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Game Theoretical Energy Management with Storage Capacity Optimization and Photo-Voltaic Cell Generated Power Forecasting in Micro Grid^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Problem Statement and Contributions

- Game theory and data-centric approaches are adapted in order to address MG electric load management problem. In order to overcome uncertainties caused by PVC generation, linear forecasting technique ARIMA has been used for forecasting. Parameters of ARIMA, i.e., AR and Moving Average (MA) are optimized through GWO and named as GARIMA,
- Energy management problem has been solved using two stage Stackelberg game theory to capture the dynamic interaction and interconnection among users and MG. Where, MG acts as a leader and users act like followers. Besides, if there exist a scenario where energy demand of users increases as compare to MG capacity of energy generation, MG purchases energy from utility. Furthermore, energy cost of MG has also been reduced by using energy storage mechanism,
- Two proposed techniques, i.e., GARIMA and CARIMA have been used for forecasting purpose. Parameters optimization of ARIMA has been performed using Gray Wolf Optimizer (GWO) and Cuckoo Search (CS) algorithm, where GARIMA gives better result as compare to CARIMA and other conventional techniques. Forecasting results of GARIMA technique are used in DEM algorithm in order to reduce uncertainties that are caused by renewable resources historic data and
- For non cooperative game of MG and users, existence of NE is proved using Stackelberg game theory. Furthermore, iterative DEM algorithm is proposed for MG to prove NE.

## 4. Material and Method

#### 4.1. Cost Model of Users

- MG is responsible for providing energy to user at any time. Hence, the cost function of user regarding energy consumption by user at any time slot k $\epsilon $ $\mathcal{K}$ is function of energy consumption ${X}_{k}$ by $\mathbb{N}$ users,
- In daily life, energy consumption by user at certain time slot is smooth function or at least it is piecewise smooth function and always increasing. Likewise, cost function of user follows the demand ${X}_{k}$,
- Cost function also depends on timings of energy consumption, apart of energy consumption by user.

#### 4.2. MG Cost Model with Storage Capacity

#### 4.3. Game Formulation and Analysis

- Users cost function $\mathcal{U}$ shows cost of energy consumption that is received by $\mathbb{N}$ users in time slot k,
- Whereas, $\mathcal{B}$ captures the benefit that is gained by MG after supplying energy ${x}_{m}^{k}$ to $\mathbb{N}$ set of users,
- ${P}_{m}^{k}$ defines price of energy that is defined by MG against each time slot k,
- ${y}_{m}$ define optimal storage capacity that is required to minimize the cost function of MG,
- Cost function of user: ${\mathcal{U}}_{n}({x}_{n},{x}_{-n},{p}_{m}^{k})$,
- Cost function of MG: $\mathcal{B}({x}_{m}^{k}\left({p}^{k}\right),{y}_{m})$.

