# Intensive Data-Driven Model for Real-Time Observability in Low-Voltage Radial DSO Grids

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## Abstract

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## 1. Introduction

- Proposing a data-driven approach for nodal voltage estimation in unbalanced LV grids;
- Combining a grey-box modeling approach to gain explainability and a generalized additive modeling approach to reduce the computational burden significantly, which makes the method practical for online monitoring;
- Deriving the method for a real-world experimental setup and validating the results with high accuracy.

## 2. Problem Definition

## 3. Workflow of the Proposed Method for Voltage Estimation

## 4. Experimental Setup Description

## 5. Method

#### 5.1. Physics of the System—Voltage Drop

#### 5.2. Data Analysis

#### 5.3. Model Selection

#### 5.4. GAM Model

- Adding a smooth term relating to the reactive-current term in the voltage drop equation by using the line current and $sin\left({\varphi}_{d}\right)=sin(arccos(cos\left({\varphi}_{d}\right)))$ as inputs, where $cos\left({\varphi}_{d}\right)$ is the power factor measured by device d. This was done to investigate the impact of the reactance in the cable.
- Adding voltage drop terms using ${I}_{\mathrm{N},\mathrm{T}1}$ and $cos\left({\varphi}_{\mathrm{N},\mathrm{T}1}\right)$ to investigate the impact of the voltage drop in the neutral conductor. It was impossible to use the neutral current data in ${C}_{\mathrm{E}1}$ due to a lack of data availability.
- Adding the temperature as an input by incorporating it into the smooth functions related to cable resistance ($s({I}_{d},cos\left({\varphi}_{d}\right))$) to investigate whether the temperature has an impact on the resistance.
- Adding a smooth term for solar radiation to investigate the potential impact of PV panels in the network. Here, a smooth term was used due the complicated functional relationship.
- Adding a seasonal term to investigate whether there is an additional daily or hourly variation not explained by other data. This was done using cubic splines with periodic incremental time step inputs (i.e., a vector $[1,$…$,m]$, where m is the period length of a day or hour).

#### 5.5. Grey-Box Model

- Adding a state for the voltage drop in the neutral conductor using ${I}_{\mathrm{N},\mathrm{T}1}$ and $cos\left({\varphi}_{\mathrm{N},\mathrm{T}1}\right)$.

#### 5.6. Model Evaluation

## 6. Results and Analysis

#### 6.1. GAM Model

#### 6.2. Grey-Box Model

#### 6.3. End Node Estimation

#### 6.4. Analysis of Measurement Device Setup Configuration

- Case 1: Installing a measuring device at node ${C}_{\mathrm{M}}$ and estimating the end node voltages at ${C}_{\mathrm{E}1}$, ${C}_{\mathrm{E}2}$, and ${C}_{\mathrm{E}3}$.
- Case 2: Installing a measuring device at end node ${C}_{\mathrm{E}1}$ and estimating the voltage at ${C}_{\mathrm{E}2}$ and ${C}_{\mathrm{E}3}$.
- Case 3: Installing two measuring devices at end nodes ${C}_{\mathrm{E}1}$ and ${C}_{\mathrm{E}2}$ and estimating the voltage at ${C}_{\mathrm{E}3}$.

#### 6.5. Application of the Proposed Method and Future Setup Extension

^{®}1.90 Ghz, with 16 GB RAM, running on Linux Pop!_OS version 21.10. It should be noted that for online operation, the computation times can be further improved—for instance, by choosing the previously estimated parameters as initial values. Similarly, the computation times for the grey-box modeling could be improved if the software CTSM-R was able to use several cores for parallel computation of the value of the likelihood function.

- Improve measurements at ${C}_{\mathrm{E}1}$, to measure all customers at the end node as well as the neutral conductor current;
- Improve measurements at ${C}_{\mathrm{M}}$, to measure all cables, including neutral conductors.

