do not receive any timely or actionable

information about their consumption.

The conventional forms of electricity generation cause about 40 percent of the human

emission of CO2. The need to reduce carbon emissions has become an urgent global

priority to mitigate climate change.

Smart sensors can allow the utilities to receive more information about the power

system to get more control in form of reliability. However, with most utilities, the

integration of all the information available has not become a reality yet. This approach,

which operates solely from cause and effect, while useful, only provides the utility the

ability to fix the problem after it occurs while some faults can be avoided by planning and

maintenance. The current practices of most utilities can be defined as a reactive approach

to power system operation rather than proactive approach.

5

1.2.3 The Smart Grid Goals

Although a precise and comprehensive definition of Smart Grid has not been proposed

yet, according to the report from NIST1 [7], the anticipated benefits and requirements of

Smart Grid are the following:

1) Improving power reliability and quality.

2) Optimizing facility utilization and averting construction of back-up (peak load)

power plants.

3) Enhancing capacity and efficiency of existing electric power networks.

4) Improving resilience to disruption.

5) Enabling predictive maintenance and self-healing responses to system disturbances.

6) Facilitating expanded deployment of renewable energy sources.

7) Accommodating distributed power sources.

8) Automating maintenance and operation.

9) Reducing greenhouse gas emissions by enabling electric vehicles and new power

sources.

10) Reducing oil consumption by reducing the need for inefficient generation during

peak usage periods

11) Presenting opportunities to improve grid security.

12) Enabling transition to plug-in electric vehicles and new energy storage options.

13) Increasing consumer choice.

14) Enabling new products, services, and markets.

1 NISTNISTNISTNIST – The National Institute of Standards and Technology – A nonregulatory science agency within the U.S. Department of Commerce, which is responsible to coordinate the development of interoperability standards for the U.S. Smart Grid.

6

1.2.4 Professional Literature

1) Smart Grid: Fundamentals of Design and AnalysisSmart Grid: Fundamentals of Design and AnalysisSmart Grid: Fundamentals of Design and AnalysisSmart Grid: Fundamentals of Design and Analysis [9] – A primer handbook which

addressing the fundamentals of Smart Grid. The book provides a fundamental

discussion on the motivation for the Smart Grid development, the working

definition and the tools for analysis and development of the Smart Grid.

2) Smart Power: Climate Change, the Smart Grid, and the Future of Electric Smart Power: Climate Change, the Smart Grid, and the Future of Electric Smart Power: Climate Change, the Smart Grid, and the Future of Electric Smart Power: Climate Change, the Smart Grid, and the Future of Electric UtilitiesUtilitiesUtilitiesUtilities

[10] – This book starts with the deregulatory efforts of the 1990s and their gradual

replacement by concerns over climate change, promoting new technologies, and

developing stable prices and supplies. Later on, it explains the revolutionary

changes that the Smart Grid is bringing to utility operations.

3) Smart Grid: Integrating Renewable, Distributed and Efficient EnergySmart Grid: Integrating Renewable, Distributed and Efficient EnergySmart Grid: Integrating Renewable, Distributed and Efficient EnergySmart Grid: Integrating Renewable, Distributed and Efficient Energy [11] – This

book explain the most recent innovations supporting Smart Grid development. It

includes topics like smart metering, renewable energy resources, plug-in hybrids,

flexible demand response, micro-grids, and specific in-depth coverage of wind and

solar power integration.

4) Smart Grid: Technology and ApplicationsSmart Grid: Technology and ApplicationsSmart Grid: Technology and ApplicationsSmart Grid: Technology and Applications [12] – This book provides a basic

discussion of the Smart Grid concept and describes the technologies that are

required for its realization. The content of the book is grouped into three main

technologies: Information and communication systems; Sensing, measurement,

control and automation and Power electronics and energy storage.

5) Control and Optimization Methods for Electric Smart GridsControl and Optimization Methods for Electric Smart GridsControl and Optimization Methods for Electric Smart GridsControl and Optimization Methods for Electric Smart Grids [13] – This book

consolidate some of the most promising and transformative recent research in Smart

Grid control. The book contains eighteen chapters written by leading researchers in

power, control, and communication systems. The essays are organized into three

broad sections, namely Architectures and Integration, Modeling and Analysis, and

Communication and Control.

7

1.3 Research Topics on Smart Grid

The new needs of more energy knowledgeable, computer savvy, and environmentally

conscious customers, combined with regulatory changes, availability of more intelligent

technologies, and ever greater demands for enough energy to drive the global economy,

arises few challenges for the future grid [14]:

1) AAAAutomated utomated utomated utomated SSSSensors and ensors and ensors and ensors and CCCControlsontrolsontrolsontrols – Dynamic optimization of voltage levels and

reactive power may permit reduction of voltage levels by a few percent and reduce

power consumption.

2) Advanced Advanced Advanced Advanced MMMMetering etering etering etering IIIInfrastructure (AMI)nfrastructure (AMI)nfrastructure (AMI)nfrastructure (AMI) – Smart meters that electronically record

interval data provides near real-time information about electricity usage and cost to

an in-home display or software application, allows consumers to make informed

choices about energy use and control their cost.

3) DemandDemandDemandDemand----Side ManagementSide ManagementSide ManagementSide Management (DSM)(DSM)(DSM)(DSM) – Enable signaling between the grid and the

consumer in order to reduce consumption during peak hours and shift demand to

off-peak periods. That can be achieved for example using dynamic pricing scheme or

direct control.

4) Clean Energy Sources Clean Energy Sources Clean Energy Sources Clean Energy Sources – Reducing the production of carbon dioxide in electricity

generation will require a variety of clean or cleaner energy sources, including coal

with carbon capture and sequestration, natural gas, nuclear, hydro, geothermal,

biomass, and increased use of wind and solar. Utilities will need to have real-time

information about these systems to maintain reliable grid operation.

5) Energy Storage Energy Storage Energy Storage Energy Storage – Since the grid must always maintain a real-time balance of load

and generation, a significant increase in the use of wind and solar will require

increasing use of storage and a greater ability to modulate demand in order to keep

the grid in balance. The operation of the system, which today is generally

controllable and deterministic, will become much more dynamic and stochastic in

nature.

8

6) Grid Reliability Grid Reliability Grid Reliability Grid Reliability – The reliability of the grid can be enhanced through the

deployment of sensors that provide real-time situational awareness. Sensors will

allow earlier detection of and response to anomalies and make widespread cascading

failures less likely.

7) CommunicationCommunicationCommunicationCommunication System System System System – Communications and information technology (IT) play a

critical role in the smart grid. The smart grid will ultimately involve networking

large numbers of sensors in transmission and distribution facilities, smart meters,

SCADA systems, back-office systems, and devices in the home which will interact

with the grid. Large amounts of data will be generated by meters, sensors and

synchrophasors. Techniques for managing, analyzing and acting on this data will

need to be developed.

8) Cyber Cyber Cyber Cyber SecuritySecuritySecuritySecurity – Ensuring cyber security of the Smart Grid is a critical priority

[15]. Security must be designed in at the architectural level, not added on later.

Ongoing research is needed to help ensure security of the grid. New threats will

continually surface, and ongoing development of new technologies and

methodologies to detect and mitigate threats and vulnerabilities will continue to be

a top priority for smart grid efforts.

9) Standards Standards Standards Standards – Development of standards for the Smart Grid requires efforts at

national, regional and international levels. Many of the suppliers of equipment and

systems used in the smart grid are global companies that seek to address markets

around the world. Unnecessary variations in equipment and systems add cost, which

eventually gets passed on to consumers. International standards promote supplier

competition and expand the range of options available to utilities, resulting

ultimately in lower costs for consumers.

9

1.4 Demand-Side Management (DSM)

1.4.1 Definition

DSM is the planning, implementation, and monitoring of those utility activities

designed to influence customer use of electricity in ways that will produce desired changes

in the utility’s load shape, like changes in the time pattern and magnitude of a utility’s

load [16].

1.4.2 Benefits

DSM programs provide a number of benefits. From the utility perspective, it can reduce

electricity consumption and defer the construction of new power plants and transmission

lines. DSM can also bring economic benefits in the form of reduced capital expenditure,

reduced operating costs, fuel savings, improved system efficiencies, and reduced losses.

From the customer perspective, DSM can reduce energy bills and improve the service and

comfort levels achieved.

1.4.3 Demand-Side Management in Smart Grid

DSM programs have existed across the globe since the 1970s. The initial generations of

DSM programs were limited by the technology available [17]. Lack of ICT infrastructure,

lack of understanding of the benefits of DSM solutions, not competitive compared with

traditional approaches, operational complexity, inappropriate market structure and lack of

incentives resulted in a lack of efficiency DSM programs.

Smart grid provides the framework to make DSM programs cost-effective and

convenient [18]. The increasing penetration of smart meters, the widespread networks and

the intelligent grid the gives utilities visibility into real-time supply and demand balancing

gives crucial advantages over those of the past.

10

1.4.4 Classification

Figure Figure Figure Figure 3333 – DSM Programs ClassificationDSM Programs ClassificationDSM Programs ClassificationDSM Programs Classification

1) Energy ReductionEnergy ReductionEnergy ReductionEnergy Reduction ProgramsProgramsProgramsPrograms – Reducing demand through more efficient processes,

buildings or equipment. This category covers a large number of measures in all

sectors include examples of typical energy reduction measures and a series of

”energy saving tips”.

