# Towards Cost and Comfort Based Hybrid Optimization for Residential Load Scheduling in a Smart Grid

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## Abstract

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## 1. Introduction

- GAPSO: In this paper, we focus on designing a load shifting technique with day-ahead pricing (DAP) mechanism. We demonstrate the performance of a traditional optimization technique and two heuristic optimization techniques. After analyzing GA and BPSO, it is observed that these techniques show pre mature convergence when dealing with high dimension problems. So, there is a need to develop such an optimization method which can improve search efficiency and precision and adequate to handle multiple constraints. Based on these heuristic techniques, a hybrid technique is proposed with the objectives of cost and discomfort minimization. Extensive simulations are conducted to validate the results. The efficiency of the proposed technique is validated by analyzing the performance metrics, which show high cost savings with minimum user discomfort. Furthermore, our proposed model has less computational complexity and more generality.
- We formulate the binary optimization problem through multiple knapsack problem (MKP). MKP helps in the effort of finding an optimal solution while employing GAPSO and respecting the total capacity of available amount of power.

## 2. System Model

#### 2.1. Energy Management Controller

#### 2.2. Communication Network

#### 2.3. Pricing Schemes

#### 2.3.1. DAP Model

#### 2.3.2. CPP Model

## 3. Problem Formulation

#### 3.1. Multiple Knapsack Problem

- It can be referred as a simplest integer linear programming (LP).
- It can be viewed as subproblems in many complex problems.
- It may represent the great practical situations.

#### 3.2. MKP in Energy Management System

- m knapsacks = m time interval.
- n objects = n appliances.
- w weight of an object = ${E}_{i}$ Energy consumed by an appliance i.
- value of an object = consumption cost of an appliance at time t.
- Capacity of knapsack = user demand with respect to the maximum amount of energy that can be drawn from the grid at time t.

## 4. Optimization Techniques

#### 4.1. Heuristic Optimization Techniques

#### 4.1.1. Brief Description of GA

#### 4.1.2. Brief Description of BPSO

- The first component is often known as “inertia” or “momentum”, it tends to move a particle in the same direction as it was travelling in. The inertia component can be scaled with a constant factor known as inertia constant. The inertia constant controls the velocity of a particle so that the particle cannot move beyond or below the scope of optimal search space. Mathematically inertia constant can be given as,$$\phi ={\phi}_{f}+({\phi}_{f}-{\phi}_{i})\times \left(\frac{{k}^{th}iteration}{maximum\phantom{\rule{0.277778em}{0ex}}\phantom{\rule{0.277778em}{0ex}}iterations}\right)$$
- The second component represents the local best solution found for the first time in search space. It tends to converge the solution toward local optima.
- The third component can be referred as the linear attraction towards the global best solution from the entire search space. It tends to fetch the optimum solution by using group knowledge of all the particles.

#### 4.2. Deterministic Optimization Technique

#### Brief Description of DP

## 5. Proposed Technique

#### GAPSO

^{−10}) for numerous (i.e., 50) successive generations. Algorithm 1 shows the working of the proposed technique.

Algorithm 1: GAPSO |

## 6. Simulations and Discussions

#### 6.1. Performance Parameters Definitions

#### 6.2. Peak Power Consumption

#### 6.3. Electricity Cost

#### 6.4. PAR

#### 6.5. User Comfort

- Since in this model, the maximization of user comfort is considered equivalent to the minimization of user discomfort, so both the terms can be used interchangeably. Figure 16 portrays the user discomfort of all the residential devices over the 24 h time horizon. Through performing extensive simulations it has been noticed that by minimizing the user discomfort, electricity cost is increased. The waiting time associated with discomfort is also analyzed and discussed.
- Figure 17 demonstrates the waiting time of all the appliances. The average waiting time of 5 h is considered in the proposed scheme. Moreover, in this work, the length of operation time of fan is 24 h and it is demonstrated that the associated waiting time is zero for this device. Generally, by delaying the appliance’s operation time more monetary benefits are achieved at consumers’ end. It is also observed in the proposed technique, that with the incorporation of user comfort, comparatively less savings are achieved. In the proposed scenario half an hour is considered as an operational time slot of appliances (i.e., 1 slot = 30 min).
- Figure 16 shows the discomfort faced by each corresponding residential device. Whereas, Figure 17 shows that average waiting time for each device. No comparison is being made in these figures, as the purpose of these figures is to demonstrate the user discomfort and average waiting for each corresponding residential device.