## 7. Conclusions

#### Future Work

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- D’Ettorre, F.; Banaei, M.; Ebrahimy, R.; Pourmousavi, S.A.; Blomgren, E.; Kowalski, J.; Bohdanowicz, Z.; Łopaciuk-Gonczaryk, B.; Biele, C.; Madsen, H. Exploiting demand-side flexibility: State-of-the-art, open issues and social perspective. Renew. Sustain. Energy Rev.
**2022**, 165, 112605. [Google Scholar] [CrossRef] - Táczi, I.; Sinkovics, B.; Vokony, I.; Hartmann, B. The challenges of low voltage distribution system state estimation—An application oriented review. Energies
**2021**, 14, 5363. [Google Scholar] [CrossRef] - Dehghanpour, K.; Wang, Z.; Wang, J.; Yuan, Y.; Bu, F. A survey on state estimation techniques and challenges in smart distribution systems. IEEE Trans. Smart Grid
**2019**, 10, 2312–2322. [Google Scholar] [CrossRef] - Wang, H.; Schulz, N.N. A Revised Branch Current-Based Distribution System State Estimation Algorithm and Meter Placement Impact. IEEE Trans. Power Syst.
**2004**, 19, 207–213. [Google Scholar] [CrossRef] - Pau, M.; Pegoraro, P.A.; Sulis, S. Efficient branch-current-based distribution system state estimation including synchronized measurements. IEEE Trans. Instrum. Meas.
**2013**, 62, 2419–2429. [Google Scholar] [CrossRef] - Baran, M.E.; Jung, J.; McDermott, T.E. Including voltage measurements in branch current state estimation for distribution systems. In Proceedings of the 2009 IEEE Power and Energy Society General Meeting, PES ’09, Calgary, AB, Canada, 26–30 July 2009. [Google Scholar] [CrossRef]
- Monticelli, A. State Estimation in Electric Power Systems: A Generalized Approach; Springer: New York, NY, USA, 1999; Volume 7. [Google Scholar]
- Lin, W.M.; Teng, J.H. State Estimation for Distribution Systems with Zero-Injection Constraints. In IEEE Transactions on Power Systems; IEEE: Piscataway, NJ, USA, 1996. [Google Scholar]
- Chen, Q.; Kaleshi, D.; Fan, Z.; Armour, S. Impact of Smart Metering Data Aggregation on Distribution System State Estimation. IEEE Trans. Ind. Inform.
**2016**, 12, 1426–1437. [Google Scholar] [CrossRef] - Nie, Y.; Chung, C.Y.; Xu, N.Z. System State Estimation Considering EV Penetration with Unknown Behavior Using Quasi-Newton Method. IEEE Trans. Power Syst.
**2016**, 31, 4605–4615. [Google Scholar] [CrossRef] - Yao, Y.; Liu, X.; Zhao, D.; Li, Z. Distribution System State Estimation: A Semidefinite Programming Approach. IEEE Trans. Smart Grid
**2019**, 10, 4369–4378. [Google Scholar] [CrossRef] - Zhu, H.; Giannakis, G.B. Power system nonlinear state estimation using distributed semidefinite programming. IEEE J. Sel. Top. Signal Process.
**2014**, 8, 1039–1050. [Google Scholar] [CrossRef] - Wu, J.; He, Y.; Jenkins, N. A robust state estimator for medium voltage distribution networks. IEEE Trans. Power Syst.
**2013**, 28, 1008–1016. [Google Scholar] [CrossRef] - Liu, B.; Wu, H.; Zhang, Y.; Yang, R.; Bernstein, A. Robust Matrix Completion State Estimation in Distribution Systems. In Proceedings of the 2019 IEEE Power & Energy Society General Meeting (PESGM), Piscataway, NJ, USA, 4–8 August 2019. [Google Scholar]
- Lin, C.; Wu, W.; Guo, Y. Decentralized Robust State Estimation of Active Distribution Grids Incorporating Microgrids Based on PMU Measurements. IEEE Trans. Smart Grid
**2020**, 11, 810–820. [Google Scholar] [CrossRef] - Dahale, S.; Karimi, H.S.; Lai, K.; Natarajan, B. Sparsity based approaches for distribution grid state estimation—A comparative study. IEEE Access
**2020**, 8, 198317–198327. [Google Scholar] [CrossRef] - Raghuvamsi, Y.; Teeparthi, K. Detection and reconstruction of measurements against false data injection and DoS attacks in distribution system state estimation: A deep learning approach. Meas. J. Int. Meas. Confed.
**2023**, 210, 112565. [Google Scholar] [CrossRef] - Zamzam, A.S.; Fu, X.; Sidiropoulos, N.D. Data-Driven Learning-Based Optimization for Distribution System State Estimation. IEEE Trans. Power Syst.
**2019**, 34, 4796–4805. [Google Scholar] [CrossRef] - Dehghanpour, K.; Yuan, Y.; Wang, Z.; Bu, F. A Game-Theoretic Data-Driven Approach for Pseudo-Measurement Generation in Distribution System State Estimation. IEEE Trans. Smart Grid
**2019**, 10, 5942–5951. [Google Scholar] [CrossRef] - Kim, D.; Dolot, J.M.; Song, H. Distribution System State Estimation Using Model-Optimized Neural Networks. Appl. Sci.
**2022**, 12, 2073. [Google Scholar] [CrossRef] - Zamzam, A.S.; Sidiropoulos, N.D. Physics-Aware Neural Networks for Distribution System State Estimation. IEEE Trans. Power Syst.