2) Load Load Load Load ManagementManagementManagementManagement ProgramsProgramsProgramsPrograms ((((Load ShapeLoad ShapeLoad ShapeLoad Shape / Demand Response/ Demand Response/ Demand Response/ Demand Response)))) – These programs

offer payments to participants to reduce their electricity usage when called upon by

the system operator either for reliability or economic reasons.

a. Direct Load Control (DLC) Direct Load Control (DLC) Direct Load Control (DLC) Direct Load Control (DLC) – In this way, loads (e.g. heating, cooling,

ventilation and lighting) can be switched on or off, often remotely, by the

utility. In this case, the customers may have back-up generators or energy

storage capability and generally have an interruptible agreement with the

utility in return for a special rate. Utilities may even call on on-site

generators to meet peak demand on the grid. The energy distribution

industry may use rolling blackouts to reduce demand when the demand

surpasses the capacity. Rolling blackouts are the systematic switching off of

supply to areas within a supplied region such that each area takes turns to

DSMDSMDSMDSM

Load growth and conservation

programs

Strategic load growth

Strategic load conservation

Load Management

Programs

Tariff incentives and penalties

Real Time Pricing (RTP)

Clitical Peak Pricing (CPP)

Time Of Use (TOU)

Load Leveling

Load ShiftingValley FillingPeak Clipping

Direct Load Control (DLC)

Energy Reduction Programs

11

”lose” supply. Utilities or municipalities in these cases would try to publish

or announce a schedule so that businesses and homes can plan their use of

energy for that period.

b. Load Leveling Load Leveling Load Leveling Load Leveling – Optimize the current generating base-load without the need

for reserve capacity to meet the periods of high demand. A common term to

describe these approaches called PAR (Peak to Average Ratio), where the

target is to minimize it in the system consumption profile.

i. Peak Clipping Peak Clipping Peak Clipping Peak Clipping – Reduction of load by using utility direct load

control (DLC) of customer’s appliances during peak times.

ii. Valley Filling Valley Filling Valley Filling Valley Filling – Load construction during off-peak period by using

techniques like electric-based thermal energy storage (water and / or

space heating or cooling).

iii. Load ShiftingLoad ShiftingLoad ShiftingLoad Shifting – Shifting load from on-peak to off-peak periods by

using of energy storage and customer load shifts. This can be

regarded as a combination of peak clipping and valley filling.

Figure Figure Figure Figure 4444 – Load LevelingLoad LevelingLoad LevelingLoad Leveling

12

c. Tariff incentives and penaltiesTariff incentives and penaltiesTariff incentives and penaltiesTariff incentives and penalties – Utilities encourage a certain pattern of use

by tariff incentives where customers use energy at certain times to achieve a

better-priced rate for their energy use.

i. Time Of Use (TOU) Time Of Use (TOU) Time Of Use (TOU) Time Of Use (TOU) – The electricity prices differ in different blocks

of time. Generally, the rate during peak periods is higher than the

one during off-peak periods. The simplest TOU rate has two time

blocks: the peak and the off-peak.

ii. Critical Peak Pricing (CPP)Critical Peak Pricing (CPP)Critical Peak Pricing (CPP)Critical Peak Pricing (CPP) – Typical goal of CPP is to more

dramatically reduce load during the relatively few, very expensive

hours. Very high ”critical peak” prices are assessed for certain hours

on event days (often limited to 10-15 per year). Prices can be 3-10

times as much during these few hours.

iii. Real Time Pricing Real Time Pricing Real Time Pricing Real Time Pricing (RTP) (RTP) (RTP) (RTP) – An hourly fluctuating prices reflecting

the real cost of electricity in the wholesale market. Customers are

informed about the prices on a day-ahead or hour-ahead basis based

on the utility’s load, power market and power producers who

participate in satisfying the demand. Implementing a RTP program

requires significant technology investment, including automated

interval metering, along with more complex price forecasting,

communications and billing systems. Many economists are convinced

that RTP is the most direct and efficient load management method

suitable for competitive electricity markets and should be the focus

of policymakers. At the moment, there are some obstacles to

implement this program in terms of the aspects of technologies,

incentive to consumers and utility companies, supportive policies and

regulations, and pricing schemes.

13

3) Load growth and Load growth and Load growth and Load growth and CCCConservationonservationonservationonservation – Load growth programs are implemented with the

intention of improving customer productivity and environmental compliance while

increasing the sale of kW for the utilities. This increases the market share of the

utility and enables an ability to fill valleys and increase peaks.

a. Strategic Strategic Strategic Strategic Load Load Load Load ConservationConservationConservationConservation – Load shape changes occur as a response to

utility programs like appliance efficiency improvement. ’Strategic’ is

intended to distinguish between naturally occurring and utility-stimulated.

b. StrategicStrategicStrategicStrategic Load GrowthLoad GrowthLoad GrowthLoad Growth – Utility encouragements for customers aim to adopt

electro-technologies (electrification), either to replace inefficient fossil fuel

equipment or to improve customer productivity and quality of life. This

results in the increase of electric energy intensity and lowering the average

cost of service by spreading the fixed cost over a larger base of energy sales,

and thus benefiting both the utility companies and the customers.

Figure Figure Figure Figure 5555 – Load Growth and ConservationLoad Growth and ConservationLoad Growth and ConservationLoad Growth and Conservation

14

1.5 The Motivation of Using Game Theory

Game Theory is a strategic analysis of situations involving a number of factors

(Players) aspires for different purposes. More formally, it is the study of mathematical

models of conflict and cooperation between intelligent rational decision-makers. On the one

hand, Game Theory attempts to predict the players moves, on the other hand, is trying to

offer players the best move for them [19] [20].

The smart grid is expected to be influenced by many deciding factors. In order to make

independent and inter-dependent decisions, game theory has been adopted by a number of

researchers. Through game theory, researchers aim at finding optimal solutions to

situations of conflict and cooperation, under the assumption that the involved players act

in their best interest. The most commonly used solution concepts are equilibrium concepts,

most famously Nash Equilibrium. In this case, even though all players are selfish, by

seeking to optimize their individual objective they end up optimizing a global objective.

Some initiatives have considered centralized demand management approaches where the

electrical companies might control the domestic appliances. The disadvantage of these

approaches includes social and legal barriers, large flow of information and scalability.

Recently, distributed approaches, where the decisions are made locally and directly by the

end consumer, have taken more relevance. In this scenario, game theory provides a

framework to evaluate and design active side management policies, since it naturally

models interactions in distributed decision making processes.

Finally, despite the importance of an efficient energy consumption system, such large-

scale plans cannot be implemented unless intelligent pricing schemes are used to provide

incentives for the subscribers to follow them. The incentives can be in form of lower utility

charges. Game theory provides a natural framework for developing pricing mechanisms to

solve various problems in networks, such as fair allocation of resources among users. A well

pricing mechanism can provide the subscribers with the incentives to cooperate in order to

not only improve the system overall performance, but also to pay less individually.

15

1.6 Thesis Objectives

1) Study how to implement relevant Game Theory tools for Demand-Side Management

in Smart Grid.

2) Propose a Control System Model for Demand-Side Management in Smart Grid

Using Game Theory to solve the fundamental problem.

The Model should include:

a. Practical Consumer Characterization Method.

b. An Algorithm for Fair Consumption Allocation.

c. An Energy Consumption Controller.

1.7 Thesis Organization

The rest of this thesis is structured as follows. In chapter 2 we review some

preliminaries from game theory and the relevant tools which can be used for DSM. In

chapter 3 we outline related works and point at open issues that we identify. In chapter 4

we describe our DSM control system model based on game theory tools. In chapter 5 we

present some simulation results and conclude in chapter 6.

1.8 Conclusions

In this chapter we introduced the fundamental problem of this thesis, we presented the

main terms and research topics of smart grid, we made a detail survey on demand-side

management and we explained the motivation of using game theory in the context of this

subject.

16

2 Game Theory as a Tool for Demand-Side Management

2.1 Introduction

Game theory is a wide discipline in mathematics which applies to a wide range of

behavioral relations, both human and non-human, as a logical method of decision science.

It is used in economics, political, psychology, biology, and today also in computer science.

Game theory defines a very wide range of topics include different kind of games, strategies,

information types, solution concepts, incentives, etc.

The first goal of this thesis is to research relevant tools in game theory which can be

practically applied in order to solve DSM problems. In this chapter we will introduce the

theoretical aspect of these tools in a dedicated form for DSM.

The main question that game theory tries to deal with in the context of DSM is how to

cause the consumer to act in a way that serves the utility interests without hurt the

consumer’s benefit. For this, we should choose game theoretic tools which allow us to

design a fair algorithm includes appropriate incentives that motivate the consumer to

cooperate with the DSM program.

In this chapter we will focus especially in Mechanism Design and Fair Division topics as

a theoretical basis for the proposed control system. Mechanism Design serves us in the

part of consumer characterization and the game formulation, Fair Division serve us in the

part of energy allocation of the shared source.

17

2.2 A Problem Representation Using Game Theory

We define a normal form (strategic form) game as follows [21]:

• A finite set of players � = �1,2, …� • Each player ∈ � chooses actions from a strategy set � • Outcomes are defined by strategy profiles which consist of all the strategies

chosen by individual players. Mathematically, the set of strategy profiles are

defined as � = �� × �� × …× �� • Players have preferences over the outcomes (note, NOT preferences over their

actions), denoted as ≼ .Usually these preferences are defined by a utility

function, � ∶ � → � that maps each outcome to a real number (sometimes called

a payoff function).

An instance of a game might be represented by the tuple (�, (� �, (≼ ��, containing the

players, strategy sets, and preferences.

For any outcomes � and ��, � ≼� �� if ��(� � ≤ ��(���. That is, a player � prefers one

outcome, ��, over another, � , if and only if that player’s utility function is higher for that

outcome. The best response function for a player ∈ � is defined as:

�� (� � = �� ∈ � ∶ � (� �, � � ≤ � (� , � �∀� � ∈ � (2.1)

where � represent the set of strategy choices of all players except . The best response function gives the strategy � for player from his possibly strategy

set � , given that he knows all the other players’ strategies in � , that maximizes player

′� utility function.

18

2.3 Nash Equilibrium

Now that we showed how to define games, we will explain the meaning of ”solving”

them. In game theory, a solution concept is a formal rule for predicting how a game will be

played. These predictions are called ”solutions”, and describe which strategies will be

adopted by players and, therefore, the result of the game. The most commonly used

solution concepts are equilibrium concepts, most famously Nash Equilibrium (NE).

The NE is conceptually the state of the game where if each player was given the chance

to change strategies given all of the other players’ strategies, the player would not be able

to profitably deviate from its current strategy.

