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Applied Sciences
, Volume 9 (4) – Feb 23, 2019

/lp/multidisciplinary-digital-publishing-institute/time-constrained-nature-inspired-optimization-algorithms-for-an-u3ksRcOdUt

- Publisher
- Multidisciplinary Digital Publishing Institute
- Copyright
- © 1996-2019 MDPI (Basel, Switzerland) unless otherwise stated
- ISSN
- 2076-3417
- DOI
- 10.3390/app9040792
- Publisher site
- See Article on Publisher Site

applied sciences Article Time-Constrained Nature-Inspired Optimization Algorithms for an Efﬁcient Energy Management System in Smart Homes and Buildings 1, 2 Ibrar Ullah * and Sajjad Hussain Department of Electrical Engineering, Capital University of Science and Technology, Islamabad 44000, Pakistan School of Engineering, University of Glasgow, Glasgow G12 8QQ, UK; Sajjad.Hussain@glasgow.ac.uk * Correspondence: ibrarullah@uetpeshawar.edu.pk; Tel.: +92-333-905-1548 Received: 14 December 2018; Accepted: 15 February 2019; Published: 23 February 2019 Abstract: This paper proposes two bio-inspired heuristic algorithms, the Moth-Flame Optimization (MFO) algorithm and Genetic Algorithm (GA), for an Energy Management System (EMS) in smart homes and buildings. Their performance in terms of energy cost reduction, minimization of the Peak to Average power Ratio (PAR) and end-user discomfort minimization are analysed and discussed. Then, a hybrid version of GA and MFO, named TG-MFO (Time-constrained Genetic-Moth Flame Optimization), is proposed for achieving the aforementioned objectives. TG-MFO not only hybridizes GA and MFO, but also incorporates time constraints for each appliance to achieve maximum end-user comfort. Different algorithms have been proposed in the literature for energy optimization. However, they have increased end-user frustration in terms of increased waiting time for home appliances to be switched ON. The proposed TG-MFO algorithm is specially designed for nearly-zero end-user discomfort due to scheduling of appliances, keeping in view the timespan of individual appliances. Renewable energy sources and battery storage units are also integrated for achieving maximum end-user beneﬁts. For comparison, ﬁve bio-inspired heuristic algorithms, i.e., Genetic Algorithm (GA), Ant Colony Optimization (ACO), Cuckoo Search Algorithm (CSA), Fireﬂy Algorithm (FA) and Moth-Flame Optimization (MFO), are used to achieve the aforementioned objectives in the residential sector in comparison with TG-MFO. The simulations through MATLAB show that our proposed algorithm has reduced the energy cost up to 32.25% for a single user and 49.96% for thirty users in a residential sector compared to unscheduled load. Keywords: energy management system; energy optimization techniques; genetic algorithm; moth-ﬂame optimization; smart grid; time-constrained optimization techniques 1. Introduction Energy utilization efﬁciency is increasing with increased use of technology and smart appliances in every ﬁeld of life in the residential, commercial and industrial sectors. At the same time, a reliable and high-quality electrical power system is extremely vital to fulﬁl the residential energy demand. Meanwhile, there is a rapid increase in demand for global natural resources. Throughout the world, major blackouts occur due to consumer demand and utility supply mismatch and system automation deﬁciencies. Hence, a transition process from the Traditional Electric Power Grid (TEPG) to the Smart Grid (SG), to integrate communication and information technologies, is the demand of the future. Presently, about 40% of the total generated energy is consumed by residential users, and approximately 30–40% of carbon emission is due to these residential areas [1]. The unnecessary and inefﬁcient use of electrical energy brings sustainability issues to the forefront, such as economic growth, heavy Appl. Sci. 2019, 9, 792; doi:10.3390/app9040792 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, 792 2 of 25 pollution and global warming. Conventionally, the service provider power systems run on fossil fuel and add to global warming with high carbon emissions. Furthermore, in the present power systems, electricity power ﬂow is uni-directional, i.e., from the supply- to the demand-side. Conversely, SG’s purpose is to make the ﬂow of electricity supply and demand bidirectional [2]. Secondly, the search for and integration of new green renewable energy resources are obligatory in such circumstances. The integration of green renewable energy resources needs a broader perspective of design, planning and optimization. Up to this time, different conventional optimization techniques, such as Linear Programming (LP) [3], Non-Linear Programming (NLP) [4], Integer Linear Programming (ILP) [5], Mixed Integer Linear Programming (MILP) [6], Dynamic Programming (DP) [7] and Constrained Programming (CP), have been practised. However, in the present situations, the integration of renewable energy resources is mandatory, and the problems are non-linear and have numerous local optima, making conventional optimization techniques obsolete. In the last decade, bio-inspired modern heuristic optimization techniques have grown in popularity due to their stochastic search mechanisms and avoidance of large convergence time for the exact solution [1]. In this research work, we propose a new meta-heuristic optimization algorithm, named Time-constrained Genetic-Moth-Flame Optimization (TG-MFO), and applied it for efﬁcient energy optimization in smart homes and buildings. We have also explored and analysed ﬁve bio-inspired heuristic algorithms for the energy optimization problem, namely the ACO, GA, Cuckoo Search Algorithm (CSA), Fireﬂy Algorithm (FA) and MFO algorithms. For analysis and validation of the proposed algorithm, we applied these algorithms in different consumer scenarios, such as a single home for one day, a single home for thirty days, thirty different sizes of homes for one day and thirty homes for thirty days. Simulation results show that our proposed algorithm reduced the end-user discomfort in terms of appliance waiting time being nearly equal to zero, as compared to the bio-inspired optimization algorithms, along with minimization of total energy cost and minimum PAR. Renewable energy sources are also integrated for further minimization of the total load and its cost. To achieve this goal, the smart electric grid is modelled as a residential sector comprised of 30 homes having different sizes, different Lengths of Operational Time (LOTs) and appliance power ratings. Appliance power ratings are different due to the home size requirements. For example, a small-sized home runs a one-ton (12,000 BTU) air conditioner compared to a large-sized home that runs 1.5 tons (18,000 BTU) or even more. Some homes have a Renewable Energy Source (RES) and a Battery Storage Unit (BSU). In the considered model, we have forty-eight (48) Operational Time Intervals (OTIs) in a day, by dividing one hour into two-time slots of thirty minutes each. In each OTI, a smart home checks appliances’ power demand, i.e., whether an appliance is ON or OFF. According to the appliances’ ON/OFF status, the Energy Management Controller (EMC) checks the availability of RES and BSU to fulﬁll the appliances’ power demand. If it is available, the appliance will be ON, and the consumer will not wait for appliance scheduling. If the generation and stored energy are insufﬁcient for running the load, the proposed algorithm will check the time span, in which a user has no problem with