**2019**, 35, 4347–4356. [Google Scholar] [CrossRef] - Menke, J.H.; Bornhorst, N.; Braun, M. Distribution system monitoring for smart power grids with distributed generation using artificial neural networks. Int. J. Electr. Power Energy Syst.
**2019**, 113, 472–480. [Google Scholar] [CrossRef] - Weng, Y.; Negi, R.; Faloutsos, C.; Ilic, M.D. Robust Data-Driven State Estimation for Smart Grid. IEEE Trans. Smart Grid
**2017**, 8, 1956–1967. [Google Scholar] [CrossRef] - Anubi, O.M.; Konstantinou, C. Enhanced resilient state estimation using data-driven auxiliary models. IEEE Trans. Ind. Inform.
**2020**, 16, 639–647. [Google Scholar] [CrossRef] - Pertl, M.; Douglass, P.J.; Heussen, K.; Kok, K. Validation of a robust neural real-time voltage estimator for active distribution grids on field data. Electr. Power Syst. Res.
**2018**, 154, 182–192. [Google Scholar] [CrossRef] - Procopiou, A.T.; Ochoa, L.F. Voltage Control in PV-Rich LV Networks Without Remote Monitoring. IEEE Trans. Power Syst.
**2017**, 32, 1224–1236. [Google Scholar] [CrossRef] - Mokaribolhassan, A.; Nourbakhsh, G.; Ledwich, G.; Arefi, A.; Shafiei, M. Distribution System State Estimation Using PV Separation Strategy in LV Feeders with High Levels of Unmonitored PV Generation. IEEE Syst. J.
**2023**, 17, 684–695. [Google Scholar] [CrossRef] - Rigoni, V.; Soroudi, A.; Keane, A. Use of fitted polynomials for the decentralised estimation of network variables in unbalanced radial LV feeders. IET Gener. Transm. Distrib.
**2020**, 14, 2368–2377. [Google Scholar] [CrossRef] - IEEE Std. 141-1993; Recommended Practice for Electric Power Distribution for Industrial Plants. The Institute of Electrical and Electronics Engineers, Inc.: New York, NY, USA, 1994. [CrossRef]
- Degroote, L.; Renders, B.; Meersman, B.; Vandevelde, L. Neutral-point shifting and voltage unbalance due to single-phase DG units in low voltage distribution networks. In Proceedings of the 2009 IEEE Bucharest PowerTech: Innovative Ideas Toward the Electrical Grid of the Future, Bucharest, Romania, 28 June–2 July 2009; pp. 1–8. [Google Scholar] [CrossRef]
- Jung, T.H.; Gwon, G.H.; Kim, C.H.; Han, J.; Oh, Y.S.; Noh, C.H. Voltage Regulation Method for Voltage Drop Compensation and Unbalance Reduction in Bipolar Low-Voltage DC Distribution System. IEEE Trans. Power Deliv.
**2018**, 33, 141–149. [Google Scholar] [CrossRef] - Pandian, S.S. Various considerations for estimating steady-state voltage drop in low voltage AC power distribution systems. In Proceedings of the Conference Record—Industrial and Commercial Power Systems Technical Conference, Detroit, MI, USA, 30 April–3 May 2006. [Google Scholar] [CrossRef]
- Wood, S.N. Generalized Additive Models: An Introduction with R, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2017. [Google Scholar] [CrossRef]
- Wood, S.N. Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. J. R. Stat. Soc. B
**2011**, 73, 3–36. [Google Scholar] [CrossRef] - Wood, S.; Pya, N.; Säfken, B. Smoothing parameter and model selection for general smooth models (with discussion). J. Am. Stat. Assoc.
**2016**, 111, 1548–1575. [Google Scholar] [CrossRef] - Wood, S.N. Stable and efficient multiple smoothing parameter estimation for generalized additive models. J. Am. Stat. Assoc.
**2004**, 99, 673–686. [Google Scholar] [CrossRef] - Wood, S.N. Thin-plate regression splines. J. R. Stat. Soc. B
**2003**, 65, 95–114. [Google Scholar] [CrossRef] - Bacher, P.; Madsen, H. Identifying suitable models for the heat dynamics of buildings. Energy Build.
**2011**, 43, 1511–1522. [Google Scholar] [CrossRef] - Stentoft, P.A.; Munk-Nielsen, T.; Vezzaro, L.; Stentoft, P.A.; Madsen, H.; Møller, J.K.; Vezzaro, L.; Mikkelsen, P.S. Towards model predictive control: Online predictions of ammonium and nitrate removal by using a stochastic ASM. Water Sci. Technol.
**2019**, 79, 51–62. [Google Scholar] [CrossRef] [PubMed] - Juhl, R.; Møller, J.K.; Madsen, H. Ctsmr—Continuous Time Stochastic Modeling in R. arXiv
**2016**, arXiv:1606.00242. [Google Scholar] - Kristensen, N.R.; Madsen, H.; Jørgensen, S.B. Parameter estimation in stochastic grey-box models. Automatica
**2004**, 40, 225–237. [Google Scholar] [CrossRef] - Juhl, R.; Møller, J.K.; Jørgensen, J.B.; Madsen, H. Modeling and Prediction Using Stochastic Differential Equations. In Prediction Methods for Blood Glucose Concentration; Springer: Berlin/Heidelberg, Germany, 2016; pp. 183–209. [Google Scholar] [CrossRef]

