# Game Theoretical Demand Response Management and Short-Term Load Forecasting by Knowledge Based Systems on the basis of Priority Index

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Game Theoretical Problem Formulation

#### 3.1. Analysis of User and Utility Company

#### 3.1.1. Analysis of User Side

#### Case 1

#### Case 2

#### Case 3

#### Case 4

#### 3.1.2. Analysis of Utility Companies

#### Case 1

#### Case 2

**Theorem**

**1.**

**Proof**

**of Theorem 1.**

**Theorem**

**2.**

**Proof**

**of Theorem 2.**

#### 3.2. Proposed Stackelberg Game Modeling

#### 3.3. Distinctiveness of Stackelberg Equilibrium

**Theorem**

**3.**

**Proof**

**of Theorem 3.**

#### 3.4. Distributed Algorithm

**Theorem**

**4.**

**Proof**

**of Theorem 4.**

Algorithm 1: Distributed Algorithm |

## 4. Knowledge Based Short-Term Load Forecasting

#### 4.1. Classic Knowledge Based Short Term Load Forecasting

#### 4.2. Proposed Knowledge Based Short-Term Load Forecasting

#### 4.2.1. Distribution of Historic Load Data

#### 4.2.2. Priority Index for Same Day

#### 4.2.3. Distribution of PNPN

#### 4.2.4. Proposed Strategy

## 5. Application of Proposed Method on Vast Topographical Zone

- At first, the days having a similar category of day are chosen on the basis of categorization of target day. In this scenario, Tuesday is included in the second category of day classification as discussed above. Moreover, all the days between Tuesday to Friday are selected. However, all the distinct days is overlooked for analytical purposes. Subsequently, these days are distributed in two data-sets, as discussed in Section II.
- The priority index of every region is evaluated by Equation (45), for all chosen days. Table 3 presents the priority index of selected days for a sample region Islamabad as an example of 30 June 2015. Moreover, in this scenario the value of ${\wp}_{temp,reg.}$ is 0.03 and ${\wp}_{1,reg.}$ is 1.5 $\times {10}^{-5}$. All the values and Table 3 are associated with the second data-set of Islamabad for the specified date. Every region and every data-set are different from one another.
- The priority index and short-term load forecasting of every region is evaluated by Equations (42) and (43) as discussed in Section II. In this scenario, ${\mathcal{D}}_{\gamma}$ and final best suitable chosen similar days are 25 June 2016, 26 June 2016, 27 June 2016, 4 June 2015, and 7 June 2015 in Islamabad. Moreover, Table 3 depicts that few same days show less difference in temperature rather than choosing same days. However, they are overlooked in this paper as along with the difference in temperature, the proximity of date has also significant worth. For instance, 10 June 2015 and 11 June 2015 will have less difference in temperature as compared to 15 June 2015. However, such days are neglected because they have maximum values of date proximity. Therefore, this paper can choose a similar day that has maximum difference in temperature in the proposed methodology because of proximities in date. Moreover, this phenomenon can produce more similar load curve shapes. Besides, the same chosen days in Islamabad and other regions can cause a discrepancy in selecting the same days from Islamabad for prediction of 28 June 2016.
- The predicted demand load of the entire system is combined load that is obtained from all regions after short-term load forecasting is done for every respective region.

#### 5.1. Deep Belief Network

- ${\mathcal{S}}_{0}$: The preceding data are disseminated autonomously, i.e., the correlation is 0 in the preceding data from where the sample is chosen. Therefore, any experimental correlations in the preceding data are the resultant from the unpredictability of the test group.
- ${\mathcal{S}}_{1}$: The preceding data are not disseminated autonomously, i.e., the data show serial correlation.

#### 5.2. Fuzzy Local Linear Model Tree Algorithm

## 6. Results and Discussion

#### 6.1. Evaluational Measures

- MAPE of short-term load forecasting throughout the year (${\mathcal{D}}_{f}$ = 9750)
- Average of DME throughout the year, which is referred as maximum distance and minimum error
- Total number of days, which have MAPE higher than 3% (${\Im}^{3}$)
- Total number of days, which have maximum error higher than 5% (${\Im}^{5}$)

#### 6.2. Discussion of Results

#### 6.2.1. Evaluation of Priority Index and Splitting Consequences on Knowledge Based Systems

- Case 1: Short-term load forecasting of PNPN without taking temperature and distribution of data
- Case 2: Short-term load forecasting of PNPN including consequences of data distribution without taking the temperature
- Case 3: Short-term load forecasting of PNPN including including temperature without taking the consequences of data distribution
- Case 4: Short-term load forecasting of PNPN with temperature and distribution of data

#### 6.2.2. Evaluation of Consequences on knowledge Based Systems from Preceding Data

- Case 1: Load forecasting by collected similar days in initial data-set, ${\mathsf{\Gamma}}_{tar,\mathcal{H}}^{d{s}_{1}}$
- Case 2: Load forecasting by collected similar days in last data-set, ${\mathsf{\Gamma}}_{tar,\mathcal{H}}^{d{s}_{2}}$
- Case 3: Load forecasting by ${\mathsf{\Gamma}}_{tar,\mathcal{H}}^{d{s}_{1}}$ and ${\mathsf{\Gamma}}_{tar,\mathcal{H}}^{d{s}_{2}}$, i.e., ${\mathsf{\Gamma}}_{tar,\mathcal{H}}\Rightarrow $ Equation (44)