appliance scheduling with the lowest energy price (time interval) for running that appliance. In order to achieve this objective, time constraints have been deﬁned for a maximum interval of time in which an appliance has to complete its operation. Consequently, if the utility gives incentives to the user in the form of real-time lower prices in off-peak hours, the end-user will be encouraged to produce his/her own energy from RES and schedule the load accordingly. The rest of the paper is organized as follows: Related work is illustrated in Section 2. Contributions are brieﬂy discussed in Section 3. Section 4 depicts the proposed system model architecture. The problem formulation is described in Section 5, and Section 6 gives the heuristic algorithms. Section 7 presents the simulation results to demonstrate some of the achievements. The paper is concluded in the last section. Appl. Sci. 2019, 9, 792 3 of 25 2. Related Work Countless researchers around the world are investigating different technologies in order to fulﬁll the needs of energy-efﬁcient and intelligent smart homes. Many algorithms have been proposed for optimal use of existing energy resources. In this regard, we illustrate some prior research works in SG. Yi Peizhong et al. [8] have proposed the Optimal Stopping Rule (OSR) for energy-efﬁcient scheduling of home appliances. The limitation of this work is that OSR runs on a threshold-based strategy. The end-user has to wait until the price comes down below the threshold level. In [9], the authors have proposed an approach to optimize their objective function using the Genetic Algorithm (GA). Electricity prices are varying between on-peak hours and off-peak hours. Therefore, an optimized task scheduling module is used in smart homes, which can reduce the consumption of the entire energy and operation times. Having an optimal scheduling of power, a heuristic-based GA was used for Demand-Response (DR) in Home Energy Management (HEM) systems in [10]. The authors proposed GA-, TLBO- (Teaching Learning-Based Optimization), EDE (Enhanced Differential Evolution) and EDTLA- (Enhanced Differential Teaching Learning-based Algorithm) based approaches, which are used for minimization of the residential total energy cost and maximization of the end-user comfort level. The problem of optimal scheduling of household appliances has been explored in [11]. The authors used the day-ahead changeable peak pricing technique for the minimization of the consumer ’s energy consumption cost using a combination problem approach. This approach enables customers to schedule their household appliance using MKP (Multiple knapsack problem) formulation. In [12], the authors implemented GPSO (Gradient-based Particle Swarm Optimization) for DR in smart homes by considering load and energy price uncertainties. The authors employed GA and BPSO (Binary Particle Swam Optimization) for optimal scheduling of home appliances in [13]. They proposed GAPSO (Genetic Algorithm with Particle Swam Optimization), a hybrid scheme of both these techniques, to obtain better results in terms of reducing PAR, minimization of electricity cost and especially end-user discomfort. Day-Ahead Pricing (DAP) and Critical Peak Pricing (CPP) are used as pricing schemes for single and several days. The authors used GA and TLBO and their hybrid TLGO (Teacher Learning-based Optimization with Genetic algorithm) for appliance scheduling in [14]. They categorized ﬂexible appliances as time ﬂexible and power ﬂexible for proﬁcient energy consumption of consumers in SG. This approach enables energy consumers to schedule their appliances to obtain optimized energy consumption. This approach also maximizes the comfort level of customers with restricted total energy consumption. The authors in [15] discussed the strategy for scheduling appliances in order to reduce carbon emissions along with the reduction of the electricity bill and waiting time. They applied the cooperative multi-swarm PSO technique to achieve their goals; however, they did not consider PAR. The authors implemented the 0/1 multiple knapsack problem with the genetic algorithm to ﬁnd a good solution in [16]. A simple ﬁtness function is evaluated for each appliance in every time slot to obtain the desired results. The authors proposed a Demand-Side Management (DSM) strategy. This technique is based on a load shifting strategy during peak hours to reduce electricity bills using an Evolutionary Algorithm (EA). The authors discussed the strategy of the load shifting-based generalized technique, from on-peak hours to off-peak hours of a day, to minimize energy cost. This mechanism can support a large number of controlled devices of numerous types to minimize end-user electricity bills. An adaptive energy model for DSM in smart homes has been proposed by the authors in [17]. Distributed RESs’ usage is optimized using the ACO algorithm. In [18], Kusakana et al. used the TOU pricing model along with the integration of RESs and BSUs to minimize the end-user ’s electricity bill and achieve energy consumption balancing. The authors proposed a model to sale extra generated energy back to the utility, as per their prior agreement. For minimization of the end-user electricity bill, Bharathi et al. suggested a model in [19], which works in industrial, commercial and residential areas. For optimization, the authors used GA. They also compared the different EA with GA and found that it gave a maximum decrease of 21.9% in the consumption of energy. Appl. Sci. 2019, 9, 792 4 of 25 In [20], the authors proposed objective function generalization using the DR program to minimize the residential consumer electricity bill. The authors showed that by shifting the load, unexpected peaks were observed in off-peak hours. They evaluated this later peak formation with multi-CPP and multi-TOU pricing schemes combined with DAP concepts. In [21], in order to lessen the end-user electricity cost and minimize the end-user discomfort, Ogunjuyigbe et al. developed a GA-based optimization technique for scheduling of appliances. In [22], authors presented a DSM strategy, by shifting the load from on-peak hours to off-peak hours, using DAP signal and Evolutionary Algorithm (EA). However, consumer comfort is not considered. In [23], the authors proposed a Quality of Experience (QoE)-based home energy management system. They gave the priority to the end-user ’s frustration. Two algorithms that run the HEM system are: “QoE-aware Cost Saving Appliance Scheduling (Q-CSAS)” for scheduling of controlled load and “QoE-aware Renewable Source Power Allocation (Q-RSPA)” for management of appliances for renewable energy sources’ surplus energy. They reduced energy cost to 30–33% without RES and 43–46% with RESs for the end-user annoyance rates of 1.67–3.36 and 1.70–3.43, respectively. In [24], the authors introduced three heuristic-based algorithms: GA, ACO and BPSO, to maximize user comfort, minimize PAR and minimize electricity cost, as well. In [25], the authors proposed a hybrid GA-PSO, which is a combination of the GA and PSO algorithm, for energy management and obtaining maximum end-user comfort in smart homes. K. Muralitharan et al. [26] presented multi-objective EA for the minimization of electricity bill and appliances waiting time. As soon as the running appliances’ load increases from a threshold, they are switched off. A multi-residential energy scheduling issue with multi-class appliances in a smart grid was discussed in [27]. The authors proposed a PL-generalized Benders