**Figure 1.**Workflow for the model selection process. Solid arrows represent the offline model selection approach using data collected from the power grid. Dotted arrows represent how the model would operate in real time using measurements and model estimates from a radial with high observability to estimate end nodes with lower observability.

**Figure 2.**Grid topology and installation of devices (blue dotted circles). The naming of the devices is constructed from the letter of the feeder (i.e., A, B, C, D, and F), subscript M indicates that it is a middle node, and subscript E indicates an end node. ${T}_{1}$ and ${T}_{2}$ represent the two devices installed at the transformer. It is also indicated whether the device measures both voltage and current $[V,I]$ or only voltage [V]. Squares represent customers in the grid.

**Figure 3.**Phase L3 voltage measurements of all devices on feeder C. ${V}_{\mathrm{T}1}$ is the voltage at the transformer (device ${T}_{1}$) and ${V}_{\mathrm{CM}}$, ${V}_{\mathrm{CE}1}$, ${V}_{\mathrm{CE}2}$, and ${V}_{\mathrm{CE}3}$ are voltages at the corresponding devices on the feeder.

**Figure 4.**Scatter plots, data density, and correlation for voltages and neutral current, for all devices on feeder C (i.e., ${T}_{1}$, ${C}_{\mathrm{M}}$, ${C}_{\mathrm{E}1}$, ${C}_{\mathrm{E}2}$, and ${C}_{\mathrm{E}3}$) using a time resolution of 10 min. “***” indicates a p-value < 0.001, “.” indicate a p-value < 0.10.

**Figure 5.**Scatter plots, data density, and correlation for voltages and input variables, using a time resolution of 10 min. “***” indicates a p-value < 0.001, “**” indicate a p-value < 0.01, “*” indicate a p-value < 0.05, “.” indicate a p-value < 0.10.

**Figure 6.**Phase L3 voltage time series for device ${C}_{\mathrm{M}}$ filtered to time resolutions 1 min, 5 min, 10 min, and 15 min.

