# An Efficient Power Scheduling Scheme for Residential Load Management in Smart Homes

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## Abstract

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## 1. Introduction

- We build a model by classifying electrical appliances into three groups based on power usage and user comfort requirements. This model incorporates the three proposed classes of appliances based on hourly electricity prices (TOU) during on-peak and off-peak hours in conjunction with user preferences.
- On the proposed model, we devise a binary version of WDO algorithm for minimum electricity cost and maximum user comfort. Moreover, a knapsack-based WDO (K-WDO) algorithm is also designed for maximum electricity cost saving that can be used as a benchmark for the performance evaluation of energy consumption in home area networks. The min-max regret-based knapsack optimization technique is used to minimize the maximum energy consumption.
- The said optimization techniques are mapped for scheduling electrical appliances. Moreover, we incorporate a renewable energy resource during critical hours for grid stability, electricity cost reduction and user comfort (we assume that fixed electric power is stored via a renewable energy resource that can be utilized in peak or crucial hours).
- Finally, we validate our proposed schemes and analytic framework via extensive simulations and comparisons of unscheduled and scheduled cases.

## 2. Related Work

## 3. Home Energy Management Architecture

## 4. Price-Based DR

#### 4.1. TOU and DAP

#### 4.2. RTP

#### 4.3. CPP

## 5. Home Appliance Energy Usage Pattern

#### 5.1. Appliance Waiting Time

## 6. System Model

## 7. Types of Appliances

Sr. No. | Appliance | Power Rating (kWh) | ${\mathit{T}}_{\mathit{l}\mathit{o}\mathit{t}}$/(Hours) |
---|---|---|---|

1 | Stove | 3.0 | 9 |

2 | Tumble Dryer | 3.3 | 15 |

3 | Clothes Dryer | 3.4 | 8 |

4 | Washing Machine | 3.0 | 3 |

5 | Oven | 3.0 | 13 |

6 | Air-conditioner | 5.0 | 7 |

#### 7.1. Class 1

#### 7.2. Class 2

#### 7.3. Class 3

## 8. Load Optimization and Scheduling

#### 8.1. Scheduling Algorithm

- The first term shows that the air particles continue their movements to the previous path with some opposition of frictional force.
- The second term is gravitational force, which attracts the air particles to the centre (in the coordinate system).
- The third term describes the force exerted on air particles to move them towards the highest pressure location, which is the global best position in the WDO optimization problem.
- The fourth term shows the Coriolis force, which is a deflecting force, because the movement of air particles in one direction is affected by the movement in the second direction. Similarly, in PSO, weights ${w}_{1}$ and ${w}_{2}$ are used to control the movement of air particles in order to find the global best position.

Symbol | Description | Symbol | Description |
---|---|---|---|

${v}_{new}$ | new velocity | v | velocity vector of air particles |

${v}_{old}$ | current velocity | ${F}_{c}$ | Coriolis force |

${x}_{curr}$ | current position | Ω | Earth rotation |

${x}_{opt}$ | optimal position | ρ | density of air particles |

${P}_{old}$ | pressure at current location | ${V}_{g}$ | vertical force on air particles |

${P}_{opt}$ | optimal pressure | ${F}_{sig}$ | sigmoid function |

$\Omega \times v$ | Coriolis force | ${p}_{gb}$ | local best position |

α | constant in update position | ${\delta}_{V}$ | volume of air |

R | universal gas constant | ${F}_{sphere}$ | sphere function |

v | velocity of air particles | ω | inertia factor |

${F}_{g}$ | gravitational force of the Earth | n | total No. of air particles (Equation (23)) |

g | gravitational acceleration | T | temperature |

$\Delta t$ | unit step time | ${v}_{i,n}$ | velocity of the i-th particle in n-dimensions |

${c}_{1}and{c}_{2}$ | weights for local and global positions | ${p}_{lb}$ | local best position |

Algorithm | Evaluation Function | No. of Iterations | Global Pressure/${\mathit{p}}_{\mathit{g}\mathit{b}}$ | Converge |
---|---|---|---|---|