**Proposition**

**1.**

**Proof.**

**Proposition**

**2.**

**Proof.**

**Proposition**

**3.**

**Proof.**

**Proposition**

**4.**

#### 4.3.1. PVC Power Forecasting Algorithm

Algorithm 1: Executed by MG |

## 5. Simulation and Discussion

#### 5.1. Data Description

#### 5.2. Experimental Results

## 6. Conclusions and Future Work

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Acronyms | |

Abbreviations | Full Form |

AR | Auto regressive |

AI | Artificial intelligence |

ARIMA | Auto Regressive Integrated Moving Average |

ACF | Auto Correlation Function |

ADF | Augmented Dickey Fuller |

AIC | Akaike Information Criteria |

BIC | Bayesian Information Criteria |

BP | Back Propagation |

CARIMA | Cuckoo Search Optimized ARIMA |

CS | Cuckoo Search |

CNN | Convolution Neural Network |

DEM | Distributed Energy Management |

DR | Demand Response |

DSM | Demand Side Management |

ES | Exponential Smoothing |

GARIMA | Gray Wolf Optimized ARIMA |

GSAE | Genetic Stacked Auto encoder |

GA | Genetic Algorithm |

GWO | Grey Wolf Optimization |

ICT | Information and Communication Technology |

MG | Micro Grid |

MAPE | Mean Absolute Percentage Error |

RMSE | Root Mean Square Error |

NN | Neural Network |

NE | Nash Equilibrium |

PSO | Particle Swarm Optimization |

PVC | Photo Voltaic Cell |

PAR | Peak Average Ratio |

PACF | Partial Auto Correlation Function |

RTP | Real Time Pricing |

RMSE | Root Mean Square Error |

SG | Smart Grid |

SVM | Support Vector Machine |

ToU | Time of Use |

Nomenclature | |

Symbols | Descriptions |

${A}_{v}$ | Actual Time Series |

${X}_{average}$ | Average User Consumption |

${\eta}_{ch}$ | Charging Efficiency of Battery |

${\sigma}_{\u03f5}^{2}$ | Constant Variance |

$\mathcal{U}$ | Cost Function of Users |

$\mathcal{B}$ | Cost Function of Micro Grid |

${l}_{n}$ | Daily Energy Usage of User |

${\eta}_{disch}$ | Discharging Efficiency of Battery |

${C}_{m}^{bat}\left(y\right)$ | Daily Depreciation Cost Function |

${C}_{k}{x}_{k}$ | Cost Function of User |

${\u03f5}_{t}$ | Error at Time t |

${x}_{n}\left(k\right)$ | Energy Demand in Particular Slot |

${e}_{n}$ | Energy Demanded from Users |

${e}_{m}^{b}\left(k\right)$ | Energy Required to Charge Battery |

${a}_{k},{b}_{k}$ | Fixed Parameters |

${y}_{l}^{m}$ | Lower Limit of Battery Capacity |

$\mathbb{N}$ | Multiple Residential Users |

${Q}^{*}$ | Micro Grid |

${\sigma}^{2}$ | Mean Square Error |

${X}_{peak}$ | Peak Consumption |

${U}_{n}$ | Profit of Micro grid |

F | Penalty Factor |

$\delta $ | Prediction Error |

${F}_{v}$ | Predicted Time Series |

${h}_{ch}^{k}$ | Pattern of Battery Charging |

${h}_{disch}^{k}$ | Pattern of Battery Discharging |

${P}^{k}$ | Real Time Price of Each Slot |

${X}_{k}$ | Sum of Total Energy |

$\varsigma $ | Strategy Form |

${\lambda}_{s}$ | Solar Power Selling Price |

s | State of Battery |

$\mathcal{K}$ | Time Slots in a Period |

${b}^{l}\left(k\right)$ | Total Energy Required to Discharge Battery |

${C}_{n,k}$ | Total Cost of $\mathbb{N}$ Users |

T | Total no. of Observations |

${C}_{n}^{sp}$ | Total Cost of Solar Power Generation |

${Q}^{*}$ | Test Static |

${y}_{m}^{u}$ | Upper Limit of Battery Capacity |

${\varphi}_{i}$ | Vector Based on Rules of AR |

${\theta}_{i}$ | Vector Based on Rules of MA |

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Time Chunks | ${\mathit{a}}_{\mathit{h}}$ (cents/kWh) | ${\mathit{b}}_{\mathit{h}}$ (cents/kWh) |
---|---|---|

0.00–6:00 | 0.03 | 4.9 |

6:00–1400 | 0.06 | 12.1 |

1400–2000 | 0.07 | 18.1 |

2100–2400 | 0.06 | 12.5 |

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

y | [1.0, 5.0] |

${B}_{disch}$ | 2.0 |

${B}_{ch}$ | 2.0 |

${\eta}_{disch}$ | 92% |

${\eta}_{ch}$ | 92% |

${\lambda}^{bat}\left(y\right)$ | 7.2 |

${\lambda}_{s}$ | 7.1 |

${\lambda}^{PVC}$ | 4.3 |

$ChargeTime$ | 6.00–1700 |

$DischargeTime$ | 1700–2200 |

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## Share and Cite

**MDPI and ACS Style**

Naz, A.; Javaid, N.; Rasheed, M.B.; Haseeb, A.; Alhussein, M.; Aurangzeb, K.
Game Theoretical Energy Management with Storage Capacity Optimization and Photo-Voltaic Cell Generated Power Forecasting in Micro Grid. *Sustainability* **2019**, *11*, 2763.
https://doi.org/10.3390/su11102763

**AMA Style**

Naz A, Javaid N, Rasheed MB, Haseeb A, Alhussein M, Aurangzeb K.
Game Theoretical Energy Management with Storage Capacity Optimization and Photo-Voltaic Cell Generated Power Forecasting in Micro Grid. *Sustainability*. 2019; 11(10):2763.
https://doi.org/10.3390/su11102763

**Chicago/Turabian Style**

Naz, Aqdas, Nadeem Javaid, Muhammad Babar Rasheed, Abdul Haseeb, Musaed Alhussein, and Khursheed Aurangzeb.
2019. "Game Theoretical Energy Management with Storage Capacity Optimization and Photo-Voltaic Cell Generated Power Forecasting in Micro Grid" *Sustainability* 11, no. 10: 2763.
https://doi.org/10.3390/su11102763