# Data-Driven Mitigation of Energy Scheduling Inaccuracy in Renewable-Penetrated Grids: Summerside Electric Use Case

## Abstract

**:**

## 1. Introduction

- Leveraging a relatively large island grid’s actual data to reveal the potential of state-of-the-art time series prediction techniques, in particular for wind energy. Note that, due to commercial IP confidentiality, the details of the prediction engine cannot be revealed; however, general procedures for enhancing RES prediction accuracy is discussed using actual data.
- Proposing a data-driven approach toward BESS sizing for energy balancing purposes. Using actual data, a novel probabilistic approach is proposed that accounts for intra-interval variations, thus enhancing the accuracy of BESS sizing. In general, the proposed method mitigates the trade-off between time resolution and accuracy; as a result, increasing the computation time-interval would have a less significant negative impact on accuracy of the results. Hence, such a method would also alleviate computational burden of analytical methods for BESS sizing. To the knowledge of the author, this is the first time such an approach is proposed in the literature.
- Proposing an optimal BESS energy management based on the presented data-driven approach.
- Quantitative analysis of wind-BESS impact on energy cost using a large amount of actual data.

## 2. Summerside Electric Grid

## 3. Wind Power Prediction

#### 3.1. Experimental Data

#### 3.2. Data Processing

#### 3.3. Feature Selection

#### 3.4. Results

## 4. Data-Driven BESS Sizing

#### 4.1. Battery Characteristics

#### 4.2. Methodology

- Populate a set of import inaccuracies vector, $\mathcal{S}$, based on the results presented in Figure 11.
- Populate a set of BESS energy capacity, $\mathcal{E}$. For each element in $\mathcal{E}$, populate a set of C-rates, $\mathcal{C}$.
- For each element in $\mathcal{E}$ and its corresponding elements in $\mathcal{C}$, calculate the charged and discharged energies for each element in $\mathcal{S}$. Calculate the savings by reducing investment cost from energy savings. Thus, for each simulation scenario $b,c$, there exist s simulation scenarios $b,c,s$.
- Calculate the final savings for each element in $\mathcal{E}$ and its corresponding elements in $\mathcal{C}$ by averaging the savings calculated for the elements in $\mathcal{S}$.

- Calculate the hourly averaged power.
- Populate a set of power threshholds. In this case, the power threshold ranges from 0–1000 kW with steps of 50 kW.
- Calculate the energy above and below the average required power for each power threshold.
- Calculate the average of calculated energies for each power threshold.
- Fit the appropriate trendline to the calculated average energy of power thresholds [52]. In this case, an exponential trendline is chosen based on the observed data. The trendline expression can be used to estimate the energy above and below the hourly average required power for a certain power threshold.

- ${\alpha}_{i}$ = 1, i.e., there is surplus of energy $\Delta {e}_{i}$.
- If Equation (13) is true, i.e., the average surplus power within the time interval does not exceed the battery power rating, go to step 3, otherwise go to step 6:$$\frac{\Delta {e}_{i}}{\Delta \tau}\le {P}^{b,c}.$$
- Estimate BESS charged energy using Equation (14):$$Ec{h}_{s,i}^{b,c}=\Delta {e}_{i}-ef\left(\right)open="("\; close=")">{P}^{b,c}-\frac{\Delta {e}_{i}}{\Delta \tau}$$
- If Equation (15) is true, i.e., the battery energy content at the end of the time interval does not exceed the maximum acceptable energy capacity, end the process and go to the next time step, otherwise go to step 5:$${E}_{s,i-1}^{b,c}+Ec{h}_{s,i}^{b,c}\times \eta \le 0.9\times {\mathrm{SOH}}_{s,i-1}^{b,c}\times {E}^{b}.$$
- Estimate the BESS charged energy using Equation (16); end the process and go to the next time step:$$Ec{h}_{s,i}^{b,c}=\frac{0.9\times {\mathrm{SOH}}_{s,i-1}^{b,c}\times {E}^{b}-{E}_{s,i-1}^{b,c}}{\eta}.$$
- Estimate BESS charged energy using Equation (17):$$Ec{h}_{s,i}^{b,c}={P}^{b,c}\times \Delta \tau -ef\left(\right)open="("\; close=")">\frac{\Delta {e}_{i}}{\Delta \tau}-{P}^{b,c}$$
- If Equation (15) is true, end the process and go to the next time step, otherwise go to step 8.
- Estimate the charged energy using Equation (16); end the process and go to the next time step.