#### 6.6. Feasible Region

#### 6.6.1. Feasible Region for Consumption Cost and Power

#### 6.6.2. Feasible Region for Cost and Waiting Time

#### 6.7. Performance Trade-Off

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Geng, Y.; Chen, W.; Liu, Z.; Chiu, A.S.; Han, W.; Liu, Z.; Zhong, S.; Qian, Y.; You, W.; Cui, X. A bibliometric review: Energy consumption and greenhouse gas emissions in the residential sector. J. Clean. Prod.
**2017**, 159, 301–316. [Google Scholar] [CrossRef] - Samadi, P.; Bahrami, S.; Wong, V.W.; Schober, R. Power dispatch and load control with generation uncertainty. In Proceedings of the 2015 IEEE Global Conference on Signal and Information Processing (GlobalSIP), Orlando, FL, USA, 14–16 December 2015; pp. 1126–1130. [Google Scholar]
- Gelazanskas, L.; Gamage, K.A. Demand side management in smart grid: A review and proposals for future direction. Sustain. Cities Soc.
**2014**, 11, 22–30. [Google Scholar] [CrossRef] - Rastegar, M.; Fotuhi-Firuzabad, M.; Zareipour, H. Home energy management incorporating operational priority of appliances. Int. J. Electr. Power Energy Syst.
**2016**, 74, 286–292. [Google Scholar] [CrossRef] - Yalcintas, M.; Hagen, W.T.; Kaya, A. An analysis of load reduction and load shifting techniques in commercial and industrial buildings under dynamic electricity pricing schedules. Energy Build.
**2015**, 88, 15–24. [Google Scholar] [CrossRef] - Zazo, J.; Zazo, S.; Macua, S.V. Robust Worst-Case Analysis of Demand-Side Management in Smart Grids. IEEE Trans. Smart Grid
**2017**, 8, 662–673. [Google Scholar] [CrossRef] - Tan, O.; Gómez-Vilardebó, J.; Gündüz, D. Privacy-cost trade-offs in demand-side management with storage. IEEE Trans. Inf. Forensics Secur.
**2017**, 12, 1458–1469. [Google Scholar] [CrossRef] - Ahmed, N.; Levorato, M.; Li, G.P. Residential Consumer-Centric Demand Side Management. IEEE Trans. Smart Grid
**2017**. [Google Scholar] [CrossRef] - Vardakas, J.S.; Zorba, N.; Verikoukis, C.V. Power demand control scenarios for smart grid applications with finite number of appliances. Appl. Energy
**2016**, 162, 83–98. [Google Scholar] [CrossRef] - Ogunjuyigbe, A.S.O.; Ayodele, T.R.; Akinola, O.A. User satisfaction-induced demand side load management in residential buildings with user budget constraint. Appl. Energy
**2017**, 187, 352–366. [Google Scholar] [CrossRef] - Shirazi, E.; Jadid, S. Optimal residential appliance scheduling under dynamic pricing scheme via HEMDAS. Energy Build.
**2015**, 93, 40–49. [Google Scholar] [CrossRef] - Althaher, S.; Mancarella, P.; Mutale, J. Automated demand response from home energy management system under dynamic pricing and power and comfort constraints. IEEE Trans. Smart Grid
**2015**, 6, 1874–1883. [Google Scholar] [CrossRef] - Muralitharan, K.; Sakthivel, R.; Shi, Y. Multiobjective optimization technique for demand side management with load balancing approach in smart grid. Neurocomputing
**2016**, 177, 110–119. [Google Scholar] [CrossRef] - Ma, J.; Chen, H.H.; Song, L.; Li, Y. Residential load scheduling in smart grid: A cost efficiency perspective. IEEE Trans. Smart Grid
**2016**, 7, 771–784. [Google Scholar] [CrossRef] - Kusakana, K. Energy management of a grid-connected hydrokinetic system under Time of Use tariff. Renew. Energy
**2017**, 101, 1325–1333. [Google Scholar] [CrossRef] - Zhang, D.; Shah, N.; Papageorgiou, L.G. Efficient energy consumption and operation management in a smart building with microgrid. Energy Convers. Manag.
**2013**, 74, 209–222. [Google Scholar] [CrossRef] - Muratori, M.; Rizzoni, G. Residential demand response: Dynamic energy management and time-varying electricity pricing. IEEE Trans. Power Syst.
