# Real-Time Demand Side Management Algorithm Using Stochastic Optimization

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Proposed Approach: DSM via Stochastic Optimization

#### 2.1. Dynamic-Interval Density Forecast

#### 2.2. Dimensionality Reduction Module

#### 2.2.1. Time-Of-Use (TOU) Partitioning

- Obtain the value of dimension reduction
- Accurate TOU Pricing: the objective of the stochastic optimization is to minimize electric cost, the electric cost in turn depends on TOU price which varies depending on the time of day. Figure 1 represents TOU policy of the Korean electric power company (KEPCO) which shows the different periods (partitions) in a day horizon with different time of use prices. The price changes are different depending on the day of the week and season [26]. Periods marked red have the highest price tag, followed by the yellow periods, with the green periods having the lowest price tag.

#### 2.2.2. Piecewise Peak Approximation

Algorithm 1. PPA ($\mathit{X}$). |

begin1. $q=TOU\_band(X)$ 2. $c=(w-f)1\{w=m\}+(m-f)1\{m>w\}$ 3. for i = 1 to c4. $Z=\mathrm{max}\_sub\_divide(q)$ 5. Endfor6. for each partition in Z,k7. ${H}_{k}=\mathrm{max}\_peak\_propensity(Z(k),Z(k-1),X)$ 8. ${r}_{k}=Z(k)$ 9. Endforend |

#### 2.3. Stochastic Optimization

## 3. Problem Formulation

- Energy Cost (TOU), which is computed at every time interval
- Demand (Peak) Cost, which is evaluated at the end of every month

#### 3.1. Energy Cost

#### 3.2. Demand Cost

#### 3.3. Optimization

## 4. Case Study

^{−10}is used to implement the stochastic optimization procedure using the parameters in Table 1 at intervals following DIDF. TOU pricing is based on data from KEPCO [26].