#### 6.3. Comparative Analysis of Proposed Method, DBN, and F-LOLIMOT

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Schleicher-Tappeser, R. How renewables will change electricity markets in the next five years. Energy Policy
**2012**, 48, 64–75. [Google Scholar] [CrossRef] - Farhangi, H. The path of the smart grid. IEEE Power Energy Mag.
**2010**, 8, 18–28. [Google Scholar] [CrossRef] - Zipperer, A.; Aloise-Young, P.A.; Suryanarayanan, S.; Roche, R.; Earle, L.; Christensen, D.; Bauleo, P.; Zimmerle, D. Electric Energy Management in the Smart Home: Perspectives on Enabling Technologies and Consumer Behavior. Proc. IEEE
**2013**, 101, 2397–2408. [Google Scholar] [CrossRef] - Beaudin, M.; Zareipour, H. Home energy management systems: A review of modelling and complexity. Renew. Sustain. Energy Rev.
**2015**, 45, 318–335. [Google Scholar] [CrossRef] - Luo, X.; Wang, J.; Dooner, M.; Clarke, J. Overview of current development in electrical energy storage technologies and the application potential in power system operation. Appl. Energy
**2015**, 137, 511–536. [Google Scholar] [CrossRef] - Pothitou, M.; Hanna, R.F.; Chalvatzis, K.J. Environmental knowledge, pro-environmental behaviour and energy savings in households: An empirical study. Appl. Energy
**2016**, 184, 1217–1229. [Google Scholar] [CrossRef][Green Version] - O’Neill, R.P.; Sotkiewicz, P.M.; Hobbs, B.F.; Rothkopf, M.H.; Stewart, W.R. Efficient market-clearing prices in markets with nonconvexities. Eur. J. Oper. Res.
**2005**, 164, 269–285. [Google Scholar] [CrossRef][Green Version] - Ghasemi, A.; Mortazavi, S.S.; Mashhour, E. Hourly demand response and battery energy storage for imbalance reduction of smart distribution company embedded with electric vehicles and wind farms. Renew. Energy
**2016**, 85, 124–136. [Google Scholar] [CrossRef] - Azizipanah-Abarghooee, R.; Terzija, V.; Golestaneh, F.; Roosta, A. Multiobjective Dynamic Optimal Power Flow Considering Fuzzy-Based Smart Utilization of Mobile Electric Vehicles. IEEE Trans. Ind. Inform.
**2016**, 12, 503–514. [Google Scholar] [CrossRef] - Khan, M.; Javaid, N.; Iqbal, M.N.; Bilal, M.; Zaidi, S.F.A.; Raza, R.A. Load Prediction Based on Multivariate Time Series Forecasting for Energy Consumption and Behavioral Analytics. In Proceedings of the Conference on Complex, Intelligent, and Software Intensive Systems, Matsue, Japan, 4–6 July 2018; Springer: Cham, Switzerland, 2018; pp. 305–316. [Google Scholar]
- Rahim, S.; Javaid, N.; Ahmad, A.; Khan, S.A.; Khan, Z.A.; Alrajeh, N.; Qasim, U. Exploiting heuristic algorithms to efficiently utilize energy management controllers with renewable energy sources. Energy Build.
**2016**, 129, 452–470. [Google Scholar] [CrossRef] - Zhu, G.; Chow, T.T.; Tse, N. Short-term load forecasting coupled with weather profile generation methodology. Build. Serv. Eng. Res. Technol.
**2018**, 39, 310–327. [Google Scholar] [CrossRef] - Ahmad, A.; Javaid, N.; Guizani, M.; Alrajeh, N.; Khan, Z.A. An Accurate and Fast Converging Short-Term Load Forecasting Model for Industrial Applications in a Smart Grid. IEEE Trans. Ind. Inform.
**2017**, 13, 2587–2596. [Google Scholar] [CrossRef] - Ahmad, T.; Chen, H.; Huang, R.; Yabin, G.; Wang, J.; Shair, J.; Azeem Akram, H.M.; Hassnain Mohsan, S.A.; Kazim, M. Supervised based machine learning models for short, medium and long-term energy prediction in distinct building environment. Energy
**2018**, 158, 17–32. [Google Scholar] [CrossRef] - Lima, F.J.; Martins, F.R.; Pereira, E.B.; Lorenz, E.; Heinemann, D. Forecast for surface solar irradiance at the Brazilian Northeastern region using NWP model and artificial neural networks. Renew. Energy
**2016**, 87, 807–818. [Google Scholar] [CrossRef] - Vrbsky, L.; da Silva, M.S.; Cardoso, D.L.; Frances, C.R.L. Clustering techniques for data network planning in Smart Grids. In Proceedings of the IEEE 14th International Conference on Networking, Sensing and Control (ICNSC), Calabria, Italy, 16–18 May 2017; pp. 7–12. [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] - Silva, G.C.; Silva, J.L.R.; Lisboa, A.C.; Vieira, D.A.G.; Saldanha, R.R. Advanced fuzzy time series applied to short term load forecasting. In Proceedings of the IEEE Latin American Conference on Computational Intelligence (LA-CCI), Arequipa, Peru, 8–10 November 2017; pp. 1–6. [Google Scholar] [CrossRef]
- Mayrink, V.; Hippert, H.S. A hybrid method using Exponential Smoothing and Gradient Boosting for electrical short-term load forecasting. In Proceedings of the IEEE Latin American Conference on Computational Intelligence (LA-CCI), Cartagena, Colombia, 2–4 November 2016; pp. 1–6. [Google Scholar] [CrossRef]