algorithm (Property (P) and L-Dual-Adequacy) for bill minimization and bounded user comfort. In [28], the authors proposed a distributed algorithm for shifting the load from on-peak hours to off-peak hours. They used the game theory approach for scheduling the residential load. The Nash equilibrium convergence rate was also accelerated by the Newton technique. PAR and end-user discomfort were minimized. The aforementioned research works achieved the cost minimization and reduction of PAR at the cost of end-user ’s waiting time. Therefore, in this paper, using TG-MFO, we achieved a nearly-zero waiting time along with cost and PAR minimization. Table 1 depicts the achievements and limitations of the aforementioned research work. Appl. Sci. 2019, 9, 792 5 of 25 Table 1. Critical analysis of the related work. OSR, Optimal Stopping Rule; TLBO, Teaching Learning-Based Optimization; DAP, Day-Ahead Pricing; GPSO, Gradient-based Particle Swarm Optimization; TLGO, Teacher Learning-based Optimization with Genetic algorithm; CPP, Critical Peak Pricing; CP, Constrained Programming. Mechanisms/Techniques Objectives/Requirements Achievements Limitations Threshold based OSR [8] Minimization of electricity bills. Reduced cost. Threshold-based cost minimization. GA [9] Minimization of electricity bills. Reduced electricity bill. No PAR is considered. GA, TLBO [10] Minimization of PAR and electricity bills. Reduced cost and PAR with RES. No end-user comfort priority. MKPwith DAP [11] Minimization of total energy and electricity bill. Reduced power consumption and electricity bill. Less end-user comfort level. No end-user comfort level and no RES and GPSO with DR [12] Minimization of PAR and electricity bills. PAR and minimization of electricity bill. congestion problem. MKP with GA, PSO and GAPSO [13] Minimization of total energy and electricity bill. Minimization of electricity bill. Less end-user comfort level and no RES. GA and TLGO algorithm [14] Cost minimization plus congestion control. Minimization of electricity bill. Waiting time increased. PSO [15] Optimization of the appliances. Carbon emission, bill and waiting time minimization. Less end-user comfort level and no RES. 0/1 MKP and GA [16] Minimization of PAR and electricity bills. Minimization of PAR and peak load shifting. Less end-user comfort level and no RES. ACO [17] Distributed RES usage is optimized. Minimization of PAR and peak load shifting. End-user comfort has been compromised. TOU along with RES and BSUs [18] To minimize the end-user electricity bill. Energy consumption balancing. User comfort has been compromised. Bill minimization for industrial, commercial and GA-based DSM [19] Compared with EA, 20.9% reduction in bill. End-user comfort has been compromised. residential consumers. Objective function generalization using the DR DR with CPP and ToU [20] Minimized residential consumer electricity bill. End-user comfort is ignored. program to minimize bill. Bill minimization keeping consumers’ maximum GA [21] Managed the load as per end-user budget. PAR has been compromised. satisfaction. EA with DAP [22] Energy bill minimization. Bill is minimized. User comfort has been compromised. Q-CSAS and Q-RSPA [23] Energy bill minimization. Bill is minimized. User comfort has been compromised. GA, ACO and BPSO [24] Cost minimization plus congestion control. Minimization of electricity bill. Less end-user comfort level. Bill minimization keeping consumers’ GA-PSO [25] Minimized electricity bill. Less end-user comfort. maximum satisfaction. Minimization of electricity bill and appliances Multiobjective EA [26] Minimized electricity bill and appliances waiting time. Appliances’ interruptions increased. waiting time. Bill minimized with upper and lower bounds on PL-generalized Benders algorithm [27] Multi-residence and multi-class appliance. No RESs and BSUs are integrated. user comfort. Used distributed algorithm, minimization of PAR Game theory, Nash equilibrium [28] PAR and end-user discomfort have been minimized. No RES integration. and discomfort. Appl. Sci. 2019, 9, 792 6 of 25 3. Key Contributions The key contributions of this research work are summarized as follows: We have proposed a new hybrid end-user comfort-based TG-MFO algorithm for an efﬁcient EMS in smart homes. We have explored and analysed the performance of ﬁve bio-inspired algorithms for the energy optimization problem in the residential sector. Through simulations, we have shown that using TG-MFO, the energy cost can be reduced up to 49.96% compared to existing methods, with nearly-zero end-user discomfort and PAR up to 60%. We have integrated RESs and BSUs for further minimization of the total load and its cost. We have applied the proposed algorithms on different consumer scenarios, such as: (a) A single home for one day, (b) A single home for 30 days, (c) Thirty different sizes of homes for one day and (d) Thirty different sizes of homes for 30 days, compared to the existing techniques. We have considered different sizes of homes with different power ratings of appliances and different LOTs as compared to earlier techniques, which are applied on either one home or multiple homes with the same lifestyle. 4. Proposed System Model 4.1. Architecture In SG, in order to obtain a reliable and efﬁcient operation, DSM is used. Two main objectives of DSM are end-user controlling activities and energy management. A Smart Home (SH) consists of a smart meter along with the EMC, for a reliable bi-directional power and information ﬂow between SG and SH [29]. All appliances, connected sensors, RESs and BSUs are connected to EMC through a Home Area Network (HAN), which is further connected to SG through a Wide Area Network (WAN). Different WAN solutions are available like PLC, Wi-Fi, Wi-Max and GSM [30]. End-users manage their energy consumption activities as per incentives offered by the utilities. In each SH, the end-user puts various parameters of all appliances in EMC. EMC is then responsible for the ON/OFF status of all appliances. Figure 1 shows the proposed system model architecture. 4.2. Appliances’ Categorization and Their Energy Models TO design an optimized model, we have divided the load according to the end-user ’s priorities, as given below. 4.2.1. The Fixed Load These are those regular appliances whose starting time remains ﬁxed. That is, a consumer can start and stop these appliances any time. Refrigerator and interior lights are examples of Fixed Load (FL). The energy consumed by all ﬁxed appliances in the total time interval of 24 h can be found as in Equation (1) [24]. E = r X t (1) f å å f f ,n f a p 2 AP n=1 f f subject to: a t b f f f where “a p ” denotes each ﬁxed appliance, AP is the set of ﬁxed appliances, r is the power f f f rating, X is the ON (1) and OFF (0) states of the nth ﬁxed appliance, t is the LOT, a is the earliest f ,n f f starting time and b is the latest ending time of ﬁxed appliances, respectively. f Appl. Sci. 2019, 9, 792 7 of 25 Most of the research works have considered 24 intervals for their energy calculations, which are usually not applicable to all appliances. Usually, an appliance, for example a microwave oven, a clothes dryer, etc., operates for less than an hour. Hence, further dividing an hour into two sub-intervals of thirty minutes each generates a total of forty-eight (48) time slots, which results in accurate manipulation. However, this slightly increased the manipulation time, but that can be ignored. UtUiltiitlyity Figure 1. A typical overview of a house with smart appliances. EMC, Energy Management Controller. 