Heuristic Algorithm based Home Energy Management ...

Heuristic Algorithm based Home Energy Management System in Smart Grid

By

Sardar Mudassar Naseem CIIT/SP15-REE-053/ISB MS Thesis In Electrical Engineering

COMSATS Institute of Information Technology Islamabad – Pakistan Fall, 2016

Heuristic Algorithm based Home Energy Management System in Smart Grid A Thesis Presented to

COMSATS Institute of Information Technology, Islamabad

In partial fulfillment of the requirement for the degree of

MS (Electrical Engineering) By

Sardar Mudassar Naseem CIIT/SP15-REE-053/ISB

Fall, 2016

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A Graduate Thesis submitted to Department of Electrical Engineering as partial fulfillment of the requirement for the award of Degree of M.S (Electrical Engineering).

Name

Registration Number

Sardar Mudassar Naseem

CIIT/SP15-REE-053/ISB

Supervisor Dr. Shahid A. Khan, Professor, Department of Electrical Engineering, COMSATS Institute of Information Technology (CIIT), Islamabad Campus. November 2016

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Final Approval This thesis titled

Heuristic Algorithm based Home Energy Management System in Smart Grid By

Sardar Mudassar Naseem CIIT/SP15-REE-053/ISB has been approved For the COMSATS Institute of Information Technology, Islamabad

External Examiner: ___________________________________ Dr. Muhammad Sher Professor, Department of Computer Science, IIU, Islamabad

Co-Supervisor: _________________________________________ Dr. Nadeem Javaid Associate Professor, Department of Computer Science, Islamabad

Supervisor: ______________________________________ Dr. Shahid A. Khan Professor, Department of Electrical Engineering, Islamabad

HoD: ______________________________________________ Dr. M. Junaid Mughal Professor, Department of Electrical Engineering, Islamabad

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Declaration I Mr. Sardar Mudassar Naseem, CIIT/SP15-REE-053/ISB, hereby declare that I have produced the work presented in this thesis, during the scheduled period of study. I also declare that I have not taken any material from any source except referred to wherever due that amount of plagiarism is within acceptable range. If a violation of HEC rules on research has occurred in this thesis, I shall be liable to punishable action under the plagiarism rules of the HEC.

Date: ____________________________ Signature of the student:

_________________________ Sardar Mudassar Naseem CIIT/SP15-REE-053/ISB

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Certificate It is certified that Sardar Mudassar Naseem CIIT/SP15-REE-053/ISB has carried out all the work related to this thesis under my supervision at the Department of Electrical Engineering, COMSATS Institute of Information Technology, Islamabad and the work fulfills the requirements for the award of the MS degree.

Date: ____________________________ Supervisor:

____________________________ Dr. Shahid A. Khan Professor, Department of Electrical Engineering,

Islamabad Co- Supervisor:

____________________________ Dr. Nadeem Javaid Associate Professor, Department of Computer Science,

Islamabad Head/Chairperson:

____________________________ Dr. M. Junaid Mughal

Professor, Department of Electrical Engineering.

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DEDICATION This thesis is dedicated to my teachers, my family and my friends.

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ACKNOWLEDGMENT I am heartily grateful to my supervisor, Dr. Shahid A. Khan and co-supervisor Dr. Nadeem Javaid who not only guided me but also motivated me via insightful criticism from the beginning to the final level that enabled me to complete this thesis. I would like to acknowledge my family, my friends, and the cooperative COMSENCE lab attendants. They all kept me motivated and energetic, and this work have not been possible without them. Finally, I offer my regard and blessing to everyone who supported me in any regard during the completion of my thesis.

Sardar Mudassar Naseem CIIT/SP15-REE-053/ISB

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ABSTRACT


Recently, Home Energy Management (HEM) controllers have been widely used for residential load management in a smart grid. Generally, residential load management aims at reducing the electricity bills and curtailing the Peak-to-Average Ratio (PAR). In this thesis, we design a HEM controller on the bases of four heuristic algorithms: Bacterial Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA), Binary Particle Swarm Optimization (BPSO), and Wind Driven Optimization (WDO). Moreover, we proposed the hybrid algorithm which is Genetic BPSO (GBPSO). All the selected algorithms are tested with the consideration of essential home appliances in Real Time Pricing (RTP) environment. Simulation results show that each algorithm in the HEM controller reduces the electricity cost and curtails the PAR. GA based HEM controller performs relatively better in term of PAR reduction; it curtails approximately 34% PAR. Similarly, BPSO based HEM controller performs relatively better in term of cost reduction it reduces approximately 36% cost. Moreover, GBPSO based HEM controller performs better than the other algorithms based HEM controllers in terms of both cost reduction and PAR curtailment.

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TABLE OF CONTENTS

1 Introduction 1.1 The Smart Grid . . . . . . . . . . . . . . . . . . . . . . . . .

1 2

2 Related Work 2.0.1 Mathematical modeling based optimization . . . . . . 2.0.2 Heuristic based scheduling . . . . . . . . . . . . . . .

5 6 8

3 System Model 3.0.1 HEM System . . . . . . . . . . . . . . . . . . 3.0.2 Load Categorization: . . . . . . . . . . . . . . 3.0.2.1 Shiftable Interruptible Appliances . . 3.0.2.2 Shiftable Un-interruptible Appliances 3.0.2.3 Regular Appliances . . . . . . . . . 3.0.3 Energy Cost and Unit Price . . . . . . . . . . 4 Problem Formulation and Proposed 4.0.1 Problem Formulation . . . . 4.0.2 Heuristic Algorithms . . . . 4.0.2.1 BFOA . . . . . . . 4.0.2.2 GA . . . . . . . . 4.0.2.3 BPSO . . . . . . . 4.0.2.4 WDO . . . . . . . 4.0.2.5 GBPSO . . . . . . 4.0.3 Feasible Region . . . . . . . 4.0.3.1 Single Home . . . 4.0.3.2 Ten Homes . . . . 4.0.3.3 Fifty Homes . . . .

Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Simulation and Discussion 44 5.0.1 Scenario 1: Single home . . . . . . . . . . . . . . . . 46 5.0.2 Scenario 2: Ten homes . . . . . . . . . . . . . . . . . 48 5.0.3 Scenario 3: Fifty homes . . . . . . . . . . . . . . . . 52 x

6 Conclusion 62 6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7 References

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LIST OF FIGURES

1.1

Abstract view of smart grid model . . . . . . . . . . . . . . .

3.1

HEMS Architecture . . . . . . . . . . . . . . . . . . . . . . . 17

4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8

Flow chart of BFOA . . . . Flow chart of GA . . . . . . Flow chart of BPSO . . . . Flow chart of WDO . . . . . Flow chart of GBPSO . . . Feasible region: Single home Feasible region: Ten homes . Feasible region: Fifty homes

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5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 5.11 5.12 5.13

RTP signal . . . . . . . . . . . . Load profile: Scenario 1 . . . . . Cost per day profile: Scenario 1 . Cost per hour profile: Scenario 1 PAR: Scenario 1 . . . . . . . . . . Load profile: Scenario 2 . . . . . Cost per day profile: Scenario 2 . Cost per hour profile: Scenario 2 PAR: Scenario 2 . . . . . . . . . . Load profile: Scenario 3 . . . . . Cost per day profile: Scenario 3 . Cost per hour profile: Scenario 3 PAR: Scenario 3 . . . . . . . . . .

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LIST OF TABLES

2.1 2.1 2.2 2.2

Mathematical modeling based optimization Continue Table 2.1 . . . . . . . . . . . . . Heuristic based scheduling . . . . . . . . . Continue Table 2.2 . . . . . . . . . . . . .

3.1 3.2

Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Description of appliances . . . . . . . . . . . . . . . . . . . 19

4.1 4.2 4.3 4.4 4.5 4.6 4.7

Parameters of BFOA . . . . Parameters of GA . . . . . . Parameters of BPSO . . . . Parameters of WDO . . . . Possible cases: Single home Possible cases: Ten homes . Possible cases: Fifty homes .

