# Optimal Residential Load Scheduling Under Utility and Rooftop Photovoltaic Units

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. System Model

## 4. Problem Formulation

#### 4.1. Energy Consumption

#### 4.2. Electricity Cost

#### 4.3. PAR

#### 4.4. Scheduling Problem Formulation

## 5. Proposed Scheme

#### 5.1. GA

#### 5.2. BPSO

#### 5.3. WDO

#### 5.4. GWDO

## 6. Simulations and Discussions

#### 6.1. Feasible Region

#### 6.2. Energy Consumption Behavior of Appliances

#### 6.3. Electricity Cost per Timeslot Analysis

#### 6.4. Total Cost Analysis

#### 6.5. PAR Analysis

## 7. Conclusions and Future Work

## Author Contributions

## Conflicts of Interest

## Abbreviations

A | Set of total appliances |

${A}^{IA}$ | Set of interruptible appliances |

SM | Smart meter |

AMI | Advanced metering infrastructure |

IHD & MCU | In-home display and monitoring control unit |

INV | Inverter |

${A}^{Non-IA}$ | Set of non-interruptible appliances |

${A}^{MR-A}$ | Set of must-run appliances |

${p}_{r}^{i}$ | Power rating of an appliance |

$\chi $ | Status of appliance |

t | Timeslot |

${T}_{h}$ | Scheduling time horizon |

${E}_{c}^{i}\left(t\right)$ | Energy consumption at timeslot |

$\chi \left({E}_{c}^{i}\left(t\right)\right)$ | Combined RTP and IBR pricing scheme |

$\phi \left(t\right)$ | Real-time electricity price at timeslot |

${E}_{th}^{i}$ | Energy consumption threshold |

${b}_{t}$ | Greater price when threshold of energy consumption is exceeded |

${S}_{t}^{i}$ | Current position of an appliance |

${r}_{t}^{i}$ | Remaining operation timeslots |

${w}_{t}^{i}$ | Waiting timeslots |

${X}_{t}$ | Status indicator of an appliance |

${S}_{t+1}^{i}$ | Appliance position at next timeslot |

${T}_{o}^{i}$ | Operation timeslots of an appliance |

$\alpha $ | Operation start time of an appliance |

$\beta $ | Operation end time of an appliance |

${E}^{PV}\left(t\right)$ | Output power of PV unit |

${\eta}^{PV}$ | Percentage efficiency of PV unit |

${A}^{PV}$ | Area of PV unit |

$Ir\left(t\right)$ | Solar irradiance |

${T}^{a}\left(t\right)$ | Temperature |

$f\left({I}_{r}\left(t\right)\right)$ | Weibull probability density function |

$\zeta $ | Weighted factor |

${\alpha}_{1},{\alpha}_{2}$ | Shape factors |

${\beta}_{1},{\beta}_{2}$ | Scale factors |

${E}^{ESS}\left(t\right)$ | Stored energy in ESS |

${\eta}^{ESS}$ | Efficiency of ESS |

$E{P}^{Ch}\left(t\right),E{P}^{Dch}\left(t\right)$ | Energy charge and discharge of ESS |

$E{P}_{UB}^{Ch}$ | Upper limit of charging |

$E{P}_{LB}^{Dch}$ | Lower limit of discharge |

${{E}^{ESS\_}}_{UB}^{Ch}$ | Upper limit of stored energy |

${E}_{T}$ | Aggregated energy consumption |

${C}_{T}$ | Total cost |

$Capcity$ | Capacity of the grid |

${E}_{T}^{\mathrm{unsch}}$ | Unscheduled load total energy consumption |

${E}_{T}^{\mathrm{sch}}$ | Scheduled load total energy consumption |

${T}_{o}^{i-\mathrm{unsch}}$ | Unscheduled load operation timeslots |

${T}_{o}^{i-\mathrm{sch}}$ | Scheduled load operation timeslots |

${X}_{t}^{\mathrm{unsch}}$ | Unscheduled load status |

${X}_{t}^{\mathrm{sch}}$ | Scheduled load status |

${P}_{C}$ | Probability of crossover |

${P}_{m}$ | Probability of mutation |

${w}_{i}$ | Initial weight |

${w}_{f}$ | Final weight |

${v}_{max}$ | Maximum velocity |

${v}_{min}$ | Minimum velocity |

${v}_{i}$ | Initial velocity |

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**Figure 13.**Energy consumption profile of users: (

**a**) Without RESs and ESS; (

**b**) With RESs; (

**c**) With RESs and ESS.

**Figure 14.**Electricity cost profile: (

**a**) Without RESs and ESS; (

**b**) With RESs; (

**c**) With RESs and ESS.

**Figure 15.**Aggregated cost analysis: (

**a**) Without RESs and ESS; (

**b**) With RESs; (

**c**) With RESs and ESS.

References | Techniques | Objectives | Limitations |
---|---|---|---|

Demand-side energy consumption scheduling in presence of peak to average ratio (PAR) constraint and users’ preference [15] | Distributed algorithm | Minimization of cost | renewable energy sources (RESs) integration are not addressed |

Electricity storage and appliances scheduling schemes for residential sector [5] | energy management control (EMC) and day-ahead pricing | Electricity cost reduction | Uncoordinated charging and discharging of batteries results in discomfort |