**Figure 7.**GAM model state estimates on training (

**a**) and test (

**b**) data sets for three days, respectively. The black and blue lines represent the observations and the model predictions, respectively. There is also a 95% confidence interval indicated by the blue area, but it is visually difficult to see in the graph due to the low standard deviation in the model.

**Figure 8.**Residual ACFs and cumulative periodograms, for the GAM model in (

**a**,

**b**) and for the grey-box model in (

**c**,

**d**). Blue horizontal and diagonal lines indicate a 95% confidence interval.

**Figure 9.**Grey-box model estimations on the training, (

**a**) and test (

**b**) data sets for three days, respectively. The black line represents the observations, and the blue line shows the model predictions. A blue area also indicates a 95% confidence interval, but it is visually difficult to see in the graph due to the low standard deviation in the model.

**Figure 10.**GAM model estimations on the training (

**a**) and test (

**b**) data sets for ${V}_{\mathrm{CE}2}$ for three days, respectively. The black line represents the observations and the blue line represents the model predictions. There is also a 95% confidence interval indicated by a blue area.

**Figure 11.**GAM model estimations on the training (

**a**) and test (

**b**) data sets for ${V}_{\mathrm{CE}3}$ zooming in on three days, respectively. The black line represents the observations and the blue line represents the model predictions. There is also a 95% confidence interval indicated by a blue area.

**Figure 12.**RMSE for voltage estimations at end nodes ${C}_{\mathrm{E}1}$ (red circle), ${C}_{\mathrm{E}2}$ (green triangle), and ${C}_{\mathrm{E}3}$ (blue square). Case 1 corresponds to installation of a measuring device at node ${C}_{\mathrm{M}}$ and estimating the end node voltages at ${C}_{\mathrm{E}1}$, ${C}_{\mathrm{E}2}$, and ${C}_{\mathrm{E}3}$; Case 2 corresponds to installation of a measuring device at end node ${C}_{\mathrm{E}1}$ and estimating voltage at ${C}_{\mathrm{E}2}$ and ${C}_{\mathrm{E}3}$; Case 3 corresponds to installation of two measuring devices at end nodes ${C}_{\mathrm{E}1}$ and ${C}_{\mathrm{E}2}$ and estimating the voltage at ${C}_{\mathrm{E}3}$.

**Table 1.**Measured input variables used in the model selection process. All electrical measurements from the experimental setup are per phase, and their placements in the LV grid are seen in Figure 2.

Variable | Notation | Unit |
---|---|---|

${V}_{\mathrm{T}1}$ | voltage at ${T}_{1}$ | V |

${V}_{\mathrm{CM}}$ | voltage at ${C}_{\mathrm{M}}$ | V |

${V}_{\mathrm{CE}1}$ | voltage at ${C}_{\mathrm{E}1}$ | V |

${V}_{\mathrm{CE}2}$ | voltage at ${C}_{\mathrm{E}2}$ | V |

${V}_{\mathrm{CE}3}$ | voltage at ${C}_{\mathrm{E}3}$ | V |

${I}_{\mathrm{T}1}$ | current at ${T}_{1}$ | A |

$cos\left({\varphi}_{\mathrm{T}1}\right)$ | power factor at ${T}_{1}$ | - |

${I}_{\mathrm{N},\mathrm{T}1}$ | neutral conductor current at ${T}_{1}$ | A |

$cos\left({\varphi}_{\mathrm{N},\mathrm{T}1}\right)$ | neutral conductor power factor at ${T}_{1}$ | - |

${I}_{\mathrm{N},\mathrm{CM}}$ | neutral conductor current at ${C}_{\mathrm{M}}$ | A |

$cos\left({\varphi}_{\mathrm{N},\mathrm{CM}}\right)$ | neutral conductor power factor at ${C}_{\mathrm{M}}$ | - |

${I}_{\mathrm{CM}}$ | current at ${C}_{\mathrm{M}}$ | A |

$cos\left({\varphi}_{\mathrm{CM}}\right)$ | power factor at ${C}_{\mathrm{M}}$ | - |

${I}_{\mathrm{CE}1}$ | current at ${C}_{\mathrm{E}1}$ | A |

$cos\left({\varphi}_{\mathrm{CE}1}\right)$ | power factor at ${C}_{\mathrm{E}1}$ | - |