DefinitionDefinitionDefinitionDefinition:::: [22] in the n-player normal-form game # = (��, … , ��; ��, … , ��, the

strategies (��∗, … , ��∗� are a Nash Equilibrium if, for each player , � ∗ is player i’s best

response to the strategies specified for the � − 1 other players, (��∗, … , � �∗ , � (�∗ , … , ��∗�: � (��∗, … , � �∗ , � ∗, � (�∗ , … , ��∗� ≥ � (��∗, … , � �∗ , � , � (�∗ , … , ��∗� (2.2)

for every feasible strategy � in � ; that is, � ∗ solves

max-.∈/. � (��∗, … , � �∗ , � , � (�∗ , … , ��∗�. (2.3)

Such a notion of equilibrium presents three issues [23]. The first one is efficiency. In

many situations of practical interest, Nash equilibria tend to be rather inefficient in terms

of social welfare. The second issue relates to the assumption that players are rational, i.e.,

that a player would always choose a best response to the system state, in terms of

maximizing his own utility. When agents are humans, they may behave in an irrational

way or may not be aware of the complete structure of the game, thereby taking non-

optimal decisions. The third issue relates the reachability of equilibrium: under which

conditions the system’s dynamics is actually able to drive the system to a certain

configuration and how much it would take for the system to stabilize there.

19

2.4 Mechanism Design

2.4.1 Preface

Mechanism Design, sometimes called reverse game theory, can be consider as the

”engineering” part of game theory. In classic game theory models, we usually try to figure

out or predict the outcomes of a given conflict. In mechanism design we do exactly the

opposite. That is, we start with the outcome (the goal we want to achieve) and we ask

what kind of procedure could be designed to achieve those goals.

It is best to view the goals of the designed mechanisms in the very abstract terms of

social choice [24]. A social choice is simply an aggregation of the preferences of the

different participants towards a single joint decision. Mechanism Design attempts

implementing desired social choices in a strategic setting, assuming that the different

members of society each act rationally in a game theoretic sense. Such strategic design is

necessary since usually the preferences of the participants are private.

In order to describe the player preference, it is not enough to say that one alternative is

preferred compered to another, the model should took into account also ”how much” it

preferred. Money is a common yardstick that allows measuring this. In a world with

money our mechanisms will not only choose a social alternative but will also determine

monetary payments to be made by the different players. The complete social choice is then

composed of the alternative chosen as well as of the transfer of money.

A well designed mechanism should cause players to be true in relation to their

preferences. Such mechanism usually called incentive compatibility or truthfulness.

Intuitively this means that player whose valuation is � would prefer ”telling the truth”

� to the mechanism rather than any possible ”lie” � �, since this gives him higher utility.

20

2.4.2 Mechanism design as a tool for Demand-Side Management

Mechanism design helps us to build a DSM model in the part of characterize the

consumer preferences and write the game formulation. Each individual subscriber in a

power system is an entity which can behave independently. The energy demand of each

subscriber may vary based on different parameters like the time of day, climate conditions,

and also the price of electricity. The different response of different users to various price

scenarios can be modeled analytically by adopting the concept of utility function from

microeconomics [25]. We can model the behavior of different users through their different

choices of utility function � . The utility function represents the level of satisfaction

obtained by the user as a function of its power consumption. The utility function � (1�, where 1 represent the consumption level, should fulfill the following properties:

Property 1Property 1Property 1Property 1:::: Utility functions � (1� are non-decreasing. Users are always interested to

consume more power if possible until they reach their maximum consumption level.

2� (1�21 ≥ 0 (2.4)

DefinitionDefinitionDefinitionDefinition 1111:::: We define 4 (1� ≜ � �(1� as the marginal benefit of the user.

Property 2: Property 2: Property 2: Property 2: The marginal benefit 4 (1� of customers is a non-increasing function.

24 (1�21 ≤ 0 (2.5)

In other words, the utility functions are concave and the level of satisfaction for users

can gradually get saturated.

Property 3: Property 3: Property 3: Property 3: We assume the expectation that no power consumption brings no benefit.

� (0� = 0 (2.6)

21

2.5 Fair Division

2.5.1 Preface

Fair division is the problem of dividing a set of goods between several people [26] [27].

This problem arises in various real-world settings: auctions, divorce settlements, frequency

allocation and territory. This is an active research area in Mathematics, Economics and

Game theory. The problem of fair division goes back at least to the Hebrew Bible.

Abraham and Lot had to decide who would get Canaan and who Jordan; Solomon had to

decide which of two women, was the mother of a disputed baby.

There are many different kinds of fair division problems, depending on the nature of

goods to divide, the criteria for fairness, the nature of the players and their preferences,

and other criteria for evaluating the quality of the division.

2.5.2 What is divided?

We define 6 as a set of items which should be divided between a group of � players

7�, 7�, 78…7�. The set of 6 can be of several types:

Invisible Invisible Invisible Invisible andandandand DivisibleDivisibleDivisibleDivisible::::

• Indivisible itemsIndivisible itemsIndivisible itemsIndivisible items – A finite set of items such that each item should be given

entirely to a single person. For example: computer, car and apartment.

• Divisible itemsDivisible itemsDivisible itemsDivisible items – An infinite set of resources, usually modeled as a subset of a

real space like [0, 1] section. For example: money, cake and water.

Homogeneous and HeterogeneousHomogeneous and HeterogeneousHomogeneous and HeterogeneousHomogeneous and Heterogeneous::::

• Homogeneous itemsHomogeneous itemsHomogeneous itemsHomogeneous items – Uniform in composition or characters like money.

• Heterogeneous itemsHeterogeneous itemsHeterogeneous itemsHeterogeneous items – Nonuniform in characters like cake.

22

Desirable and UndesirableDesirable and UndesirableDesirable and UndesirableDesirable and Undesirable::::

• Desirable itemsDesirable itemsDesirable itemsDesirable items – Items that is considered a favorable outcome like car or cake.

• Undesirable itemsUndesirable itemsUndesirable itemsUndesirable items – Such as house chores (which can also be indivisible, such as

dumping the trash, or divisible, like mowing the lawn).

2.5.3 Common Fair Division Problems

• Fair Fair Fair Fair AAAAllocation or Fair Allocation or Fair Allocation or Fair Allocation or Fair Assignmentssignmentssignmentssignment – Dividing a set of indivisible and

heterogeneous items.

• Cake Cutting Cake Cutting Cake Cutting Cake Cutting – Dividing a set of divisible, heterogeneous and desirable resource.

• Chore Division Chore Division Chore Division Chore Division – Dividing a set of heterogeneous and undesirable items.

• Housemate Problem Housemate Problem Housemate Problem Housemate Problem – Dividing the rooms in the apartment (a set of indivisible,

heterogeneous, desirable goods), and divide the rent to pay (divisible,

homogeneous, undesirable good).

• Inheritance Problem Inheritance Problem Inheritance Problem Inheritance Problem – Dividing desirable indivisible heterogeneous items,

desirable divisible heterogeneous property such as land, and desirable divisible

homogeneous property such as money.

2.5.4 Fairness Criteria

According to the Subjective theory of value, there cannot be an objective measure of

the value of each item. Therefore, objective fairness is not possible, as different people may

assign different values to each item. Therefore, most current research on fairness focuses on

concepts of subjective fairness. Each of the � Players is assumed to have a personal,

subjective utility function or value function � which assigns a numerical value to each

subset of 6. Usually the functions are assumed to be normalized for the interval [0, 1],

where � (∅� = 0 and � (6� = 1.

23

According to this, we will define several concepts of subjective fairness:

• Proportional Proportional Proportional Proportional DivisionDivisionDivisionDivision – Every person gets at least his due share, according to

his own value function. That means each of the � players gets a subset of 6

which he values as at least 1/�:

� (1 � ≥ 1/�∀ (2.7)

For example if three people divide up a cake, each one gets at least a third by

their own valuation.

• EnvyEnvyEnvyEnvy----free Divisionfree Divisionfree Divisionfree Division – Every person gets a share that he values at least as much

as all other shares:

� (1 � ≥ � ;1�<∀, = (2.8)

An Envy-Free guarantees no one will want somebody else’s share more than his

own. This kind of criteria is relevant only for heterogeneous goods.

• Equitable DivisionEquitable DivisionEquitable DivisionEquitable Division – Every person feels exactly the same happiness, i.e., got

exactly the same value:

� (1 � = ��;1�<∀, = (2.9)

This is the more social criteria.

• UtilitarianUtilitarianUtilitarianUtilitarian DivisionDivisionDivisionDivision – A solution that maximizes the sum of the individual

utilities:

max> � (1 � (2.10)

24

2.5.5 Main challenges in Fair Division problems

• The The The The DDDDividersividersividersividers – The real life problem is the one of dividing goods or resources

fairly between players, who has an entitlement to them. The central assumption

of fair division is that such a division should be performed by the players

themselves. The players may be use a mediator but certainly not an arbiter as

only the players really know how they value the goods. In computerized

systems, the division performed by agents which represent the player’s utility.

• The PreferencesThe PreferencesThe PreferencesThe Preferences – In the real world people sometimes have a good idea of how

the other players value the goods and they may care very much about it. The

case where they have complete knowledge of each other’s valuations can be

modeled by game theory. In many cases, the preferences of the participants are

private. In these cases, partial knowledge is very hard to model. A major part of

the practical side of fair division is the devising and study of procedures that

work well despite such partial knowledge or small mistakes.

• TTTThe Procedure he Procedure he Procedure he Procedure – The main goal of fair division theory is to provide a procedure

or algorithm to achieve a fair division, or prove their impossibility. In practice,

the suggested algorithm should be applicable and converge by finite number of

steps. In order to demonstrate the complexity of this challenge we can indicate

for example that a bounded envy-free algorithm for the five-players case was

just recently proposed by Saberi and Wang in 2009 [28]. Actually, up to now,

the bounded n-player envy-free algorithm is still an open question.

• The TThe TThe TThe Truth ruth ruth ruth – Fair division cases might cause the players to lie about their

preferences in order to increase their part of the shared resource. When people

buy bread for example, he uses social resources like wheat, fuel and human

resources that invested in making the bread. What prevents overuse of these

resources is the bread price. This is the penalty should be paid to compensate

the society on resource utilization. The model must include mechanism to

motivate the consumer to be true about his needs.