- He, Y.; Xu, Q.; Wan, J.; Yang, S. Short-term power load probability density forecasting based on quantile regression neural network and triangle kernel function. Energy
**2016**, 114, 498–512. [Google Scholar] [CrossRef] - Li, S.; Wang, P.; Goel, L. A novel wavelet-based ensemble method for short-term load forecasting with hybrid neural networks and feature selection. IEEE Trans. Power Syst.
**2016**, 31, 1788–1798. [Google Scholar] [CrossRef] - Wang, J.; Hu, J. A robust combination approach for short-term wind speed forecasting and analysis—A robust combination approach for short-term wind speed forecasting and analysis—Combination of the ARIMA (Autoregressive Integrated Moving Average), ELM (Extreme Learning Machine), SVM (Support Vector Machine) and LSSVM (Least Square SVM) forecasts using a GPR (Gaussian Process Regression) model. Energy
**2015**, 93, 41–56. [Google Scholar] - Jackson, E.A. Comparison between Static and Dynamic Forecast in Autoregressive Integrated Moving Average for Seasonally Adjusted Headline Consumer Price Index. SSRN Electron. J.
**2018**, 1–14. [Google Scholar] [CrossRef] - Mitchell, G.; Bahadoorsingh, S.; Ramsamooj, N.; Sharma, C. A comparison of artificial neural networks and support vector machines for short-term load forecasting using various load types. In Proceedings of the IEEE Manchester PowerTech, Manchester, UK, 18–22 June 2017; pp. 1–4. [Google Scholar]
- Di Persio, L.; Cecchin, A.; Cordoni, F. Novel approaches to the energy load unbalance forecasting in the Italian electricity market. J. Math. Ind.
**2017**. [Google Scholar] [CrossRef] - Barman, M.; Dev Choudhury, N.; Sutradhar, S. A regional hybrid GOA-SVM model based on similar day approach for short-term load forecasting in Assam, India. Energy
**2018**, 145, 710–720. [Google Scholar] [CrossRef] - Sepasi, S.; Reihani, E.; Howlader, A.M.; Roose, L.R.; Matsuura, M.M. Very short term load forecasting of a distribution system with high PV penetration. Renew. Energy
**2017**, 106, 142–148. [Google Scholar] [CrossRef] - Eapen, R.R.; Simon, S.P. Performance Analysis of Combined Similar Day and Day Ahead Short Term Electrical Load Forecasting using Sequential Hybrid Neural Networks. IETE J. Res.
**2018**. [Google Scholar] [CrossRef] - Ahmad, A.; Anderson, T.N.; Rehman, S.U. Prediction of Electricity Consumption for Residential Houses in New Zealand; Springer: Cham, Switzerland, 2018; pp. 165–172. [Google Scholar]
- Hoverstad, B.A.; Tidemann, A.; Langseth, H.; Ozturk, P. Short-Term Load Forecasting With Seasonal Decomposition Using Evolution for Parameter Tuning. IEEE Trans. Smart Grid
**2015**, 6, 1904–1913. [Google Scholar] [CrossRef] - Kavanagh, K.; Barrett, M.; Conlon, M. Short-term electricity load forecasting for the integrated single electricity market (I-SEM). In Proceedings of the 52nd International Universities Power Engineering Conference (UPEC), Heraklion, Greece, 28–31 August 2017; pp. 1–7. [Google Scholar] [CrossRef]
- Alobaidi, M.H.; Chebana, F.; Meguid, M.A. Robust ensemble learning framework for day-ahead forecasting of household based energy consumption. Appl. Energy
**2018**, 212, 997–1012. [Google Scholar] [CrossRef] - Lydia, M.; Suresh Kumar, S.; Immanuel Selvakumar, A.; Edwin Prem Kumar, G. Linear and non-linear autoregressive models for short-term wind speed forecasting. Energy Convers. Manag.
**2016**, 112, 115–124. [Google Scholar] [CrossRef] - Bramer, L.; Rounds, J.; Burleyson, C.; Fortin, D.; Hathaway, J.; Rice, J.; Kraucunas, I. Evaluating penalized logistic regression models to predict Heat-Related Electric grid stress days. Appl. Energy
**2017**, 205, 1408–1418. [Google Scholar] [CrossRef] - Yukseltan, E.; Yucekaya, A.; Bilge, A.H. Forecasting electricity demand for Turkey: Modeling periodic variations and demand segregation. Appl. Energy
**2017**, 193, 287–296. [Google Scholar] [CrossRef] - Abdoos, A.; Hemmati, M.; Abdoos, A.A. Short term load forecasting using a hybrid intelligent method. Knowl.-Based Syst.
**2015**, 76, 139–147. [Google Scholar] [CrossRef] - Carvallo, J.P.; Larsen, P.H.; Sanstad, A.H.; Goldman, C.A. Long term load forecasting accuracy in electric utility integrated resource planning. Energy Policy
**2018**, 119, 410–422. [Google Scholar] [CrossRef] - Hawarah, L.; Ploix, S.; Jacomino, M. User Behavior Prediction in Energy Consumption in Housing Using Bayesian Networks; Springer: Berlin/Heidelberg, Germany, 2010; pp. 372–379. [Google Scholar]
- Basu, K.; Debusschere, V.; Bacha, S. Appliance usage prediction using a time series based classification approach. In Proceedings of the IECON 2012—38th Annual Conference on IEEE Industrial Electronics Society, Montreal, QC, Canada, 25–28 October 2012; pp. 1217–1222. [Google Scholar] [CrossRef]
