# Optimized Charge Controller Schedule in Hybrid Solar-Battery Farms for Peak Load Reduction

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

#### 2.1. Demand Forecasting Review

#### 2.2. Solar Forecasting Review

#### 2.3. Scheduling of Battery Review

## 3. Methodology

- Demand forecasting problem
- Solar forecasting problem
- Battery optimization problem

#### 3.1. Machine Learning Approach

#### 3.1.1. Random Forest

#### 3.1.2. Gradient Boosting Regression Trees

- -
- N is the number of individual trees built,
- -
- ${F}_{0}$ is the initial prediction,
- -
- ${F}_{i}$ is the prediction at stage i,
- -
- h is the prediction of an individual tree learner,
- -
- ν ∈ (0, 1] is the shrinkage parameter to reduce the effect of an individual tree in the sequence.

#### 3.1.3. Feed-Forward Neural Networks

#### 3.1.4. Combined Forecasts

#### 3.1.5. Hyperparameter Tuning

#### 3.2. Demand Forecasting

#### 3.3. Solar Forecasting

- There is an inherent bias of NWP forecasts, as the grid points of NWP data are usually not precisely on a solar plant. To overcome this bias, there was a linear-regression-based debias method developed for the GHI predictions, so that the closest grid points would be used to predict GHI measurements at the site.
- Then, this irradiance and the temperature were used as features for modeling the active power on the PV site.
- To capture the possible timewise degradation of solar modules [27], as well as to see any effect of seasonality, numerous cyclic features were utilized in the modeling.
- The final modeling was done with scikit-learn-based Linear modeling and Random Forest.

- -
- First, the Mean Absolute Percentage Error was used. The physical meaning of this error metric is the average absolute percentage difference of the prediction from the ground truth.
- -
- Secondly, the normalized Mean Absolute Error was used for the basis of model selection. The basis of normalization is the maximum measured power. The physical meaning of this error metric is the percentage of how high the average absolute error is compared to the farm capacity.

#### 3.4. Battery Scheduling

#### 3.4.1. Scheduler with Perfect Forecasts

#### 3.4.2. Scheduler with Imperfect Forecasts

## 4. Case Study: PoD Data Science Challenge

#### 4.1. Competition Background

#### 4.2. Input Sources and Data

- Maximize the daily evening peak reduction,
- Maximize the amount of daily solar photovoltaic energy charging.

#### 4.3. Challenge Rounds

#### 4.4. Evaluation Metric

- -
- ${S}_{d}$ is the peak reduction score for a particular day,
- -
- ${R}_{d,peak}$ is the percentage peak reduction during the evening period on day d (old peak–new peak)/old peak,
- -
- ${p}_{d,1}$, ${p}_{d,2}$ indicate the proportion of energy stored in the battery from solar energy and from the grid, respectively, on day d
- -
- ${C}_{1}$, ${C}_{2}$ are the given constants and weights for the solar and grid energy, respectively. These weights are based on the relatively lifetime Greenhouse Gas emission intensity of solar and electricity from the grid around the substation.

#### 4.5. Battery Operational Constraints

- 1.
- The maximum charge and discharge of power is 2.5 MW.$$-2.5\mathrm{MW}=-D\le {b}_{t}\le D=2.5\mathrm{MW}$$
- 2.
- The battery cannot charge beyond its capacity, ${q}_{t}$ (in MWh)$$0\le {q}_{t}\le C=6\mathrm{MWh}$$
- 3.
- The total charge in the battery at the next time step ${q}_{d,k+1}$ is related to how much is currently in the battery and how much is charged within the battery at time k, i.e.,$${q}_{t}-{q}_{t-1}-{b}_{t-1}*0.5=0$$
- 4.
- Charging (${b}_{t}\ge 0$) is only allowed from midnight to 3.30 P.M. (t = 1 to 31).
- 5.
- Discharging (${b}_{t}\le 0$) is only allowed from 3.30 P.M. to 9 P.M. t = 31 to 42.
- 6.
- The battery must be empty after discharging, i.e., ${q}_{t}=0$ for $t=43,\dots ,48$.

#### 4.6. Results of the Proposed Methodology

#### 4.6.1. Demand Forecasting Results

#### 4.6.2. Solar Forecasting Results

- ◦
- Average CSI stands for Clear Sky Index, indicating how clear a day is, on average, when compared to a modeled clearsky day. (Clearsky modeling has been performed with a default parameter set of the corresponding PVLIB modules.)
- ◦
- UF stands for Utilization Factor, that is the overall real produced energy of the power plant as a percentage of the hypothetical case that the power plant was producing electricity on nominal capacity during the entire period.

#### 4.6.3. Battery Scheduler Results

## 5. Discussion and Future Work

#### 5.1. Improved Forecasting Framework

#### 5.1.1. Additional Input Features

#### 5.1.2. Sophistication of Modeling

#### 5.2. Battery Scheduling Improvements

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Demand forecasts for Extra Trees, XGBoost, LightGBM, the combined forecast and the actual demand on a weekday (

**left**), weekend day (

**middle**) and holiday (

**right**).

**Figure 5.**Peak reduction scores of our solution, the benchmark, and the competitors’ solutions in the 4 + 1 rounds. Rounds 3 and 4 correspond to Christmas and COVID lockdown periods, respectively.

