# Predicting Energy Demand in Semi-Remote Arctic Locations

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## Abstract

**:**

## 1. Introduction

## 2. Background and Related Work

#### 2.1. Statistical Methods

#### 2.2. Machine Learning Methods

#### 2.3. Transfer Learning

## 3. Methodology

#### 3.1. Prediction Strategy

#### 3.1.1. Training, Validation, and Test

#### 3.1.2. Transferability

#### 3.2. Normalized Root Mean Squared Error

## 4. Case Study

#### 4.1. Real-World Time Series

#### 4.2. The Industry Time Series in Location 1

## 5. Results and Discussion

#### 5.1. Result of Short-Term Predictions (1-h Forecasting Horizon)

#### 5.1.1. Industry Energy Prediction for Location 1

#### 5.1.2. Short-Term Transferability Predictions of Industry Consumption at Location 2

- the energy consumption at location 2 is predicted with the models trained on the time series on location 1;
- the energy consumption at location 1 is predicted with the models trained on the time series on location 2.

#### 5.1.3. All Periods and Sectors for Both Locations

#### 5.2. Predicting at Longer (2, 6, 12, 24, and 165-h) Forecasting Horizons

## 6. Conclusions

## Supplementary Materials

_{r}, specifies how each convolutional layer L, are dilated with a factor a factor 2i. Here i are the specific layer of the network. The hyperparameter configuration are trained over 50 epochs. Table S4: Each hyperparameter is searched in the interval [min,max]. The parameters in the table are the following: Neurons in the reservoir (N

_{r}), connectivity (R

_{c}), noise in the state uptdate (ξ), spectral radius (ρ), the scaling of input, teaching and feedback weights (ω