5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

Comparison Comparison Comparison Comparison Comparison Comparison Comparison Comparison

of of of of of of of of

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cost: Scenario 1 . . . . PAR: Scenario 1 . . . . cost: Scenario 2 . . . . PAR: Scenario 2 . . . . cost: Scenario 3 . . . . PAR: Scenario 3 . . . . percentage decrement in percentage decrement in

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Chapter 1 Introduction

1

1.1

The Smart Grid

The ever increasing energy demand has created problems like a blackout, load shedding, voltage instability, frequency drop, etc. As a solution, two approaches are nowadays in practice: (i) increasing the generation capacity, and (ii) managing the load according to existing power generation capacity through Home Energy Management (HEM) system [1]. The earlier approach majorly depends on the installation of new power generation substations. In the later approach, Demand Side Management (DSM) programs are utilized which aim to manage the load according to existing generation capacity through scheduling techniques. In fact, the scheduling techniques are optimization algorithms for managing the load between ONpeak hours and OFF-peak hours while taking into account user and utility requirements. Substantial research efforts have been made to investigate the scheduling problem in the residential sector (refer to Fig. 1.1 for a pictorial view of the residential area based smart grid). For example, the authors in [2] use Mixed Integer Linear Programming (MILP) to schedule residential appliances, Photovoltaic (PV) system, storage system, lighting system, and heating and air conditioning system. Case study results show a reduction in cost and PAR, however, system complexity is increased. In [3], Mixed Integer Non-Linear Programming (MINLP) is used to schedule appliances belonging to multiple classes. Similarly, in [4, 5] MILP and MINLP are used for appliance scheduling to reduce the electricity cost. In [6], Bacterial Foraging Optimization Algorithm (BFOA) is implemented for resource scheduling problem in grid computing aiming at electricity cost minimization. MINLP and Genetic Algorithm (GA) are used in [7] for controlling home appliances. The authors in [8] use GA for scheduling in residential appliances subject to electricity cost reduction. In [9], Binary Particle Swarm Optimization (BPSO) is used for scheduling interruptible load. Their simulation results verify the effectiveness of BPSO in terms of electricity bill reduction and energy profile stability. Similarly, [10] studied load shifting techniques in HEM system by using Particle Swarm Optimization (PSO). Cost and energy minimization were the objectives of this study. A comparative study of PSO and Wind Driven Optimization (WDO) is conducted in [11] to solve the problem of residential load management. The simulation results show that the performance of WDO is better than PSO in terms of user comfort and electricity cost reduction. The mathematical techniques like MILP and MINLP are quite beneficial but at the cost of high computational complexity [2, 7]. On the other hand, heuristic algorithms (e.g., GA, BPSO, and BFOA) are flexible for specified 2

Figure 1.1: Abstract view of smart grid model

constraints, easy in terms of implementation and have low computational complexity [12]. In this thesis, we use four heuristic algorithms; BFOA, GA, BPSO, and WDO to solve the load scheduling problem. We choose these algorithms due to their self-organization, self-optimization, self-protection, self-healing and decentralized control system [12]. These algorithms are tested with the simulative consideration of a HEM system in Real Time Pricing (RTP) environment. Simulation results show that each algorithm is capable of reducing cost and PAR in comparison to the unscheduled load, however, there is a trade-off between cost and PAR in each scheme. We proposed Genetic BPSO (GBPSO). This hybrid technique incorporates the functionalities of GA and BPSO to create new individuals. In our proposed scheme, we modified the method of updating position by using genetic operators (crossover and mutation) to further improve the performance of BPSO. We follow all steps of BPSO to achieve better position vector, then it is updated by applying crossover and mutation process to further improve the results. Simulation results show that GBPSO outperforms other heuristic algorithms in terms of cost and PAR. The rest of the thesis is organized as follows. Chapter 2 presents Related work. System Model is presented chapter 3. Problem formulation and pro-

3

posed solution are presented in chapter 4. Simulation results are discussed Chapter 5. Chapter 6 concludes the thesis. Finally, references are provided at the end of the thesis.

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Chapter 2 Related Work

5

In the literature, many DSM based load scheduling techniques are presented to reduce the electricity bill and PAR. HEM system is an important feature in residential scheduling. For the development of HEM system, a substantial work has been done. For example, authors in [13], present a brief survey of the design and essential functions of HEM system. They discuss configuration and implementation challenges, like the method of integrating renewable energy sources with the existing system in HEM environment. Moreover, an overview of existing literature regarding residential appliance scheduling is also discussed. Similarly, a detailed literature survey on residential energy management system is presented in [14]. The main objectives of this study are to focus on modelling approaches and their effects on the development of HEM system. The authors also discuss the challenges, like load forecasting limitations, heterogeneity of residential appliances, computational complexity, etc., in the implementation of HEM system. Moreover, they give an intuition of scheduling techniques like mathematical, meta-heuristic and heuristic algorithms. [13, 14] mention several problems in HEM system. To solve such problems, many mathematical and heuristic algorithms are presented. Some of the latest techniques are discussed below. 2.0.1

Mathematical modeling based optimization

The smart charging mechanism in [15] enhances the efficiency of energy storage systems and scheduling approaches in DSM under RTP scheme. An aggregator is introduced which optimally schedules the appliances and battery charging based on Day Ahead Pricing (DAP) scheme. The objectives of this study are to benefit consumers in term of cost reduction and comfort maximization. To solve optimization problem Linear Programming (LP) has been used. The results show that with appropriate scheduling of storage devices and carefully designed RTP, customers can apprehend significant saving on their electricity bills. Authors in [16], proposed Integer Linear Programming (ILP) based HEM system. Cost minimization and peak reduction are the main objectives of this work along with the integration of PV system. To achieve better control of peak load, 24 hours are divided into 96 time slots. Simulation results show, by integrating PV and division of time slots, an effective reduction in cost and peak load is achieved. However, system complexity is increased. In [17], authors investigate the scheduling problem of residential appliances under RTP scheme. This paper proposes an effective home automation system to minimize the trade-off between electricity bill and user satisfaction. They 6

also consider seasonal price variations and study their effects on cost and solve the optimization problem by using MINLP. Authors in [18], proposed a general and comprehensive optimization based Automated Demand Response (ADR). They schedule the operation of several classes of domestic appliances (deferrable, non-deferrable, thermal, curtailable and critical) to minimize energy cost and maximize user comfort. In this paper, MINLP is implemented in Advanced Integrated Multidimensional Modeling (AIMM) software to solve the mathematical models. Case studies are conducted to show the effectiveness of the proposed controller, results show a prominent reduction in electricity bill while maintaining comfort level. Authors in [19] present a novel cost efficient framework for scheduling of residential load. This cost-effective algorithm is developed by using Fractional Programming (FP) tools. Distributed Energy Resources (DREs) are included in their framework to enhance the cost efficiency. In [20], Heating, Ventilating, and Air-Conditioning (HVAC) system is presented in HEM environment. HVAC model has been proposed for scheduling in HEM system while considering user preferences (cost) and properties of HVAC. MINLP model is used to formulate the problem. Moreover, a prototype software is developed on the basis of the proposed model. Numerical results show a reduction in cost, however, PAR is not considered. Authors in [21], present a new algorithm for a HEM system for managing high power residential appliances. Proper mathematical model of each high energy consumption appliance is presented. Moreover, a simulator and user interface is developed in c++. This model is based on MILP and a heuristic algorithm. The objectives of this work are to minimize energy consumption while keeping user comfort maximum. Different case studies are conducted to prove the effectiveness of the proposed algorithm. Results show that proposed scheme keeps the load below the pre-defined level and power consumption is controlled while keeping user comfort maximum, however, the cost is not discussed. A novel scheduling model of residential appliances is proposed in [22]. In this work, the Energy Box (eBox) software architecture is presented which acts as a communicator between utility and consumer. Authors model MILP and heuristic based eBox. Simulation results show that heuristic based eBox performs better in terms of consumption time and quality. However, PAR is not considered, also system complexity is increased. Demand side scheduling scheme has been proposed in [23]. The PAR constrained mathematical model is presented to reduce cost and PAR. Authors classify residential appliances in two categories, shift-able and throttle-able appliances. To solve cost model, the centralized and distributed algorithms are presented which are solved without consumers’ preferences and with consumers’ preferences. 7

Simulation results show the effectiveness of proposed algorithms. However, system complexity is increased. In [24], the authors discuss the power demand control scenarios to reduce peak demand. These are default scenario, finite delay request scenario, finite postpone request scenario and finite compressed demand scenario. Recursive formulas are modeled for calculation of peak demand under each scenario. In their modeling, they consider a finite number of appliances. They associate four different power demand control scenarios with RTP scheme to derive a social welfare model for reducing cost and peak demand. The results of the proposed model show an efficient reduction in the peak demand for a finite number of devices. Simulation results show that by including DERs, a prominent cost reduction are achieved. However, computational time and system complexity is increased. Table 2.1 shows a summary of mathematical model based optimization algorithms. 2.0.2