**2016**, 31, 1108–1117. [Google Scholar] [CrossRef] - Yi, P.; Dong, X.; Iwayemi, A.; Zhou, C.; Li, S. Real-time opportunistic scheduling for residential demand response. IEEE Trans. Smart Grid
**2013**, 4, 227–234. [Google Scholar] [CrossRef] - Yaagoubi, N.; Mouftah, H.T. User-aware game theoretic approach for demand management. IEEE Trans. Smart Grid
**2015**, 6, 716–725. [Google Scholar] [CrossRef] - Liu, Y.; Yuen, C.; Yu, R.; Zhang, Y.; Xie, S. Queuing-based energy consumption management for heterogeneous residential demands in smart grid. IEEE Trans. Smart Grid
**2016**, 7, 1650–1659. [Google Scholar] [CrossRef] - Liu, Y.; Yuen, C.; Huang, S.; Hassan, N.U.; Wang, X.; Xie, S. Peak-to-average ratio constrained demand-side management with consumer’s preference in residential smart grid. IEEE J. Sel. Top. Signal Process.
**2014**, 8, 1084–1097. [Google Scholar] [CrossRef] - Fakhrazari, A.; Vakilzadian, H.; Choobineh, F.F. Optimal energy scheduling for a smart entity. IEEE Trans. Smart Grid
**2014**, 5, 2919–2928. [Google Scholar] [CrossRef] - Miao, H.; Huang, X.; Chen, G. A genetic evolutionary task scheduling method for energy efficiency in smart homes. Int. Rev. Electr. Eng. (IREE)
**2012**, 7, 5897–5904. [Google Scholar] - Zhao, Z.; Lee, W.C.; Shin, Y.; Song, K.B. An optimal power scheduling method for demand response in home energy management system. IEEE Trans. Smart Grid
**2013**, 4, 1391–1400. [Google Scholar] [CrossRef] - Anvari-Moghaddam, A.; Monsef, H.; Rahimi-Kian, A. Optimal smart home energy management considering energy saving and a comfortable lifestyle. IEEE Trans. Smart Grid
**2015**, 6, 324–332. [Google Scholar] [CrossRef] - Bahrami, S.; Wong, V.W.; Huang, J. An Online Learning Algorithm for Demand Response in Smart Grid. IEEE Trans. Smart Grid
**2017**. [Google Scholar] [CrossRef] - Samadi, P.; Mohsenian-Rad, A.H.; Schober, R.; Wong, V.W.; Jatskevich, J. Optimal real-time pricing algorithm based on utility maximization for smart grid. In Proceedings of the 2010 First IEEE International Conference on Smart Grid Communications (SmartGridComm), Gaithersburg, MD, USA, 4–6 October 2010; pp. 415–420. [Google Scholar]
- Erdinc, O.; Paterakis, N.G.; Mendes, T.D.; Bakirtzis, A.G.; Catalão, J.P. Smart household operation considering bi-directional EV and ESS utilization by real-time pricing-based DR. IEEE Trans. Smart Grid
**2015**, 6, 1281–1291. [Google Scholar] [CrossRef] - Agnetis, A.; de Pascale, G.; Detti, P.; Vicino, A. Load scheduling for household energy consumption optimization. IEEE Trans. Smart Grid
**2013**, 4, 2364–2373. [Google Scholar] [CrossRef] - Belhaiza, S.; Baroudi, U. A game theoretic model for smart grids demand management. IEEE Trans. Smart Grid
**2015**, 6, 1386–1393. [Google Scholar] [CrossRef] - Marzband, M.; Yousefnejad, E.; Sumper, A.; Domínguez-García, J.L. Real time experimental implementation of optimum energy management system in standalone microgrid by using multi-layer ant colony optimization. Int. J. Electr. Power Energy Syst.
**2016**, 75, 265–274. [Google Scholar] [CrossRef][Green Version] - Chakraborty, S.; Ito, T.; Senjyu, T.; Saber, A.Y. Intelligent economic operation of smart-grid facilitating fuzzy advanced quantum evolutionary method. IEEE Trans. Sustain. Energy
**2013**, 4, 905–916. [Google Scholar] [CrossRef] - Derakhshan, G.; Shayanfar, H.A.; Kazemi, A. The optimization of demand response programs in smart grids. Energy Policy
**2016**, 94, 295–306. [Google Scholar] [CrossRef] - Gupta, A.; Singh, B.P.; Kumar, R. Optimal provision for enhanced consumer satisfaction and energy savings by an intelligent household energy management system. In Proceedings of the 2016 IEEE 6th International Conference on Power Systems (ICPS), New Delhi, India, 4–6 March 2016. [Google Scholar]
- Zhang, D.; Evangelisti, S.; Lettieri, P.; Papageorgiou, L.G. Economic and environmental scheduling of smart homes with microgrid: DER operation and electrical tasks. Energy Convers. Manag.
