Game Theoretical Energy Management with Storage Capacity Optimization and Photo-Voltaic Cell Generated Power Forecasting in Micro Grid †
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 is function of energy consumption by 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 ,
- 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 shows cost of energy consumption that is received by users in time slot k,
- Whereas, captures the benefit that is gained by MG after supplying energy to set of users,
- defines price of energy that is defined by MG against each time slot k,
- define optimal storage capacity that is required to minimize the cost function of MG,
- Cost function of user: ,
- Cost function of MG: .
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 |
Actual Time Series | |
Average User Consumption | |
Charging Efficiency of Battery | |
Constant Variance | |
Cost Function of Users | |
Cost Function of Micro Grid | |
Daily Energy Usage of User | |
Discharging Efficiency of Battery | |
Daily Depreciation Cost Function | |
Cost Function of User | |
Error at Time t | |
Energy Demand in Particular Slot | |
Energy Demanded from Users | |
Energy Required to Charge Battery | |
Fixed Parameters | |
Lower Limit of Battery Capacity | |
Multiple Residential Users | |
Micro Grid | |
Mean Square Error | |
Peak Consumption | |
Profit of Micro grid | |
F | Penalty Factor |
Prediction Error | |
Predicted Time Series | |
Pattern of Battery Charging | |
Pattern of Battery Discharging | |
Real Time Price of Each Slot | |
Sum of Total Energy | |
Strategy Form | |
Solar Power Selling Price | |
s | State of Battery |
Time Slots in a Period | |
Total Energy Required to Discharge Battery | |
Total Cost of Users | |
T | Total no. of Observations |
Total Cost of Solar Power Generation | |
Test Static | |
Upper Limit of Battery Capacity | |
Vector Based on Rules of AR | |
Vector Based on Rules of MA |
References
- Huang, B.; Li, Y.; Zhang, H.; Sun, Q. Distributed optimal co-multi-microgrids energy management for energy internet. IEEE/CAA J. Autom. Sin. 2016, 3, 357–364. [Google Scholar]
- Wollenberg, B.F. Toward a smart grid: Power delivery for the 21st century. Power Energy Mag. 2005, 3, 34–41. [Google Scholar]
- Ahmad, A.; Javaid, N.; Mateen, A.; Awais, M.; Khan, Z. Short-Term Load Forecasting in Smart Grids: An Intelligent Modular Approach. Energies 2019, 12, 164. [Google Scholar] [CrossRef]
- Zahid, M.; Ahmed, F.; Javaid, N.; Abbasi, R.A.; Kazmi, Z.; Syeda, H.; Javaid, A.; Bilal, M.; Akbar, M.; Ilahi, M. Electricity Price and Load Forecasting using Enhanced Convolutional Neural Network and Enhanced Support Vector Regression in Smart Grids. Electronics 2019, 8, 122. [Google Scholar]
- Wang, Y.; Mao, S.; Nelms, R.M. Distributed online algorithm for optimal real-time energy distribution in the smart grid. IEEE Internet Things J. 2014, 1, 70–80. [Google Scholar] [CrossRef]
- Muralitharan, K.; Sakthivel, R.; Shi, Y. Multiobjective optimization technique for demand side management with load balancing approach in smart grid. Neurocomputing 2016, 177, 110–119. [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]
- Rifkin, J. The Third Industrial Revolution: How Lateral Power Is Transforming Energy, the Economy, and the World; Macmillan: New York, NY, USA, 2011. [Google Scholar]
- Yi, P.; Zhu, T.; Jiang, B.; Jin, R.; Wang, B. Deploying Energy Routers in an Energy Internet Based on Electric Vehicles. IEEE Trans. Veh. Technol. 2016, 65, 4714–4725. [Google Scholar] [CrossRef]