Heuristic based scheduling

An improved model of DSM is presented in [25]. Day ahead load shifting technique for three service areas (residential, commercial and industrial) is modelled. The objective of this study is to reduce cost and minimize energy consumption. A heuristic based Evolutionary Algorithm (EA) has been used to solve scheduling problem with a large number of appliances. According to this technique, the DSM system receives an objective curve from utility and then schedules the load close to the input objective curve. A case study is conducted in three service areas to prove the effectiveness of proposed algorithm. Simulation results show that proposed DSM technique can manage a large number of appliances and efficiently reduces cost and PAR. However, cost saving in the residential sector is less than other sectors. Sergio et al. [26], formulate a constrained based multi-objective optimization problem. The objectives of this study are to minimize energy consumption and maximize a utility function. Two EA based algorithms are proposed to efficiently achieve the required objectives. However, electricity cost is not considered. Theoretical analysis of BFOA is presented in [27]. This paper explains the following: 1) basic theory of BFOA and its parameters, 2) working steps of BFOA (chemotaxis, swimming, reproduction and elimination-dispersal), 3) mathematical formulation and 4) flowchart and algorithm of BFOA. This paper provides only a theoretical foundation of BFOA, scheduling application is not studied. Authors in [28], present a brief analysis of BFOA. Comparative study of BFOA is conducted with other optimization algo8

rithms in term of scheduling, however, no simulations are conducted to validate the results. In [6], BFOA is implemented for resource scheduling problem in grid computing. A comparative study of BFOA with the existing heuristics based scheduling algorithms has been studied through the GridSim toolkit. The experimental result shows, BFOA performs better in terms of cost when compared with existing algorithms. Improved version of BFOA (IBFOA) is suggested in [29], in which elimination-dispersal and chemotaxis steps are improved, which increased convergence rate and accuracy. Implementation method of GA on residential load by using Supervisory Control And Data Acquisition (SCADA) is proposed in [7]. This paper compares the results of GA scheduled load with MINLP scheduled load under three different scenarios while considering power limits. Intelligent Energy Systems Laboratory (LASIE) is used for a case study. LASIE consists of a SCADA system, renewable energy sources (PV, wind turbine, and a fuel cell) and variable loads for testing. Authors conducted a case study to validate their scheme on three different type of loads. Results shows that GA has fast convergence rate and improved scheduling profile than MINLP. In [31], the problem of residential load scheduling is studied under DSM. The main objective of this study is to determine the optimal energy consumption to minimize electricity cost. MATLAB simulations of this study show that a prominent cost reduction is achieved. GA is implemented in [32], for solving energy optimization problem of a small-scale smart house having hybrid energy (PV and utility) sources. Authors suggest hardware based future work in which controller will be built by using GA. Authors in [33], present a model of optimal integration of Distributed Energy Storage System (DESS) in term of optimal sizing and location. A new method of integration of DESSs and capacitors with the smart grid is proposed to reduce reactive power and cost of a power system. Authors conducted a case study in which four different cases of integration of DESS are investigated. A hybrid technique in which GA is combined with Sequential Quadratic Programming (SQP) is used to achieve the objectives. Results of case studies show, by reducing reactive power and optimal charging of energy storage resources, cost minimization and peak clipping is achieved. Power scheduling technique is proposed in [8]. In this paper RTP signal is combined with Inclined Block Rate (IBR) and each hour is divided into five slots, in this way each day has 120-time slots and each slot consists of 12-minutes. This timing scheme gives more flexible way to manage power and cost of the user, but increases the complexity and burden of the system. Simulation results show a reduction in electrical power consumption, PAR and cost. Authors in [34], formulate a GA based optimization problem 9

in smart home environment to reduce cost. This model is compared with other greedy search algorithms. Results show an efficient performance of GA based system in term of cost reduction. However, PAR is not considered. The basic concept, variants, and applications of PSO in the power system are presented in [35]. In this work a detailed theoretical and mathematical modeling of PSO implementation is presented, then different variants of PSO are discussed with their respective mathematical models. Variants that are discussed in this paper are PSO-GA, hybridization of Evolutionary Programming and PSO (EPSO), Multi-Objective PSO (MOPSO), Adaptive PSO, Dynamic Neighborhood PSO (DN-PSO), Vector Evaluated PSO (VEPSO), Gaussian PSO (GPSO). In addition, authors discussed the various applications of PSO in power system based optimization problems. Authors in [9] present the scheduling of interruptible appliances over a 16 hour time period. The objective of this study is to minimize the number of interruptions and minimize the bill payments. BPSO is used for scheduling of 29 interruptible appliances, which are divided into two curtailments i.e. curtailment A and curtailment B. Both of them are scheduled according to required objectives. In [37], realistic scheduling model for HEM system is presented. The objectives of this study are to minimize cost and user frustration. To achieve both objectives, 24 hour time slot is divided into four logical sub-slots which increase the flexibility of control on load. Dynamic thresholds are defined for each sub-slot. BPSO is used to solve the optimization problem. Results show an efficient performance of proposed system. The problem of managing energy resources by using PSO-Mutation (PSO-MUT) is studied in [36]. Mathematical formulation of an objective function is presented in which energy resources like PV system, Wind and Combine Heat and Power (CHP) plant are included. Network constraints of the power system are also considered in a formulation. The case study is conducted to apply the proposed methodology. A 30 kV distribution network, supplied by substation of 60/30 kV, distributed by 6 feeders, with 937 buses and 464 MV/LV transformers are used in this study. Results of PSO-MUT shows best average results with a slightly high delay than PSO. Authors in [39], propose a variant of PSO, which is an Application Specific Modified PSO (ASMPSO). This variant of PSO is used to solve energy resource management problem associated with high penetration of distributed generation and Electric Vehicles (EVs). This algorithm includes a self-optimization technique which updates velocity and position by self-optimization which makes PSO more robust and efficient. Two case studies are conducted with 1000 and 2000 EV, ASMPSO is compared with MINLP, results show that ASMPSO is 2600 times faster than MINLP. In 10

[38], a comparative study of GA and PSO in terms of quality of solution and efficiency is conducted. Algorithms are tested for 12 different benchmark functions. Results show that quality of solution of both algorithms is 99% or more with 99% confidence interval. However, in term of efficiency PSO is better than GA. A new nature-inspired heuristic algorithm is presented in [40], which is called WDO. To implement WDO, Authors derive the equations from winds’ motion theory. A numerical study is conducted using unimodal and multi-model rest functions. Moreover, a comparative study of WDO, GA, PSO and Differential Evaluation (DE) is conducted on 3 different application of Electromagnetic problems. In [11], comparison of WDO and PSO is studied for scheduling problem. Authors investigate that performance of WDO is better than PSO in term of electric bill reduction and waiting time. Furthermore, performance of Knapsack-WDO (K-WDO) is also studied. Table 2.2 shows summary of heuristic based optimization algorithms.

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Table 2.1: Mathematical modeling based optimization

Technique

LP [15]

ILP [16]

MINLP model [17]

MINLP implemented in AIMM [18] FP [19] MINLP [20]

Objective Cost minimization and optimal charging of batteries Cost minimization and peak reduction Cost minimization Peak demand reduction and cost minimization Enhance cost efficiency Cost minimization

HEMalgorithm [21]

Maximize user comfort and minimize energy consumption

MILP and heuristic algorithm [22]

Minimized user frustration and minimize electricity bill

Features

Limitations

Proposed a method to integrate an aggregator which optimally schedules the battery charging

consider only cost reduction

Integrate PV, time slot division, achieve flexible load control

computational time increases

Consider both thermal and electrical appliances and study seasonal price variations and their effect on cost

PAR is ignored

ADR is proposed for comprehensive scheduling of residential appliances

System complexity is increased

Novel cost efficient model is proposed Effective HVAC model is proposed for HEM system Mathematical modeling of high consumption residential appliances, user interface is designed in C++ programming

PAR is not considered

Mathematical modeling, eBox solver is designed in java

PAR is ignored, system complexity increased

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Multi objectives are not considered


Table 2.1: Continue Table 2.1

Mathematical formulated algorithm [23]

Cost and PAR minimization

Mathematical recursive formulas [24]

Reducing cost and peak demand

Mathematical formulation of energy minimization problem and distributed energy schedule algorithm Mathematical formulation of four power demand scenarios and modeling of a social welfare for cost and peak energy reduction

13

System complexity increased

Consider only energy consumption reduction

Table 2.2: Heuristic based scheduling

Technique

Objective

Features

Limitations

EA [25]

Reduce cost and minimize energy consumption

Residential, commercial and industrial appliances are modelled, Case study is conducted in three service areas.

Cost reduction is not effective in residential sector

EA [26]

Minimize energy consumption and maximize utility function

Two EA based algorithms are proposed.

Cost minimization is not formulated

BFOA and hybridized BFOA [28]

Task scheduling

Hybridization of BFOA and its variants are studied

Simulations are not conducted

BFOA [6]

Minimizing cost

IBFOA [29]

Formulation of IBFOA

GA and MINLP [7]

Minimize energy consumption

GA [31]

Cost minimization

GA [32]

Minimize energy consumption and electricity cost

Comparative study of BFOA with the existing heuristics based scheduling algorithms Improved formulation of chemotactic and elimination-dispersal steps, convergence speed and accuracy is improves Case study is conducted in LASIE Laboratory by using SCADA system for 18 different loads under three different scenarios Objective function and constraints are mathematically defined Mathematical modeling of electrical, case study on real infrastructure

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PAR is ignored IBFOA is compared only by using benchmark function, no real scenarios are considered Electricity cost and PAR are ignored Limited objectives are considered i.e. cost only Only single house is considered

Table 2.2: Continue Table 2.2

Hybrid technique (GA and SQP) [33]

Minimize reactive power and cost

Integration of DESSs and capacitors is proposed to reduce cost and reactive power Mathematical formulation, time slot division is changed to control cost and PAR Novel GA optimization technique is proposed, comparison with other greedy search algorithms

GA [8]

PAR and cost minimization

System complexity is increased

GA [34]

Cost minimization

BPSO [9]

PAR and cost minimization

Mathematical formulation of objective function

Only interruptible appliance are considered

BPSO [37]

minimize cost and user frustration

PSO and PSO-MUT [36]