- Basu, K.; Hawarah, L.; Arghira, N.; Joumaa, H.; Ploix, S. A prediction system for home appliance usage. Energy Build.
**2013**, 67, 668–679. [Google Scholar] [CrossRef] - Rollins, S.; Banerjee, N. Using rule mining to understand appliance energy consumption patterns. In Proceedings of the IEEE International Conference on Pervasive Computing and Communications (PerCom), Budapest, Hungary, 24–28 March 2014; pp. 29–37. [Google Scholar] [CrossRef]
- Karatasou, S.; Santamouris, M.; Geros, V. Modeling and predicting building’s energy use with artificial neural networks: Methods and results. Energy Build.
**2006**, 38, 949–958. [Google Scholar] [CrossRef] - Chen, Y.; Yang, Y.; Liu, C.; Li, C.; Li, L. A hybrid application algorithm based on the support vector machine and artificial intelligence: An example of electric load forecasting. Appl. Math. Model.
**2015**, 39, 2617–2632. [Google Scholar] [CrossRef] - Hong, W.C. Electric load forecasting by support vector model. Appl. Math. Model.
**2009**, 33, 2444–2454. [Google Scholar] [CrossRef] - Zhao, H.X.; Magoulès, F. A review on the prediction of building energy consumption. Renew. Sustain. Energy Rev.
**2012**, 16, 3586–3592. [Google Scholar] [CrossRef] - Li, X.; Lu, J.; Ding, L.; Xu, G.; Li, J. Building Cooling Load Forecasting Model Based on LS-SVM. In Proceedings of the 2009 Asia-Pacific Conference on Information Processing, Shenzhen, China, 18–19 July 2009; pp. 55–58. [Google Scholar]
- Li, H.Z.; Guo, S.; Li, C.J.; Sun, J.Q. A hybrid annual power load forecasting model based on generalized regression neural network with fruit fly optimization algorithm. Knowl.-Based Syst.
**2013**, 37, 378–387. [Google Scholar] [CrossRef] - Wang, J.; Li, L.; Niu, D.; Tan, Z. An annual load forecasting model based on support vector regression with differential evolution algorithm. Appl. Energy
**2012**, 94, 65–70. [Google Scholar] [CrossRef] - Faris, H.; Hassonah, M.A.; Al-Zoubi, A.M.; Mirjalili, S.; Aljarah, I. A multi-verse optimizer approach for feature selection and optimizing SVM parameters based on a robust system architecture. Neural Comput. Appl.
**2018**, 30, 2355–2369. [Google Scholar] [CrossRef] - Ogliari, E.; Grimaccia, F.; Leva, S.; Mussetta, M.; Ogliari, E.; Grimaccia, F.; Leva, S.; Mussetta, M. Hybrid Predictive Models for Accurate Forecasting in PV Systems. Energies
**2013**, 6, 1918–1929. [Google Scholar] [CrossRef][Green Version] - Geng, J.; Huang, M.L.; Li, M.W.; Hong, W.C. Hybridization of seasonal chaotic cloud simulated annealing algorithm in a SVR-based load forecasting model. Neurocomputing
**2015**, 151, 1362–1373. [Google Scholar] [CrossRef] - Bedekar, P.P.; Korde, P.N. Determining optimum time multiplier setting of overcurrent relays using modified Jaya algorithm. In Proceedings of the 2017 Innovations in Power and Advanced Computing Technologies (i-PACT), Vellore, India, 21–22 April 2017; pp. 1–6. [Google Scholar] [CrossRef]
- Samuel, O.; Javaid, N.; Ashraf, M.; Ishmanov, F.; Afzal, M.; Khan, Z. Jaya based Optimization Method with High Dispatchable Distributed Generation for Residential Microgrid. Energies
**2018**, 11, 1513. [Google Scholar] [CrossRef] - Mohsenian Rad, A.H.; Wong, V.W.S.; Jatskevich, J.; Schober, R.; Leon Garcia, A. Autonomous Demand-Side Management Based on Game-Theoretic Energy Consumption Scheduling for the Future Smart Grid. IEEE Trans. Smart Grid
**2010**, 1, 320–331. [Google Scholar] [CrossRef][Green Version] - Siano, P. Demand response and smart grids—A survey. Renew. Sustain. Energy Rev.
**2014**, 30, 461–478. [Google Scholar] [CrossRef] - Wang, H.; Huang, J. Joint investment and operation of microgrid. IEEE Trans. Smart Grid
**2017**, 8, 833–845. [Google Scholar] [CrossRef] - Siano, P.; Sarno, D. Assessing the benefits of residential demand response in a real time distribution energy market. Appl. Energy
**2016**, 161, 533–551. [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] - Zhou, B.; Li, W.; Chan, K.W.; Cao, Y.; Kuang, Y.; Liu, X.; Wang, X. Smart home energy management systems: Concept, configurations, and scheduling strategies. Renew. Sustain. Energy Rev.
**2016**, 61, 30–40. [Google Scholar] [CrossRef] - Marcon, P.; Szabo, Z.; Vesely, I.; Zezulka, F.; Sajdl, O.; Roubal, Z.; Dohnal, P. A Real Model of a Micro-Grid to Improve Network Stability. Appl. Sci.