**2016**, 110, 113–124. [Google Scholar] [CrossRef] - Reka, S.S.; Ramesh, V. A demand response modeling for residential consumers in smart grid environment using game theory based energy scheduling algorithm. Ain Shams Eng. J.
**2016**, 7, 835–845. [Google Scholar] [CrossRef] - Safdarian, A.; Fotuhi-Firuzabad, M.; Lehtonen, M. Optimal residential load management in smart grids: A decentralized framework. IEEE Trans. Smart Grid
**2016**, 7, 1836–1845. [Google Scholar] [CrossRef] - Moon, S.; Lee, J.W. Multi-Residential Demand Response Scheduling with Multi-Class Appliances in Smart Grid. IEEE Trans. Smart Grid
**2016**. [Google Scholar] [CrossRef] - Wang, J.; Li, Y.; Zhou, Y. Interval number optimization for household load scheduling with uncertainty. Energy Build.
**2016**, 130, 613–624. [Google Scholar] [CrossRef] - Bharathi, C.; Rekha, D.; Vijayakumar, V. Genetic Algorithm Based Demand Side Management for Smart Grid. Wirel. Pers. Commun.
**2017**, 93, 481–502. [Google Scholar] [CrossRef] - Logenthiran, T.; Srinivasan, D.; Shun, T.Z. Demand side management in smart grid using heuristic optimization. IEEE Trans. Smart Grid
**2012**, 3, 1244–1252. [Google Scholar] [CrossRef] - Ma, K.; Yao, T.; Yang, J.; Guan, X. Residential power scheduling for demand response in smart grid. Int. J. Electr. Power Energy Syst.
**2016**, 78, 320–325. [Google Scholar] [CrossRef] - Naoyuki, M. Energy-on-Demand System Based on Combinatorial Optimization of Appliance Power Consumptions. J. Inf. Process.
**2017**, 25, 268–276. [Google Scholar] - Kumaraguruparan, N.; Sivaramakrishnan, H.; Sapatnekar, S.S. Residential task scheduling under dynamic pricing using the multiple knapsack method. In Proceedings of the 2012 IEEE PES Innovative Smart Grid Technologies (ISGT), Washington, DC, USA, 16–20 January 2012. [Google Scholar]
- Kim, D.H.; Abraham, A.; Cho, J.H. A hybrid genetic algorithm and bacterial foraging approach for global optimization. Inf. Sci.
**2007**, 177, 3918–3937. [Google Scholar] [CrossRef] - Arabali, A.; Ghofrani, M.; Etezadi-Amoli, M.; Fadali, M.S.; Baghzouz, Y. Genetic-algorithm-based optimization approach for energy management. IEEE Trans. Power Deliv.
**2013**, 28, 162–170. [Google Scholar] [CrossRef] - Del Valle, Y.; Venayagamoorthy, G.K.; Mohagheghi, S.; Hernandez, J.C.; Harley, R.G. Particle swarm optimization: basic concepts, variants and applications in power systems. IEEE Trans. Evolut. Comput.
**2008**, 12, 171–195. [Google Scholar] [CrossRef] - Bellman, R. Dynamic Programming; Princeton University Press: Princeton, NJ, USA, 1957. [Google Scholar]
- Ng, K.H.; Sheble, G.B. Direct load control-A profit-based load management using linear programming. IEEE Trans. Power Syst.
**1998**, 13, 688–694. [Google Scholar] [CrossRef] - Kurucz, C.N.; Brandt, D.; Sim, S. A linear programming model for reducing system peak through customer load control programs. IEEE Trans. Power Syst.
**1996**, 11, 1817–1824. [Google Scholar] [CrossRef] - Hsu, Y.Y.; Su, C.C. Dispatch of direct load control using dynamic programming. IEEE Trans. Power Syst.
**1991**, 6, 1056–1061. [Google Scholar] - Azadeh, A.; Ghaderi, S.F.; Tarverdian, S.; Saberi, M. Integration of artificial neural networks and genetic algorithm to predict electrical energy consumption. Appl. Math. Comput.
**2007**, 186, 1731–1741. [Google Scholar] [CrossRef]