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2.5.6 Fair Division as a tool for Demand-Side Management

Fair Division helps us to build a DSM model in the part of fairly allocate the shared

energy source capacity. Our research shown that the problem of fairly divide electrical

capacity between consumers who should pay money for the service, can describe as follows:

The The The The DDDDivided ivided ivided ivided IIIItemstemstemstems::::

• ElectricityElectricityElectricityElectricity – Divisible, Homogeneous and Desirable.

• MoneyMoneyMoneyMoney – Divisible, Homogeneous, Undesirable.

The Fairness CriteriaThe Fairness CriteriaThe Fairness CriteriaThe Fairness Criteria::::

• For different fair division cases, different fairness criteria are suitable.

The The The The MMMMain Challengesain Challengesain Challengesain Challenges::::

• The DThe DThe DThe Dividersividersividersividers – Our automatic system should be based on computerized agents

integrated in the smart meters. In order to design a distributed DSM system,

the system can use a mediator for the allocation as mentioned before.

• The Preferences The Preferences The Preferences The Preferences – The model should fit for private preferences.

• The ProcedureThe ProcedureThe ProcedureThe Procedure – The top challenge of this section is to propose an algorithm

that can be practically integrated in the local energy consumption controller.

• The TrueThe TrueThe TrueThe True – The model should include price profile that encourages the

consumers to be true about their needs.

2.6 Conclusions

In this chapter we introduced the most relevant tools in game theory that can be used

for design an algorithm for demand-side management. The most useful tools were

Mechanism Design for the consumer characterization and Fair Division for the resource

allocation.

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3 Related Works

3.1 Introduction

In this chapter, we present related works that used game theory as a tool for demand-

side management in smart grid. Most of these works can be divided into two main topics:

Consumption Scheduling and Real Time Management. At the end of this chapter, we note

a number of open issues identified in these works, during our research. These open issues

helped us to refine the objectives of this thesis and to define our system goals.

3.2 Demand-Side Management Based on Scheduling

Mohsenian-Rad et al. [29] presented an autonomous incentive based algorithm for

scheduling power consumption. In this scheme, loads are classified into Schedulable

consumption and Non-schedulable consumption. Schedulable consumption represents

usages that do not have strict time constraints, and Non-schedulable consumption

represents usages that have strict time constraints. The authors proposed the use of

Energy Consumption Scheduling devices (ECS) as a component of the smart meters. In

this model, an ECS communicates with other ECSs in its neighborhood sharing its

scheduling information. Running their proposed distributed algorithm, each ECS computes

and broadcasts its optimal schedule. The algorithm repeats until no ECS announces any

change of schedule. Simulation results confirm that the proposed algorithm significantly

reduces the PAR as well as the total energy cost in the system.

Mohsenian-Rad et al. [30] presented an autonomous and distributed demand-side

energy management system among users based on game theory. An energy consumption

scheduling game is formulated in which the users act as the players and a daily household

appliance schedules as their strategies. This work assumes that the utility company can

have appropriate pricing tariffs in order to differentiate the energy usage levels and

27

durations. The work demonstrates that for a common scenario comprising a single utility

company serving a number of customers, the global optimal performance in terms of

minimizing the energy costs is achieved at the Nash equilibrium of the game. Furthermore,

the users receive incentives to take part in this service. The experimental results reveal

that this approach is able to reduce the peak-to-average ratio of the total energy demand,

the total energy costs, and also each player’s individual daily electricity bills.

Ibars et al. [31] proposed distributed load management scheme based on the capacity of

the consumers to manage their own demands in order to minimize a cost function or price.

The system is modeled as a non-cooperative network congestion game by modeling both

demand and smart grid load using a directed graph, in which the cost of a unit load over

an edge depends on the total load over that edge. In other words, in the defined non-

cooperative congestion game amongst the users or players, the price levels are set for the

demand vector of each player. The work demonstrates that the game formulated as such

converges to a stable equilibrium point in a distributed manner. Different user demand

profiles reveal that it is possible to obtain a smoother generation curve while meeting the

user demands.

Caron and Kesidis [32] proposed a dynamic pricing scheme that encourages consumers

to adjust their power use with the objective of getting a flat overall consumption. The

authors showed that finding an optimum schedule is NP-hard, and then presented

methodologies to study how close one can get to the ideal case. This was done based on

the amount of information the consumers are willing to share with their utility company.

Furthermore, the authors studied the outcomes based on several scheduling policies,

namely, uniform, ALOHA I, ALOHA II, and Time/Slackness. In their work, the authors

have also compared the performance of these scheduling policies.

Chen et al. [33] proposed the use of a real-time pricing rate, and formed a Stackelberg

game between the utility company and energy management controllers that are to be

deployed at each home. The game was setup such that the controllers play the role of the

follower and the utility company plays the role of the leader. The authors simulated their

28

proposed methodology and concluded that their approach saves money for the consumers

and ensures that rebound peaks do not appear.

Gatsis and Giannakis [34] presented a cooperative scheduling approach between the

utility company and the consumers. In this approach, loads are classified into loads that

must run, loads that must consume a given amount of power (e.g., a rechargeable battery),

and loads that are adjustable in power consumption but the adjustment could cause

consumer dissatisfaction (e.g., climate control). This was modeled into a convex

optimization problem that was solved using the distributed subgradient method. The

authors also presented simulation results that show that it is possible to meet the

constraints above in an optimum way.

Samadi et al. [35] provided an interesting VCG-based mechanism (based on algorithmic

mechanisms design) for the utility company to effectively price users employing DSM.

They investigated some of the main properties of the proposed mechanism such as

truthfulness and efficiency. It is shown that the pricing scheme can be designed in such a

way that, by acting selfishly, users end up reaching the optimal system-level operating

point. Simulation results confirmed that by using the proposed method, along with

maximizing the social welfare, the energy provider will also benefit in terms of energy cost

and PAR.

Wang and de Groot [36] presented a mechanism to further exploit the awareness of end

users in a three-tier energy market. Their method proposes to use the middle tier, the

Energy Service Company level, to aggregate the flexible electricity consumption patterns

from individual users and reduce the peak energy consumption through load-balancing.

They also gave a method for multiple Energy Service Companies to improve their

schedules iteratively via Demand Response events. They proved that the method produces

a schedule that is a Nash Equilibrium. Extensive experiments showed the effectiveness of

their method.

Zhu et al. [37] proposed an Integer Linear Programming (ILP) and game theory based

optimization mechanism for the home demand-side management in a smart grid. The

29

proposed mechanism is able to schedule both the optimal power and the optimal operation

time for power-shiftable appliances and time-shiftable appliances respectively according to

user preference and the power consumption patterns of individual appliances. The

mechanism can be applied to both centralized control and distributed coordinative

management schemes. Simulation results demonstrate the convergence of the game

theoretical algorithm.

Nguyen et al. [38] presented a game-theoretic framework to model independent decision-

making of users’ energy consumption scheduling. They designed a new pricing model and

proposed a distributed algorithm to achieve the Nash equilibrium of the NECS (Non-

Cooperative Energy Consumption and Storage) game in which each user tries to minimize

its energy payment to an energy provider. Unlike other DSM algorithms which require the

message exchanges between users, their distributed algorithm requires only the interaction

between the energy provider and users via pricing information. Simulations showed that

the distributed algorithm can reduce the energy cost and PAR of the system compared

with the centralized design.

Chen et al. [39] proposed a novel load scheduling scheme to shift and shave the peak

load to stabilize the power demand and avoid overload. First, the smart appliances are

classified into two categories, i.e., the time-shiftable and the temperature-shiftable. Then

they constructed the Operation-Comfort Level (OCL) models which incentive consumers

to use the algorithm to cut the electricity cost with minimum uncomforting brought by the

change of energy consumption scheduling. Simulations confirm that the algorithm

significantly reduces the peak load, the PAR and the total energy cost with acceptable.

Shinwari et al. [40] used a water-filling based scheduling algorithm to obtain a flat

demand curve. The proposed algorithm does not require any communication between

scheduling nodes. The authors also study the possible errors in demand forecast and

incentives for customer participations. Their results confirm the efficiency and fairness of

the proposed scheduling algorithm.

30

3.3 Real Time Demand-Side Management

Samadi et al. [41] proposed a real-time pricing algorithm for DSM programs to

encourage desired energy consumption behaviors among users and to keep the total

consumption level below the power generation capacity. In the system model, the

subscribers and the energy provider automatically interact with each other through a

limited number of message exchanges and by running a distributed algorithm to find the

optimal energy consumption level for each subscriber, the optimal price values to be

advertised by the energy provider, and also the optimal generating capacity for the energy

provider. They formulate the real-time pricing as an optimization problem to maximize the

aggregate utility functions of all subscribers in the system while minimizing the imposed

energy cost to the energy provider. They proved the existence and the uniqueness of the

optimal solution for the formulated optimization problem. Simulation results confirmed

that both subscribers and the energy provider have benefit from the proposed algorithm.

Tarasak [42] extend the approach in [41] to consider the effect of load uncertainty. The

paper considers three uncertainty models: bounded uncertainty model, Gaussian model and

unknown distribution model. He showed that load uncertainty increases the optimal price

and that load uncertainty with unknown distribution has a higher optimal price than the

Gaussian model. Simulation results provide some insights on how different models of load

uncertainty affect the generating capacities and the aggregate power consumption.

Samadi et al. [43] proposed a VCG mechanism for DSM in smart grid. The proposed

mechanism aims to maximize the aggregate utility of all users while minimizing the total

cost of power generation. They investigated some of the main properties of the proposed

mechanism such as truthfulness, efficiency, and nonnegative transfer. Through simulation,

they showed that the proposed VCG mechanism improves the performance of the system

by encouraging users to reduce their power consumption and shift their loads to off-peak

hours. They also analyzed the impact of some key parameters on our model through

simulations. The simulations confirmed that by using our proposed VCG mechanism, in

addition to maximizing the social welfare, the energy provider will benefit as well.