4.2.2. Elastic Load These are those appliances that can be fully managed, i.e., they can be shifted to any time slot and can also be interrupted at any time keeping in view the minimization of PAR and electricity bill [24]. These include: dish washer, washing machine, spin dryer, electric car, laptop, desktop computer, vacuum cleaner, oven, cook top and microwave oven [31]. The energy consumed by all elastic appliances in the total time interval of 24 h with 48 time-slots can be found as in Equation (2). E = (r X t ) (2) e å å e,n e,n e a p 2 AP n=1 e e subject to: a t b e e e where a p denotes each elastic appliance, AP is the set of elastic appliances, r is the power rating of e e e textth elastic appliances, X is the ON (1) and OFF (0) states of the n elastic appliance, t is the LOT e,n e for each elastic appliance, a is the earliest starting time and b is the latest ending time of elastic e e appliances, respectively. The total energy consumption of the end-user “E ” is given by: E = E + E (3) T f e where “E ” is the ﬁxed appliances total energy and “E ” is the total energy of the elastic appliances. f e Appl. Sci. 2019, 9, 792 8 of 25 4.3. RES Model Photovoltaic (PV) cells and wind turbines can be used as local power generators, also known as distributed RESs, on consumer premises. These RESs can be used for the local energy generation, as well as for charging the batteries in BSUs. The RESs’ generated energy, denoted by E , can be RES calculated as in [32], by approximating a local Gaussian function (Figure 2) as follows: (tm) ( ) 2s E (t, m, s) = p e (4) RES s 2p where t denotes the prospection variable (time), m is the mean or central value and s is the standard deviation. RES 4 6 8 10 12 2 4 6 8 10 12 0 2 Time (Hours) (a) (b) Figure 2. (a) Gaussian function representing the approximate PV cells’ energy generation (Wh) [32]. (b) RES-generated energy E for a single home. RES The total daily energy generated from RESs must be positive, i.e., greater than zero and on a daily basis, it is given by: 0 E E (5) RES RES (max) where E is the maximum available RESs’ generated energy capacity. If in any time interval, the RES (max) RESs’ generated energy exceeds the end-user energy demand E , i.e., E > E (6) RES T then it is sold back to the grid as per their prior agreement or can be used for charging batteries in BSUs for later use, particularly during peak hours. 4.4. BSU Model When RESs’ generated energy exceeds the consumer energy demand, it is stored in the batteries using BSUs, which can be used during on-peak hours or night-time, when RESs are not available. This can be modelled using a binary variable X as: bat 1 for charging X = (7) bat 0 for discharging where X shows the charging and discharging states of the batteries. In this model, we ignore the bat energy losses during the charging and discharging process. RES generated from solar PV cells (Wh) Appl. Sci. 2019, 9, 792 9 of 25 4.5. Types of Users Residential users have been categorized as follows. 4.5.1. Non-Active Users Non-Active Users (NAUs) do not use RESs and/or BSUs. They fulﬁl their load demand only from the utility grid. They can reduce their electricity bill by transferring their loads to off-peak hours. The consumed energy of NAU is calculated using the following equation: E = E (8) N AU T where E is the energy consumption of all non-active users and E is the total energy consumption N AU T of all appliances. 4.5.2. Semi-Active Users Semi-Active Users (SAUs) may generate their own energy using RESs and get energy from the grid when needed, i.e., when their demand exceeds the RESs’ generated energy or when RESs are not available. That is, the end-user energy demand from the grid will be the total used energy minus their self-generated RES energy. Their consumed energy is calculated using the following equation: E = E E (9) S AU T å RES,n n=1 where E is the energy consumption of semi-active users and E is the energy generated S AU RES from RESs. 4.5.3. Fully-Active Users Fully-Active Users (FAUs) generate their own energy using RESs and store the extra generated energy in the batteries using BSUs. They obtain energy from the grid when needed, i.e., when their demand exceeds the RESs’ generated energy plus the BSUs’ stored energy. Their energy consumption pattern is calculated using the following equation: E = E E E (10) FAU T å RES,n BSU,n n=1 where E is the energy consumption of fully-active users, E is the nth consumer ’s RESs’ FAU RES,n generated energy and E is consumers’ stored energy using BSUs. Now, if E is positive, this BSU,n BSU means that RESs are charging the batteries, and if E is negative, this means batteries are discharging BSU and providing energy to the load. 5. Problem Formulation In this work, we assumed a single home and thirty homes with different power ratings of appliances, as tabulated in Table 2. Our required objectives are: (a) Consumers’ high comfort level by reducing appliances’ average waiting time, (b) Consumers’ electricity bill minimization, (c) Minimization of PAR and (d) Integration of RES and BSU in the system for further reduction of end-user waiting time. These objectives can be achieved by the optimization of the energy consumption proﬁles of home appliances, using different scheduling techniques. If V is the maximum energy capacity in every time T Appl. Sci. 2019, 9, 792 10 of 25 slot, then the end-user electricity cost along with PAR can be minimized, keeping aggregated energy consumption of cumulative home appliances within the maximum threshold limit of V . Mathematically, this constraint can be shown as follows: E V (11) T T Here, E is the total energy demand of the end-user. Table 2. Appliances and their running time constraints [31]. LOT, Length of Operational Time. Power Rating Starting Ending Time-Span LOT S. No. Appliance Category r (KW) Time (a) Time (b) (b a) (h) (h) e,n 1 Fridge-1 Fixed 0.3 00 24 24 24 2 Interior Lighting-1 Fixed 0.84 18 24 06 6.0 3 Dish Washer-1 Elastic 2.0 09 17 08 2.0 4 Washing Machine-1 Elastic 0.6 09 12 03 1.5 5 Spin Dryer-1 Elastic 2.5 13 18 05 1.0 6 Cook Top-1 Elastic 3.0 08 09 01 0.5 7 Oven-1 Elastic 5.0 18 19 01 0.5 8 Microwave-1 Elastic 1.7 08 09 01 0.5 9 Laptop-1 Elastic 0.1 18 24 06 2.0 10 Desktop-1 Elastic 0.3 18 24 06 3.0 11 Vacuum Cleaner-1 Elastic 1.2 09 17 08 0.5 12 Electrical Car-1 Elastic 3.5 18 08 14 3.0 1 Fridge-2 Fixed 0.25 00 24 24 24 2 Interior Lighting-2 Fixed 0.9 19 24 07 7.0 3 Dish Washer-2 Elastic 1.9 11 15 04 2.0 4 Washing Machine-2 Elastic 0.5 10 14 04 2.0 5 Spin Dryer-2 Elastic 2.0 10 16 06 2.0 6 Cook Top-2 Elastic 3.5 09 10 01 0.5 7 Oven-2 Elastic 5.4 17 20 03 1.5 8 Microwave-2 Elastic 1.9 07 09 02 0.8 9 Laptop-2 Elastic 0.09 16 23 07 3.0 10 Desktop-2 Elastic 0.28 14 20 06 2.0 11 Vacuum Cleaner-2 Elastic 1.4 10 16 06 1.5 12 Electrical Car-2 Elastic 3.3 16 09 17 4.0 1 Fridge-3 Fixed 0.5 00 24 24 20 2 Interior Lighting-3 Fixed 0.62 17 06 13 13 3 Dish Washer-3 Elastic 2.5 10 16 06 2.5 4 Washing Machine-3 Elastic 0.8 08 14 06 1.8 5 Spin Dryer-3 Elastic 2.5 13 19 06 1.0 6 Cook Top-3 Elastic 3.2 07 09 02 0.5 7 Oven-3 Elastic 5.3 16 18 02 1.5 8 Microwave-3 Elastic 1.9 10 14 04 1.0 9 Laptop-3 Elastic 0.2 16 24 08 2.5 10 Desktop-3 Elastic 0.4 18 20 02 1.0 11 Vacuum Cleaner-3 Elastic 1.3 11 12 01 0.5 12 Electrical Car-3 Elastic 3.4 16 07 11 5.0 1 Fridge-4 Fixed 0.4 00 24 24 18 2 Interior Lighting-4 Fixed 0.7 19 08 13 13 3 Dish Washer-4 Elastic 2.3 08 19 11 4.0 4 Washing Machine-4 Elastic 0.9 11 14 03 1.0 5 Spin Dryer-4 Elastic 2.0 14 20 06 1.0 