- ${\alpha}_{i}$ = 0, i.e., there is deficit of energy $\Delta {e}_{i}$.
- If Equation (13) is true, go to step 3, otherwise go to step 6.
- Estimate BESS charged energy using Equation (18):$$Edi{s}_{s,i}^{b,c}=\Delta {e}_{i}-ef\left(\right)open="("\; close=")">{P}^{b,c}-\frac{\Delta {e}_{i}}{\Delta \tau}$$
- If Equation (19) is true, i.e., the battery energy content at the end of the time interval is not below the minimum acceptable energy capacity, end the process and go to the next time step, otherwise go to step 5:$$0.1\times {E}^{b}\le {E}_{s,i-1}^{b,c}-\frac{Edi{s}_{s,i}^{b,c}}{\eta}.$$
- Estimate the BESS charged energy using Equation (20); end the process and go to the next time step:$$Edi{s}_{s,i}^{b,c}=Edi{s}_{s,i-1}^{b,c}-0.1\times {E}^{b}\times \eta .$$
- Estimate BESS charged energy using Equation (21):$$Edi{s}_{s,i}^{b,c}={P}^{b,c}\times \Delta \tau -ef\left(\right)open="("\; close=")">\frac{\Delta {e}_{i}}{\Delta \tau}-{P}^{b,c}$$
- If Equation (19) is true, end the process and go to the next time step, otherwise go to step 8.
- Estimate the charged energy using Equation (20); end the process and go to the next time step.

## 5. Economics of the Wind-BESS System

#### 5.1. Optimal BESS Capacity

#### 5.2. Highest Achievable Savings

#### 5.3. BESS Lifetime

#### 5.4. Interpretation and Analysis

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

AC | Autocorrelation |

ADF | Augmented Dickey–Fuller |

AI | Artificial Intelligence |

ARIMA | Autoregressive Integrated Moving Average |

BESS | Battery Energy Storage Systems |

BFE | Backward Feature Elimination |

ESS | Energy Storage Systems |

LIB | Lithium-Ion Battery |

MAE | Mean Absolute Error |

MOU | Memorandum of Understanding |

NREL | National Renewable Energy Laboratory |

NWP | Numerical Weather Prediction |

PAC | Partial Autocorrelation |

PEI | Prince Edward Island |

RES | Renewable Energy Resources |

SCADA | Supervisory Control and Data Acquisition |

SEETSS | Summerside Electric Energy Transmission Scheduling System |

SOH | State of Health |

SVM | Support Vector Machine |

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**Figure 11.**Histogram of Summerside Electric Energy Transmission Scheduling System (SEETSS) and BluWave import schedule residuals.

**Figure 13.**5-min and hourly resolution of Summerside Electric actual required power import for a sample 2-h period.

**Figure 14.**Charged and discharged energy of a 1 MW BESS for the sample period shown in Figure 13.

**Figure 16.**Flowchart of the proposed method in Section 4.2.

Number of Data Points | Resolution | Number of Features | Source | |
---|---|---|---|---|

Dataset 1 | 17,568 | Hourly | 7 | Summerside Electric |

Dataset 2 | 52,560 | 10-min | 98 | Summerside Electric |

Dataset 3 | 17,568 | Hourly | 18 | Environment and Climate Change Canada |

Wind MAE (kWh) | Load MAE (kWh) | Import MAE (kWh) | |
---|---|---|---|

Summerside | 1383 | 800 | 1872 |

BluWave | 851 | 332 | 976 |

Improvement | 62% | 58% | 48% |

$\mathit{C}=1$ | $\mathit{C}=2$ | $\mathit{C}=3$ | |
---|---|---|---|

Cost ($/kWh) | 450 | 600 | 750 |

Symbol | Type | Description | Unit |
---|---|---|---|

$\mathcal{E}$ | Set | BESS energy capacities | |

$\mathcal{C}$ | Set | BESS C-rates | |

$\mathcal{S}$ | Set | Import error scenarios | |

$\mathcal{T}$ | Set | time-steps | |

b | Index | BESS energy capacity | |

c | Index | BESS C-rate | |

i | Index | time-step | |

s | Index | Import error scenario | |

${\alpha}_{i}$ | Parameter | Binary parameter indicating energy surplus during time-step i | |

$\eta $ | Parameter | One-way converter efficiency | % |

$|\Delta {e}_{i}|$ | Parameter | Import inaccuracy at time-step i | MWh |

$\Delta \tau $ | Parameter | Time interval length | 1 h |

${E}^{b}$ | Parameter | BESS nominal energy capacity for simulation scenario b | MWh |

${P}^{b,c}$ | Parameter | BESS nominal Power capacity for simulation scenarios $b,c$ | MW |

${E}_{s,i}^{b,c}$ | Variable | BESS energy at the end of time-step i for simulation scenario $b,c,s$ | MWh |

$Ec{h}_{s,i}^{b,c}$ | Variable | BESS charged energy during time-step i for simulation scenario $b,c,s$ | MWh |

$Edi{s}_{s,i}^{b,c}$ | Variable | BESS discharged energy during time-step i for simulation scenario $b,c,s$ | MWh |

${\mathrm{L}}_{s}^{b,c}$ | Variable | BESS end of life for simulation scenario $b,c,s$ | |

${\mathrm{SOH}}_{s,i}^{b,c}$ | Variable | BESS state of health at the end of time-step i for simulation scenario $b,c,s$ |

${}_{{\mathit{\rho}}_{\mathit{sur}}}$\ ${}^{{\mathit{\rho}}_{\mathit{def}}}$ | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |
---|---|---|---|---|---|---|---|---|---|