**2017**, 7, 757. [Google Scholar] [CrossRef] - Liu, Y.; Li, T.; Chen, Y.; Wang, D.; Liu, Y.; Li, T.; Chen, Y.; Wang, D. Optimization of Solar Water Heating System under Time and Spatial Partition Heating in Rural Dwellings. Energies
**2017**, 10, 1561. [Google Scholar] [CrossRef] - Esther, B.P.; Kumar, K.S. A survey on residential Demand Side Management architecture, approaches, optimization models and methods. Renew. Sustain. Energy Rev.
**2016**, 59, 342–351. [Google Scholar] [CrossRef] - Alshehri, K.; Liu, J.; Chen, X.; Basar, T. A Stackelberg game for multi-period demand response management in the smart grid. In Proceedings of the 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, 15–18 December 2015; pp. 5889–5894. [Google Scholar]
- Liang, H.; Tamang, A.K.; Zhuang, W.; Shen, X.S. Stochastic Information Management in Smart Grid. IEEE Commun. Surv. Tutor.
**2014**, 16, 1746–1770. [Google Scholar] [CrossRef] - Luo, X.; Lee, C.K.; Ng, W.M.; Yan, S.; Chaudhuri, B.; Hui, S.Y.R. Use of Adaptive Thermal Storage System as Smart Load for Voltage Control and Demand Response. IEEE Trans. Smart Grid
**2017**, 8, 1231–1241. [Google Scholar] [CrossRef] - Lee, J.; Guo, J.; Choi, J.K.; Zukerman, M. Distributed Energy Trading in Microgrids: A Game Theoretic Model and Its Equilibrium Analysis. IEEE Trans. Ind. Electron.
**2015**, 62, 3524–3533. [Google Scholar] [CrossRef] - Erol-Kantarci, M.; Mouftah, H.T. Energy-Efficient Information and Communication Infrastructures in the Smart Grid: A Survey on Interactions and Open Issues. IEEE Commun. Surv. Tutor.
**2015**, 17, 179–197. [Google Scholar] [CrossRef] - Carnicer, J.M.; Goodman, T.N.T.; Peña, J.M. Linear conditions for positive determinants. Linear Algebra Its Appl.
**1999**, 292, 39–59. [Google Scholar] [CrossRef] - Chai, B.; Chen, J.; Yang, Z.; Zhang, Y. Demand Response Management With Multiple Utility Companies: A Two-Level Game Approach. IEEE Trans. Smart Grid
**2014**, 5, 722–731. [Google Scholar] [CrossRef] - Emami, N.; Pakzad, A. A New Knowledge-Based System for Diagnosis of Breast Cancer by a combination of the Affinity Propagation and Firefly Algorithms; Shahrood University of Technology: Shahrood, Iran, 2018. [Google Scholar]
- GhaffarianHoseini, A.; Zhang, T.; Nwadigo, O.; GhaffarianHoseini, A.; Naismith, N.; Tookey, J.; Raahemifar, K. Application of nD BIM Integrated Knowledge-based Building Management System (BIM-IKBMS) for inspecting post-construction energy efficiency. Renew. Sustain. Energy Rev.
**2017**, 72, 935–949. [Google Scholar] [CrossRef][Green Version] - Lin, J.; Wang, F.; Cai, A.; Yan, W.; Cui, W.; Mo, J. Daily Load Curve Forecasting Using Factor Analysis and RBF Neural Network Based on Load Segmentation. In Proceedings of the China International Electrical and Energy Conference (CIEEC), Beijing, China, 19–21 October 2017; pp. 601–606. [Google Scholar]
- Ashouri, M.; Haghighat, F.; Fung, B.C.; Lazrak, A.; Yoshino, H. Development of building energy saving advisory: A data mining approach. Energy Build.
**2018**, 172, 139–151. [Google Scholar] [CrossRef] - Raza, M.Q.; Nadarajah, M.; Hung, D.Q.; Baharudin, Z. An intelligent hybrid short-term load forecasting model for smart power grids. Sustain. Cities Soc.
**2017**, 31, 264–275. [Google Scholar] [CrossRef] - Golestaneh, F.; Pinson, P.; Gooi, H.B. Very Short-Term Nonparametric Probabilistic Forecasting of Renewable Energy Generation; With Application to Solar Energy. IEEE Trans. Smart Grids
**2016**, 31, 3850–3863. [Google Scholar] [CrossRef] - Cerne, G.; Dovzan, D.; Skrjanc, I. Short-term load forecasting by separating daily profile and using a single fuzzy model across the entire domain. IEEE Trans. Ind. Electron.
**2018**, 65, 7406–7415. [Google Scholar] [CrossRef] - Dedinec, A.; Filiposka, S.; Dedinec, A.; Kocarev, L. Deep belief network based electricity load forecasting: An analysis of Macedonian case. Energy
**2016**, 115, 1688–1700. [Google Scholar] [CrossRef] - Guarnaccia, C.; Tepedino, C.; Iliev, S.; Popova, S.; Quartieri, J. A Forecasting Model Based on Time Series Analysis Applied to Electrical Energy Consumption. Int. J. Math. Models Methods Appl. Sci.
**2015**, 9, 432. [Google Scholar] - Dong, Q.; Sun, Y.; Li, P. A novel forecasting model based on a hybrid processing strategy and an optimized local linear fuzzy neural network to make wind power forecasting: A case study of wind farms in China. Renew. Energy
**2017**, 102, 241–257. [Google Scholar] [CrossRef]