Energy and cost minimization

Realistic scheduling model is presented, flexible load control Mathematical formulation of objective function incorporating various energy resources, case studies are carried out to validated scheme

ASMPSO [39]

Energy resource management and cost minimization

WDO [40]

Effectiveness of WDO is Compare with other heuristic algorithms

K-WDO and PSO [11]

Electricity bill reduction and minimizing waiting time

ASMPSO, intelligently update velocity making PSO more robust Theoretical and mathematical explanation of WDO is presented, furthermore WDO is applied to solve electromagnetic problems Binary version of WDO is presented. Mathematical formulation of objective function and algorithm is presented 15

PAR and user comfort is not considered

Formulate only cost function


PAR and energy consumption are ignored

Only EVs in residential sector are considered Residential scheduling problem is not considered for comparison

Limited number of appliances are considered

Chapter 3 System Model

16

In this chapter, we describe our proposed system model, load categorization, and their mathematical formulation. Moreover, we discuss pricing signal and cost calculation methodology in our work. For nomenclature see Table 3.1. 3.0.1

HEM System

A HEM system for a smart home consists of a HEM controller, an in-home display, a set of smart appliances, and a smart meter as shown in Fig. 3.1. Smart appliances are connected (wired or wireless) to the HEM controller. The HEM controller is connected to the smart meter which receives RTP signal from the Neighbourhood Area Network (NAN). The NAN consists of Information and Communication Technology (ICT) equipment for the establishment of a link between the utility and the smart homes. The HEM controller based on RTP and DR signals, HEM controller schedules the residential appliances according to user preferences. Our modeling approach is distributive i.e. NAN connects multiple homes such that each home has its own HEM system.

Figure 3.1: HEMS Architecture

3.0.2

Load Categorization:

Let N be the total number of smart homes such that each home has a m number of appliances. For each consumer, let An = asi ∪ asni ∪ ar , represents set of appliances, where asi , asni , ar are the set of shiftable 17

Table 3.1: Nomenclature

Symbol

Description

Symbol

Description

N An τ E λ ζ Υ θ ∆ Ne Nr

m An T ρ(τ ) ε σ wi wf Fsig k kmax

Total number of appliances Set of appliances Total time peroid Pricing signal (RTP) Energy consumption Cost per hour Initial weight constant Finial weight constant Sigmoid function Current iteration Maximum number of iterations Gradient of pressure Volume Density of air parcels Friction coefficient Earth rotation Velocity of air parcel

Pc cross bits

Total number of homes Set of appliances Time interval Energy consumption Power rating of appliance Cost per day Total load demand Position of bacteria Random direction vector Number of elimination steps Number of reproduction steps Number of chemotaxis steps Number of swimming steps Number of population steps Fitness level of bacteria Step size Dimension if search space in BFOA Upper velocity limit in BPSO and WDO lower velocity limit in BPSO and WDO Probability of crossover Crossover bits

Pm

Probability of mutation

xopt

num mbits Number of mutated bits

xcur

mut row Pm vnew

Mutated row Probability of mutation Velocity in current iteration

g RT vold

xold

Position in previous iteration

w, c1, c2

Nc Ns Np ji Ci D vmax vmin

18

∆P δV ρ α ω u unew ucur popt pcur

Velocity of air parcel in new iteration Velocity of air parcel in current iteration Pressure at optimal location Pressure at current loacation Optimal location of air parcel Current location of air parcel Gravitational constant Universal gas constand Velocity in previous iteration Weight constants

interruptible appliances, shiftable uninterruptible appliances, and regular appliances respectively. These appliances are scheduled in 24 hour time horizon τ ǫ T , ∀, T = [τ1 , τ2 , ..., τ24 ]. For our scheduling problem, we consider 10 different residential appliances which are categorized into these three groups. This categorization depends on the requirement of operating time and energy consumption pattern. Appliances along with their power ratings and usage hours per day are shown in Table 3.2. Table 3.2: Description of appliances

Group

Shiftable interruptible Shiftable uninterruptible Regular appliances

3.0.2.1

Appliances

Power rating (kWh)

Daily usage (Hours)

Vacuum cleaner Water heater Water pump Dish washer Hair dryer Washing machine Cloth Dryer AC Refrigerator Oven

0.7 4 0.8 1.5 1.2 0.7 4 1.5 0.18 2

6 8 8 10 4 5 4 15 14 7

Shiftable Interruptible Appliances

These appliances can be shifted to any time slot and can be interrupted when required. These appliances include the vacuum cleaner, water heater, water pump, dishwasher, hair dryer, etc. Let Asi be the set of interruptible appliances and asi ǫAsi represents each appliance in this set. Let λsi is the power rating of each appliance. Then total energy consumption per day (εsi ) is represented by the following equation. εsi =

T X X

asi ǫAn

τ =1

λsi × α(τ )

(3.1)

Total cost per day of each interruptible appliance in time interval T can be obtained by following formula: ζsitotal

=

T X X

asi ǫAn

λτsi

τ =1

19

× ρ(τ ) × α(τ )

(3.2)

Similarly, cost per hour of interruptible appliances is X τ λτsi × ρ(τ ) × α(τ ) ∀ τ =1:T σsi =

(3.3)

asi ǫAn

Here, α(τ ) = [0, 1] shows appliance ON/OFF status. We minimize cost per hour of each appliance as a result overall cost is reduced. 3.0.2.2

Shiftable Un-interruptible Appliances

These appliances can be shifted to any time slot but once start their operation, they must complete their operation without interruption. These appliances include washing machine, cloth dryer, etc. Let Asni be the set of uninterruptible appliances and asni ǫAsni represents each appliance. The power rating of each appliance is λsni and total energy consumption εsni per day is represented by the following equation. εsni =

T X X

asni ǫAn

τ =1

λτsni

× α(τ )

(3.4)

As these appliances are uninterruptible so they must complete their length of operation. This continuous operation of an appliances may increase the cost which can be calculated by the following equation. total ζsni

=

T X X

asni ǫAn

τ =1

λτsni × ρ(τ ) × α(τ )

Cost per hour of regular appliances is calculated as follow: X τ λτsni × ρ(τ ) × α(τ ) ∀ τ =1→T σsni =

(3.5)

(3.6)

asni ǫAn

3.0.2.3

Regular Appliances

These appliances are also called thermostatically controlled appliances because their operation depends on temperature. These appliances include AC, refrigerator, oven, etc. Let Ar be the set of regular appliances and ar ǫAr represents each appliance. Let λr is the power rating of each appliance and εr is the total energy consumption per day which is represented by the following equation. εr =

T X X

ar ǫAn

τ =1

20

λτr × α(τ )

(3.7)

Regular appliances have large length of operation to fulfill user requirements. Cost of such appliance in time interval T is ζrtotal

=

T X X

ar ǫAn

λτr

τ =1

× ρ(τ ) × α(τ )

(3.8)

Cost per hour of regular appliances can be calculated by following equation: X λτr × ρ(τ ) × α(τ ) ∀ τ =1→T σrτ = (3.9) ar ǫAn

Let Υ represents total load consumed by each home in time interval T . Υτ = εsi + εsni + εr

∀ τ =1→T

The energy consumption of each appliance resented by following matrix:  τ Υa1si . . . Υτa1si Υτa2 . . . Υτa2 si  si  . . ME =   . .   . . T Υasi . . . ΥTasi 3.0.3

(3.10)

in each interval of time is rep. . . Υτa1r . . . Υτa2r . . . . . . ΥTar

       

Energy Cost and Unit Price

The Cost of consumed power is calculated with respect to the unit price of electricity. There are many schemes that define unit price, like Time of Use (TOU), RTP, Critical Peak Pricing (CPP) etc. In our work we use RTP signal, ρ(τ ) represents RTP signal at each time interval τ ǫT . Hence, to calculate the total cost per hour, total load consumed in each hour is multiplied by price rate at that hour. Eq. 3.11 shows cost per hour of total load. X τ σtotal = Υ(τ,ai ) × ρ(τ ) ∀ τ =1→T (3.11) ai ǫasi ,asni ,ar

Similarly, to find the cost per day we sum up all values of cost per hour for time T . Eq. 3.12 represents total cost per day of all appliances. ζtotal =

T X τ =1

X

ai ǫasi ,asni ,ar

21

Υ(τ,ai ) × ρ(τ )

(3.12)

Chapter 4 Problem Formulation and Proposed Solution

22

In any DSM based strategies, main objectives are: minimizing the electricity bill, minimizing the use of power from the grid, or minimizing PAR and electricity cost to benefit consumer and utility. These objectives can be achieved by various DSM strategies, like by shifting load from peak to off-peak hours or by shifting power levels [23]. In our proposed solution, load shifting is the primary technique that can be implemented by the HEM controller of the smart grid. For this purpose we formulate the PAR constrained cost function, which aims to reduce cost while taking consideration of PAR constraint. Moreover, we proposed an algorithm which is hybrid of GA and BPSO to efficiently achieve the required objectives. 4.0.1