- Xia, Z.; Chen, L.; Sun, X.; Liu, J. A multi-keyword ranked search over encrypted cloud data supporting semantic extension. Int. J. Multimed. Ubiquitous Eng. 2016, 11, 107–120. [Google Scholar] [CrossRef]
- Ellabban, O.; Abu-Rub, H.; Blaabjerg, F. Renewable energy resources: Current status, future prospects and their enabling technology. Renew. Sustain. Energy Rev. 2014, 39, 748–764. [Google Scholar] [CrossRef]
- Sato, T.; Kammen, D.M.; Duan, B.; Macuha, M.; Zhou, Z.; Wu, J.; Tariq, M.; Asfaw, S.A. Smart Grid Standards: Specifications, Requirements, and Technologies; John Wiley and Sons: Hoboken, NJ, USA, 2015. [Google Scholar]
- Uski, S.; Forssén, K.; Shemeikka, J. Sensitivity Assessment of Microgrid Investment Options to Guarantee Reliability of Power Supply in Rural Networks as an Alternative to Underground Cabling. Energies 2018, 11, 2831. [Google Scholar] [CrossRef]
- Zhang, Y.; Fu, L.; Zhu, W.; Bao, X.; Liu, C. Robust model predictive control for optimal energy management of island microgrids with uncertainties. Energy 2018, 164, 1229–1241. [Google Scholar] [CrossRef]
- 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. [Google Scholar] [CrossRef]
- Nuño, E.; Maule, P.; Hahmann, A.; Cutululis, N.; Sørensen, P.; Karagali, I. Simulation of transcontinental wind and solar PV generation time series. Renew. Energy 2018, 118, 425–436. [Google Scholar] [CrossRef]
- Zhou, Z.; Bai, J.; Dong, M.; Ota, K.; Zhou, S. Game-theoretical energy management design for smart cyber-physical power systems. Cyber-Phys. Syst. 2015, 1, 24–45. [Google Scholar] [CrossRef]
- Ahmad, F.; Rasool, A.; Ozsoy, E.; Sekar, R.; Sabanovic, A.; Elitaş, M. Distribution system state estimation—A step towards smart grid. Renew. Sustain. Energy Rev. 2018, 81, 2659–2671. [Google Scholar] [CrossRef]
- Hussain, B.; Khan, A.; Javaid, N.; Hasan, Q.U.; Malik, S.A.; Dar, A.H.; Kazmi, A.; Ahmad, O. A Weighted-Sum PSO Algorithm for HEMS: A New Approach for the Design and Diversified Performance Analysis. Electronics 2019, 8, 180. [Google Scholar] [CrossRef]
- Naz, A.; Javaid, N.; Khan, A.B.M.; Iqbal, M.M.; ur Rehman Hashmi, M.A.; Abbasi, R.A. Game-Theoretical energy management for residential user and micro grid for optimum sizing of photo voltaic battery systems and energy prices. In Proceedings of the 33rd International Conference on Advanced Information Networking and Applications (AINA), Matsue, Japan, 27–29 March 2019; pp. 1097–1106. [Google Scholar]
- Farhath, Z.A.; Arputhamary, B.; Arockiam, L. A Survey on ARIMA Forecasting Using Time Series Model. Int. J. Comput. Sci. Mob. Comput. 2016, 5, 104–109. [Google Scholar]
- Wei, W.; Liu, F.; Mei, S.; Hou, Y. Robust energy and reserve dispatch under variable renewable generation. IEEE Trans. Smart Grid 2015, 6, 369–380. [Google Scholar] [CrossRef]
- Iqbal, Z.; Javaid, N.; Iqbal, S.; Aslam, S.; Khan, Z.; Abdul, W.; Almogren, A.; Alamri, A. A Domestic Microgrid with Optimized Home Energy Management System. Energies 2018, 11, 1002. [Google Scholar] [CrossRef]
- Chen, Z.; Wu, L.; Fu, Y. Real-time price-based demand response management for residential appliances via stochastic optimization and robust optimization. IEEE Trans. Smart Grid 2012, 3, 1822–1831. [Google Scholar] [CrossRef]
- Reka, S.S.; Ramesh, V. Demand side management scheme in smart grid with cloud computing approach using stochastic dynamic programming. Perspect. Sci. 2016, 8, 169–171. [Google Scholar] [CrossRef]