_{i}, ω

_{o}, ω

_{f}), and regression parameter C. The optimum hyperparameter configurations for each sector are selected as the one yielding the highest prediction accuracy on the validation set.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- De Gooijer, J.G.; Hyndman, J.R. 25 years of time series forecasting. Int. J. Forecast.
**2006**, 22, 443–473. [Google Scholar] [CrossRef] [Green Version] - Simchi-Levi, D.; Simchi-Levi, E.; Kaminsky, P. Designing and Managing the Supply Chain: Concepts, Strategies and Cases; McGraw-Hill: New York, NY, USA, 1999. [Google Scholar]
- Bunn, D. Forecasting loads and prices in competitive power markets. Proc. IEEE
**2000**, 88, 163–169. [Google Scholar] [CrossRef] - Ruiz, P.A.; Gross, G. Short-term resource adequacy in electricity market design. IEEE Trans. Power Syst.
**2008**, 23, 916–926. [Google Scholar] [CrossRef] - Child, M.; Kemfert, C.; Bogdanov, D.; Breyer, C. Flexible electricity generation, grid exchange and storage for the transition to a 100% renewable energy system in Europe. Renew. Energy
**2019**, 139, 80–101. [Google Scholar] [CrossRef] - International Renewable Energy Agency. Power System Flexibility for the Energy Transition, Part 2: IRENA FlexTool Methodology; IRENA: Abu Dhabi, United Arab Emirates, 2018. [Google Scholar]
- Alstone, P.; Gershenson, D.; Kammen, D.M. Decentralized energy systems for clean electricity access. Nat. Clim. Chang.
**2015**, 5, 305–314. [Google Scholar] [CrossRef] - Olauson, J.; Ayob, M.N.; Bergkvist, M.; Carpman, N.; Castellucci, V.; Goude, A.; Lingfors, D.; Waters, R.; Widén, J. Net load variability in Nordic countries with a highly or fully renewable power system. Nat. Energy
**2016**, 1, 16175. [Google Scholar] [CrossRef] - Bordin, C.; Thomasgard, A. SMACS MODEL, a stochastic multihorizon approach for charging sites management, operations, design, and expansion under limited capacity conditions. J. Energy Storage
**2019**, 26, 100824. [Google Scholar] [CrossRef] - Orehounig, K.; Evins, R.; Dorer, V. Integration of decentralized energy systems in neighbourhoods using the energy hub approach. Appl. Energy
**2015**, 154, 277–289. [Google Scholar] [CrossRef] - Ringkjøb, H.-K.; Haugan, P.M.; Nybø, A. Transitioning remote Arctic settlements to renewable energy systems—A modelling study of Longyearbyen, Svalbard. Appl. Energy
**2020**, 258, 114079. [Google Scholar] [CrossRef] - Olkkonen, L.; Korjonen-Kuusipuro, K.; Grönberg, I. Redefining a stakeholder relation: Finnish energy “prosumers” as co-producers. Environ. Innov. Soc. Transit.
**2017**, 24, 57–66. [Google Scholar] [CrossRef] - Liu, N.; Yu, X.; Wang, C.; Li, C.; Ma, L.; Lei, J. Energy-sharing model with price-based demand response for microgrids of peer-to-peer prosumers. IEEE Trans. Power Syst.
**2017**, 32, 3569–3583. [Google Scholar] [CrossRef] - Morstyn, T.; Farrell, N.; Darby, S.J.; McCulloch, D.M. Using peer-to-peer energy-trading platforms to incentivize prosumers to form federated power plants. Nat. Energy
**2018**, 3, 94–101. [Google Scholar] [CrossRef] - An, J.; Lee, M.; Yeom, S.; Hong, T. Determining the peer-to-peer electricity trading price and strategy for energy prosumers and consumers within a microgrid. Appl. Energy
**2020**, 261, 114335. [Google Scholar] [CrossRef] - Xiao, X.; Wang, J.; Lin, R.; Hill, D.J.; Kang, C. Large-scale aggregation of prosumers toward strategic bidding in joint energy and regulation markets. Appl. Energy
**2020**, 271, 115159. [Google Scholar] [CrossRef] - Jiang, Y.; Zhou, K.; Lu, X.; Yang, S. Electricity trading pricing among prosumers with game theory-based model in energy blockchain environment. Appl. Energy
**2020**, 271, 115239. [Google Scholar] [CrossRef] - Hafeez, G.; Alimgeer, K.S.; Khan, I. Electric load forecasting based on deep learning and optimized by heuristic algorithm in smart grid. Appl. Energy
**2020**, 269, 114915. [Google Scholar] [CrossRef] - Arcos-Aviles, D.; Pascual, J.; Guinjoan, F.; Marroyo, L.; Sanchis, P.; Marietta, M.P. Low complexity energy management strategy for grid profile smoothing of a residential grid-connected microgrid using generation and demand forecasting. Appl. Energy
**2017**, 205, 69–84. [Google Scholar] [CrossRef] - Giaouris, D.; Papadopoulos, A.I.; Patsios, C.; Walker, S.; Ziogou, C.; Taylor, P.; Voutetakis, S.; Papadopoulou, S.; Seferlis, P. A systems approach for management of microgrids considering multiple energy carriers, stochastic loads, forecasting and demand side response. Appl. Energy
**2019**, 226, 546–559. [Google Scholar] [CrossRef] [Green Version] - Stokland, J.; Løksa, K. Omlegging til en Framtidsrettet Nettleie, NVE.
**2020**. Available online: https://www.nve.no/reguleringsmyndigheten/nytt-fra-rme/nyheter-reguleringsmyndigheten-for-energi/omlegging-til-en-framtidsrettet-nettleie/ (accessed on 9 July 2020). - Norges Vassdrags-Og Energidirektorat; Miljødirektoratet; ENOVA; Statens Vegvesen; Kystverket; Landbruksdirektoratet. Klimakur 2030: Tiltak og Virkemidler mot 2030; Miljødirektoratet: Oslo, Norway, 2020. [Google Scholar]
- ENOVA. Sluttrapport på Konseptutredning; Troms Kraft Nett AS: Tromsø, Norway, 2019. [Google Scholar]