31

Agarwal and Cui [44] presented a solution through variable-rate metering, which

indicates the real-time cost of power generation in order to influence the customers to

lower power consumption during the peak times. This work points out that the main

challenge to implementing real-time pricing consists in the lack of cost-effective two-way

smart metering for communicating the real-time prices to the customers and their

consumption levels back to the utility provider. Then, this work proposes formulation of

noncooperative games among the customers with two real-time pricing schemes under

more general load profiles and revenue models. The results indicate that both the pricing

schemes contribute to similar electricity loading patterns when the customers are

interested in the minimization of electricity costs alone.

Conejo et al. [45] presented a model for optimally adjusting the hourly load level of a

given consumer in response to hourly electricity prices is presented. The objective is to

maximize the utility of the consumer subject to a number of constraints on load levels and

aggregated consumptions. The interaction takes place on an hourly basis using a rolling

window algorithm to consider the energy consumption throughout the twenty four hours of

the day. A case study demonstrates the usefulness of the proposed algorithm to maximize

the utility, or to reduce the electricity bill, of a consumer that integrates the proposed

procedure in its EMS.

Ramchurn et al. [46] study a decentralized demand-side management scheme in which

agents coordinate to smooth load peaks. It is shown that through such schemes significant

reduction in peak demand can be achieved. In the paper, the authors also introduce an

evolutionary game model; they show that under their scheme the usage of demand-side

management mechanisms is always convenient. In such conditions the dynamics of the

game is straightforwardly converging to the single Nash equilibrium.

32

3.4 Open Issues on Related Works

In order to refine our goals for this thesis, we specially focused on the great work made

by Samadi and Mohsenian-Rad [41], because of the similarity to our research. The open

issues we will present here had confirmed by some correspondence with these authors. It

should be noted that these issues also identified in additional works.

1) Is RealIs RealIs RealIs Real----TiTiTiTime Pricing really works?me Pricing really works?me Pricing really works?me Pricing really works? – In [41] authors presented a Real-Time Pricing

algorithm for Demand-Side Management as describe in Figure 6.

Figure Figure Figure Figure 6666 – Illustration of Illustration of Illustration of Illustration of [41][41][41][41] algorithmalgorithmalgorithmalgorithm

However, in a different work of Mohsenian-Rad [47] he wrote: ”Although real-time

pricing has several potential advantages, its benefits are currently limited due to

lack of efficient building automation systems as well as user’s difficulty in manually

responding to time-varying prices”. As believers on a real-time approach which

minimally reduce the consumer comfort, we do want to propose a real-time based

system model instead of Scheduling model which significantly influence the

subscriber’s consumption habits.

33

2) What’s the connection between the calculated values to the real ones?What’s the connection between the calculated values to the real ones?What’s the connection between the calculated values to the real ones?What’s the connection between the calculated values to the real ones? – Many

algorithms, like [41], calculate few values like: optimal consumption level 1 �?@A, optimal generating capacity B�?@A and optimal price C?@A� . However, in most cases,

there is no connection between the calculated values and the real ones. This is

because the system works on open-loop manner, so, in practice, the subscriber can

consume any amount of energy he wants, and there is no way to confirm that he

consumes the theoretical optimal value that calculated for him. Our goal to offer a

system model that would work in a closed-loop manner and keep the subscriber

interests.

3) Is utility function intuitively characterizing the consumer preferences?Is utility function intuitively characterizing the consumer preferences?Is utility function intuitively characterizing the consumer preferences?Is utility function intuitively characterizing the consumer preferences? – The

algorithm proposed in many cases uses pure mathematical utility functions to

represent the consumer’s preferences like describe in Figure 7.

Marginal Benefit Function Utility Function

Figure Figure Figure Figure 7777 – Marginal and Utility Functions inMarginal and Utility Functions inMarginal and Utility Functions inMarginal and Utility Functions in [41][41][41][41]

In most cases, these functions do not give an intuitive characterization that can be

introduce to the consumer in order to draw up a contract for him. Moreover, in

many cases, there is much need for the subscriber’s involvement in performing the

required settings for the algorithm. This can lead to a lack of cooperation by the

subscriber. Our goal in this thesis is to propose a simple and intuitive

characterization method to represent the consumer preferences.

34

4) Is the algorithm can implement practical?Is the algorithm can implement practical?Is the algorithm can implement practical?Is the algorithm can implement practical? – The algorithm proposed in [41] uses

functions with many parameters to represent the subscriber and the provider

preferences like describe below:

D(1,E� = FE1 − G2 1�,H0 ≤ 1 ≤ EGE�2G ,H1 ≥ EG I�(B�� = G�B�� + K�B� + L� Consumer Utility Function Provider Cost Function

When we tried to implement this algorithm ourselves, we discovered that the

simulation actually behaves as expected but the parameters cannot be practically

calibrated. This means that this algorithm cannot be implementing in a real DSM

system at the subscriber’s houses. Our target in this thesis to propose a practical

and simple algorithm that would be applicable.

5) Is coupling between subscribers is fair?Is coupling between subscribers is fair?Is coupling between subscribers is fair?Is coupling between subscribers is fair? – In the algorithm proposed in [41], there

can be a situation that one subscriber consumes energy in his optimal consumption

value, and suddenly his neighbor decide to increase his consumption level. This

event will affect the first subscriber directly, and the total price will increase, or his

optimal consumption value will decrease. Real subscriber will not accept that as a

fair system. Our target to propose a fair system model without such coupling

between subscribers.

3.5 Conclusions

In this chapter we introduced related work that uses game theory as a tool for demand-

side management in smart grid. As can be see, the two main approaches for demand-side

management are: Consumption Scheduling and Real-Time management. It is not yet clear,

which approach will finally be in common in the future smart grid. In this thesis we try to

propose a system that combine these two approaches and will have the advantages of each.

35

4 Demand Side Management Control System Model

4.1 Introduction

In this chapter we will introduce our proposed demand-side management control system

model framework. We first declare the system goals which defined according to the thesis

objectives and the open issues we discovered on the related works.

Then we present the model and its basic principle which we called: Asynchronous

Consumption Mode (ACM). We will explain the inspiration for this method.

Finally, we detail the three main components of the model: Consumer Characterization

method, Fair Division Algorithm for energy allocation and Energy Consumption Controller

that helps to close the loop of the system.

Each of these three components can be separately expand by additional future research

and development.

36

4.2 System Goals

1) Practical Consumer Characterization MethodPractical Consumer Characterization MethodPractical Consumer Characterization MethodPractical Consumer Characterization Method – The consumer preferences

characterization method should be:

a. Can be practically calibrated.

b. Require minimum involvement by the subscriber.

c. Simple and intuitive to propose to the subscriber.

2) An Algorithm for Fair Consumption AllocationAn Algorithm for Fair Consumption AllocationAn Algorithm for Fair Consumption AllocationAn Algorithm for Fair Consumption Allocation – This section should be designed

according game theory principles as followed:

a. The system should find a fair energy allocation for each subscriber according

to the equitable fair division criteria.

b. Give the subscriber an incentive to use the system and be truthful.

c. Minimum coupling between subscribers.

3) An Energy Consumption ControllerAn Energy Consumption ControllerAn Energy Consumption ControllerAn Energy Consumption Controller – The ECC should fulfills the following goals:

a. Enable a closed-loop system that keep the subscriber interests and manage

the consumption level according to the optimal calculated value.

b. Combine the advantage of two DSM approaches: Consumption Scheduling

and Real-Time Management. Our approach is somewhere between both.

37

4.3 System Model

The general system model includes several load subscribers and shared source of energy

connected to the electrical grid as describes in Figure 8. We assume that each subscriber is

equipped with an ECC device in its smart meter for managing the household energy

consumption. The subscribers are all connected to the power line coming from the energy

source. The ECC devices are also connected to each other and also to the energy source

through a Local Area Network (LAN).

Figure Figure Figure Figure 8888 – General System ModelGeneral System ModelGeneral System ModelGeneral System Model

Let M denote the set of subscribers, where� ≜ |M|. For each subscriber� ∈ M, let O�

denote the set of appliances. For each appliance P ∈ O� we define the Consumption Level

DemandQ�RS�TU, the Operational DemandV�

R and the Quality of Service WX� which will

be explaining later on. According to these parameters the system will fairly allocate

consumption level 1�?@A

for each subscriber.

ECC1 ECC2 ECCn

Limited

Energy

Source

LAN

Power Line

38

4.4 Control Loop Description

After we presented the general system model, we can describe the closed control loop

that represents the core of our proposed model. As seen in Figure 9, the control loop

contains the two main part of the proposed system: The Fair Division allocation section

and the Energy Consumption Controller. The controller connected to the household

appliances in order to manage their operation, but it also measure their truth real-time

consumption level through measurement device in order to close the loop. The controller

calculates the error between the optimal allocated consumption level and the actually real-

time consumption level, and manages the appliances operation in a way that minimizes

this error. Each of the system components will detail explained later.

Figure Figure Figure Figure 9999 – Control Loop Control Loop Control Loop Control Loop DescriptionDescriptionDescriptionDescription

ECC

Household Consumption

Σ Fair Division Allocation

Consumption Measurement

1�?@A Computed

Consumption Level

Error

++++ ----

1�Z[ Real-Time

Consumption Level

1�Z[ Measured

Consumption Level

39

4.5 Asynchronous Consumption Mode (ACM)

Source of inspiration to our model is the revolution occurred in communication systems

at the beginning of the century. The first communication system was based on

synchronous bandwidth allocation, means each subscriber got a fixed amount of bandwidth

whether he used it or not. This method got the name STM – Synchronous Transfer Mode.

With technology development, communication vendors wanted to maximize to utilization

of the channels. That led to develop an asynchronous bandwidth allocation method called

ATM – Asynchronous Transfer Mode [48]. The basic principles of this method were

allocated bandwidth according to the type of the service, and use free channel bandwidth

when some subscribers don’t use it temporally. These principles implement mainly by

define Quality of Service (QOS) levels and queue management.