Problem Formulation

In our scheduling problem our objective function is two fold; minimize cost and PAR by optimal use of power from the grid. To minimize total cost, we reduce per hour cost of scheduled load as compared to unscheduled load. Also to curtail PAR we minimize peak load demand. So by using knapsack problem formulation, objective function is as follow: min

T X i=1

X

ai ǫAsi ,Asni ,Ar

Υ(τ,ai ) × ρ(τ )

(13)

subjected to: P AR =

maxτ ǫT (Υτ ) P ≤ Γmax 1 τ ǫT Υτ T

Tmin ≤ τ ≤ Tmax

Υτ = εsi + εsni + εr ≤ κg

(4.1a) (4.1b) (4.1c)

schedule unschedule σtotal < σtotal

(4.1d)

schedule unschedule ζtotal < ζtotal

(4.1e)

T X τ =1

Υunsch. τ

=

T X

Υsch. τ

(4.1f)

τ =1

Eq. 13 shows objective function which is to minimize cost per day. Eq. 4.1a - Eq. 4.1f are the constraints of objective function. Constraint Eq. 4.1a defines PAR and restricts the PAR of total load demand less than 23

Γmax . We select Γmax very carefully to assure the feasibility of the Eq. 13. Here, it is noted that Γmax = 1 cannot be achieved because average load and peak load cannot be same by any algorithm. Constraint Eq. 4.1b ensures that scheduling time should be in the scheduling limits. Eq. 4.1c ensures total load demand of each group of appliances should be less than grid capacity (κg ). The value of κg is defined by the electricity provider company to ensures the reliability of the grid. Constraint Eq. 4.1d and Eq. 4.1e shows that cost per hour and cost per day of scheduled load should be less than unscheduled load. Similarly, power consumption constraint in Eq. 4.1f guarantee that the total power consumption before and after scheduling remains same. It also ensures that length of operation of each appliance must not be affected by scheduling. 4.0.2

Heuristic Algorithms

The selected heuristic algorithms are described in detail in the following subsections. Table 3.1 provides nomenclature of these algorithms. 4.0.2.1

BFOA

BFOA is a well-known optimization algorithm inspired by the social foraging behavior of real bacteria (Escherichia coli). The bacteria swim in search of nutrients and finds best nutrients (solutions) to maximize their energy. The BFOA consists of three phases: chemotaxis, reproduction, and elimination-dispersal. Before the start of any phase, parameters are initialized as listed in Table 4.1. After initialization of parameters, chemoTable 4.1: Parameters of BFOA

Parameters

Values

Ne Nr Nc Np Ns Ci Θ P ed maximum generation

24 5 5 30 2 0.01 0.5 0.5 50

24

taxis phase starts. In this phase, initial population matrix of bacteria is generated randomly. Here, each bacterium position represents a candidate solution to the problem. Chemotaxis step consists of diverging (tumbling) or converging (swimming) of solution (bacteria). Due to an initial random matrix, solution diverges. However, after fitness evaluation, better solutions are selected which now converges toward a local best solution. The working procedure of chemotaxis step is given in algorithm 1. Here θ(i, :) shows a position of bacteria and Ci is the step size which bacterium takes. Step size is an important control parameter that changes the convergence behaviour of a solution. So a selection of this parameter is very important if we select a very small value solution traps in local minima while a large value takes the solution away from the global best solution. At the end of chemotaxis step, we get the local best solution (status of the appliance). Algorithm 1 BFOA: Chemotaxis steps 1: procedure Chemotaxis 2: for j = 1 : Nc do 3: for i = 1 : Np do 4: calculate initial position 5: θ(i, :) = θ(i, :) + Ci √ ∆Ti [27] ∆i ∆i

6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24:

for d = 1 : (m − 1) do Compute fitness: J = F it f unction(i) end for s=0 while s < Ns do ⊲ swimming loop if J(i) = J last(i) then ⊲ evaluating fitness J(i) = J(i) calculate new position θ(i, :) for d = 1 : (m − 1) do calculate fitness function F it f unction(i) end for else s = Ns end if end while end for current best state of appliances are recorded end for end procedure

After chemotaxis phase, reproduction phase is started, in which only feasi25

ble solutions are recorded to produce next generation. Reproduction phase accelerates and refines the search by adding more number of bacteria in the optimization domain. As chemotaxis phase provides a local best solutions and reproduction phase accelerates the convergence, the eliminationdispersion phase helps to get global best values. In this phase, least feasible solutions are discarded and new random samples are inserted with a low probability. This process is very important because non feasible solutions are eliminated and hence the chance of repetition is avoided. For example, after completion of these phases, if we get solution for 1st hour like [1 0 1 0 0 1 0 0 0 1], its mean that appliance 1, 3, 6, and 10 are ON for this particular hour. We then calculate its power consumption and electricity cost. Here, it is noted that best solutions must follow the constraints of our objective function. The general working principle of BFOA is shown by a flowchart in Fig. 4.1. 4.0.2.2

GA

GA is a heuristic optimization technique inspired by the genetic process of living organisms. New genres are formed which carry the properties of their parents. In our GA-based HEM system, Parameters of GA are initialized as shown in Table 4.2. The initial random population of chromosomes is Table 4.2: Parameters of GA

Parameters

Values

Population size n Number of iterations Pc Pm

200 10 300 0.9 0.1

generated, where each chromosome holds the solution of given problem. These solutions show the status of each appliance for the given time slot. The initial population is in m × n matrix form, where n and m represent population size and a total number of appliances, respectively. The fitness function is evaluated on initial population. Fitness is calculated for each row of solution matrix. For example if we get solution, like row 1 (1st hour) is [1 1 1 0 0 1 0 0 0 1], it means that appliance 1 − 3, 6, and 10 are ON. We then calculate its energy consumption and electricity cost. According to the results of evaluation, current best solutions are recorded. 26

Figure 4.1: Flow chart of BFOA

27

On the basis of these current best solutions, a new steam of population is generated by crossover and mutation. Algorithm 2 shows crossover and mutation steps. In the crossover, binary strings are crossover from two parents and made two new off springs. The probability of crossover rate is very important control parameter and directly depends on convergence rate. A large value of crossover rate means fast convergence at the cost of accuracy. In literature, best crossover rate is for the optimization problem is found to be: Pc = 0.9 (4.2) To create randomness in the results so that repetition of a population could be avoided we use mutation process. It changes one or more principles gene in a chromosome from its initial state. Probability of mutation is very low which is found by the following formula: pm =

1 − Pc 10

(4.3)

So for better results, crossover rate is high while mutation rate is low. Once crossover and mutation are done, again a population is generated and fitness is evaluated and compared with the previous population. This whole process keeps on repeating until an optimal solution is obtained. Fig. 4.2 shows the main steps of GA. 4.0.2.3

BPSO

BPSO is a binary variant of PSO. It is a nature-inspired optimization technique based on bird flock in search of food. When birds move for food they have some specific positions and velocities. In BPSO based HEM system, parameters are initialized which are given in Table 4.3. In next step initial position matrix is generated randomly, position of each particle represents canidate solution. Velocity function is initiliazed by using following formula: vi = vmax × 2 × (rand(swarm, n) − 0.5)

(4.4)

Position matrix is a solution matrix which shows the status of appliances while velocity controls the population generation. Initially generated position matrix is evaluated by fitness function (objective function). Best values on the basis of fitness function for current iteration are defined, 28

Algorithm 2 GA: Crossover and mutation process 1: procedure Crossover and mutation 2: Step 1 : 3: Parent vectors are selected on the basis of fitness: Parent1 and Parent2 4: Step 2 : 5: if Pc > rand then 6: crossover operation started 7: generating random crossover point as cross bits 8: if cross bits == 0 then 9: cross bits = rand(, 1, 1) 10: end if 11: of f spring1 = [parent1(1 : cross bits)P arent2(cross bits + 1 : end)] 12: of f spring2 = [parent2(1 : cross bits)P arent1(cross bits + 1 : end)] 13: end if 14: Step 3 : 15: if Pm > rand then 16: mutation operation started 17: for i=1: num mbits do 18: mut row = f loor(length(parent1) × rand 19: if mut row == 0 then 20: mut row = randi(length(parent1), 1, 1) 21: end if 22: change bit = parent1(mut row) 23: if change bit == 1 then 24: parent1(mut row) = 0 25: else 26: if change bit == 0 then 27: parent1(mut row) = 1 28: end if 29: end if 30: end for 31: end if 32: end procedure

29

Figure 4.2: Flow chart of GA

30

Table 4.3: Parameters of BPSO

Parameters

Values

Swarm size n Number of iterations c1 c2 wi wf vmax vmin

10 10 600 2 2 2 0.4 4 -4

called pbest. A collection of pbest values from all iterations are evaluated by fitness function to find global best (gbest). These gbest values are the status of appliances on which cost and PAR are minimum for a particular hour. In next step, velocity function is updated as shown in Algorithm 3. Velocity function is very important as it consists of the control parameter that changes the convergence behaviour of a solution. These control parameters include inertia factor, acceleration coefficients, previous, and best position values. These parameters are carefully selected as shown in Table 4.3. Values of velocity are in real numbers so they are converted into a binary state to obtain the status of each appliance. To convert into binary, sigmoid (Sg ) function is used, which is defined as Sig(j, i) =