- Herran, D.S.; Nakata, T. Design of decentralized energy systems for rural electrification in developing countries considering regional disparity. Appl. Energy
**2012**, 91, 130–145. [Google Scholar] [CrossRef] - Schäfer, M.; Kebir, N.; Neumann, K. Research needs for meeting the challenge of decentralized energy supply in developing countries. Energy Sustain. Dev.
**2011**, 15, 324–329. [Google Scholar] [CrossRef] - International Energy Agency. SDG7: Data and Projections–Access to Electricity; IEA: Paris, France, 2020; Available online: https://www.iea.org/reports/sdg7-data-and-projections/access-to-electricity (accessed on 15 June 2020).
- Boute, A. Off-grid renewable energy in remote Arctic areas: An analysis of the Russian Far East. Renew. Sustain. Energy Rev.
**2016**, 59, 1029–1037. [Google Scholar] [CrossRef] - Quitoras, R.M.; Campana, P.E.; Rowley, P.; Crawford, C. Remote community integrated energy system optimization including building enclosure improvements and quantitative energy trilemma metrics. Appl. Energy
**2020**, 267, 115017. [Google Scholar] [CrossRef] - Aberilla, J.M.; Gallego-Schmid, A.; Stamford, L.; Azapagic, A. Design and environmental sustainability assessment of small-scale off-grid energy systems for remote rural communities. Appl. Energy
**2020**, 258, 114004. [Google Scholar] [CrossRef] - Statistics Norway (SSB). Elektrisitet 10314: Nettoforbruk av Elektrisk Kraft, Etter Forbrukergruppe (GWh) (K) 2010–2019; Statistics Norway: Oslo, Norway, 2020; Available online: https://www.ssb.no/statbank/table/10314/ (accessed on 23 October 2020).
- Deihimi, A.; Orang, O.; Showkati, H. Short-term electric load and temperature forecasting using wavelet echo state networks with neural reconstruction. Energy
**2013**, 57, 382–401. [Google Scholar] [CrossRef] - Van Oldenborgh, G.J.; Balmaseda, M.A.; Ferranti, L.; Stockdale, T.N.; Anderson, D.L.T. Did the ECMWF seasonal forecast model outperform statistical ENSO forecast models over the last 15 years? J. Clim.
**2005**, 18, 3240–3249. [Google Scholar] [CrossRef] [Green Version] - Dang-Ha, T.H.; Bianchi, F.M.; Olssson, R. Local short term electricity load forecasting: Automatic approaches. In Proceedings of the 2017 International Joint Conference on Neural Networks (IJCNN), Anchorage, AK, USA, 14–19 May 2017; IEEE: Anchorage, AK, USA, 2017. [Google Scholar]
- Hyndman, R.; Koehler, A.; Ord, K.; Snyder, R. Forecasting with Exponential Smoothing: The State Space Approach; Springer Series in Statistics; Springer: Berlin/Heidelberg, Germany, 2008. [Google Scholar]
- Taylor, J.W. A Comparison of univariate time series methods for forecasting intraday arrivals at a call center. Manag. Sci.
**2008**, 54, 253–265. [Google Scholar] [CrossRef] [Green Version] - Taylor, S.J.; Letham, B. Forecasting at Scale. Am. Stat.
**2018**, 72, 37–45. [Google Scholar] [CrossRef] - Box, G.E.P.; Jenkins, G.M.; Reinsel, G.C.; Ljung, G.M. Time Series Analysis: Forecasting and Control; John Wiley & Sons: Hoboken, NJ, USA, 2011; Volume 74. [Google Scholar]
- Box, G.E.P.; Cox, D.R. An analysis of transformations. J. R. Stat. Soc. Ser. B Methodol.
**1964**, 26, 211–243. [Google Scholar] [CrossRef] - Alberg, D.; Last, M. Short-term load forecasting in smart meters with sliding window-based ARIMA algorithms. Vietnam J. Comput. Sci.
**2018**, 5, 241–249. [Google Scholar] [CrossRef] - Bianchi, F.M.; De Santis, E.; Rizzi, A.; Sadeghian, A. Short-term electric load forecasting using echo state networks and PCA decomposition. IEEE Access
**2015**, 3, 1931–1943. [Google Scholar] [CrossRef] - Schäfer, A.M.; Zimmermann, H.-G. Recurrent neural networks are universal approximators. Int. J. Neural Syst.
**2007**, 17, 253–263. [Google Scholar] [CrossRef] [PubMed] - Bianchi, F.M.; Maiorino, E.; Kampffmeyer, M.C.; Rizzi, A.; Jenssen, R. An Overview and Comparative Analysis of Recurrent Neural Networks for Short Term Load Forecasting. arXiv
**2018**, arXiv:1705.04378. [Google Scholar] - Gasparin, A.; Lukovic, S.; Alippi, C. Deep Learning for Time Series Forecasting: The Electric Load Case; Cornell University,: Ithaca, NY, USA, 2019. [Google Scholar]
- Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput.