**Figure 2.**Variations in load behavior of sample Thursday during 2015 of Pakistan’s National Power Network (PNPN).

**Figure 5.**Fluctuating Behavior of Load Curve in Pakistan and Difference of Monday and a Sample Week-day.

**Figure 7.**Auto-correlation of preceding demand load data for day lags in deep belief network (DBN) for original data (0, 1).

**Figure 8.**Auto-correlation of preceding demand load data for day lags in DBN for original data (0, 1).

**Figure 9.**Auto-correlation of preceding demand load data for day lags in DBN for original data (1, 2).

**Figure 10.**Auto-correlation of preceding demand load data for day lags in DBN for resampled data (1,2).

**Figure 11.**Auto-correlation of preceding demand load data for day lags in Fuzzy Local Linear Model Tree (F-LOLIMOT).

**Figure 12.**Comparative analysis and effect of proposed and traditional method for Monday, 19 September 2015.

**Figure 13.**Comparative analysis and effect of proposed and traditional method for Wednesday, 13 June 2015.

**Figure 14.**Comparative analysis and effect of proposed and traditional method for Sunday, 4 January 2015.

Symbol | Meaning |
---|---|

$\mathcal{UC}$ | Utility Companies |

$\mathtt{n}$ | All consumers |

${\mathtt{n}}_{\mathtt{0}}$ | Consumer |

${\mathtt{uc}}_{\mathtt{0}}$ | Utility Company |

${d}_{{n}_{0}}$ | Demand of consumer |

${\gamma}_{\mathtt{n}}\mathtt{0}$ | Constant for user analysis |

${\tau}_{n}0$ | Constant for user demand |

ln | Function for decision making |

${\kappa}_{u{c}_{0}}$ | Price per unit |

${B}_{{n}_{0}}$ | Total budget of consumer |

${\mathsf{\Lambda}}_{{n}_{0},1},{\mathsf{\Lambda}}_{{n}_{0},2},{\mathsf{\Lambda}}_{{n}_{0},3}$ | Lagrange multipliers |

$\nabla {\upsilon}_{cons}$ | Best condition of first order |

${\mathcal{E}}_{u{c}_{0}}$ | Available power of ${\mathtt{uc}}_{\mathtt{0}}$ |

${\xi}_{u{c}_{0}+1}$ | Price of $\mathcal{UC}$ other than ${\mathtt{uc}}_{\mathtt{0}}$ |

$\mathcal{M}$ | Invertible matrix |

$|\mathcal{M}|$ | Determinant of $\mathcal{M}$ |

${\Im}_{prod}$ | Strategy sets for $\mathcal{M}$ |

${\Im}_{cons}$ | Strategy sets for ${\mathtt{n}}_{\mathtt{0}}$ |

$\mathtt{d}$ | Game plan for all n |

$d{\kappa}^{+}$ | Best feedback of all n |

${\mathtt{d}}_{{\mathtt{n}}_{\mathtt{0}}}^{+}$ | Proposed best scheme for n |

$r$ | Iteration Number |

${\delta}_{\mathtt{uc}}\mathtt{0}$ | Speed modification constraint of ${\mathtt{uc}}_{\mathtt{0}}$ |

${I}_{i}$ | Input Vector in SVM |

${O}_{i}$ | Targeted Output in SVM |

$E$ | Total data in SVM |

$\mathcal{W}$ | Weight in SVM |

t | Threshold estimate in SVM |

**Table 2.**Mean Absolute Percentage Error (MAPE) for every pair of ${\mathcal{D}}_{\gamma}$ and ${W}_{1}$ for training data.