6 Cook Top-4 Elastic 3.5 10 12 02 1.2 7 Oven-4 Elastic 5.5 10 11 01 0.8 8 Microwave-4 Elastic 1.9 10 14 04 1.5 9 Laptop-4 Elastic 0.15 11 23 12 4.0 10 Desktop-4 Elastic 0.4 09 24 15 6.0 11 Vacuum Cleaner-4 Elastic 1.5 11 16 05 1.2 12 Electrical Car-4 Elastic 4.0 10 22 12 4.0 Appl. Sci. 2019, 9, 792 11 of 25 5.1. PAR The peak to average ratio can be minimized, using the scheduling algorithms, which is in favor of both the utility and consumer for maintaining demand-supply balance. It is the ratio of the peak load of the consumer to the average load of the consumer, in every interval of time, and is denoted by m. Mathematically, it is deﬁned as in [33]: max m = (12) T,n n=1 5.2. User’s Comfort in Terms of Waiting Time (t ) User ’s comfort in terms of waiting time is important for end-users. Waiting time must be minimized to have a high comfort level so that the end-user ’s frustration can be avoided. It is that interval of time when a consumer switches on an appliance, and due to the scheduling limitations of the system, he/she has to wait to start its operation. As we have deﬁned the earliest starting time a and the latest ending time b of an appliance, then another parameter h will be the operational starting time of the same switched-on appliance. This is shown diagrammatically in Figure 3. Here, b-a is the time span, deﬁned by the consumer, as given in Table 2. Figure 3 shows that a consumer ’s maximum waiting time could be up to h . Since LOT is already deﬁned by the consumer, so at h , the max max algorithm will have to start the appliance to complete its operation up to the ﬁnal time b. For example, Dishwasher-1 (Table 2) has a time span of 8 h (from 9:00–17:00) and LOT = 2 h. This means that our proposed algorithm (TG-MFO) must start Dishwasher-1 from 9:00–17:00 to complete its operation of 2 h, with a waiting time ranging from 0–6 h. Figure 3. Starting time, ending time, LOT and waiting time. Here, LOT is the length of the operational interval of time, in which an appliance completes its task. In the case of ﬁxed appliances, there is no issue of waiting time, as whatever time the consumer wants to switch it on, he/she can do so. Therefore, we do not include ﬁxed appliances in the scheduling problem. Now, since, (b a) LOT (13) Therefore, the range of waiting time can be a to h , as shown in Figure 3. max Appliances’ normalized waiting time (t ) can be calculated as: h a t = (14) (b LOT) a Equation (14) shows that the normalized waiting time can be from “0” (when h = a) to “1” (when (b LOT) = h). Table 2 illustrates the typical electricity demand of a single home and multiple homes, with different power ratings and types of appliances, their LOTs and (a) and (b) constraints [31]. Since Appl. Sci. 2019, 9, 792 12 of 25 different end-users have different habits and life routines, with different sizes and power ratings of appliances, we have assumed four (4) types of homes and randomly selected through the proposed algorithm, to have randomness in the consumed energy when taking multiple (here, 30) homes. 5.3. Objective Function Mathematically, our objective function can be formulated as follows: 48 N min [l (E z ) + (l t )] (15) å 1 å T,n n 2 w m=1 n=1 where z is the energy cost in every interval of time. Our proposed objective function aims to reduce electricity cost, while maintaining a higher end-user comfort level by minimization of waiting time. l and l are multiplying factors of two portions of the objective function. Their values can be either “0” or “1” so that (l + l ) = 1 [24]. This reveals that either l and l could be 0 or 1. That is, if a consumer 1 2 1 2 does not want to participate in the load scheduling process, then his/her multiplying factors will be l = 1 and l = 0 in the objective function. 6. Scheduling Algorithms Heuristic means “to discover ”, or “to ﬁnd” or “to hit upon” by experiment, trial and error approaches. The solution of an optimization problem can be found in a realistic interval of time. However, such optimization techniques cannot guarantee the optimal solution. Meta-heuristic means “to ﬁnd on a higher level” or “to ﬁnd ahead of” local optimization. This means its performance is superior to straightforward heuristics techniques. All such algorithms use the process of local search and randomization, which further provides a path to global search and optimization. The problem of scheduling home appliances optimally, using different meta-heuristic algorithms like GA, ACO, FA, MFO and CSA, is discussed in Section 6. Various classical programming techniques like LP, ILP, MILP, DP and CP have already been used by researchers for optimal scheduling of home appliances. The convergence time of these classical techniques is very large due to the exact solution, and to schedule a large number of appliances, they cannot be used. Furthermore, classical algorithms usually show the best results for local optimization, as compared to the global point of view. Therefore, due to their probabilistic nature, bio-inspired meta-heuristic algorithms give good results in the case of local, as well as global solutions. 6.1. GA GA is in the family of evolutionary algorithms. This algorithm’s name is due to it being inspired the genetic progression of living organisms. It has a quick rate of convergence. GA carries out parallel search operations in the provided solution space, which reduces the chances of being trapped in the local optimal solution. For complex non-linear problems’ formulation, GA is the best option, especially where the global optimization is a challenging job. For any solution deployment, as GA is probabilistic in nature, the optimality is usually not guaranteed [34]. GA initiates a random population known as chromosomes, and then, in every iteration, the generated population is updated. Home appliances are mapped with bits of chromosomes. The ﬁtness function of a given problem is evaluated by the suitability of each chromosome. In every iteration, the population is updated by storing the present local best solution, known as elitism. After elitism, in order to reproduce new chromosomes, two parent chromosomes are chosen using the tournament-based selection technique. Then, on the basis of selected chromosomes, the crossover procedure is performed. New offspring are added to update the present population [35]. Table 3 shows the GA parameters. Appl. Sci. 2019, 9, 792 13 of 25 Table 3. GA parameters. S.No. Parameter Value 1 Population size 200 2 Crossover probability 0.8 3 Mutation probability 0.2 4 Maximum number of generations 800 6.2. MFO The nature-inspired algorithm MFO was proposed by Seyedali Mirjalili in 2015 [36]. Moths are butterﬂy-like insects, having 160,000 plus different species in nature. They have their unique navigation mechanism known as transverse orientation when ﬂying in the moonlight. When they ﬂy in a spiral, they maintain a constant angle related to the moon, ultimately converging in the direction of light. The spiral articulates the searching region, and it assures the exploitation of the optimum solution. Since MFO is a population-based algorithm, the movement of m moths in n dimensions (variables) is given in the position matrix form as follows: 2 3 q ... q 1,1 1,n 6 7 Q = (16) 4 ... ... ... 