**1997**, 8, 1735–1780. [Google Scholar] [CrossRef] [PubMed] - Sak, H.; Senior, A.W.; Beaufays, F. Long short-term memory based recurrent neural network architectures for large vocabulary speech recognition. arXiv
**2014**, arXiv:1402.1128. [Google Scholar] - Deihimi, A.; Showkati, H. Application of echo state networks in short-term electric load forecasting. Energy
**2012**, 39, 327–340. [Google Scholar] [CrossRef] - Varshney, S.; Verma, T. Half hourly electricity load prediction using Echo State Network. Int. J. Sci. Res. (IJSR)
**2014**, 3, 885–888. [Google Scholar] - Bianchi, F.M.; Scardapane, S.; Uncini, A.; Rizzi, A.; Sadeghian, A. Prediction of telephone calls load using Echo State Network with exogenous variables. Neural Networks
**2015**, 71, 204–213. [Google Scholar] [CrossRef] - Peng, Y.; Lei, M.; Li, J.-B.; Peng, X.-Y. A novel hybridization of echo state net-works and multiplicative seasonal ARIMA model for mobile communication traffic series forecasting. Neural Comput. Appl.
**2014**, 24, 883–890. [Google Scholar] [CrossRef] - Jaeger, H.; Haas, H. Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication. Science
**2004**, 304, 78–80. [Google Scholar] [CrossRef] [Green Version] - Borovykh, A.; Bothe, S.; Oosterlee, C.W. Conditional time series forecasting with convolutional neural networks. arXiv
**2018**, arXiv:1703.04691. [Google Scholar] - Kuo, P.-H.; Huang, C.-J. A High precision artificial neural networks model for short-term energy load forecasting. Energies
**2018**, 11, 213. [Google Scholar] [CrossRef] [Green Version] - Amarasinghe, K.; Marino, D.L.; Manic, M. Deep neural networks for energy load forecasting. In Proceedings of the 2017 IEEE 26th International Symposium on Industrial Electronics (ISIE), Edinburgh, UK, 19–21 June 2017; IEEE: Edinburgh, Scotland, UK, 2017; pp. 1483–1488. [Google Scholar]
- He, W. Load forecasting via deep neural networks. Procedia Comput. Sci.
**2017**, 122, 308–314. [Google Scholar] [CrossRef] - Tian, C.; Ma, J.; Zhang, C.; Zhan, P. A deep neural network model for short-term load forecast based on long short-term memory network and convolutional neural network. Energies
**2018**, 11, 3493. [Google Scholar] [CrossRef] [Green Version] - Fawaz, H.I.; Forestier, G.; Weber, J.; Idoumghar, L.; Muller, P.-A. Transfer learning for time series classification. In Proceedings of the 2018 IEEE International Conference on Big Data (Big Data), Seattle, WA, USA, 10–13 December 2018; IEEE: Seattle, WA, USA, 2018; pp. 1367–1376. [Google Scholar]
- Xu, X.; Meng, Z. A hybrid transfer learning model for short-term electric load forecasting. Electr. Eng.
**2020**, 102, 1371–1381. [Google Scholar] [CrossRef] - Jung, S.-M.; Park, S.; Jung, S.-W.; Hwang, E. Monthly electric load forecasting using transfer learning for smart cities. Sustainability
**2020**, 12, 6364. [Google Scholar] [CrossRef] - Hooshmand, A.; Sharma, R. Energy predictive models with limited data using transfer learning. In Proceedings of the e-Energy ’19: The Tenth ACM International Conference on Future Energy Systems, Phoenix, AZ, USA, 25–28 June 2019; pp. 12–16. [Google Scholar] [CrossRef] [Green Version]
- Nikolay, L.; Yu, J.; Rajagopal, R. Applied time-series transfer learning. Stanford, CA, USA. Workshop track; ICLR; Standford university: Standford, CA, USA, 2018; pp. 1–4. [Google Scholar]
- He, Q.-Q.; Pang, P.C.-I.; Si, Y.-W. Transfer learning for financial time series forecasting. In Proceedings of the PRICAI 2019: Trends in Artificial Intellegence, Yanuca Island, Fiji, 26–30 August 2019; Nayak, A., Sharma, A., Eds.; Lectore Notes in Computer Science. Springer: Cham, Switzerland, 2019; Volume 11671. [Google Scholar] [CrossRef]
- Holmes, S. RMS Error, Stanford. 28 November 2000. Available online: https://statweb.stanford.edu/~susan/courses/s60/split/node60.html (accessed on 9 July 2020).
- Ishavskraft AS. Om Oss. Available online: https://www.ishavskraft.no/om/ (accessed on 21 April 2020).
- Hyndman, R.J.; Athanasopoulos, G. Forecasting: Principles and Practice, 2nd ed.; OTexts: Melbourne, Australia, 2018; Available online: https://otexts.com/fpp2/ (accessed on 18 January 2021).
- Omar, K. Deconstructing Time Series Using Fourier Transform, Medium. Available online: https://medium.com/@khairulomar/deconstructing-time-series-using-fourier-transform-e52dd535a44e (accessed on 9 July 2020).
- Hong, T.; Fan, S. Probabilistic electric load forecasting: A tutorial review. Int. J. Forecast.
**2016**, 32, 914–938. [Google Scholar] [CrossRef]