**Figure 16.**User Discomfort (Dr: Dryer, D.W: Dish Washer, W.M: Washing Machine, Ov: Oven, Ir: Iron, V.C: Vacuum, Ket: Kettle, To: Toaster, R.C: Rice Cooker, H.D: Hair Dryer, Bl: Blender, F.P: Frying Pan, C.M: Coffee Maker).

**Figure 17.**Average Waiting Time (Dr: Dryer, D.W: Dish Washer, W.M: Washing Machine, Ov: Oven, Ir: Iron, V.C: Vacuum, Ket: Kettle, To: Toaster, R.C: Rice Cooker, H.D: Hair Dryer, Bl: Blender, F.P: Frying Pan, C.M: Coffee Maker).

Appliance’s Type | Power Rating (kW) | Length of Operation Time (hours) | Total Devices |
---|---|---|---|

Dryer | 1.2 | 4.0 | 189 |

Dish Washer | 0.7 | 3.0 | 288 |

Washing Machine | 2.0 | 2.5 | 268 |

Oven | 1.3 | 3.0 | 279 |

Iron | 1.0 | 2.0 | 340 |

Vacuum Cleaner | 2.0 | 2.0 | 158 |

Fan | 0.2 | 24 | 288 |

Kettle | 2.0 | 4.0 | 406 |

Toaster | 0.9 | 3.0 | 048 |

Rice Cooker | 0.85 | 4.0 | 059 |

Hair Dryer | 1.5 | 2.0 | 058 |

Blender | 0.3 | 1.5 | 066 |

Frying Pan | 1.1 | 1.5 | 101 |

Coffee Maker | 0.8 | 1.5 | 056 |

Total | - | - | 2604 |

Variables | Description |
---|---|

T | Time period of a day |

${T}_{u}^{t}$ | User defined time |

${T}_{s}^{t}$ | Scheduler defined time |

$EMC$ | Energy Management Controller |

${\lambda}_{i}$ | Electricity price |

${T}_{OTI}^{i}$ | Operation time interval of appliance i |

${\alpha}_{i}$ | Start time of an appliance i |

${\beta}_{i}$ | End time of an appliance |

${T}_{LoT}^{i}$ | Length of operation time of device i |

$Ca{p}_{T}$ | Maximum allowable energy that can be used for each hour of the day |