5 q ... q m,1 m,n The resultant ﬁtness values, for “m” number of moths, are stored in an array. The ﬁtness function (objective) evaluates each moth’s ﬁtness value. Each moth’s position vector, i.e., matrix Q’s ﬁrst row, is evaluated on the ﬁtness function, and its output is then allocated to its respective moth. Similarly, a matrix U is assigned to the corresponding ﬂames as follows: 2 3 u ... u 1,1 1,n 6 7 U = ... ... ... (17) 4 5 u ... u m,n m,1 Now, in mapping our problem of the optimum scheduling of home appliances, moths act as searching agents, and ﬂames are the optimum positions. In each iteration, a moth searches for an optimum ﬂame, with updates in the next iteration for the best solution by comparing with the previous one. Moths follow the logarithmic spiral for their update positions, where moths start from some initial position, following some limited ﬂuctuating search space, and reach their destination ﬂames. In MFO, the logarithmic spiral is: bt S(X , P ) = d e cos(2pt) + P (18) i j i j where d = jP X j is the ith moth distance from jth ﬂame, b is the spiral shape deﬁning the constant i j i and the random number t lies between 1 and one. When t = 1, this means the moth is closest to its destination ﬂame, while t = 1 indicates that its farthest position from the ﬂame. Therefore, the moth is always assumed to be in a hyper-ellipse space, which guarantees the exploitation and exploration of search space. Table 4 depicts the MFO parameters. Table 4. MFO parameters. S. No. Parameter Value 1 Number of moths and ﬂames 12 2 Max. No. of Iterations 1000 3 Lower bound L 100 4 Upper bound U 100 b Appl. Sci. 2019, 9, 792 14 of 25 6.3. TG-MFO In this work, we apply the bio-inspired algorithms GA, MFO and their hybrid version TG-MFO. Then, we compare their results with some of the existing techniques like ACO, CSA and FA on randomly-generated data. Then, we apply the strategy of the time constraints of end-users, i.e., for each appliance to switch-ON, we give some time span as the initial and ﬁnal thresholds for all appliances. A user initiates the operation of an appliance, but usually, it is allowed to remain OFF for a certain time interval, in which the user has no problem or frustration. We apply this time threshold policy, to have a zero end-user waiting time. TG-MFO is based on the hybridization of GA and MFO with time constraints. Initially, MFO is applied on randomly-generated data for the optimization problem to obtain the local best positions for home appliances. Then, GA is applied to compare MFO’s local best solution with the new random data, to ﬁnd the global best solution in each iteration. The ﬁtness functions are updated accordingly. This process continues until the termination criterion is fulﬁlled. Figure 4 depicts the steps involved in the TG-MFO implementation process, while, the pseudocode of Algorithm 1 shows the step-by-step working of the proposed TG-MFO algorithm. 6.4. ACO ACO is a bio-inspired meta-heuristic iteration-based optimization technique. Using pheromone trails, chemicals as signals to other ants left on the ground known as the Stigmergy principle, starting from their nest, in search of food, ants ﬁnd the shortest routes between their origins to the destination. If an ant wants, with a certain probability, to follow a particular path, it follows the pheromone trail. It reinforces the other ants by laying more pheromone on the same trail. As the movement of ants increases on a route, the amount of pheromone increases. Since pheromones’ nature is volatile, so the shortest path has more pheromone as compared to the longer one. As a result, ants’ movement increases on the shortest route. Using this principle, ACO is used for the solution of discrete combinatorial search optimized-solution problems. Self-organization and self-healing are the distinguishing properties of ACO. ACO is used for the residential consumer ’s energy optimization, which is a novel scheme for such energy management problems [24]. The ACO parameters are given in Table 5. Table 5. ACO parameters. S. No. Parameter Value S. No. Parameter Value 1 No. of Ants 12 4 Evaporation rate 5 2 Pheromone intensity factor a 2 5 Trail decay factor 0.5 3 Visibility intensity factor b 6 6 Max. iterations 600 1 Appl. Sci. 2019, 9, 792 15 of 25 Start Initialize all parameters: α, β,ρ, τ etc GA phase Random generation of MFO phase population Yes Random generation End New population is generated > Max. generation Yes No Fitness function is evaluated No Does mutation finished Position of individual Moth is updated Mutation Yes No of iteration > population size One offspring is On the basis of P best selected new population is No generated Yes No Check wither P is best Two parent No achieved values are Does crossover finished selected as: 1 : 2 Yes Present P is best Crossover assigned to old P best Figure 4. Flowchart for the proposed algorithm Time-constrained Genetic (TG)-MFO. Appl. Sci. 2019, 9, 792 16 of 25 Algorithm 1: Pseudocode of the proposed TG-MFO algorithm. 1 Initialization: GA parameters, MFO parameters, the maximum size of the population, No. of iterations. 2 Input: RTP z , AP, r, X, a, b, V , X , l. n T bat 3 MFO phase: 4 Random generation of the initial population of moths Q matrix using Equation (16) i,j 5 Random generation of the initial population of ﬂames U matrix using Equation (17) i,j 6 Fitness function O is evaluated by objective function f ( M) = (U (i) l (i)) rand() + l (i) b b b 7 Position of individual moths Q is updated as per the position of ﬂame U i,j i,j 8 while No. of iterations < population size do 9 for i =1:M do 10 for j =1:N do 11 end 12 New solution is evaluated 13 Present P is assigned to the old P best best 14 GA phase: 15 On the basis of P , generate chromosomes x for i = 1,2,...,n best i 16 Two parent values are selected as 1:2 17 if (The crossover is done then 18 One offspring is selected 19 Mutation is done 20 else 21 Two parent values are selected again till the crossover is ﬁnished 22 end 23 end 24 if (Mutation is ﬁnished then 25 The new population is generated 26 else 27 One offspring is again selected until the mutation is ﬁnished 28 end 29 Present P is assigned to old P best best 30 end 31 Output: E , E , t , m T RES w 6.5. CSA The cuckoo search algorithm was proposed by [37] and belongs to the family of bio-inspired meta-heuristic algorithms. It is used to solve the optimization problems using the mating and production behaviour of some cuckoo species and the characteristics of Lèvy ﬂights of some birds and fruit ﬂies. Certain cuckoo species use nests of other birds to lay their eggs, selected randomly, known as host nests. The birds who own these nests may ﬁnd these eggs and raise the cuckoo’s young. CSA uses certain rules to ﬁnd the best local solution by mapping pattern of eggs (1,0) with home appliances’ ON-OFF condition, stated as follows: The nest is randomly selected, in which each cuckoo lays one egg at a time. For upcoming production, those nests will be selected having the higher quality eggs. The host bird determines that the cuckoo laid the eggs, while the number of host nests is ﬁxed. The algorithm starts the discovery of the local best solution from randomly-given eggs (either one or zero) in the host nests. This one or zero shows the ON and OFF states of home appliances to Appl. Sci. 2019, 9, 792 17 of 25 be scheduled in a given time-slot. According to the ﬁtness function, each egg (probable solution) is assessed. This solution will be our objective of minimum cost and PAR with reduced waiting time constrained. The production step is repeated, while discovering the superior eggs with a probability of 0.25. Lèvy ﬂights are carried out to ﬁnd the global best solution, out of the local best solution [38]. Table 6 gives the CSA parameters. Table 6. CSA parameters. S. No. Parameter Value 1 