Input Type | Input Features |
---|---|

Weather features | Lagged weather features 1–3 h Rolling mean and rolling standard deviation on 3–48 h horizons Heating degree days and cooling degree days Temperature–datetime interaction variables |

Datetime features | Hour of day, day of week, day of month, day of year, week of year, month of year, year |

Holiday features | Holidays and days immediately before and after holidays are marked as special |

Solar features | PV generation forecast |

Variables | |
---|---|

${b}_{t}$ | The rate of charge or discharge for period t |

${p}_{t}$ | Charge rate from solar for period t |

${q}_{t}$ | Energy stored in the battery at beginning of period t |

$r$ | Minimum daily net load across peak hours |

Constants | |

${S}_{t}$ | Day-ahead solar forecast for period t |

${L}_{t}$ | Day-ahead load forecast for period t |

${P}_{{S}_{t}}=\frac{{e}^{{S}_{t}}}{{{\displaystyle \sum}}_{t\in \Omega}^{}{e}^{{S}_{t}}}$ | Weights/Pseudo probabilities to calculate expected generation |

${P}_{{L}_{t}}=\frac{{e}^{{L}_{t}}}{{{\displaystyle \sum}}_{t\in {\Omega}^{\prime}}^{}{e}^{{L}_{t}}}$ | Weights/Pseudo probabilities to calculate expected net demand |

B | Deviation factor from average net demand |

$D=\left(\frac{{{\displaystyle \sum}}_{t\in {\Omega}^{\prime}}^{}{L}_{t}-C*0.5}{11}\right)$ | Forecasted net demand during peak hours |

Data Type | Granularity | Comments |
---|---|---|

Historical temperature and irradiance data; temperature and irradiance predictions for the upcoming round’s period | 60 min | The data are from multiple grid points of a Numerical Weather Prediction model MERRA-2. The precise prediction cycles of these points were unknown but are assumed to be constant. |

Historical demand data on the substation | 30 min | No data about the upcoming round’s period. |

Historical photovoltaic generation data of the 5 MW Newton Downs Solar Plant. | 30 min | No data about the upcoming round’s period. |

Challenge Round: | Given Historical Dataset: | Submission Dataset: |
---|---|---|

0 | 3 November 2017–22 July 2018 | 23 July 2018–29 July 2018 |

1 | 3 November 2017–15 October 2018 | 16 October 2018–22 October 2018 |

2 | 3 November 2017–9 March 2019 | 10 March 2019–16 March 2019 |

3 | 3 November 2017–17 December 2019 | 18 December 2019–24 December 2019 |

4 | 3 November 2017–2 July 2020 | 3 July 2020–9 July 2020 |

**Table 5.**MAPE (%) values on the submission period for individual models and the combined result. Lowest error rate in

**bold**, second lowest in italic.

Round | Extra Trees | XGBoost | LightGBM | Combined Forecast |
---|---|---|---|---|

1 | 4.531 | 8.301 | 5.347 | 5.292 |

2 | 2.965 | 4.704 | 3.371 | 3.359 |

3 | 5.419 | 4.501 | 4.042 | 4.522 |

4 | 5.637 | 5.731 | 4.864 | 5.330 |

Round | R^{2} | CVRMSE (%) |
---|---|---|

0 | 0.92 | 6.59 |

1 | 0.92 | 8.01 |

2 | 0.97 | 4.78 |

3 | 0.82 | 5.21 |

4 | 0.72 | 7.33 |

Round | Test Month | Average CSI | UF | MAPE [%] | nMAE [%] | R^{2} | CVRMSE |
---|---|---|---|---|---|---|---|

1 | March | 0.6 | 0.12 | 24.5 | 4.02 | 0.85 | 72.46 |

2 | July | 0.86 | 0.27 | 25.1 | 6.98 | 0.87 | 45.39 |

3 | October | 0.97 | 0.13 | 28.5 | 5.92 | 0.76 | 87.12 |

4 | December | 0.66 | 0.03 | 69.8 | 1.39 | 0.72 | 134.04 |

Round | Scheduler That Assumes No Error in Forecasts (a) | Scheduler That Accounts for Error in Forecasts (b) | Improvement in Score (b-a) | Best Possible Score |
---|---|---|---|---|

Round 0 | 99.65 | 103.83 | 4.18 | 120.97 |

Round 1 | 90.16 | 98.16 | 8 | 110.82 |

Round 2 | 76.17 | 80.69 | 4.52 | 91.15 |

Round 3 | 48.65 | 53.16 | 4.51 | 63.11 |

Round 4 | 99.57 | 113.33 | 13.76 | 128.98 |

Overall | 82.84 | 89.83 | 6.99 | 103.0 |

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## Share and Cite

**MDPI and ACS Style**

Barta, G.; Pasztor, B.; Prava, V.
Optimized Charge Controller Schedule in Hybrid Solar-Battery Farms for Peak Load Reduction. *Energies* **2021**, *14*, 7794.
https://doi.org/10.3390/en14227794

**AMA Style**

Barta G, Pasztor B, Prava V.
Optimized Charge Controller Schedule in Hybrid Solar-Battery Farms for Peak Load Reduction. *Energies*. 2021; 14(22):7794.
https://doi.org/10.3390/en14227794

**Chicago/Turabian Style**

Barta, Gergo, Benedek Pasztor, and Venkat Prava.
2021. "Optimized Charge Controller Schedule in Hybrid Solar-Battery Farms for Peak Load Reduction" *Energies* 14, no. 22: 7794.
https://doi.org/10.3390/en14227794