WDO | Sphere | 204 | 0 | Yes |

WDO | Step | 500 | 0.6616 | No |

PSO | Sphere | 500 | $9.{069}^{-6}$ | No |

PSO | Step | 370 | 0 | Yes |

#### 8.1.1. Population Evaluation Functions

Parameter | Value | Parameter | Value |
---|---|---|---|

Particle Size | 10 | RT-coefficient | 3 |

No. of Iterations | 500 | Gravitational const | 0.2 |

Max-V | 0.4 | Coriolis effect | 0.4 |

Dimensions | [−1, +1] | α | 0.4 |

Parameter | Value | Parameter | Value |
---|---|---|---|

Particle Size | 10 | ${c}_{1}$ | 2 |

No. of Iterations | 500 | ${c}_{2}$ | 2 |

Max-V | 0.3 | ${w}_{i}$ | 1.0 |

Dimensions | [−1, +1] | ${w}_{f}$ | 0.4 |

## 9. Peak-to-Average Ratio

## 10. Simulation Results and Discussion

#### 10.1. Electricity Cost vs. Appliance Waiting Time

**Figure 7.**(

**a**) Appliance I starting time; (

**b**) Appliance II starting time; (

**c**) Appliance III starting time; (

**d**) Appliance IV starting time; (

**e**) Appliance V starting time; (

**f**) Appliance Istarting time; appliance staring time of the unscheduled and scheduled cases.

#### 10.2. Electricity Cost vs. Electricity Price

#### 10.3. Energy Consumption

#### 10.4. PAR Reduction

**Figure 12.**Total peak-to-average ratio (PAR) reduction comparison of the WDO and PSO algorithms for a simple household based on the TOU price signals adopted from NYISO.

#### 10.5. Electricity Cost with Renewable Sources

## 11. Conclusions

Algorithms | Unscheduled Cost (Cents) | Scheduled Cost (Cents) | Saving % Age | Scheduled Cost + RE (Cents) | Saving % Age |
---|---|---|---|---|---|

K-WDO | 2390 | 1629 | 31.85 | 1457 | 39.04 |

WDO | 2390 | 1842 | 22.93 | 1620 | 32.22 |

K-PSO | 2390 | 1867 | 21.89 | 1756 | 26.16 |

PSO | 2390 | 2003 | 16.20 | 1753 | 26.66 |

## Acknowledgements

## Author Contributions

## Conflicts of Interest

## Nomenclature

Symbol | Description | Symbol | Description |

${T}_{f}$ | appliance finishing time | ${T}_{on}$ | appliance scheduled on time |

${T}_{0}$ | initial appliance starting time | $\delta {t}_{w}^{n}$ | appliance waiting time |

${T}_{lot}$ | length of operation time | T | total time horizon |

${E}_{con}$ | energy consumption of appliance | ${E}_{th}$ | energy consumption threshold |

${E}_{con}^{min}$ | minimum energy consumption | ${E}_{ss}$ | energy consumption using scheduler |

${E}_{con}^{max}$ | maximum energy consumption | ${E}_{ssd}$ | energy consumption with delay |

${E}_{mr}$ | energy consumption of must run appliances | ${E}_{con}^{max}$ | maximum energy consumption |

${T}_{sch}$ | scheduling horizon | ${T}_{s}$ | unscheduled appliance starting time |

${E}_{t}$ | total energy consumption | ${\lambda}_{a}$ | boolean variable for on/off status |

$Cos{t}_{sa{v}_{n}}^{s}$ | set of electricity cost saving for appliance n | $Cos{t}_{sav}^{min}$ | minimum electricity cost saving |

$Cos{t}_{sav}^{max}$ | maximum electricity cost saving | S | set of all possible scenario |

${S}_{0}$ | set of all possible solutions | ${z}^{s}({i}_{n})$ | given solution |

${z}^{\ast s}({i}_{n})$ | optimal solution | ${r}_{max}^{s}$ | maximum regret |

${C}_{t}$ | total energy capacity | C | electricity cost |

${C}_{RE}$ | electricity cost with renewable energy source | ${r}^{s}$ | associated regret of solution s |

$ma{x}_{load}$ | maximum electricity load | $averag{e}_{load}$ | average electricity load |

${x}_{(t,i)}$ | energy unit price | ${\delta}_{t}$ | small change in time |

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**MDPI and ACS Style**

Rasheed, M.B.; Javaid, N.; Ahmad, A.; Khan, Z.A.; Qasim, U.; Alrajeh, N.
An Efficient Power Scheduling Scheme for Residential Load Management in Smart Homes. *Appl. Sci.* **2015**, *5*, 1134-1163.
https://doi.org/10.3390/app5041134

**AMA Style**

Rasheed MB, Javaid N, Ahmad A, Khan ZA, Qasim U, Alrajeh N.
An Efficient Power Scheduling Scheme for Residential Load Management in Smart Homes. *Applied Sciences*. 2015; 5(4):1134-1163.
https://doi.org/10.3390/app5041134

**Chicago/Turabian Style**

Rasheed, Muhammad Babar, Nadeem Javaid, Ashfaq Ahmad, Zahoor Ali Khan, Umar Qasim, and Nabil Alrajeh.
2015. "An Efficient Power Scheduling Scheme for Residential Load Management in Smart Homes" *Applied Sciences* 5, no. 4: 1134-1163.
https://doi.org/10.3390/app5041134