**Figure 1.**Overview of methodology for making predictions with statistical-and machine-learning models. The advantages and disadvantages of each approach are given.

**Figure 2.**Real-world time series of consumption for location 1 and 2. The demand for the industry sector is strongly correlated with the fishing season, while the energy demand for households is correlated with temperature changes, where cold temperatures during wintertime give higher energy demand for heating purposes.

**Figure 3.**Real-world time series of consumption for location 1 (upper) and 2 (lower). The periods of holidays are removed, leaving a time series of 6544 samples instead of 8129 samples (1 March 2019 to 1 February 2020).

**Figure 5.**Frequency domain of consumption data by Fourier transformation with autocorrelation function (ACF) and partial autocorrelation functions (PACF) functions. The correlation outside the standard deviations are correlations and not a statistical fluke. The red color represents the ACF and PACF after differencing the time series.

**Figure 7.**Short-term transferability predictions. The models are trained on the time series at location 1 to predict the energy consumption at location 2.

Prediction Results on 1-h Forecasting Horizon | ||||
---|---|---|---|---|

Case 1: Train on Location 1 to Predict Location 1 and 2 | ||||

Location 1 | Location 2 (Transferability) | |||

Company | Household | Company | Household | |

Model | NRMSE | NRMSE | NRMSE | NRMSE |

LSTM | 0.066 | 0.055 | 0.084 | 0.096 |

GRU | 0.074 | 0.047 | 0.084 | 0.063 |

Elman | 0.074 | 0.047 | 0.085 | 0.063 |

CNN | 0.068 | 0.048 | 0.075 | 0.062 |

ESN | 0.012 | 0.013 | 0.096 | 0.034 |

ARIMA | 0.070 | 0.039 | 0.368 | 0.110 |

Prophet | 0.160 | 0.093 | - | - |

Average | 0.075 | 0.049 | 0.132 | 0.071 |

Case 2 (Validation): Train on Location 2 to Predict Location 2 and 1 | ||||

Location 2 | Location 1 (Transferability) | |||

Company | Household | Company | Household | |

Model | NRMSE | NRMSE | NRMSE | NRMSE |

LSTM | 0.045 | 0.035 | 0.149 | 0.064 |

GRU | 0.046 | 0.036 | 0.129 | 0.047 |

Elman | 0.046 | 0.036 | 0.129 | 0.047 |

CNN | 0.050 | 0.029 | 0.075 | 0.046 |

ESN | 0.032 | 0.004 | 0.395 | 0.040 |

ARIMA | 0.052 | 0.027 | 0.843 | 0.215 |

Prophet | 0.220 | 0.076 | - | - |

Average | 0.070 | 0.034 | 0.286 | 0.077 |

Multistep Prediction Results (NRMSE) | ||||||
---|---|---|---|---|---|---|

Timestamp | LSTM | GRU | Elman | CNN | ESN | ARIMA |

1 h | 0.066 | 0.046 | 0.046 | 0.068 | 0.012 | 0.070 |

2 h | 0.071 | 0.072 | 0.067 | 0.079 | 0.078 | 0.070 |

6 h | 0.078 | 0.086 | 0.094 | 0.074 | 0.163 | 0.083 |

12 h | 0.077 | 0.101 | 0.119 | 0.093 | 0.182 | 0.108 |

24 h | 0.518 | 0.441 | 0.531 | 0.524 | 0.142 | 0.139 |

165 h | 0.164 | 0.181 | 0.083 | 0.114 | 0.166 | 0.159 |

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## Share and Cite

**MDPI and ACS Style**

Foldvik Eikeland, O.; Bianchi, F.M.; Apostoleris, H.; Hansen, M.; Chiou, Y.-C.; Chiesa, M.
Predicting Energy Demand in Semi-Remote Arctic Locations. *Energies* **2021**, *14*, 798.
https://doi.org/10.3390/en14040798

**AMA Style**

Foldvik Eikeland O, Bianchi FM, Apostoleris H, Hansen M, Chiou Y-C, Chiesa M.
Predicting Energy Demand in Semi-Remote Arctic Locations. *Energies*. 2021; 14(4):798.
https://doi.org/10.3390/en14040798

**Chicago/Turabian Style**

Foldvik Eikeland, Odin, Filippo Maria Bianchi, Harry Apostoleris, Morten Hansen, Yu-Cheng Chiou, and Matteo Chiesa.
2021. "Predicting Energy Demand in Semi-Remote Arctic Locations" *Energies* 14, no. 4: 798.
https://doi.org/10.3390/en14040798