CBR – Constant Bit Rate

STMSTMSTMSTM

UBR – Unspecified Bit Rate

ABR – Available Bit Rate

VBR – Variable Bit Rate

CBR – Constant Bit Rate

ATMATMATMATM

Figure Figure Figure Figure 10101010 – Synchronous Transfer Mode vs. Asynchronous Transfer ModeSynchronous Transfer Mode vs. Asynchronous Transfer ModeSynchronous Transfer Mode vs. Asynchronous Transfer ModeSynchronous Transfer Mode vs. Asynchronous Transfer Mode

Very similarly, traditional electricity networks have the same features like STM

networks. Each subscriber gets a fixed energy allocation, irrespective of the level of

consumption of other subscriber and the level of importance of his appliances.

In order to propose an asynchronous model similarly to ATM, we define a novel term

we call: ACM ACM ACM ACM – Asynchronous Consumption ModeAsynchronous Consumption ModeAsynchronous Consumption ModeAsynchronous Consumption Mode. This method will affect the way we

characterize the consumer preferences and on the operating principle of the Energy

Consumption Controller (ECC).

40

4.6 Consumer Characterization

This section would be the first part of our ACM (Asynchronous Consumption Mode)ACM (Asynchronous Consumption Mode)ACM (Asynchronous Consumption Mode)ACM (Asynchronous Consumption Mode)

method. At this section we present new approach to characterize the consumer preferences

by defining three QOS (Quality of Service) levels for the consumer appliances. Moreover,

our method will fulfill the principles of mechanism design introduced in section 2.4.

In order to be more intuitive, we decided to characterize the consumer preferences

starting with the marginal utility function4 (1� instead of the utility function. According

to Property 2, this function should be a non-increasing function.

As it is said, we define three QOS levels to describe the priority of the appliance

operation:

1) CCR CCR CCR CCR – Constant Consumption RateConstant Consumption RateConstant Consumption RateConstant Consumption Rate – This level includes appliances that must

work when they demand for energy. For example: refrigerator and indoor light.

2) AAAACRCRCRCR – AvaiAvaiAvaiAvailablelablelablelable Consumption RateConsumption RateConsumption RateConsumption Rate – This level includes appliances at secondary

priority that can operate according to available energy capacity and can tolerate

delay in operation time. For example: electric kettle and boiler.

3) UCR UCR UCR UCR – Unspecified Consumption RateUnspecified Consumption RateUnspecified Consumption RateUnspecified Consumption Rate – This level includes appliances at third

priority that can operate according to surplus energy capacity and are sensitive for

breaking off operation. For example: under-floor heating and outdoor lighting.

Table Table Table Table 1111 – Typical QOS level featuresTypical QOS level featuresTypical QOS level featuresTypical QOS level features

QOSQOSQOSQOS PriorityPriorityPriorityPriority Operation timeOperation timeOperation timeOperation time Sensitive to Sensitive to Sensitive to Sensitive to delay before delay before delay before delay before

actionactionactionaction

Can disconnect Can disconnect Can disconnect Can disconnect during during during during

operationoperationoperationoperation

Energy Energy Energy Energy consumption consumption consumption consumption

levellevellevellevel

CCRCCRCCRCCR 1 Short / Long Yes No Low

ACRACRACRACR 2 Short No Yes Low / High

UCRUCRUCRUCR 3 Short No Yes Low

41

These definitions would give us a piecewise constant marginal utility function.

According to definition 1, the relationship between the marginal utility function and the

utility function itself can be describes as:

� (1� = \4 (1�]1 (4.1)

For example:

\ →

Marginal Utility Function 4(1� Utility Function �(1� Figure Figure Figure Figure 11111111 – Consumer Characterization exampleConsumer Characterization exampleConsumer Characterization exampleConsumer Characterization example

In this way we do not need to calibrate values of the utility function parameters that

cannot be calibrating. It can easily show that the received utility function does fulfill all

the properties it should satisfy.

It is clearly, that this method is very simple and intuitive to propose to the subscriber.

All he needs to do is to map all the appliances in his home and define their consumption

level and priority. If we want to make a simplest system and minimize the involvement of

the subscriber, we can predefine a table of appliances with typical consumption level and

priority, and all would remain to the subscriber is to select the appliances he has. In a real

system we should allow the subscriber to change his priorities each time interval of the

system. That because one appliance can be very important at evening but less important

at morning when nobody home.

The incentive to the consumer to use such of service can be by giving a different price

for each QOS level. Where CCR service would be the most expensive service and UCR

would be the cheapest. That should motivate the subscriber truly declare his preferences.

0

0.5

1

0 0.5 1

QO

SQ

OS

QO

SQ

OS

Consumption DemandConsumption DemandConsumption DemandConsumption Demand

0

0.5

1

0 0.5 1

Uti

lity

Uti

lity

Uti

lity

Uti

lity

Consumption DemandConsumption DemandConsumption DemandConsumption Demand

CCRCCRCCRCCR

AAAACRCRCRCR

UUUUCRCRCRCR

42

4.7 Fair Division Algorithm

4.7.1 Preface

In this section we explain the fair division algorithms for the component that makes the

allocation of the shared source between all the consumers. That would be the second tool

of game theory that we implement in our model as described in section 2.5. Our research

showed that there are almost non works that used fair division as a tool in their model.

As described above, our shared resource is electricity, means it Divisible, Homogeneous

and Desirable. We will present three algorithms for the use of three relevant fairness

criteria called: Proportional Division, Equitable Division and Utilitarian Division. In the

next chapter we’ll show some simulation results to demonstrate the difference between

these criteria.

Generally, the proportional division method will allocate each QOS level relative to

consumer demand, the equitable division method will allocate the resource in order to

equalized the consumer utility and the utilitarian division method will allocate the resource

in a way that maximize the social utility and the provider profit.

For convenience, we denote each method with the following acronyms:

• PDPDPDPD – Proportional Division.

• EDEDEDED – Equitable Division.

• UDUDUDUD – Utilitarian Division.

43

4.7.2 Proportional Allocation

Algorithm 1Algorithm 1Algorithm 1Algorithm 1 Fair Division Allocation – Proportional Division

Require:Require:Require:Require: Set of marginal utility functions 4 (1� Ensure:Ensure:Ensure:Ensure: Allocation (1�̂ _ , 1�̂ _ , … , 1�̂_� ForForForFor = = 1,… ,3 (represents three QOS levels) dodododo

IfIfIfIf ;∑ Q�, R� b� < P4PdPKdeLPfPLgh< 1�, ̂_ = Q�, R (4.2)

ElseElseElseElse

1�, ̂_ = Q�, R∑ Q�, R� b� × P4PdPKdeLPfPLgh (4.3)

End forEnd forEnd forEnd for

ReturnReturnReturnReturn (1�̂ _ , 1�̂_ , … , 1�̂_� which, for all ∈ M, gives a relative allocation.

Above is an algorithm for a simple proportional division allocation. The algorithm

allocates each QOS level separately. In each level, it checks if the is enough capacity in

order to satisfy all subscribers, if there is; it allocates according to the demand (4.2). Else,

it allocates the availably capacity relatively to the demand (4.3).

44

4.7.3 Equitable Allocation

Algorithm 2Algorithm 2Algorithm 2Algorithm 2 Fair Division Allocation – Equitable Division

Require:Require:Require:Require: Set of marginal utility functions 4 (1� Ensure:Ensure:Ensure:Ensure: Allocation (1�i_ , 1�i_ , … , 1�i_� ForForForFor = 1,… , � dodododo

� (1� = j4 (1�]1 End forEnd forEnd forEnd for

Solve the following Fair Division problem using Bisection Method:

max (��(1�, ��(1�, … , ��(1�� (4.4)

s.t. � (1 � = ��;1�<∀, = (4.5)

>1 i_� b� = 1 (4.6)

1 i_ ≥ 0∀ ∈ M (4.7)

ReturnReturnReturnReturn (1�i_ , 1�i_ , … , 1�i_� which, for all ∈ M, gives a maximum utility.

Above is an algorithm for equitable division allocation. First, the algorithm calculates

the utility functions set of all subscribers. Then it solves the fair division problem (4.4) by

using bisection numerical method according to the given constrains.

(4.6) and (4.7) ensure that the allocation produced is both feasible and complete.

Furthermore, (4.5) guarantees that the allocation will fulfill the equitable division criteria,

means each subscriber gets the same benefit.

It should be noted, that there can be edge cases where some subscribers demand a very

low amount of capacity from the shared source. In this cases, constrain (4.5) will cause

that not all the source capacity will be allocated between the subscribers. In such cases, we

45

will allocate this subscriber his maximum capacity demand, means maximum benefit, and

get him out of the game. The rest of the capacity will be allocated between the rests of the

subscribers as describe above.

The bisection method in mathematics is a root-finding method which repeatedly bisects

an interval and then selects a subinterval in which a root must lie for further processing.

We used that method since that graphic description of the problem can be describes as a

cross section finding between all the utility functions graphs and a horizon line at a

maximum possible level.

4.7.4 Utilitarian Allocation

Algorithm 3Algorithm 3Algorithm 3Algorithm 3 Fair Division Allocation – Utilitarian Division

Require:Require:Require:Require: Set of marginal utility functions 4 (1� Ensure:Ensure:Ensure:Ensure: Allocation (1�k_ , 1�k_, … , 1�k_� ForForForFor = 1,… , � dodododo

� (1� = j4 (1�]1 End forEnd forEnd forEnd for

Solve the following Fair Division problem:

max >� (1 �� b� (4.8)

s.t. >1 k_� = 1 (4.9)

1 k_ ≥ 0∀ ∈ M (4.10)

ReturnReturnReturnReturn (1�k_ , 1�k_ , … , 1�k_� which, for all ∈ M,

gives a maximum social utility and provider profit.

46

Above is an algorithm for utilitarian division allocation. First, the algorithm calculates

the utility functions set of all subscribers and then it solves the fair division problem (4.8).

(4.9) and (4.10) ensure that the allocation produced is both feasible and complete.

Since it can be more than one solution for this problem, the algorithm will return an

allocation vector that both maximize the social utility and the provider profit.

4.8 Price Profile

A main question should be asked is how to cause the subscribers to be honest about

their needs in order to truly allocate the resource fairly. As mentioned before, the only way

to balance the market is by using a price profile that encourages the subscriber to present

real needs. In other words, the mechanism should be such that it would be inexpedient for

the subscriber to lie about his preferences.