1 1 + e−vnew

(4.5)

By applying equation 4.5 position matrix is updated as follow xnew = 1 if xnew = 0 if

rand(1) ≤ Sig(j, i) rand(1) > Sig(j, i)

(4.6)

Fitness is evaluated on a new position, this process continues until the stopping criteria is met. At the end of this process, we get ”gbest” values which are the optimum solution for scheduling of our appliances. For example, a ten bit binary pattern [0 1 1 1 1 0 0 0 0 1] is generated as we have ten appliances, where 1 shows ON and 0 shows OFF state of appliances. This process recaps for each time slot to obtain optimal power consumption pattern. So according to the above formulation, flowchart of BPSO is given Fig.4.3 31

Algorithm 3 BPSO: Velocity updating 1: procedure Updating velocity 2: Initialize velocity by using equation 4.9 3: for j = 1 : swarm do 4: for i = 1 : m do 5: vnew = w ×vold +c1 ×rand(1)×(pbest−xold )+c2 ×rand(1)× (gbest − xold ) [35] 6: if vnew < V max && vnew > V min then 7: vnew (i, j) = vnew (i, j) 8: else 9: if vnew < V min then 10: vnew = V min 11: else 12: if vnew > V max then 13: vnew = V max 14: end if 15: end if 16: end if 17: end for 18: end for 19: end procedure

32

Figure 4.3: Flow chart of BPSO

33

4.0.2.4

WDO

WDO is a nature-inspired optimization technique based on an atmospheric motion of wind. When the wind blows, it equalizes the horizontal imbalances. In this algorithm, we consider small air parcels as a candidate solution that are moving in N-dimensional space which experience different type of forces. In WDO-HEM system, parameters of WDO are initialized. These are shown in Table 4.4 along with their values. Table 4.4: Parameters of WDO

Parameters

Values

Population size n Number of iterations RT g α dimMin dimMax vmax vmin

20 10 400 3 0.2 0.4 -5 5 0.3 -0.3

In next step initial position matrix is generated randomly which shows the status of appliances. Similarly, the initial velocity is generated which is mathematically defined as: vi = vmax × 2 × (rand(populationsize, n) − 0.5);

(4.7)

This initially generated position matrix is evaluated by fitness function (objective function) and states of the appliances for a particular time slot are achieved, then velocity function is updated. In WDO velocity function is different from BPSO. In this function, we consider four different forces as control parameters. These parameters include gravitational force, pressure gradient force, coriolis force, and frictional force. In [40] an equation is derived for updating velocity by using these control parameters. In our scheme velocity is updated as per algorithm 4. Here posnew shows the current status of appliances. At each iteration velocity and position, values must be updated. By using Eq. 4.8 new position of air parcel for each iteration is defined, xnew = xcur + unew ∆t (4.8) 34

Algorithm 4 WDO: Velocity updating 1: procedure Updating velocity 2: Initialize velocity 3: for j = 1 : popsize do 4: for i = 1 : m do 5: unew = (1 − α) × ucur − (g × pos) + (| 1i − 1|) × ((gbest − pos) × cucur RT ) + ( i ) [40] 6: if unew < vmax && unew > vmin then 7: unew = unew 8: else 9: if unew < vmin then 10: unew = minV 11: else 12: if unew > vmax then 13: unew = vmax 14: end if 15: end if 16: end if 17: posnew = pos + unew 18: end for 19: end for 20: end procedure

35

Here ∆t is step time which is equal to 1, velocity at each iteration must be bounded by its maximum and minimum values which are define as unew = umax if unew > umax unew = −umax if unew < umax

(4.9)

After updating velocity function again new ”position” matrix is generated and evaluated. This process will continue until stopping criteria is met. At the end of this process, we get ”gbest” values which are the optimum solution for scheduling of our appliances. Fig. 4.4 shows the implementation of WDO. 4.0.2.5

GBPSO

GBPSO is our proposed algorithm which is a hybrid of BPSO and GA. We choose these two algorithms because simulation results (refer to section IV) of GA and BPSO show that, GA is effective in PAR reduction and BPSO is effective in cost reduction. So we combine the features of GA and BPSO so that resulting algorithm should reduce both cost and PAR. Working procedure of GBPSO consists of two phases, in the first phase we follow all the steps as in BPSO which are explained above. In next phase genetic operations (crossover and mutation) are applied to gbest values of BPSO. It improves results because crossover and mutation are applied on the best values instead of random values. For example if we take pattern of 7th hour which is a peak hour, result after completion of first phase is [0 0 0 0 1 1 1 1 1 1], in which 6 appliances are ON while result after second phase is [1 0 0 1 0 1 1 0 0 0] in which only 4 appliances are in ON state. Similarly, other time slots are improved due to which cost and PAR is improved. Fig. 4.5 shows flow chart of GBPSO. 4.0.3

Feasible Region

Feasible region is an area which defined by a specific set of points in which objective function satisfies the result. A specific set of points are actually constraints of the problem. We find the feasible region of a cost function for single as well as for multiple homes.

36

Figure 4.4: Flow chart of WDO

37

Figure 4.5: Flow chart of GBPSO

38

Table 4.5: Possible cases: Single home

Case

Min. Min. Max. Max.

load, Min. ρ load, Max. ρ load, Min. ρ load, Max. ρ

4.0.3.1

Single Home

Load (kWh) Electricity price ($/kWh)

Cost ($)

1.5 1.5 10.7 10.7

0.12 0.41 0.86 2.98

0.08 0.27 0.08 0.27

First of all, we consider single home in which our objective function is to minimize cost by controlling energy consumption. Cost per time slot is defined as: X τ Υ(τ,ai ) × ρ(τ ) ∀ τ =1→T σtotal = (4.10) ai ǫasi ,asni ,ar

We have to minimize cost in each time slot. So our objective function is defined as: τ min(σtotal ) To find constraints of this objective function, we consider RTP signal ρ(τ ) whose range is (0.081:0.2735) $/kWh. So we calculate four possible cases as shown in Table 4.5. Moreover, maximum cost per hour of an unscheduled unsch. load is σmax = $2.2. Based upon these values we define our constraints so that cost of scheduled load should be less than or equal to unscheduled cost in each time slot. Hence constraints are C1 : 0.12 ≤ στsch. ≤ 2.2 C2 : ζtotal < 15.69 C3 : 1.5 ≤ Υsch. ≤ 10.7 τ C1 shows that maximum cost in each time slot is $2.2, so we schedule load such that cost should not be greater than $2.2 in any time slot. Similarly, C2 shows that total cost per day should be less than unscheduled cost. C3 represents that maximum unscheduled load in any time slot can be 10.7 kWh, so scheduled load should be less than or equal to this load. In Fig. 4.6 total cost range is shown by trapezium (P1 P3 P6 P2 ) while shaded portion which is surrounded by (P1 , P2 , P3 , P4 ,P5 ) is a feasible region. Now cost under this region in any time slot will be feasible and it reduces overall electricity cost. Note that at P4 and P5 cost is same, however, the load is changed. So we calculate values of RTP at these load values which are 0.27 39

$/kWh and 0.20 $/kWh when load is 8.8 kWh and 10.7 kWh respectively. Hence when load is 10.7 kWh then it must not be scheduled in time slots having price ρ(τ ) > 0.20 $/kWh.

3 P6(10.7, 2.9)

Electricity bill per hour ($)

2.5

P5(8, 2.2)

P4(10.7, 2.2)

2

1.5

1 P2(1.5, 0.41)

0.5 P3(10.7, 0.86) P1(1.5, 0.12)

0 0

2

4

6

8

10

12

Energy consmption (kWh)

Figure 4.6: Feasible region: Single home

4.0.3.2

Ten Homes

In this scenario our objective function is same, however, limits of constraints are changed due to increase in a number of homes. Cost per time slot of ten homes can be calculated as follow N,τ σtotal

=

10 X n=1

X

ai ǫasi ,asni ,ar

Υ(τ,ai ) × ρ(τ )

∀ τ =1→T

(4.11)

To find range of constraints we calculate four possible cases as shown in Table 4.6. Based upon these values new range of constraints are sch. C1 : 1.2 ≤ σN,τ ≤ 21.9 C2 : ζN,total < 156 C3 : 15 ≤ Υsch. N,τ ≤ 107 40

Table 4.6: Possible cases: Ten homes

Case

Min. Min. Max. Max.

load, Min. ρ load, Max. ρ load, Min. ρ load, Max. Eρ


Cost($)

15 15 107 107

1.2 4.1 8.6 29.26

0.08 0.27 0.08 0.27

Fig. 4.7 shows that shaded region (P1 P3 P6 P2 ) is a feasible region. It shows unsch. that maximum cost for each time slot is σN,max = $21.9. So C1 restricts our unsch. scheduled cost per hour for N number of homes to be less σN,max . Similarly, C2 and C3 constraints restrict total cost per day and maximum load for multiple homes. Note that at P4 and P5 load is increased, however, cost is constant because we shift load in low peak hours.