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

- Gelazanskas, L.; Gamage, K.A.A. Demand side management in smart grid: A review and proposals for future direction. Sustain. Cities Soc.
**2014**, 11, 22–30. [Google Scholar] [CrossRef] - Rahmani-Andebili, M. Nonlinear demand response programs for residential customers with nonlinear behavioral models. Energy Build.
**2016**, 119, 352–362. [Google Scholar] [CrossRef] - Palensky, P.; Dietrich, D. Demand side management: Demand response, intelligent energy systems, and smart loads. IEEE Trans. Ind. Inform.
**2011**, 7, 381–388. [Google Scholar] [CrossRef] - Logenthiran, T.; Srinivasan, D.; Shun, T.Z. Demand side management in smart grid using heuristic optimization. IEEE Trans. Smart Grid
**2012**, 3, 1244–1252. [Google Scholar] [CrossRef] - Ipakchi, A.; Albuyeh, F. Grid of the future. IEEE Power Energy Mag.
**2009**, 7, 52–62. [Google Scholar] [CrossRef] - Liu, W.; Niu, S.; Xu, H. Optimal planning of battery energy storage considering reliability benefit and operation strategy in active distribution system. J. Mod. Power Syst. Clean Energy
**2017**, 5, 177–186. [Google Scholar] [CrossRef] - Akhil, A.A.; Huff, G.; Currier, A.B.; Kaun, B.C.; Rastler, D.M.; Chen, S.B.; Cotter, A.L.; Bradshaw, D.T.; Gauntlett, W.D. DOE/EPRI Electricity Storage Handbook; United States National Nuclear Security Administration: Washington, DC, USA, 2015. [Google Scholar]
- Tsekouras, G.J.; Kanellos, F.D.; Mastorakis, N. Computational Problems in Science and Engineering; Springer: Berlin, Germany, 2015; Volume 343, pp. 19–59. [Google Scholar]
- Aneiros, G.; Vilar, J.; Raña, P. Short-term forecast of daily curves of electricity demand and price. Int. J. Electr. Power Energy Syst.
**2016**, 80, 96–108. [Google Scholar] [CrossRef] - Khan, G.M.; Khan, S.; Ullah, F. Short-term daily peak load forecasting using fast learning neural network. In Proceedings of the 2011 11th International Conference on Intelligent Systems Design and Applications, Cordoba, Spain, 22–24 November 2011; pp. 843–848. [Google Scholar]
- Dash, P.K.; Satpathy, H.P.; Liew, A.C. A real-time short-term peak and average load forecasting system using a self-organising fuzzy neural network. Eng. Appl. Artif. Intell.
**1998**, 11, 307–316. [Google Scholar] [CrossRef] - Feinberg, E.A.; Genethliou, D. Peak demand control in commercial buildings with target peak adjustment based on load forecasting. Appl. Math. Power Syst.
**2005**, 2, 269–285. [Google Scholar] - Dabbagh, M.; Hamdaoui, B.; Rayes, A.; Guizani, M. Shaving Data Center Power Demand Peaks through Energy Storage and Workload Shifting Control. IEEE Trans. Cloud Comput.
**2017**. [Google Scholar] [CrossRef] - Lin, Q.; Yin, M.; Shi, D.; Qu, H. Optimal Control of Battery Energy Storage System Integrated in PV Station Considering Peak Shaving. Chin. Autom. Congr. (CAC)
**2017**, 2017, 2750–2754. [Google Scholar] - Lu, C.; Xu, H.; Pan, X.; Song, J. Optimal sizing and control of battery energy storage system for peak load shaving. Energies
**2014**, 7, 8396–8410. [Google Scholar] [CrossRef] - Cho, K.; Kim, S.; Kim, J.; Kim, E.; Kim, Y.; Cho, C. Optimal ESS Scheduling considering Demand Response for Electricity Charge Minimization under Time of Use Price Key words. Renew. Energy Power Qual. J.
**2016**, 264–267. [Google Scholar] [CrossRef] - Elizabeth, F.Q.; Nghiem, T.X.; Behl, M.; Mangharam, R.; Pappas, G.J. Scalable Scheduling of Building Control Systems for Peak Demand Reduction. Am. Control Conf.
**2012**, 3050–3055. [Google Scholar] [CrossRef] - Nghiem, T.X.; Behl, M.; Mangharam, R.; Pappas, G.J. Green scheduling of control systems for peak demand reduction. In Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, USA, 12–15 December 2011; pp. 5131–5136. [Google Scholar]
- Carpinelli, G.; Khormali, S.; Mottola, F.; Proto, D. Optimal operation of electrical energy storage systems for industrial applications. IEEE Power Energy Soc. Gen. Meet.
**2013**, 7, 1–5. [Google Scholar] - Carpinelli, G.; Celli, G.; Mocci, S.; Mottola, F.; Pilo, F.; Proto, D. Optimal Integration of Distributed Energy Storage Devices in Smart Grids. IEEE Trans. Smart Grid
**2013**, 4, 985–995. [Google Scholar] [CrossRef] - Chiodo, E.; Lauria, D. Probabilistic description and prediction of electric peak power demand. In Proceedings of the Electrical Systems for Aircraft, Railway and Ship Propulsion (ESARS), Bologna, Italy, 16–18 October 2012. [Google Scholar]
- Rahmani-Andebili, M.; Venayagamoorthy, G.K. Stochastic optimization for combined economic and emission dispatch with renewables. In Proceedings of the 2015 IEEE Symposium Series on Computational Intelligence, Cape Town, South Africa, 7–10 December 2015; pp. 1252–1258. [Google Scholar]
- Wang, Y.; Wang, B.; Zhang, T.; Nazaripouya, H.; Chu, C.C.; Gadh, R. Optimal energy management for Microgrid with stationary and mobile storages. In Proceedings of the IEEE Power Engineering Society Transmission and Distribution Conference, Dallas, TX, USA, 2–5 May 2016. [Google Scholar]
- Yudong, M.; Matuško, J.; Borrelli, F. Stochastic Model Predictive Control for Building HVAC Systems: Complexity and Conservatism. IEEE Trans. Control Syst. Technol.
**2015**, 23, 101–116. [Google Scholar] - Shapiro, A.; Philpott, A. A Tutorial on Stochastic Programming. 2007, pp. 1–35. Available online: http://stoprog.org/stoprog/SPTutorial/TutorialSP.pdf (accessed on 3 April 2018).
- June, S.; Mar, S. Korea Electric Power Corporation Tariff. 2013. Available online: https://cyber.kepco.co.kr/kepco/EN/F/htmlView/ENFBHP00101.do?menuCd=EN060201. (accessed on 3 April 2018).
- Keogh, E.; Chakrabarti, K.; Pazzani, M.; Mehrotra, S. Dimensionality Reduction for Fast Similarity Search in Large Time Series Databases. Knowl. Inf. Syst.
**2001**, 3, 263–286. [Google Scholar] [CrossRef] - Chakrabarti, K.; Keogh, E.; Mehrotra, S.; Pazzani, M. Locally adaptive dimensionality reduction for indexing large time series databases. ACM Trans. Database Syst.
**2002**, 27, 188–228. [Google Scholar] [CrossRef] - Kennedy, J.; Eberhart, R. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, Perth, Australia, 27 November–1 December 1995; Volume 4, pp. 1942–1948. [Google Scholar]