- Hu, W.; Wang, P.; Gooi, H.B. Toward optimal energy management of microgrids via robust two-stage optimization. IEEE Trans. Smart Grid 2018, 9, 1161–1174. [Google Scholar] [CrossRef]
- Cui, S.; Wang, Y.W.; Xiao, J.; Liu, N. A Two-Stage Robust Energy Sharing Management for Presumer Microgrid. IEEE Trans. Ind. Inform. 2018. [Google Scholar] [CrossRef]
- Lew, D.; Bird, L.; Milligan, M.; Speer, B.; Carlini, E.M.; Estanqueiro, A.; Flynn, D.; Gómez-Lázaro, E.; Holttinen, H.; Menemenlis, N.; et al. Wind and solar curtailment: International experience and practices. In Proceedings of the 12th International Workshop on Large-Scale Integration of Wind Power into Power Systems as Well as on Transmission Networks for Offshore Wind Power Plants, London, UK, 22–24 October 2013. [Google Scholar]
- Ibanez, E.; Brinkman, G.; Hummon, M.; Lew, D. A solar reserve methodology for renewable energy integration studies based on sub-hourly variability analysis. In Proceedings of the 2nd International Workshop on Integration of Solar Power in Power Systems Proceedings, Lisbon, Portugal, 12–13 November 2012. [Google Scholar]
- Mills, A.; Ahlstrom, M.; Brower, M.; Ellis, A.; George, R.; Hoff, T.; Kroposki, B.; Lenox, C.; Miller, N.; Stein, J.; et al. Understanding Variability and Uncertainty of Photovoltaics for Integration with the Electric Power System; No. LBNL-2855E; Lawrence Berkeley National Lab. (LBNL): Berkeley, CA, USA, 2009. [Google Scholar]
- Taylor, J.; McSharry, P. Short-term load forecasting methods: An evaluation based on European data. IEEE Trans. Power Syst. 2007, 22, 2213–2219. [Google Scholar] [CrossRef]
- Melin, P.; Soto, J.; Castillo, O.; Soria, J. A new approach for time series prediction using ensembles of ANFIS models. Expert Syst. Appl. 2012, 39, 3494–3506. [Google Scholar] [CrossRef]
- Potter, C.; Negnevitsky, M. Very short-term wind forecasting for Tasmanian power generation. IEEE Trans. Power Syst. 2006, 21, 965–972. [Google Scholar] [CrossRef]
- Hippert, H.; Pedreira, C.; Souza, R. Neural networks for short-term load forecasting: A review and evaluation. IEEE Trans. Power Syst. 2001, 16, 44–55. [Google Scholar] [CrossRef]
- Amjady, N.; Keynia, F.; Zareipour, H. Wind power prediction by a new forecast engine composed of modified hybrid neural network and enhanced particle swarm optimization. IEEE Trans. Sustain. Energy 2011, 2, 265–276. [Google Scholar] [CrossRef]
- Adamowski, K.; Dalezios, N.R.; Mohamed, F.B. Space-time ARIMA modeling for regional precipitation forecasting. J. Comput. Math. 1987, 5, 249–263. [Google Scholar]
- Ong, C.-S.; Huang, J.-J.; Tzeng, G.-H. Model identification of ARIMA family usinggenetic algorithms. Appl. Math. Comput. 2005, 164, 885–912. [Google Scholar]
- Yeh, W.-C.; Yeh, Y.-M.; Chang, P.-C.; Ke, Y.-C.; Chung, V. Forecasting wind powerin the Mai Liao wind farm based on the multi-layer perceptron artificialneural network model with improved simplified swarm optimization. Int. J. Electr. Power Energy Syst. 2014, 55, 741–748. [Google Scholar] [CrossRef]
- Chen, R.; Liang, C.-Y.; Hong, W.-C.; Gu, D.-X. Forecasting holiday daily touristflow based on seasonal support vector regression with adaptive geneticalgorithm. Appl. Soft Comput. 2015, 26, 435–443. [Google Scholar] [CrossRef]
- Zhou, D.; An, Y.; Zha, D.; Wu, F.; Wang, Q. Would an increasing block carbon tax be better? A comparative study within the Stackelberg Game framework. J. Environ. Manag. 2019, 235, 328–341. [Google Scholar] [CrossRef] [PubMed]