${\mathcal{D}}_{\mathit{\gamma}}$ | ${\mathit{W}}_{1}$ | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 | |

5 | 1.430 | 1.722 | 1.322 | 1.517 | 1.113 | 1.321 | 1.612 | 1.421 | 1.117 | 1.220 | 1.312 |

6 | 1.128 | 1.787 | 1.316 | 1.501 | 1.119 | 1.313 | 1.611 | 1.417 | 1.113 | 1.216 | 1.307 |

7 | 1.418 | 1.712 | 1.312 | 1.509 | 1.102 | 1.325 | 1.609 | 1.415 | 1.111 | 1.215 | 1.305 |

8 | 1.418 | 1.711 | 1.321 | 1.507 | 1.100 | 1.303 | 1.615 | 1.420 | 1.119 | 1.217 | 1.311 |

9 | 1.418 | 1.713 | 1.217 | 1.599 | 1.102 | 1.307 | 1.617 | 1.425 | 1.123 | 1.206 | 1.315 |

10 | 1.419 | 1.715 | 1.311 | 1.503 | 1.105 | 1.311 | 1.621 | 1.430 | 1.125 | 1.213 | 1.321 |

11 | 1.431 | 1.715 | 1.311 | 1.505 | 1.106 | 1.312 | 1.622 | 1.433 | 1.130 | 1.219 | 1.320 |

12 | 1.491 | 1.710 | 1.331 | 1.501 | 1.107 | 1.315 | 1.625 | 1.432 | 1.132 | 1.220 | 1.320 |

13 | 1.431 | 1.713 | 1.360 | 1.599 | 1.108 | 1.324 | 1.629 | 1.435 | 1.131 | 1.223 | 1.319 |

14 | 1.472 | 1.721 | 1.366 | 1.502 | 1.109 | 1.327 | 1.630 | 1.440 | 1.131 | 1.227 | 1.326 |

15 | 1.414 | 1.789 | 1.363 | 1.503 | 1.111 | 1.328 | 1.631 | 1.441 | 1.134 | 1.228 | 1.329 |

Date | Day | Difference of Temperature | Proximity of Date | Index Value |
---|---|---|---|---|

4 June 2015 | Thursday | 1 | 371 | 0.1393 |

7 June 2015 | Sunday | 0 | 366 | 0.1282 |

10 June 2015 | Wednesday | 2 | 337 | 0.2859 |

11 June 2015 | Thursday | −1 | 332 | 0.2747 |

15 June 2015 | Monday | −2 | 266 | 0.1549 |

16 June 2015 | Tuesday | −5 | 265 | 0.3295 |

17 June 2015 | Wednesday | −3 | 264 | 0.3791 |

19 June 2015 | Friday | −4 | 263 | 0.3795 |

24 June 2016 | Friday | −1 | 4 | 0.0212 |

25 June 2016 | Saturday | −3 | 7 | 0.5701 |

26 June 2016 | Sunday | −2 | 6 | 0.1210 |

27 June 2016 | Monday | 0 | 5 | 0.0021 |

Original Data | Experimental Data | Region Size | |
---|---|---|---|

(0, 1) | 1.00 $\times {10}^{-7}$ | 0.5510981 | 8175 |

(0, 2) | 6.75$\times {10}^{-4}$ | 0.6528330 | 14,798 |

(1, 1) | 0.00$\times {10}^{0}$ | 0.4384530 | 16,856 |

(1, 2) | 0.00$\times {10}^{0}$ | 0.7561250 | 15,087 |

**Table 5.**Consequences of priority index and data distribution on the forecasting results for ${\Im}^{5}$ and ${\Im}^{3}$.

Nature of Days | ${\mathit{\Im}}^{5}$ | ${\mathit{\Im}}^{3}$ | ||||||
---|---|---|---|---|---|---|---|---|

Case 1 | Case 2 | Case 3 | Case 4 | Case 1 | Case 2 | Case 3 | Case 4 | |

Weekdays | 10 | 8 | 7 | 6 | 5 | 4 | 6 | 8 |

Weekend | 3 | 4 | 4 | 3 | 1 | 1 | 2 | 1 |

Yearly Mean | 25 | 26 | 20 | 19 | 20 | 13 | 11 | 12 |

**Table 6.**Consequences of priority index and data distribution on the forecasting results for Maximum Distance Minimum Error (MDME) and MAPE.