**Figure 2.**Deterministic forecast and battery energy-storage systems BESS schedule analysis (

**a**) when forecast coincides with observed (

**b**) when observed deviates from the forecast.

**Figure 3.**(

**a**) Demand forecast as a probability distribution (DPD); (

**b**) Demand distribution forecast with confidence interval.

**Figure 5.**(

**a**) Converting distributions in a partition distribution to a single distribution using piecewise peak approximation (PPA) (

**b**) Peak propensity or failure region of demand distribution.

**Figure 7.**(

**a**) Demand side management (DSM) algorithm results considering only energy arbitrage (

**b**) DSM algorithm results considering only peak demand control.

**Figure 9.**(

**a**) Day ahead forecast and observed demand; (

**b**) BESS schedule on forecasted demand using deterministic optimization (DO).

**Figure 10.**(

**a**) BESS schedule on observed demand using DO (

**b**) BESS schedule on observed demand using proposed approach.

Parameters | Symbols | Symbols |
---|---|---|

Peak demand limit | Pl | 6610 kW |

BESS capacity | ${S}_{\mathrm{BESS}}$ | 500 kWh |

BESS efficiency | $\gamma $ | 90% |

Initial SOC | $so{c}_{0}$ | 0.2 |

Maximum/Minimum SOC | $so{c}_{\mathrm{max}}/so{c}_{\mathrm{min}}$ | 0.9/0.2 |

Number of sample points | m | 24 |

Number of distributions in a day | n | 96 |

Number of samples in a distribution | a | 250 |

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

Original Peak (Without BESS) | 1763 kW | |

New Peak (With BESS) | Energy arbitrage | 2072 kW |

Peak Control | 1330 kW | |

Ensemble | 1308 kW | |

Peak Reduction | Energy arbitrage | −18% |

Peak Control | 25% | |

Ensemble | 26% | |

Original Cost (Without BESS) | ₩235,084,438 | |

Yearly Cost Reduction (With BESS) | Energy arbitrage | ₩35,296,338 |

Peak Control | ₩2,937,306 | |

Ensemble | ₩9,636,600 | |

Yearly Cost Reduction | Energy arbitrage | 15% |

Peak Control | 1% | |

Ensemble | 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**

Amoasi Acquah, M.; Kodaira, D.; Han, S. Real-Time Demand Side Management Algorithm Using Stochastic Optimization. *Energies* **2018**, *11*, 1166.
https://doi.org/10.3390/en11051166

**AMA Style**

Amoasi Acquah M, Kodaira D, Han S. Real-Time Demand Side Management Algorithm Using Stochastic Optimization. *Energies*. 2018; 11(5):1166.
https://doi.org/10.3390/en11051166

**Chicago/Turabian Style**

Amoasi Acquah, Moses, Daisuke Kodaira, and Sekyung Han. 2018. "Real-Time Demand Side Management Algorithm Using Stochastic Optimization" *Energies* 11, no. 5: 1166.
https://doi.org/10.3390/en11051166