Number of host nests 12 2 Number of iterations 1000 3 Discovery rate 100 6.6. FA Fireﬂies are in the insect family. They live mostly in humid environments. They generate green, yellow and pale-red limited intensity ﬂashing lights chemically. There are more than 2000 different species. Their unique ﬂashing light pattern is used for communication, i.e., to attract partners and probable prey and as a defensive cautionary mechanism. Some female species apply the ﬂashing light mating pattern for the hunting of other species [39]. Like PSO, in FA, inspired by nature, three assumptions are made: (a) all ﬁreﬂies must be of the same sex, (b) the attractiveness of a ﬁreﬂy is directly proportional to its brightness and inversely proportional to the square of the distance between two ﬁreﬂies and (c) brightness is calculated by an objective function: the brighter one will attract the less bright ones. The ﬁreﬂy’s ﬂashing light intensity in complete darkness is related to the solution quality. The brighter ﬁreﬂy will attract less bright ones, depending on the brightness intensity, which is calculated as follows: I( I , r ) = (19) o i,j i,j where I is the ﬂashing light intensity at the origin and r is the distance of ﬁreﬂy j from ﬁreﬂy i. Let g o i,j be the coefﬁcient of the ﬁreﬂy’s ﬂashing light absorption in a medium, then, in the above equation, the light intensity I will vary with the distance between ﬁreﬂies r using the following equation: i,j gr i,j I( I , g, r ) = I e (20) o o i,j Both Equations (19) and (20) can be combined using the Gaussian form as follows: gr i,j I( I , g, r ) = I e (21) o i,j o The following approximation can be used for a slower rate of decrease in the light intensity between the origin and the target. I( I , g, r ) = (22) i,j 1 + gr i,j As the less bright ﬁreﬂy will be attracted to the brighter ﬁreﬂy, this attractiveness b between two ﬁreﬂies can now be mapped as: gr i,j b(b , g, r ) = b e (23) o i,j o Appl. Sci. 2019, 9, 792 18 of 25 where b is the attractiveness at the zero distance. For b = b at the zero distance, r = 0. Therefore, o o i,j for a characteristic distance of r = , Equation (23) becomes: b(b , g, r ) = b e . The distance o i,j o between any two ﬁreﬂies x and y at positions i and j is calculated by: r = Dist.(x , y ) = jjx y jj = (x y ) (24) i,j i j i j å i,k j,k k=1 The ﬁreﬂy movement towards another ﬁreﬂy has two parts: (a) The movement will be for ﬁnding a better solution using attractiveness. (b) The movement will be random. x = x + ( Attractiveness Distance) + Randomness (25) i i gr i,j x = x + b e .(y x ) + a(Rand() 0.5) (26) i i j i where a is the randomness parameter and Rand is a random number generated lying between zero and one. Two extreme points are that when g is zero, attractiveness will be constant, and when g is ¥, attractiveness will almost be zero. Practically, g lies between zero and ¥, so FA gives good results in ﬁnding local, as well as global optima [39]. Table 7 depicts the FA parameters. Table 7. FA parameters. S. No. Parameter Value 1 Randomness parameter (a) 0.2 2 Attractiveness (b) 2 3 Absorption coefﬁcient (g) 1 7. Results and Discussions 7.1. Consumer Scenarios In the present work, four types of consumer scenarios were simulated and discussed. In the ﬁrst case, a single home was taken, and its hourly load, hourly energy cost, PAR and waiting time were determined both in the unscheduled and scheduled (with ACO, CSA, GA, FA, MFO and TG-MFO) environment for a single day. In the second case, a residential building with thirty homes having users with different habits with different LOTs and different power ratings of appliances were considered. Again, their hourly average load, hourly cost, PAR and waiting time were determined both for unscheduled and scheduled (with ACO, CSA, GA, FA, MFO and TG-MFO) scenarios for a single day. In the third case, we considered a single home, found all four of its parameters for unscheduled and scheduled scenarios for a complete month, i.e., thirty (30) days, and found its monthly bill. In the fourth case, a residential building with thirty homes was considered, and we determined its daily average load, daily cost, daily PAR and average waiting time for a complete month, i.e., thirty (30) days, as well as calculated its monthly electricity consumption and electricity bill. In all four cases, the RTP scheme was used. For the system’s stability, further reduction of electricity consumption and maximum user comfort, RES and BSUs were also integrated. Additionally, for photovoltaic cells’ electricity generation, temperature, solar irradiance, battery charging/discharging rates and its storage system, different assumptions were considered from [40]. 7.2. Pricing Signal Different pricing signals were available. We used the day-ahead real time pricing (RTP) signal in our simulations, as shown in Figure 5. Appl. Sci. 2019, 9, 792 19 of 25 RTP 8 12 16 20 24 4 8 Time (hours) Figure 5. Day-ahead real-time pricing signal. 7.3. The Average Waiting Time Waiting time is a very important feature of appliance scheduling for optimal energy consumption in the smart grid. To reduce electricity cost, usually, waiting time increases. A user wants to start an appliance, but due to scheduling time constraints, the user has to wait for to start its operation. Our main objective in this work was to minimize the user electricity bill, keeping in view the maximum comfort level of the end-user. Figure 6 shows that we achieved our objective using heuristic techniques for optimal scheduling. The graphs show that TG-MFO outperformed ACO, CSA, GA, FA and MFO in achieving a nearly-zero waiting time for the end-user. Un-sch GA -sch MFO-sch ACO -sch CSA -sch FA -sch TG-MGO-sch 1 Home 1 day 1 Home 30 days 30 Homes 1 day 30 Homes 30 days No. of homes/days Figure 6. Average waiting time for a single home and 30 homes. 7.4. The Total Electricity Cost Figure 7 shows the electricity cost for the unscheduled and scheduled (with ACO, CSA, GA, FA, MFO and TG-MFO) load. The results show that the electricity cost of the meta-heuristic algorithms-based scheduled load was very low as compared to the unscheduled load cost. In Figure 7a, the operation of a single home for a single day is considered. In this case, ACO-based scheduling showed better results as compared to all scheduled and unscheduled costs. Similarly, in Figure 7b, the case of a single home for 30 days (one month) is shown, in Figure 7c, that of 30 homes with different LOTs and power ratings for 30 days (one month), and in Figure 7d, the case of 30 homes for 30 days; the scheduled cost was very much as compared to the un-scheduled cost. In all four cases, ACO outperformed all scheduling techniques. Avg. waiting time (h)) Electricity Cost (Cents) Appl. Sci. 2019, 9, 792 20 of 25 8 400 4 200 2 100 Un−sch GA MFO ACO CSA FA GT−MFO Un−sch GA MFO ACO CSA FA GT−MFO (a) (b) 600 10000 0 0 Un−sch GA MFO ACO CSA FA GT−MFO Un−sch GA MFO ACO CSA FA GT−MFO (c) (d) Figure 7. Total cost for un-scheduled, and GA, MFO, ACO, CSA, FA and TG-MFO Scheduled load (a) Total cost for a single home for 1 day. (b) Total cost for single home for 30 days. (c) Total cost for 30 homes for 1 day. (d)Total cost for 30 homes for 30 days. 7.5. Hourly Load Figure 8 shows the total hourly load of a single home and 30 homes with unscheduled and scheduled loads with the bio-inspired algorithms ACO, CSA, GA, FA, MFO and TG-MFO. The results show that as compared to the unscheduled load, meta-heuristic algorithm-based scheduled load was shifted to the off-peak hours, where