Variables | Values |
---|---|

Probability of crossover | 0.9 |

Probability of mutation | 0.1 |

Insite | 1.0 |

Vmax | 4.0 |

Vmin | −4 |

${\Omega}_{1}$ | 2.0 |

${\Omega}_{2}$ | 2.0 |

Population size | 200 |

Maximum Iterations | 600 |

$\rho $ | 0.001 |

k | 3.0 |

Technique | Parameters | Without EMC | With EMC | Reduction (%) |
---|---|---|---|---|

GA | Cost ($) | 1581.9 | 1480.7 | 29.9702 |

Peak-Load (kW) | 1706.3 | 1572.3 | 7.8532 | |

BPSO | Cost ($) | 1581.9 | 1591.2 | 24.0470 |

Peak-Load (kW) | 1706.3 | 1232.3 | 27.7794 | |

GAPSO | Cost ($) | 1581.9 | 1181.8 | 25.2923 |

Peak-Load (kW) | 1706.3 | 1085.3 | 36.39 | |

DP | Cost ($) | 1581.9 | 1297.2 | 25.6467 |

Peak-Load (kW) | 1706.3 | 1108.8 | 35.0172 |

Technique | Parameters | Lower Value | Upper Value |
---|---|---|---|

GA | Cost ($) | 1106.7 | 1116.0 |

Discomfort | 0.1240 | 0.8941 | |

PAR | 5.8204 | 6.1599 | |

BPSO | Cost ($) | 1201.4 | 1205.2 |

Discomfort | 0.2310 | 0.8421 | |

PAR | 4.5706 | 4.7336 | |

GAPSO | Cost ($) | 1179.6 | 1182.8 |

Discomfort | 0.1102 | 0.8100 | |

PAR | 4.4858 | 4.5283 | |

DP | Cost ($) | 1175.6 | 1175.6 |

Discomfort | 0.1102 | 0.8100 | |

PAR | 4.2350 | 4.2315 |

Technique | Parameters | Without EMC | With EMC | Reduction (%) |
---|---|---|---|---|

GA | Cost ($) | 57,584 | 45,771 | 20.5143 |

Peak-Load (kW) | 41,088 | 32,136 | 21.7873 | |

BPSO | Cost ($) | 57,584 | 48,550.5 | 15.6883 |

Peak-Load (kW) | 41,088 | 26,928 | 34.4626 | |

GAPSO | Cost ($) | 57,584 | 43,765 | 23.9979 |

Peak-Load (kW) | 41,088 | 27,476 | 33.1288 | |

DP | Cost ($) | 57,584 | 43,840 | 23.8677 |

Peak-Load (kW) | 41,088 | 27,400 | 33.331 |

Techniques | Computation Time (Seconds) |
---|---|

GA | 0.68 |

BPSO | 0.59 |

GAPSO | 0.55 |

DP | 0.7 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. 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/).

## Share and Cite

**MDPI and ACS Style**

Javaid, N.; Ahmed, F.; Ullah, I.; Abid, S.; Abdul, W.; Alamri, A.; Almogren, A.S. Towards Cost and Comfort Based Hybrid Optimization for Residential Load Scheduling in a Smart Grid. *Energies* **2017**, *10*, 1546.
https://doi.org/10.3390/en10101546

**AMA Style**

Javaid N, Ahmed F, Ullah I, Abid S, Abdul W, Alamri A, Almogren AS. Towards Cost and Comfort Based Hybrid Optimization for Residential Load Scheduling in a Smart Grid. *Energies*. 2017; 10(10):1546.
https://doi.org/10.3390/en10101546

**Chicago/Turabian Style**

Javaid, Nadeem, Fahim Ahmed, Ibrar Ullah, Samia Abid, Wadood Abdul, Atif Alamri, and Ahmad S. Almogren. 2017. "Towards Cost and Comfort Based Hybrid Optimization for Residential Load Scheduling in a Smart Grid" *Energies* 10, no. 10: 1546.
https://doi.org/10.3390/en10101546