There are many methods in the literature of game theory to formulate a price profile of

the system, and actually this can be a whole subject for Master thesis. Famous methods

family for designing price profiles called Clarkes Groves Mechanisms. These models are

subject of auction theory. The special property of these auctions is that the dominant

strategy of each player is to honestly declare his demand value. In other words, these

models are ’truth inducing’. This branch of game theory also belongs to the field of

mechanism design mentioned before.

In this thesis we define a simple price profile that gives the most expensive price for the

CCR QOS level, a medium price for the ACR QOS level, and the cheapest price for the

UCR QOS level. This method should encourage the subscriber to well define his appliances

needs in order to save money.

It should be noted here, that one of the basic assumptions of game theory is that the

player is rational. It means that the player make actions in a way that serves his targets

and his benefit. Therefore it can be conclude, this simple price profile should be an

incentive for the subscriber to define his needs truly.

47

4.9 Energy Consumption Controller (ECC)

All the subscriber’s appliances are connected to the ECC as describes in Figure 12. The

ECC manage the appliances operation on the one hand, and measure their truth real-time

consumption on the other hand.

Figure Figure Figure Figure 12121212 – Appliances connected to ECCAppliances connected to ECCAppliances connected to ECCAppliances connected to ECC

The real time consumption measurement functions as the feedback branch of the

system control loop. Moreover, the controller receive a measurement of the total

consumption from the shared source, in order to identify moments of low consumption by

other subscriber that can by use temporarily.

The main principle of operation of the controller includes the application of the three

QOS levels defined per each appliance. Appliances which classify as CCR will receive

service on demand. Appliances which classify as ACR will receive service immediately if

the consumer have available capacity or will be delayed if not. Appliances which classified

as UCR will receive service according to surplus capacity of the shared resource. The

controller will shut down these appliances instantaneously if there will be demand for

applying more important appliance. The overall goal of the control loop is to stick as much

as possible to the energy amount allocated to the consumer.

Consumption Control

Consumer Parameters

Supply

A1

Mea

sure

An

Supply

Mea

sure

Supply

Mea

sure

ECC

A2

Source Measurement

48

4.10 Conclusions

In this chapter we introduced the theoretic aspects of our proposed model. Our starting

point was the system goals which we define according to the thesis objectives and the open

issues we identify at related works. Later we present the system model and the basic

notations. At the core of this chapter we introduced our Asynchronous Consumption Mode

concept and the closed control loop designed according to it.

The three main parts of the model was the Consumer Characterization approach based

on the mechanism design principles, the Fair Division algorithm that allocates the share

source energy and the Energy Consumption Controller the manage the appliances

operation. Next we show some simulation examples to demonstrate the model concept.

49

5 Performance Demonstration

5.1 Introduction

In this chapter we will demonstrate the system operation. We will describe the

experimental setup and present some simulation results. As described above, the system

consists of two main independent parts: the fair division allocation section and the real-

time closed loop section. The output allocation of the first part is the input set point of the

second. Therefore, we divide the simulation demonstration into these two parts.

Our example would be for two typical subscribers that shared the same source while

each of them demands almost all the capacity with different level of priorities. That

means, the total demand for capacity from the subscribers exceeded the ability of the

shared source.

First we map the subscriber’s appliances and their characterization, after that we

describe the characterization of each subscriber preferences, later we demonstrate the

allocation method and eventually we show an example for consumption graph for each

subscriber. Finally we explain the simulation results and conclude.

50

5.2 Experimental Setup

Figure Figure Figure Figure 13131313 – Experimental SetupExperimental SetupExperimental SetupExperimental Setup

Table Table Table Table 2222 – Subscriber’s DemandsSubscriber’s DemandsSubscriber’s DemandsSubscriber’s Demands

SubscriberSubscriberSubscriberSubscriber1111 SubscriberSubscriberSubscriberSubscriber2222

lm no poqSrsU tuvo lm nw pwqSrsU tuvw 1 Lighting 0.2 CCR 1 Lighting 0.15 CCR

2 Refrigerator 0.3 CCR 2 Refrigerator 0.35 CCR

3 Washing Machine 1.2 CCR 3 Microwave 0.8 CCR

4 Dishwasher 0.8 CCR 4 Boiler 0.8 ACR

5 Boiler 0.8 ACR 5 Electric Kettle

0.9 ACR

6 Electric Kettle 1.5 ACR 6 Radiator 0.4 UCR

7 Under-floor

Heating 0.4 UCR

8 Mini Bar 0.1 UCR

9 Toaster 0.8 UCR

LAN

Power Line

ECC1 ECC2

Limited Energy Source

4.5kW

Subscriber1 Subscriber2

51

5.3 Simulation Results

5.3.1 Consumer Characterization

According to our method, the characterization of the consumer’s preferences will be by

marginal utility function 4 (1� and utility function � (1� as described in section 4.6.

As shown in Figure 14, subscriber1 needs more energy that subscriber2, and especially

for the first QOS level, CCR.

Subscriber1’s Marginal Utility Function Subscriber2’s Marginal Utility Function

Subscriber1’s Utility Function Subscriber2’s Utility Function

Figure Figure Figure Figure 14141414 – Customer CharacterizationCustomer CharacterizationCustomer CharacterizationCustomer Characterization

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

Marginal Utility Function

x

v(x)

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

Marginal Utility Function

x

v(x)

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

Utility Function

x

u(x)

0 0.2 0.4 0.6 0.8 1 1.20

0.2

0.4

0.6

0.8

1

Utility Function

x

u(x)

CCRCCRCCRCCR

AAAACRCRCRCR

UUUUCRCRCRCR

CCRCCRCCRCCR

AAAACRCRCRCR

UUUUCRCRCRCR

52

5.3.2 Fair Division Allocation

At the next step of the simulation, we operate the three different algorithms for fair

division that mentioned in section 4.7. In Table 3 we collect the results of each allocation

method. As describe in section 2.5.4, the relevant criteria for homogeneous resource

allocation are: Proportional Division, Equitable Division and Utilitarian Division. In this

simulation we use three of them in order to demonstrate the differences.

Table Table Table Table 3333 – Allocation ResultsAllocation ResultsAllocation ResultsAllocation Results

CriterionCriterionCriterionCriterion SubscriberSubscriberSubscriberSubscriber1111 SubscriberSubscriberSubscriberSubscriber2222 TotalTotalTotalTotal

AllocationAllocationAllocationAllocation UtilityUtilityUtilityUtility AllocationAllocationAllocationAllocation UtilityUtilityUtilityUtility AllocationAllocationAllocationAllocation UtilityUtilityUtilityUtility

ProportionalProportionalProportionalProportional 0.657

(2957W) 0.634

0.343

(1543W) 0.322

1

(4500W) 0.956

EquitableEquitableEquitableEquitable 0.4469

(2011W) 0.4469

0.5531

(2489W) 0.4469

1

(4500W) 0.8938

UtilitarianUtilitarianUtilitarianUtilitarian 0.71

(3195W) 0.67

0.29

(1305W) 0.29

1

(4500W) 0.956

As appear from the table, in this case, the proportional criterion and the utilitarian

criterion give similar results. Both criteria allocated more energy to subscriber1 rather than

subscriber2. On the other hand, the use of the equitable criterion, allocates more energy

actually to subscriber2 counterintuitive. The reason for that is that the Equitable criterion

in a social criterion which its goal to equalize utilities. This means that the least significant

subscriber will get more energy allocation than the other. This result indicates that this

criterion is not suitable for most applications described in this work.

53

5.3.3 Energy Consumption Control Loop

General 5.3.3.1

In this section we describe the control loop operation for each of the three allocation

result presented in Table 3. In order to do that, we assumed a consumption profile for each

of the appliances mentioned above. At section 5.3.3.2 we use the proportional allocation

results, at section 5.3.3.3 we use the equitable allocation results and at section 5.3.3.4 we

use the utilitarian allocation results.

In each example we first show the total consumption graph of each subscriber with and

without the algorithm. It can clearly see that the expected theoretical consumption graph

exceeds the ability of the source to provide power. Of course, in the case of standard

system, the circuit protection breaker was operating and disconnects the feed. Later we

show graphs for each appliance which describe the consumption demand and the actually

consumption.

In the total consumption graphs, the blue color represent the CCR appliances, the

green color represent the ACR appliances and the light blue represent the UCR appliances.

Also, the red line represents the allocation level of the subscriber according to the results

of the previous section. The magenta line represents the available capacity in the system

form to point of view of each subscriber.

In the appliances consumption graphs, the red color represent the energy demand

profile and the green color the actually operation profile.

We now explain the behavior of the system on some important points. The goal of this

simulation is to describe the asynchronous principle of the real-time control loop.

54

Example 1 – Consumption Graphs for the Proportional Division case 5.3.3.2

Figure Figure Figure Figure 15151515 – Consumption GraphConsumption GraphConsumption GraphConsumption Graph for the for the for the for the Proportional DivisionProportional DivisionProportional DivisionProportional Division casecasecasecase withwithwithwith algorithmalgorithmalgorithmalgorithm

Figure Figure Figure Figure 16161616 – Consumption GraphConsumption GraphConsumption GraphConsumption Graph for the for the for the for the Proportional DivisionProportional DivisionProportional DivisionProportional Division casecasecasecase withoutwithoutwithoutwithout algorithmalgorithmalgorithmalgorithm

CCR

ACR

UCR

Allocation

Available

2957W

1543W

4500W

2957W

1543W

4500W

1111 2222

3333

4444

55

Figure Figure Figure Figure 17171717 – SubscriberSubscriberSubscriberSubscriber1111’s Appliances’s Appliances’s Appliances’s Appliances

Figure Figure Figure Figure 18181818 – SubscriberSubscriberSubscriberSubscriber2222’s Appliances’s Appliances’s Appliances’s Appliances

Demand

Operation

CC

RC

CR

CC

RC

CR

A

CR

AC

RA

CR

AC

R

UU UUCC CC

RR RR

Lighting

Refrigerator

Washing machine

Dishwasher

Boiler

Kettle

Floor Heating

Mini Bar

Toaster

CC

RC

CR

CC

RC

CR

A

CR

AC

RA

CR

AC

R

UU UUCC CC

RR RR

Lighting

Refrigerator

Microwave

Boiler

Kettle

Radiator

56

In this example, subscriber 1 gets more energy allocation than subscriber 2 according to

their needs. As seen in the graphs, the controller manages the appliances operation in a

way that maximizes the utilization of the energy allocation of the subscriber. Moreover,

the controller enables to operate UCR appliances on account of free energy of the other

subscriber. The total overall consumption is obtained in the limits of the shared resource.