not only the price was low, but RES was also available, considering the end-user ’s time constraints for the maximum comfort level. The ﬁgure shows that our proposed algorithm gave comparative results for both single and multiple homes with different sizes, power ratings and LOTs. 7.6. Integration of RES and BSU In order to minimize the consumed energy for further reduction of the total cost, RES and BSUs were integrated in homes. Figure 9 shows that the day-time load will be supported by RES, while extra energy will be stored in BSUs for running the load in peak hours. It drastically reduced the cost. The ﬁgure depicts that our proposed TG-MFO algorithm has intelligently not only shifted the load to day-time off-peak hours for cost minimization, but also reduced the PAR. 7.7. PAR PAR plays an important role in the optimal scheduling of smart home appliances. Due to high PAR, the utility faces huge peak loads during peak hours, and the rest of the day, most of the generating units remain idle. Therefore, researchers try to reduce PAR for economical load dispatch in smart grids. Figure 10 shows that, in the case of a single home for a single day and thirty homes for a single day, MFO performed better than FA, while in the case of a single home for thirty days and thirty homes for thirty days, FA showed better results than MFO. In our proposed hybrid model, we tried to not only schedule appliances optimally, economically and having maximum end-user comfort, but also gave the lowest PAR, for the beneﬁt of utility, and hence, to further increase the end-user comfort level. Total Cost ($) Total Cost ($) Total Cost ($) Total Cost ( $ ) Appl. Sci. 2019, 9, 792 21 of 25 Un−sch GA Sch MFO Sch ACO Sch CSA Sch FA Sch GT−MFO Sch 8 10 12 14 16 18 20 22 24 2 4 6 8 Time (Hours) (a) Un−Sch GA Sch MFO Sch ACO Sch CSA Sch FA Sch GT−MFO Sch 8 10 12 14 16 18 20 22 24 2 4 6 8 Time (hours) (b) Figure 8. The hourly load for un-scheduled and GA-, MFO-, ACO-, CSA-, FA- and TG-MFO-scheduled load. (a) The hourly load for a single home. (b) The hourly load for 30 homes. Un−Sch demand GA Sch MFO Sch TG−MFO Sch RES BSU charge BSU discharge Un−Sch demand Plot −50 8.00 12.00 16.00 20.00 00.00 4.00 8.00 Time (hours) Figure 9. Energy demand curves of the scheduled and the un-scheduled load along with RES and BSUs. A comparison of the proposed algorithm with state-of-the-art research works in the smart grid environment for energy optimization and end-user comfort is depicted in Table 8. Most of the existing techniques have used trade-offs between user comfort and bill minimization. Load (kWh) Load (kWh) Electricity Demand(KW) Appl. Sci. 2019, 9, 792 22 of 25 Un−sch GA MFO ACO CSA FA GT−MFO (a) Un−sch GA MFO ACO CSA FA GT−MFO (b) Figure 10. PAR for un-scheduled and GA-, MFO-, ACO-, CSA-, FA- and TG-MFO-scheduled load. (a) PAR for a single home. (b) PAR for 30 homes. Table 8. Comparison of TG-MFO with the state-of-the-art work. Cost Techniques No. of Homes/Days Waiting Time Reduction K. Ma et al. [5] 34% 1.76 h Y. Peizhong et al. [8] 30 days 20% 7.64 h TLGO [14] 33% 1.83 h TLBO 31.5% 2.14 h GA 31% 2.37 h Ogunjuyigbe et al. [23] 9.6 (dis-satisfaction level) 20.2= 30.9= Pilloni et al. [25] 33% 1.65 to 1.70 (Annoyance rate) K. Muralitharan et al. [28] 10 Home appliances 38% 73.32 s 11 76.28 s 12 86.83 s 13 94.39 s 14 107.58 s TG-MFO (Proposed) 1 home for 1 day 32.25% 0.62 h 1 home for 30 days 19.39% 0.48 h 30 homes for 1 day 43.98% 0.38 h 30 homes for 30 days 49.96% 0.26 h Table 9 shows the performance of the proposed TG-MFO algorithm, compared to unscheduled load and scheduled with the GA, MFO, ACO, FA and CSA algorithms. PAR PAR Appl. Sci. 2019, 9, 792 23 of 25 Table 9. Comparison of the un-scheduled load with GA, MFO, ACO, CSA, FA and TG-MFO. %Cost Waiting % PAR Techniques No. of Homes/Days Cost ($) PAR Reduction Time (h) Change Un- Single home for 1 day 6.2 – – 4.58 – Schedule Single home for 30 days 366 – – — – 30 homes for 1 day 582 – – 3.84 – 30 homes for 30 days 8476 – – — – GA Single home for 1 day 5.8 06.45% 1.75 4.19 8.5% Scheduled Single home for 30 days 332 09.28% 7.41 — — 30 homes for 1 day 340 41.58% 1.45 2.13 44.5% 30 homes for 30 days 4320 49.03% 6.76 — — MFO Single home for 1 day 4.2 32.26% 2.81 3.82 16.6% Scheduled single home for 30 days 296 19.12% 4.62 — — 30 homes for 1 day 490 15.8% 4.67 1.21 68.5% 30 homes for 30 days 4992 41.10% 4.61 — — TG-MFO Single home for 1 day 4.2 32.25% 0.62 2.02 49.8% Scheduled single home for 30 days 295 19.39% 0.48 — — 30 homes for 1 day 326 43.98% 0.38 1.48 61.4% 30 homes for 30 days 4241 49.96% 0.26 — — ACO Single home for 1 day 4.4 29.03% 2.74 2.34 48.9% Scheduled Single home for 30 days 245 33.06% 5.02 — — 30 homes for 1 day 242 58.41% 1.48 1.37 64.3% 30 homes for 30 days 3212 62.10% 1.39 — — CSA Single home for 1 day 4.38 29.35% 2.46 4.26 6.9% Scheduled Single home for 30 days 336 08.19% 5.21 — — 30 homes for 1 day 239 58.93% 6.82 2.67 30.4% 30 homes for 30 days 4295 49.32% 1.18 — — FA Single home for 1 day 5.2 16.12% 4.54 2.45 46.5% Scheduled Single home for 30 days 338 07.65% 2.38 — — 30 homes for 1 day 398 31.61% 1.17 1.83 52.3% 30 homes for 30 days 4852 42.75% 2.32 — — Table 10 shows the runtime of the proposed algorithms using an Intel (R) Core (TM) i5 processor, with 4.00 GB of installed memory (RAM) and the 32-bit Windows 7 Operating system. Table 10. Runtime of the proposed algorithm in four different scenarios. Proposed Algorithm No. of Homes/Days Run Time (s) TG-MFO Single home for 1 day 47.65 Single home for 30 days 123.02 Thirty homes for 1 day 129.18 Thirty homes for 30 days 841.65 8. Conclusions and Future Work In this paper, we mapped GA, MFO and a new efﬁcient and robust hybrid TG-MFO meta-heuristic bio-inspired algorithm for optimal scheduling of home appliances in the smart grid and compared their results with existing techniques of CSA, FA and ACO. We considered a single- and multiple home scenarios in a residential sector. In multiple homes, we took different LOTs and power ratings of appliances to make it more practical. Day-ahead RTP signalling was used for demand response in smart homes. The results show that there was a 6.45%–49.03%, 32.26%–41.10% and 32.25%–49.96% decrease in the total cost with GA, MFO and TG-MFO scheduling, respectively, for single and multiple users. RESs and BSUs were also integrated to obtain a further decrease in the total cost and end-user Appl. Sci. 2019, 9, 792 24 of 25 waiting time. In this work, we tried to not only reduce the total cost, but to achieve a high comfort level of the end-user by minimizing the waiting time of home appliances using the time constraints of a maximum average delay of 0.26–0.62 h. This algorithm can be applied to actual data when and where they are provided. It not only reduces the energy cost, but also increases the stability and reliability of the grid. Future work includes exploration of more bio-inspired algorithms for intelligent and efﬁcient energy optimization, and a multi-objective approach will be applied. Author Contributions: I.U. wrote the ﬁrst draft of the manuscript, proposed the idea and topology design method. S.H. provided technical supervision, insights and additional ideas on presentation. Both of the authors equally contributed, revised and approved the manuscript. 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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

Applied Sciences – Multidisciplinary Digital Publishing Institute

**Published: ** Feb 23, 2019

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