- Ji, X.; Yang, K.; Na, X.; Lv, C.; Liu, Y. Shared Steering Torque Control for Lane Change Assistance: A Stochastic Game-Theoretic Approach. IEEE Trans. Ind. Electron. 2019, 66, 3093–3105. [Google Scholar] [CrossRef]
- Han, L.; Morstyn, T.; McCulloch, M. Incentivizing Prosumer Coalitions With Energy Management Using Cooperative Game Theory. IEEE Trans. Power Syst. 2019, 34, 303–313. [Google Scholar] [CrossRef]
- Li, C.; Cai, W.; Luo, H.; Zhang, Q. Power utilization strategy in smart residential community using non-cooperative game considering customer satisfaction and interaction. Electr. Power Syst. Res. 2019, 166, 178–189. [Google Scholar] [CrossRef]
- Haupt, S.E.; Kosović, B. Variable generation power forecasting as a big data problem. IEEE Trans. Sustain. Energy 2017, 8, 725–732. [Google Scholar] [CrossRef]
- Gao, B.; Liu, X.; Yu, C.; Tang, Y. Game-theoretic energy management with storage capacity optimization in the smart grids. J. Mod. Power Syst. Clean Energy 2018, 6, 656–667. [Google Scholar] [CrossRef]
- Su, J.; Zhou, L.; Li, R. Cost-benefit analysis of distributed grid-connected photovoltaic power generation. Proc. CSEE 2013, 33, 50–56. [Google Scholar]
- Liang, X.; Li, X.; Lu, R.; Lin, X.; Shen, X. UDP: Usage-based dynamic pricing with privacy preservation for smart grid. IEEE Trans. Smart Grid 2013, 4, 141–150. [Google Scholar] [CrossRef]
- Stephens, E.R.; Smith, D.B.; Mahanti, A. Game theoretic model predictive control for distributed energy demand-side management. IEEE Trans. Smart Grid 2015, 6, 1394–1402. [Google Scholar] [CrossRef]
- Sinha, A.; Malo, P.; Frantsev, A.; Deb, K. Finding optimal strategies in a multi-period multi-leader–follower Stackelberg game using an evolutionary algorithm. Comput. Oper. Res. 2014, 41, 374–385. [Google Scholar] [CrossRef]
- Iwueze, I.S.; Nwogu, E.C.; Nlebedim, V.U.; Imoh, J.C. Comparison of Two Time Series Decomposition Methods: Least Squares and Buys-Ballot Methods. Open J. Stat. 2016, 6, 1123. [Google Scholar] [CrossRef]
- Cadenas, E.; Rivera, W.; Campos-Amezcua, R.; Heard, C. Wind speed prediction using a univariate ARIMA model and a multivariate NARX model. Energies 2016, 9, 109. [Google Scholar] [CrossRef]
- Dickey, D.A.; Fuller, W.A. Distribution of the estimators for autoregressive time series with a unit root. J. Am. Stat. Assoc. 1979, 74, 427–431. [Google Scholar]
- Yang, X.S.; Deb, S. Cuckoo search via Lévy flights. In Proceedings of the 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC), Coimbatore, India, 9–11 December 2009. [Google Scholar]
- Naz, M.; Iqbal, Z.; Javaid, N.; Khan, Z.A.; Abdul, W.; Almogren, A.; Alamri, A. Efficient Power Scheduling in Smart Homes Using Hybrid Grey Wolf Differential Evolution Optimization Technique with Real Time and Critical Peak Pricing Schemes. Energies 2018, 11, 384. [Google Scholar] [CrossRef]
- Mirjalili, S.; Mirjalili, S.M.; Lewis, A. Grey wolf optimizer. Adv. Eng. Softw. 2014, 69, 46–61. [Google Scholar] [CrossRef]
- Available online: http://www.elia.be/en/grid-data/power-generation/Solar-power-generation-data/Graph (accessed on 1 January 2019).
Time Chunks | (cents/kWh) | (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] |
2.0 | |
2.0 | |
92% | |
92% | |
7.2 | |
7.1 | |
4.3 | |
6.00–1700 | |
1700–2200 |
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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
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 StyleNaz, 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