4 | 0.5 | 1 | 2.75 | 4 | 5.25 | 5.75 | 6.5 | 7.5 | 8 |

8 | 1.25 | 3 | 4.25 | 5.25 | 5.75 | 6.5 | 7.5 | 8.25 | 9.25 |

12 | 3.25 | 4.5 | 5.25 | 5.75 | 7.25 | 8 | 8.25 | 9.25 | 9.25 |

16 | 4.5 | 5.5 | 6.5 | 7.5 | 8 | 8.5 | 9.25 | 9.25 | 10.75 |

20 | 5.5 | 6.5 | 7.5 | 8 | 8.5 | 9.25 | 10.5 | 10.75 | 11.25 |

24 | 6.5 | 7.5 | 8 | 8.5 | 9.25 | 10.5 | 11.25 | 11.25 | 11.25 |

28 | 7.5 | 8 | 8.75 | 9.25 | 10.5 | 11.25 | 11.25 | 11.25 | 12 |

32 | 8 | 9.25 | 9.25 | 10.75 | 11.25 | 11.25 | 11.25 | 12 | 12.75 |

36 | 9.25 | 9.25 | 10.75 | 11.25 | 11.25 | 11.25 | 12 | 14 | 14 |

${}_{{\mathit{\rho}}_{\mathit{sur}}}$\ ${}^{{\mathit{\rho}}_{\mathit{def}}}$ | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |
---|---|---|---|---|---|---|---|---|---|

4 | −0.021 | 0.003 | 0.076 | 0.179 | 0.295 | 0.419 | 0.547 | 0.681 | 0.817 |

8 | 0.008 | 0.086 | 0.191 | 0.308 | 0.432 | 0.561 | 0.695 | 0.837 | 0.971 |

12 | 0.097 | 0.203 | 0.322 | 0.446 | 0.575 | 0.710 | 0.847 | 0.987 | 1.128 |

16 | 0.216 | 0.335 | 0.460 | 0.590 | 0.725 | 0.862 | 1.002 | 1.143 | 1.288 |

20 | 0.348 | 0.474 | 0.604 | 0.739 | 0.876 | 1.017 | 1.159 | 1.304 | 1.451 |

24 | 0.4875 | 0.619 | 0.754 | 0.891 | 1.032 | 1.174 | 1.320 | 1.467 | 1.614 |

28 | 0.633 | 0.769 | 0.906 | 1.048 | 1.190 | 1.336 | 1.483 | 1.630 | 1.777 |

32 | 0.784 | 0.922 | 1.063 | 1.206 | 1.352 | 1.499 | 1.646 | 1.793 | 1.943 |

36 | 0.937 | 1.078 | 1.221 | 1.368 | 1.515 | 1.662 | 1.809 | 1.959 | 2.112 |

**Table 7.**Optimal BESS size energy capacity (MWh) for a 15 year-project lifetime; optimal power capacity (MW) is the same as Table 5; penalties are in c/kWh.

${}_{{\mathit{\rho}}_{\mathit{sur}}}$\ ${}^{{\mathit{\rho}}_{\mathit{def}}}$ | 4 | 8 | 12 | 16 | 20 | 24 | 28 | 32 | 36 |
---|---|---|---|---|---|---|---|---|---|

4 | 2.5 | 4.5 | 10 | 12.75 | 15 | 15.75 | 16.75 | 18.25 | 19 |

8 | 5.5 | 10.75 | 13.25 | 15 | 15.75 | 16.75 | 18.25 | 19.25 | 20.5 |

12 | 11.25 | 13.75 | 15 | 15.75 | 18 | 19 | 19.25 | 20.5 | 20.5 |

16 | 13.75 | 15.25 | 16.75 | 18.25 | 19 | 19.5 | 20.5 | 20.5 | 22.25 |

20 | 15.25 | 16.75 | 18.25 | 19 | 19.5 | 20.5 | 22 | 22.25 | 23 |

24 | 16.75 | 18.25 | 19 | 19.5 | 20.5 | 22 | 23 | 23 | 23 |

28 | 18.25 | 19 | 20 | 20.5 | 22 | 23 | 23 | 23 | 23.75 |

32 | 19 | 20.5 | 20.5 | 22.25 | 23 | 23 | 23 | 23.75 | 24.75 |

36 | 20.5 | 20.5 | 22.25 | 23 | 23 | 23 | 23.75 | 26.25 | 26.25 |

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**MDPI and ACS Style**

Farrokhabadi, M.
Data-Driven Mitigation of Energy Scheduling Inaccuracy in Renewable-Penetrated Grids: Summerside Electric Use Case. *Energies* **2019**, *12*, 2228.
https://doi.org/10.3390/en12122228

**AMA Style**

Farrokhabadi M.
Data-Driven Mitigation of Energy Scheduling Inaccuracy in Renewable-Penetrated Grids: Summerside Electric Use Case. *Energies*. 2019; 12(12):2228.
https://doi.org/10.3390/en12122228

**Chicago/Turabian Style**

Farrokhabadi, Mostafa.
2019. "Data-Driven Mitigation of Energy Scheduling Inaccuracy in Renewable-Penetrated Grids: Summerside Electric Use Case" *Energies* 12, no. 12: 2228.
https://doi.org/10.3390/en12122228