30

P6(107, 29.26) 25

Electricity bill per hour ($)

P5(21.9, 80)

P4(21.9, 107)

20

15

10 P2(15, 4.10)

5 P3(107, 8.67)

P1(15, 1.21) 0 0

20

40

60

80

100

Energy Consumption (kWh)

Figure 4.7: Feasible region: Ten homes

41

120

Table 4.7: Possible cases: Fifty homes

Case

Min. Min. Max. Max.

load, Min. ρ load, Max. ρ load, Min. ρ load, Max. ρ

4.0.3.3

Fifty Homes


Cost($)

75 75 535 535

6.1 20.51% 43.34% 146.32%

0.08 0.27 0.08 0.27

In this scenario we consider 50 homes. Cost per time slot of fifty homes can be calculated as follow N,τ σtotal =

50 X

N =1

X

ai ǫasi ,asni ,ar

Υ(τ,ai ) × ρ(τ )

∀ τ =1→T

(4.12)

In this case load and cost is increased which change the constraint limits as sch. shown in Table 4.7. Maximum cost in this case is now σN,τ $109.9. Based upon these values new range of constraints are sch. C1 : 6.1 ≤ σN,τ ≤ 146.32 C2 : ζN,total < 784 C3 : 75 ≤ Υsch. N,τ ≤ 535 Fig. 4.8 shows that shaded region (P1 P3 P6 P2 ) is feasible region. It shows that maximum cost for each time slot is $21.9. So constraints C1 , C2 , C3 restricts cost per hour, cost per day and maximum load respectively.

42

150 P5(535, 146.32)

Elecricity bill per hour ($)

P5(400, 109.96)

100

P4(535, 109.96)

50 P2(75, 20.51) P3(535, 43.32)

P1(75, 6.1) 0 0

100

200

300

400

500

Energy consumption (kWh)

Figure 4.8: Feasible region: Fifty homes

43

600

Chapter 5 Simulation and Discussion

44

In this thesis, four heuristic algorithms; BFOA, GA, BPSO, and WDO are compared in term of cost and PAR. We consider 10 different residential appliances which are categorised into three groups: shiftable interruptible, shiftable uninterruptible and regular appliances as show in Table 3.1 (refer to chapter 3). We use RTP signal as shown in Fig. 5.1. This profile shows that 7 − 10 hours are ON-peak hours, 11 − 15 hours are shoulder peak hours. 1 − 6 and 15 − 24 hours are OFF-peak hours. Below is the list of 30 RTP Pricing

Electricity price (cents/kWh)

25

20

15

10

5

0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hours)

Figure 5.1: RTP signal

formulas that we used for cost and PAR calculations. App hour Cost = Σ24 hour=1 (EPRate ∗ PRate )

(5.1)

Total unscheduled load formula is: App lod = PRate ∗ App

(5.2)

PAR is calculated by using the formula: P AR =

S max(lod ) S Avg(lod)

45

(5.3)

5.0.1

Scenario 1: Single home

11 Unscheduled BFOA GA BPSO WDO GBPSO

10 9

Load(kWh)

8 7 6 5 4 3 2 1 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hours)

Figure 5.2: Load profile: Scenario 1

Fig. 5.2 shows daily energy consumption pattern of unscheduled and scheduled load for a single home. In unscheduled energy consumption pattern, user activities are high in 6 − 9 and 13 − 17 hours leading to high cost and high PAR. Maximum energy consumption of BFOA, GA, BPSO, WDO, and GBPSO scheduled load is limited to 8.044 kWh, 8.248 kWh, 9.586 kWh, 8.962 kWh, and 7.478 kWh respectively. The difference between peak values of unscheduled and scheduled load in each case is 2.6 kWh, 2.4 kWh, 1.1 kWh, 1.7 kWh, and 3.2 kWh respectively. It is concluded that our proposed scheme has minimum peak load and has stable load pattern which reduces PAR. In BFOA peak load is in 1 − 7 hours because uninterruptible appliances along with AC and water heater are scheduled in these hours. Similarly, next peaks are at 15 − 17 hour, however, these are less than previous peak and in low peak hours. This pattern decreases PAR, however, cost is not effectively reduced. GA schedule uninterruptible appliances in first 9 hours along with other interruptible appliances, due to which load of 7 kWh is scheduled in peak hour. Also, consumption is increasing in 17 − 24 hours from 5.7 kWh to 8.2 kWh which increases cost. In 10 − 17 46

hours load is under 3 kWh, hence the only peak is at 24th hour. Due to less number of peaks PAR decreases. In BPSO and WDO, it is noticed that load distribution pattern is similar. However, BPSO shows higher peak values. The similar behavior of BPSO and WDO is because both have same controlling parameters i.e. velocity and position. However, WDO has more controlling factors in updating velocity function which makes it better than BPSO. From Fig. 5.2 we can see that both schedules maximum load in 1st and in 6 − 10 hour. BPSO schedule uninterruptible appliances in 1 − 9 hours along with water heater and oven in 6 − 10 hour. WDO schedule most of interruptible and regular appliances in 1−7 hours and uninterruptible appliances in 7 − 14 hours. This type of energy consumption pattern increases peak load in both cases. Due to small difference between unscheduled peak and BPSO, WDO scheduled peak, PAR is not efficiently decreased. Our proposed scheme GBPSO shows most regular pattern as compared to others. A constant load profile has been shown in 1 −14 hours expect at 2 − 3 hour. It maintains the balance between low and high power consumption devices with respect to RTP. Uninterruptible appliances are scheduled in 1 − 9 hours along with low power consumption appliances. It efficiently follows the PAR constraint defined in section IV. Peak load of GBPSO is 7.478 kWh while peak unscheduled load is 10.7 kWh. So a difference of 3.22 kWh is observed which reduces PAR. Furthermore, after 14th hour BPSO, WDO and GBPSO shows a similar pattern, however, GBPSO consumes less power which reduces its cost. Fig. 5.3 shows the electricity cost comparison of unscheduled and scheduled load. The per day cost of unscheduled, BFOA, GA, BPSO, WDO, and GBPSO scheduled load is $15.69, $14.59, $14.97, $9.90, $10.08, and $9.76 respectively. Table 5.1 shows percentage decrement in cost. GBPSO shows the highest percentage decrement which is 37.76% while BFOA, GA, BPSO, and WDO reduces 6.99%, 4.5%, 36.87%, and 32.29% cost. It is noted that each algorithm follows the objective function and its constraints, however, GBPSO shows best results as compared to other algorithms under study. Although percentage cost reduction between BPSO and GBPSO is very small, however, GBPSO reduces PAR which makes it prominent. Fig. 5.4 shows cost per hour profile. It shows that every algorithm is capable of maintaining cost per hour in the bounds define by feasible region (refer to Chapter 4). Also, the total cost is always less than unscheduled cost. It is noticed that GA and BFOA have more per hour cost due to which overall cost is not effectively reduced. In BPSO, WDO and GBPSO per hour cost for each time slot is under $0.75 due to which overall cost is commendably reduced. Fig. 5.5 illustrates the performance of unscheduled and scheduled load 47

16

14

Total cost per day ($)

12

10

8

6

4

2

0 Unschedule

BFOA

GA

BPSO

WDO

GBPSO

Figure 5.3: Cost per day profile: Scenario 1

with respect to PAR. We formulate PAR in section IV, In which we set a limit that PAR should be greater than Γmax . In case of single home, we set Γmax = 4.5. We get the values of PAR in unscheduled, BFOA, GA, BPSO, WDO, and GBPSO scheduled load is 4.51, 3.46, 3.02, 4.22, 4.20, and 2.56 respectively. Table 5.2 shows percentage decrement of PAR. Results show that each scheme is able to reduce PAR and follows the constraint, however, GBPSO shows the highest percentage decrement which is 43.08%. Similarly, BFOA, GA, BPSO, and WDO reduces 23.24%, 32.69%, 6.38%, and 6.67% PAR. GBPSO shows the best result because peak load is 7.6 kWh for only 1 hour and load distribution is uniform. In the case of BPSO and WDO PAR is not effectively reduced due to high peaks for multiple times. 5.0.2

Scenario 2: Ten homes

Energy consumption pattern for 10 homes, by using BFOA, GA, BPSO, WDO, and GBPSO is shown in Fig. 5.6. It shows that maximum energy consumption of unscheduled load is 107 kWh. In the case of BFOA, GA, 48

Table 5.1: Comparison of cost: Scenario 1

Scheduling techniques

Cost

Difference

Percentage decrement in cost

Unscheduled BFOA GA BPSO WDO GBPSO

15.69 14.59 14.97 9.90 10.08 9.76

1.09 0.72 5.78 5.61 5.92

6.99% 4.2% 36.87% 32.29% 37.76%

Table 5.2: Comparison of PAR: Scenario 1


PAR


4.51 3.46 3.02 4.22 4.21 2.57

Difference

1.05 1.48 0.29 0.30 1.94

49

Percentage decrement in PAR 23.28% 32.69% 6.43% 6.65% 43.08%

2.5 Unscheduled BFOA GA BPSO WDO GBPSO

Cost per hour ($)

2

1.5

1

0.5

0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hours)

Figure 5.4: Cost per hour profile: Scenario 1

BPSO, WDO, and GBPSO HEM systems this value is limited to 80.44 kWh, 88.04 kWh, 99.40 kWh, 100 kWh and 75.68 kWh respectively. It is noticed that energy consumption pattern for each HEM system is under predefined limits. It is also noted that by increasing number of homes, energy consumption is increased, however, consumption pattern for each case nearly same. Unscheduled energy consumption pattern is same because we consider same appliances and same power consumption pattern for each home. The behavior of BFOA shows some variations, peak load is now in 6 − 7 hour which increases its cost because this is a peak hour. Similarly, in GA energy consumption is under 40 kWh in 2 − 6 hours and 10 − 17 hours. However, load is increased to 65 kWh in 6 − 10 hours and it is further increased from 60 kWh to 90 kWh 17 − 24 hours which increases its cost. In BPSO and WDO peak values are increased by increasing number of users, however, overall pattern remains same. In GBPSO, scheduling pattern is more regular as compare to others. A constant load profile has been shown in 0 − 13 hours. The peak load of GBPSO is 76.82 kWh while peak unscheduled load is 107 kWh. So a difference of 31.32 kWh is observed which reduces PAR.