Nature of Days | MDME | MAPE | ||||||
---|---|---|---|---|---|---|---|---|

Case 1 | Case 2 | Case 3 | Case 4 | Case 1 | Case 2 | Case 3 | Case 4 | |

Weekdays | 3.70 | 3.65 | 2.95 | 2.58 | 1.23 | 1.33 | 1.25 | 1.29 |

Weekend | 2.96 | 2.92 | 2.75 | 2.49 | 1.19 | 1.15 | 1.17 | 1.01 |

Yearly Mean | 2.70 | 2.26 | 2.51 | 2.24 | 1.09 | 1.07 | 1.03 | 1.02 |

${\mathcal{D}}_{\mathit{\gamma}}$ | ${\mathcal{W}}_{1}$ | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

0 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 | 0.8 | 0.9 | 1 | |

5 | 1.115 | 1.161 | 1.089 | 1.075 | 1.096 | 1.049 | 1.078 | 1.088 | 1.117 | 1.121 | 1.125 |

6 | 1.015 | 1.029 | 1.021 | 1.017 | 1.019 | 1.022 | 1.026 | 1.031 | 1.040 | 1.045 | 1.050 |

7 | 1.043 | 1.012 | 1.011 | 1.009 | 1.016 | 1.025 | 1.043 | 1.045 | 1.052 | 1.105 | 1.106 |

8 | 1.301 | 1.318 | 1.313 | 1.314 | 1.321 | 1.325 | 1.329 | 1.342 | 1.378 | 1.389 | 1.391 |

9 | 1.208 | 1.219 | 1.217 | 1.216 | 1.223 | 1.234 | 1.249 | 1.265 | 1.290 | 1.301 | 1.315 |

10 | 1.305 | 1.315 | 1.321 | 1.311 | 1.326 | 1.336 | 1.349 | 1.367 | 1.387 | 1.403 | 1.421 |

11 | 1.308 | 1.329 | 1.325 | 1.326 | 1.331 | 1.341 | 1.352 | 1.353 | 1.376 | 1.391 | 1.415 |

12 | 1.309 | 1.301 | 1.327 | 1.328 | 1.345 | 1.347 | 1.358 | 1.367 | 1.395 | 1.412 | 1.428 |

13 | 1.309 | 1.302 | 1.324 | 1.331 | 1.337 | 1.348 | 1.362 | 1.381 | 1.413 | 1.426 | 1.443 |

14 | 1.403 | 1.436 | 1.431 | 1.435 | 1.443 | 1.453 | 1.466 | 1.487 | 1.503 | 1.529 | 1.525 |

15 | 1.404 | 1.414 | 1.416 | 1.423 | 1.439 | 1.465 | 1.494 | 1.511 | 1.534 | 1.529 | 1.549 |

**Table 8.**Consequences of taking ${\mathsf{\Gamma}}_{tar,\mathcal{H}}^{d{s}_{1}}$ and ${\mathsf{\Gamma}}_{tar,\mathcal{H}}^{d{s}_{2}}$ on forecasting.

Nature of Days | ${\mathit{\Im}}^{5}$ | ${\mathit{\Im}}^{3}$ | MDME | MAPE | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Case 1 | Case 2 | Case 3 | Case 1 | Case 2 | Case 3 | Case 1 | Case 2 | Case 3 | Case 1 | Case 2 | Case 3 | |

Weekdays | 10 | 13 | 7 | 8 | 7 | 7 | 3.21 | 2.73 | 2.71 | 1.81 | 1.52 | 1.26 |

Weekend | 5 | 3 | 2 | 2 | 1 | 1 | 2.89 | 2.35 | 2.35 | 1.09 | 1.23 | 1.17 |

Yearly Mean | 39 | 16 | 16 | 18 | 14 | 13 | 2.68 | 2.24 | 2.24 | 1.31 | 1.10 | 1.03 |

**Table 9.**Comparison of Fuzzy Local Linear Model (F-LOLIMOT), deep belief network (DBN), and proposed method.

Technique | ${\mathit{\Im}}^{5}$ | ${\mathit{\Im}}^{3}$ | MDME | MAPE | Operational Time (s) | |
---|---|---|---|---|---|---|

Training Time | Executing Time | |||||

Proposed | 17 | 10 | 2.83 | 1.10 | 15 | 0.41 |

DBN | 50 | 42 | 2.89 | 1.21 | 29 | 0.52 |

F-LOLIMOT | 42 | 35 | 3.43 | 1.50 | 215 | 0.81 |

© 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**

Khan, M.; Javaid, N.; Sajjad; Abdullah; Naseem, A.; Ahmed, S.; Riaz, M.S.; Akbar, M.; Ilahi, M.
Game Theoretical Demand Response Management and Short-Term Load Forecasting by Knowledge Based Systems on the basis of Priority Index. *Electronics* **2018**, *7*, 431.
https://doi.org/10.3390/electronics7120431

**AMA Style**

Khan M, Javaid N, Sajjad, Abdullah, Naseem A, Ahmed S, Riaz MS, Akbar M, Ilahi M.
Game Theoretical Demand Response Management and Short-Term Load Forecasting by Knowledge Based Systems on the basis of Priority Index. *Electronics*. 2018; 7(12):431.
https://doi.org/10.3390/electronics7120431

**Chicago/Turabian Style**

Khan, Mahnoor, Nadeem Javaid, Sajjad, Abdullah, Adnan Naseem, Salman Ahmed, Muhammad Sajid Riaz, Mariam Akbar, and Manzoor Ilahi.
2018. "Game Theoretical Demand Response Management and Short-Term Load Forecasting by Knowledge Based Systems on the basis of Priority Index" *Electronics* 7, no. 12: 431.
https://doi.org/10.3390/electronics7120431