Smart home energy management system for joint scheduling of electrical and thermal appliances [6] | Heuristic-based EMC | Optimal scheduling of appliances and cost reduction | Achieved economical solution at cost of users’ comfort |

Intelligent decision support systems under generic and flexible cost model for load scheduling [7] | Generic and flexible cost model | Peaks reduction and enhancement of the power system efficiency | Reduced the peaks and cost while user comfort was comprised |

Joint access and load scheduling under DR schemes [8] | Markov chain and derive the steady-state distribution | Cost reduction | PAR is increased while reducing the cost |

Residential load control algorithm for demand-side management [9] | Energy consumption scheduling algorithm | Reduction of electricity bill and PAR | Reduced peaks in demand while user comfort is minimized |

Prosumers demand-side management [10] | Smart scheduler | Reduction of electricity cost | Peaks in consumption emerged while reducing electricity cost, which may damage the entire power system |

Optimal scheduling method for distributed generations, battery ESS, tap transformer, and controllable loads [16] | Binary particle swarm optimization (BPSO) | Minimization of total system losses | Objectives are achieved at the cost of system complexity |

Two market models in order to cope with the gap between demand and supply [11] | Distributed demand response (DR) algorithms | Minimization of cost | Higher communication overhead and computing complexity |

Optimal scheduling of appliances under operational constraints and economical consideration [12] | Novel appliances commitment algorithm | Comfort maximization and cost reduction | Peaks may emerge while reducing cost |

Demand curve smoothing by controlling the charging strategies of electric vehicles [13] | Decentralized algorithm | Minimization of the peak demand loads | User comfort is compromised while reducing peaks in demand |

Optimal power scheduling method for DR in home energy management system [17] | Genetic algorithm (GA) | Electricity cost and PAR reduction | The complexity of the system increased due to the division of scheduling time horizon |

An efficient heuristic-based EMC is utilized with RESs for load scheduling in the SG [18] | GA, BPSO, and ACO algorithms | Minimization of electricity cost, PAR, and maximization of user comfort | Complexity of the system is increased while achieving the desired objectives |

An optimized home energy management system in the smart grid (SG) for demand-side management [19] | GA, wind-driven optimization (WDO), BPSO, and hybrid of GA and BPSO algorithms | Cost and PAR minimization | User comfort is compromised |

Home load management in the SG [20] | Decentralized framework and proposed scheduling algorithm | Cost reduction, comfort, and privacy reservation | PAR is compromised while reducing desired objectives |

Parameters | Values |
---|---|

Population size | 100 |

n | 9 |

Number of iterations | 100 |

${P}_{c}$ | 0.9 |

${P}_{m}$ | 0.1 |

Parameters | Values |
---|---|

Swarm size | 9 |

n | 9 |

Number of iterations | 100 |

${c}_{1}$ | 2 |

${c}_{2}$ | 2 |

${w}_{i}$ | 2 |

${w}_{f}$ | 0.4 |

$vmax$ | 4 |

$vmin$ | −4 |

Parameters | Values |
---|---|

Population size | 20 |

n | 9 |

Number of iterations | 100 |

$RT$ | 3 |

g | 0.2 |

$\alpha $ | 0.4 |

$dimMin$ | −5 |

$dimMax$ | 5 |

$vmax$ | 0.3 |

$vmin$ | −0.3 |

Category | SA | OTS | Power Rating (kW) |
---|---|---|---|

Must-run appliances | Air conditioner | 75 | 1.5 |

Water cooler | 70 | 1 | |

Refrigerator | 60 | 0.5 | |

Interruptible appliances | Washing machine | 40 | 0.7 |

Clothes dryer | 40 | 2 | |

Water motor | 36 | 0.8 | |

Non-interruptible appliances | Electric kettle | 20 | 1.5 |

Electric iron | 30 | 1.8 | |

Oven | 25 | 2 |

Techniques | Cost Reduction: Scenario 1 | Cost Reduction: Scenario 2 | Cost Reduction: Scenario 3 | PAR Reduction: Scenario 1 | PAR Reduction: Scenario 2 | PAR Reduction: Scenario 3 |
---|---|---|---|---|---|---|

GA | 4.2% | 11.6% | 13.46% | 8.3% | 4.5% | 17.39% |

BPSO | 15.49% | 9.3% | 21.5% | 16.5% | 11.36% | 13.04% |

WDO | 18.3% | 13.95% | 25% | 20.8% | 13.6% | 26.08% |

GWDO | 22.5% | 47.7% | 49.2% | 29.1% | 30.% | 35.4% |

© 2018 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**

Hafeez, G.; Javaid, N.; Iqbal, S.; Khan, F.A. Optimal Residential Load Scheduling Under Utility and Rooftop Photovoltaic Units. *Energies* **2018**, *11*, 611.
https://doi.org/10.3390/en11030611

**AMA Style**

Hafeez G, Javaid N, Iqbal S, Khan FA. Optimal Residential Load Scheduling Under Utility and Rooftop Photovoltaic Units. *Energies*. 2018; 11(3):611.
https://doi.org/10.3390/en11030611

**Chicago/Turabian Style**

Hafeez, Ghulam, Nadeem Javaid, Sohail Iqbal, and Farman Ali Khan. 2018. "Optimal Residential Load Scheduling Under Utility and Rooftop Photovoltaic Units" *Energies* 11, no. 3: 611.
https://doi.org/10.3390/en11030611