# Enhanced Time-of-Use Electricity Price Rate Using Game Theory

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## Abstract

**:**

## 1. Introduction

#### Problem Statement

## 2. Related Work

## 3. System Model

#### 3.1. Formulation of GTToU

#### 3.1.1. Modified ToU Tariff

#### 3.1.2. Electricity Cost Minimization

## 4. Proposed Methodology

#### 4.1. GT Based Price Model

#### 4.2. SSA Based Scheduling Model

Algorithm 1 Pseudocode of Salp swarm optimization |

#### SAA

#### 4.3. RFA Based Scheduling Model

#### 4.3.1. RFA

Algorithm 2 Pseudocode of Rain-fall optimization |

#### 4.3.2. Raindrop

#### 4.3.3. Neighborhood

#### 4.3.4. Neighbor Point

#### 4.3.5. Dominant Drop

#### 4.3.6. Active Drop

#### 4.3.7. Inactive Drop

#### 4.3.8. Explosion Process

#### 4.3.9. Raindrops Rank

#### 4.3.10. Merit Order List

## 5. Simulation Results and Discussion

#### 5.1. Experiment Configuration

#### 5.2. Experimental Results for GTToU

#### 5.3. Experimental Results for Day-Ahead RTP

#### 5.4. Experimental Results for Ensemble Regression

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

Symbols | Description | Symbols | Description |

C/I | Curtailable/Interruptible | $E.{L}^{US}$ | Total aggregated load of N homes |

CPP | Critical Peak Pricing | $\gamma $ | Constant value |

CPR | Critical Peak Rebate | $E.{C}^{total}$ | Total electricity cost |

DR | Demand Response | $\wp [0,1]$ | ON and OFF status of appliance d |

EMC | Energy Management Controller | U | Uniform distribution function |

GT | Game Theory | ${\Im}_{hour}^{h}$ | Pay-off of each home |

GTToU | GT-based Price Signal | $\aleph ,\hslash $ | Tuple of the game |

NN | Neural Network | m | Size of the population |

PAR | Peak to Average Ratio | i | Drop numbers |

RFA | Rain Fall Algorithm | $lo{w}_{k}u{p}_{k}$ | Lower and upper limits |

RTP | Real Time Pricing | $N{P}_{j}^{i}$ | Neighbor point j of raindrop i |

SH | Smart Home | r | Real vector |

SHEMS | SH Energy Management System | ${r}_{initial}$ | Initial neighborhood size |

SSA | Salp Swarm Algorithm | $np$ | Neighborhood points |

ToU | Time-of-Use | $N{P}_{i}^{d}$ | Dominant drop |

VPP | Variable Peak Pricing | F | Objective function |

$\Xi {P}^{h}(hour)$ | Modified TOU Price Signal | $F{D}_{i}$ | Value of raindrop |

${H}_{p}^{off}$ | Off Peak Hours | $F(N{P}_{j}^{i})$ | Neighbor point |

h | Set of N number of homes | $np(ex)$ | Neighbors in explosion process |

${\Im}_{hour}^{h}$ | Depends on extra cost | $C{1}_{t}^{i}$ | Rank of rain drops |

ß% | Extra generated energy | ${\omega}_{1},{\omega}_{2}$ | Weighting co-efficients |

$std$ | Standard deviation | $C{1}_{t}^{i},C{2}_{t}^{i}$ | Change in value of objective function for |

raindrops at iteration |

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Group | Appliances | Power Rate (kWh) | Daily Usage (h) |
---|---|---|---|

Water motor | 1 | 2 | |

Interruptible load | Dish washer | 1.8 | 2 |

Iron | 1 | 1 | |

Non-interruptible load | Washing machine | 0.7 | 1.5 |

Cloth dryer | 5 | 1 | |

Oven | 2.15 | 1.5 | |

Blender | 0.3 | 1.5 | |

Light1 | 0.03 | 9 | |

Non-schedule able load | Light2 | 0.03 | 9 |

Light3 | 0.011 | 20 | |

Light4 | 0.18 | 28 | |

Refrigerator | 0.225 | 24 |

Unscheduled | SSA | RFA | ||||||
---|---|---|---|---|---|---|---|---|

Home 1 | Home 2 | Home 3 | Home 1 | Home 2 | Home 3 | Home 1 | Home 2 | Home 3 |

ToU | ||||||||

643.99¢ | 617.84¢ | 645.61¢ | 603.21¢ | 590.74¢ | 563.38¢ | 554.58¢ | 586.760¢ | 567.70¢ |

GTToU | ||||||||

639.73¢ | 611.07¢ | 640.66¢ | 458.76¢ | 456.48¢ | 456.33¢ | 436.42¢ | 435.59¢ | 438.95¢ |

Unscheduled | SSA | RFA | ||||||
---|---|---|---|---|---|---|---|---|

Home 1 | Home 2 | Home 3 | Home 1 | Home 2 | Home 3 | Home 1 | Home 2 | Home 3 |

ToU | ||||||||

791.11 | 790.84 | 804.80 | 889.48 | 892.40 | 875.95 | 818.66 | 843.91 | 839.73 |

GTToU | ||||||||

791.05 | 783.01 | 791.96 | 681.27 | 676.54 | 676.51 | 663.18 | 667.30 | 661.77 |

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## Share and Cite

**MDPI and ACS Style**

Khalid, A.; Javaid, N.; Mateen, A.; Ilahi, M.; Saba, T.; Rehman, A. Enhanced Time-of-Use Electricity Price Rate Using Game Theory. *Electronics* **2019**, *8*, 48.
https://doi.org/10.3390/electronics8010048

**AMA Style**

Khalid A, Javaid N, Mateen A, Ilahi M, Saba T, Rehman A. Enhanced Time-of-Use Electricity Price Rate Using Game Theory. *Electronics*. 2019; 8(1):48.
https://doi.org/10.3390/electronics8010048

**Chicago/Turabian Style**

Khalid, Adia, Nadeem Javaid, Abdul Mateen, Manzoor Ilahi, Tanzila Saba, and Amjad Rehman. 2019. "Enhanced Time-of-Use Electricity Price Rate Using Game Theory" *Electronics* 8, no. 1: 48.
https://doi.org/10.3390/electronics8010048