As seen in Figure 15, at and there are two gaps in the CCR consumption

profile. These gaps were used to operate two appliances of the ACR level. As seen in

Figure 17, the first time interval was used to operate the kettle after small delay, and the

second interval was used to operate the boiler without delay.

The marked points and demonstrate a situation where each subscriber use free

capacity of the other subscriber. This is another way to maximize the utilization of the

shared resource.

The marked point represents a moment that the total demand exceeds the ability of

the source to provide energy while the system operates without the control loop algorithm.

Figure 17 and Figure 18 demonstrate the operation of each appliance. As seen in the

figures, CCR devices are working on demand. ACR devices are working immediately on

demand or after delay to a moment with available energy. UCR devices are working

according to surplus energy and they can be shut down any time. Nevertheless, only the

UCR devices allow operating according to free energy capacity of the other subscriber.

These results are very similar to the results of the third example and therefore we won’t

explain the third example separately.

1111 2222

2222 3333

4444

57

Example 2 – Consumption Graphs for the Equitable Division case 5.3.3.3

Figure Figure Figure Figure 19191919 – Consumption GraphConsumption GraphConsumption GraphConsumption Graph for the for the for the for the Equitable DivisionEquitable DivisionEquitable DivisionEquitable Division casecasecasecase withwithwithwith algorithmalgorithmalgorithmalgorithm

Figure Figure Figure Figure 20202020 – Consumption GraphConsumption GraphConsumption GraphConsumption Graph for the for the for the for the Equitable DivisionEquitable DivisionEquitable DivisionEquitable Division casecasecasecase withoutwithoutwithoutwithout algorithmalgorithmalgorithmalgorithm

CCR

ACR

UCR

Allocation

Available

2011W

2489W

4500W

2011W

2489W

4500W

58

Figure Figure Figure Figure 21212121 – SubscriberSubscriberSubscriberSubscriber1111’s Appliances’s Appliances’s Appliances’s Appliances

Figure Figure Figure Figure 22222222 – SubscriberSubscriberSubscriberSubscriber2222’s Appliances’s Appliances’s Appliances’s Appliances

Demand

Operation

CC

RC

CR

CC

RC

CR

A

CR

AC

RA

CR

AC

R

UU UUCC CC

RR RR

Lighting

Refrigerator

Washing machine

Dishwasher

Boiler

Kettle

Floor Heating

Mini Bar

Toaster

CC

RC

CR

CC

RC

CR

A

CR

AC

RA

CR

AC

R

UU UUCC CC

RR RR

Lighting

Refrigerator

Microwave

Boiler

Kettle

Radiator

59

In this case, subscriber 1 didn’t get enough energy because of the equitable division

principle. As seen in the graphs, the subscriber utilized almost all his allocation and still

couldn’t apply the first QOS level. Actually, subscriber 1 operates his devices mainly with

free capacity of the other subscriber.

As seen in Figure 21, the dishwasher, which is a CCR device, was temporary shout

down. Of course this is unacceptable situation which emphasize that the equitable criterion

doesn’t fit our needs.

On the other hand, the second subscriber, which got extra capacity allocation, could

operate all his devices without any problems.

60

Example 3 – Consumption Graphs for the Utilitarian Division case 5.3.3.4

Figure Figure Figure Figure 23232323 – Consumption GraphConsumption GraphConsumption GraphConsumption Graph for the for the for the for the Utilitarian DivisionUtilitarian DivisionUtilitarian DivisionUtilitarian Division casecasecasecase withwithwithwith algorithmalgorithmalgorithmalgorithm

Figure Figure Figure Figure 24242424 – Consumption GraphConsumption GraphConsumption GraphConsumption Graph for the for the for the for the Utilitarian DivisionUtilitarian DivisionUtilitarian DivisionUtilitarian Division casecasecasecase withoutwithoutwithoutwithout algorithmalgorithmalgorithmalgorithm

CCR

ACR

UCR

Allocation

Available

3195W

1305W

4500W

3195W

1305W

4500W

61

Figure Figure Figure Figure 25252525 – SubscriberSubscriberSubscriberSubscriber1111’s Appliances’s Appliances’s Appliances’s Appliances

Figure Figure Figure Figure 26262626 – SubscriberSubscriberSubscriberSubscriber2222’s Appliances’s Appliances’s Appliances’s Appliances

Demand

Operation

CC

RC

CR

CC

RC

CR

A

CR

AC

RA

CR

AC

R

UU UUCC CC

RR RR

Lighting

Refrigerator

Washing machine

Dishwasher

Boiler

Kettle

Floor Heating

Mini Bar

Toaster

CC

RC

CR

CC

RC

CR

A

CR

AC

RA

CR

AC

R

UU UUCC CC

RR RR

Lighting

Refrigerator

Microwave

Boiler

Kettle

Radiator

62

5.4 Interpretation of the results

5.4.1 Consumer Characterization

In this example we show the simplicity of the consumer characterization according to

our method. This process includes appliances mapping and feature description for each.

Next we construct the marginal utility function 4 (1� and the utility function � (1� of the

subscriber. Recall that, this method relies on the assumption that the subscriber truly

describes his needs due to the pricing profile of the service. As we have seen, we didn’t

need to calibrate complex function’s parameter in the characterization process.

5.4.2 Fair division

Simulation results show that the most relevant criteria for fair energy allocation in

electrical system are the proportional criterion and the utilitarian criterion. The

proportional criterion can be good for cases which the characterization of each subscriber is

heterogeneous and there are few subscribers.

On the other hand, in cases where there are many subscribers with similar utility

function, that criterion would not fit. That because each subscriber will get very little

amount of energy allocation which he could do anything with it. In this case, utilitarian

criterion will be more suitable. That because the algorithm will allocate as much energy as

it can for each QOS level for each subscriber. Of course, there can be situations that some

subscriber will get no allocation at all.

The conclusion is that we should select to most appropriate criterion for each case and

not rely on the same one all the time.

63

5.4.3 Energy Consumption Control Loop

Simulation results demonstrate the principles of our method called Asynchronous

Consumption Mode. According to this method we allocate energy for each subscriber in

asynchronous way. That means the allocation is made according to the needs of each

appliances and its QOS level. The main goal of the control loop is to maximize the

utilization of each allocation by manage the operation time of the appliances. For example,

instead of preventing service for appliance because there is not available capacity

temporally, we remember the demand in the controller memory and operate the appliance

when it’s possible. Moreover, we are using available capacity of the other subscriber to

operate low level QOS appliances.

5.5 Conclusions

In this chapter we demonstrate the performances of our system model framework. We

show the use of the consumer characterization method, the fair division allocation and the

real time control loop. We show a dynamic simulation to demonstrate three different cases

and we focused on few interesting points on the graphs.

64

6 Summary

6.1 Conclusions

In this thesis we study the field of smart grid and the application of game theory in

demand-side management problems. According to the fundamental problem we tried to

solve, we define the main thesis objectives: Study how to implement relevant game theory

tools for demand-side management and propose a control system model that uses these

principles to solve the fundamental problem. The thesis objectives were redefined after the

literature survey which leads to define the control system goals.

According to these goals, we proposed a system model framework contain three main

components: consumer characterization method, fair division allocation and an energy

consumption controller. The model framework was based on a new method that we

present, called Asynchronous Consumption Mode.

Simulation results demonstrate how our model framework satisfies the fundamental

problem and the thesis objectives. This study showed that the general smart grid and

demand management sector in particular, present complex problems that require

considerable investment in research and development. Game theory in this case can be a

powerful tool to design mechanisms that maximize consumer’s and provider’s benefit.

6.2 Thesis Presentations

This work was presented several times. Once during a seminar held in the Department

of Electrical and Computer Engineering at Ben-Gurion University [49]. Once more, in front

of the IEC smart grid leaders headed by Mr. Emil Koifman [50]. And last time at the

Annual Convention of the Society of Electrical and Electronics Engineers in Israel [51].

65

6.3 Thesis Contributions

• This thesis was the basis for the first research that combines smart grid issues

with game theory principles in the Electrical and Computer Engineering

department in Ben-Gurion University. During this research we open a window

for understanding the ability to use game theory tools to solve electrical

engineer problems.

• We proposed a novel method that we called Asynchronous Consumption Mode

(ACM) as a framework for management an electrical network.

• We proposed a method for characterize the consumer preferences in a practical,

simple and intuitive fashion. One of the innovations in this method is that we

characterize each appliance separately and not just the total demand.

• We first use the fair division method in order to make a fair allocation of the

shared resource. We showed that it is possible to use several criteria which give

some interesting results.

• We emphasize the need for well-designed price profile in order to motivate the

subscriber to use the service and to be true about his needs.

• We proposed a closed loop system model that manages the user appliances

operation in order to maximize the utilization of his allocation.

66

6.4 Future Directions

• Demand-side management is a very wide field of research. There are still many

open issues that need to be solved in order to make smart grid come true. One

future direction can be to deal with different fundamental problems. This

research showed that every tiny change in the problem definition can cause a

huge change in the solution direction especially when it comes to game theory.

• Those interested in game theory can continue to explore additional tools and

criteria for demand-side management in smart grid. The amount of abilities that

game theory makes available to the researcher is almost limitless.

• Each of the main components in our system model framework can be extended

by additional research and development. For example, by providing response to

changes in requirements over the hours of the day and days of the year.

• A major future direction can be by research method for designing smart price

profiles as a core mechanism in the system. This price profile can be managed in

real time fashion. An interesting case to explore can be by using a progressive

price which means that subscriber that demand more electricity will absorb

more the price changes.

67

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