$solar$ | solar radiation (from DMI) | W/m${}^{2}$ |

${T}_{\mathrm{amb}}$ | ambient temperature (from DMI) | °C |

**Table 2.**Estimated parameters and function terms in Equation (12), as well as corresponding p-values.

Parameter/Term | Estimated | p-Value |
---|---|---|

Intercept | $230.6$ | <$2\times {10}^{-16}$ |

$s\left({V}_{\mathrm{T}1,t}\right)$ | $6.229$ | <$2\times {10}^{-16}$ |

$te({I}_{\mathrm{T}1,t},cos\left({\varphi}_{\mathrm{T}1,t}\right)){T}_{\mathrm{amb},t}$ | $8.595$ | $1.03\times {10}^{-5}$ |

$te({I}_{\mathrm{T}1,t},sin\left({\varphi}_{\mathrm{T}1,t}\right))$ | $9.831$ | $0.09692$ |

$s(I{N}_{\mathrm{T}1,t},cos\left({\varphi}_{\mathrm{T}1}\right))$ | $10.546$ | $0.00115$ |

$s\left({V}_{\mathrm{CE}1,t}\right)$ | $4.733$ | <$2\times {10}^{-16}$ |

$te({I}_{\mathrm{CE}1,t},cos\left({\varphi}_{\mathrm{CE}1,t}\right)){T}_{\mathrm{amb},t}$ | $15.979$ | $6.86\times {10}^{-6}$ |

$te({I}_{\mathrm{CE}1,t},sin\left({\varphi}_{\mathrm{CE}1,t}\right))$ | $0.306$ | <$2\times {10}^{-16}$ |

**Table 3.**Comparison of log-likelihood between the GAM and grey-box models, as well as RMSEs of the training and test data sets.

GAM | Grey-Box | |
---|---|---|

Log likelihood | 1678 | 1685 |

RMSE training data set | 0.099 | 0.100 |

RMSE test data set | 0.109 | 0.107 |

Parameter | Estimated | Std. Error | p-Value |
---|---|---|---|

Initial state ${V}_{\mathrm{R},\mathrm{CM}-\mathrm{CE}1}$ | $2.3693\times {10}^{2}$ | $18.476$ | <$2.2\times {10}^{-16}$ |

Initial state ${V}_{\mathrm{X},\mathrm{CM}-\mathrm{CE}1}$ | $2.3716\times {10}^{2}$ | $18.498$ | <$2.2\times {10}^{-16}$ |

a | $1.5318\times {10}^{-1}$ | $3.7564\times {10}^{-3}$ | <$2.2\times {10}^{-16}$ |

b | $9.8561\times {10}^{-6}$ | $1.8247\times {10}^{-6}$ | $7.48\times {10}^{-8}$ |

c | $9.5597\times {10}^{-1}$ | $2.0718\times {10}^{-3}$ | <$2.2\times {10}^{-16}$ |

d | $2.1358\times {10}^{-2}$ | $9.9780\times {10}^{-4}$ | <$2.2\times {10}^{-16}$ |

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## Share and Cite

**MDPI and ACS Style**

Blomgren, E.M.V.; Banaei, M.; Ebrahimy, R.; Samuelsson, O.; D’Ettorre, F.; Madsen, H.
Intensive Data-Driven Model for Real-Time Observability in Low-Voltage Radial DSO Grids. *Energies* **2023**, *16*, 4366.
https://doi.org/10.3390/en16114366

**AMA Style**

Blomgren EMV, Banaei M, Ebrahimy R, Samuelsson O, D’Ettorre F, Madsen H.
Intensive Data-Driven Model for Real-Time Observability in Low-Voltage Radial DSO Grids. *Energies*. 2023; 16(11):4366.
https://doi.org/10.3390/en16114366

**Chicago/Turabian Style**

Blomgren, Emma M. V., Mohsen Banaei, Razgar Ebrahimy, Olof Samuelsson, Francesco D’Ettorre, and Henrik Madsen.
2023. "Intensive Data-Driven Model for Real-Time Observability in Low-Voltage Radial DSO Grids" *Energies* 16, no. 11: 4366.
https://doi.org/10.3390/en16114366