50

5 4.5 4 3.5

PAR

3 2.5 2 1.5 1 0.5 0 Unscheduled

BFOA

GA

BPSO

WDO

GBPSO

Figure 5.5: PAR: Scenario 1

Fig. 5.7 shows the cost per day of unscheduled and scheduled load for 10 homes. The maximum electricity cost in unscheduled model is $156.93. It is reduced to $145.93, $146.46, $99.04, $100.85, and $96.83 in the case of BFOA, GA, BPSO, WDO, and GBPSO respectively. Here, it is important to note that by increasing number of users cost is increased, however, all HEM system follow objective function. Table 5.3 shows percentage decrement in cost for each case. GBPSO shows the highest percentage decrement which is 38.29% while BPSO and WDO reduce 36.88% and 35.73% respectively. GA and BFOA show least percentage decrement in cost. However, it is greater than scenario 1. It is noticed that cost reduction is nearly same for GBPSO and BPSO based HEM systems, however, PAR is effectively reduced in GBPSO-HEM which make it more suitable. Fig. 5.8 represents cost per hour for unscheduled and scheduled load. It is noticed that each algorithm limits the cost within feasible region defines in section IV. So results of Fig. 5.7 and Fig. 5.8 show that each algorithm successfully schedule the load to reduce cost and follow the constraints C1 and C2 (refer to Chapter 4). However, GA and BFOA reduces a very small percentage as compared to other algorithms. Also, our proposed algorithm

51


100 90

Load (kWh)

80 70 60 50 40 30 20 10 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hours)


GBPSO reduces a highest percentage of cost. Fig. 5.9 illustrates the performance of unscheduled and scheduled (BFOA, GA, BPSO, WDO, and GBPSO) load with respect to PAR reduction for 10 homes. In this scenario we set Γmax = 45. From Fig. 5.9 it is clear that each design model is capable of reducing PAR with respect to unscheduled load. However, performance of GBPSO-HEM is best among other HEM systems. Table 5.4 shows percentage decrement in PAR. GBPSO has highest percentage decrement which is 39.57% while WDO has least which 7.78%. It is noticed that due to increasing in the number of homes more peaks are incorporated in BFOA and GA based HEM systems which increase PAR. 5.0.3

Scenario 3: Fifty homes

Fig. 5.10 shows an energy consumption pattern for 50 homes. It shows that the peak unscheduled load is 535 kWh while maximum energy consumption for BFOA, GA, BPSO, WDO, and GBPSO is 398.42 kWh, 415.80 kWh, 493.30 kWh, 470.96 kWh and 367.22 kWh respectively. It is noticed that by 52



Cost

Difference



156.93 145.57 146.46 99.04 100.85 96.83

11.36 10.47 57.89 56.08 60.1

7.23% 6.67% 36.88% 35.73% 38.29%



PAR

Difference

Percentage decrement in PAR


45.10 35.11 29.98 41.32 41.59 26.25

9.99 15.12 3.78 3.51 18.85

22.15% 33.52% 8.38% 7.78% 41.79%

53

160

140


120

100

80

60

40

20

0 Unschedule

BFOA

GA

BPSO

WDO

GBPSO


increasing number of homes overall load is increased, however, simulation pattern is same as for single home. GBPSO limits the load to 367.22 kWh, which is 31.6% decrement as compare to unscheduled peak. Similarly, in case of BFOA, GA, BPSO, and WDO percentage reduction in energy consumption is 25.52%, 22.2%, 6.19%, and 12.14% respectively. Our proposed technique performs best because now crossover and mutation are applied on the best values which further improve the results. Fig. 5.11 shows a comparison of cost for unscheduled and scheduled load. The maximum cost in an unscheduled model is $784.66. In BFOA, GA, BPSO, WDO, and GBPSO HEM system cost are reduced to $727.16, $758.58, $495.1, $502.25, and $488.3 respectively. Table 5.5 shows percentage decrement in cost for each case. GBPSO and BPSO show a prominent decrement in cost. Results show that our proposed scheme GBPSO ensures better results even for multiple home scenario. Fig. 5.12 represents cost per hour for unscheduled and scheduled load. Our system efficiently reduces the cost even if the number of homes are increased. Results show that each HEM system successfully schedules the load under pre-define constraints of feasible region (refer to Chapter 4).

54


Cost per hour ($)

20

15

10

5

0 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hours)


Performance of unscheduled and scheduled load with respect to PAR is shown in Fig. 5.13. It shows that each design model is capable of reducing PAR with respect to unscheduled load even if number of homes are increased. Table 5.6shows the difference of scheduled and unscheduled PAR and percentage decrement in PAR. Results show that GBPSO HEM system shows highest percentage decrement while BPSO has least percentage decrement. For this scenario BPSO However, Performance of GBPSOHEM is best among GA-HEM and BPSO-HEM. So it is concluded that our proposed scheme efficiently reduces PAR even if the number of homes are increased. Table 5.7 and 5.8 show the comparison of the simulated algorithms in terms of cost and PAR for three scenarios. It can be clearly seen that for single as well as for multiple homes BFOA and GA based HEM controller reduces PAR while compromising cost. Similarly, BPSO and WDO based HEM controller reduces cost but compromises on PAR for each scenario. Moreover, GBPSO performs best for each scenario, it efficiently reduces costs and curtails PAR. Hence our proposed HEM model is more efficient for multi objective function even if complexity is increased.

55



Cost

Difference



784.66 727.16 758.58 495.10 502.25 488.3

57.5 26.08 289.56 282.41 296.36

7.32% 3.32% 36.90% 35.99% 37.76%



PAR


225.50 173.15 149.66 219.91 208.93 129.34

Difference

52.35 75.84 5.59 16.57 96.16

Percentage decrement in PAR 23.21% 33.63% 2.4% 7.34% 42.64%

Table 5.7: Comparison of percentage decrement in cost


Scenario Scenario 2 1

Scenario 3

BFOA GA BPSO WDO GBPSO

6.99% 4.5% 36.87% 32.29% 37.76%

7.32% 3.32% 36.90% 37.99% 37.36%

7.23% 6.67% 36.88% 35.73% 38.29%

56

50 45 40 35

PAR

30 25 20 15 10 5 0 Unscheduled BFOA

GA

BPSO

WDO

GBPSO


Table 5.8: Comparison of percentage decrement in PAR


Scenario Scenario 2 1

Scenario 3

BFOA GA BPSO WDO GBPSO

23.24% 32.69% 6.38% 6.67% 43.08%

23.21% 33.63% 2.4% 7.34% 42.64%

22.15% 33.52% 8.38% 7.78% 41.79%

57


500 450

Load (kWh)

400 350 300 250 200 150 100 50 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hours)


58

800

700


600

500

400

300

200

100

0 Unschedule

BFOA

GA

BPSO

WDO

GBPSO


59


Cost per hour ($)

100

80

60

40

20

0 1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Time (hours)


60

250

200

PAR

150

100

50

0 Unscheduled BFOA

GA

BPSO

WDO


61

GBPSO

Chapter 6 Conclusion

62

6.1

Conclusion

In this thesis, we have presented a HEM controller for residential energy management in a smart grid. Our formulated objective function is evaluated in terms of selected performance metrics by using four heuristic algorithms (BPSO, GA, BFOA and WDO). Simulations are conducted with the consideration of essential home appliances using RTP scheme. Results show that GA based HEM controller is better than the other algorithms based HEM controllers in term of PAR reduction. The execution time of GA-HEM is less the other ones. On the other hand, BPSO-HEM performs better than the other ones in term of cost reduction. Furthermore, GBPSO-HEM outperforms other HEM systems. Additionally, multiple user scenarios account for effective scalability of the proposed techniques. Results also show that there is a trade-off between cost and PAR in each algorithm, however, GBPSO efficiently reduces both cost and PAR.

63

Chapter 7 References

64

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