# A Mixed Receding Horizon Control Strategy for Battery Energy Storage System Scheduling in a Hybrid PV and Wind Power Plant with Different Forecast Techniques

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## Abstract

**:**

## 1. Introduction

## 2. Architecture of Hybrid PV and Wind Power Plant

## 3. Forecasting Techniques

## 4. Problem Formulation

#### 4.1. Cost Function

#### 4.2. Constraints

#### 4.3. Reformulation

## 5. Mixed Receding Horizon Control Strategy

- Case NB: No battery—used for benchmarking with no battery installed;
- Case DD: Day-ahead dispatch—use the results from day-ahead forecasting;
- Case DR: Day-ahead RHC dispatch—use the results from day-ahead forecasting with a receding horizon;
- Case MR: Mixed RHC dispatch—applies results from both day-ahead and hour-ahead forecasting with a receding horizon.

- Step 1:
- Forecast. The day-ahead and hour-ahead forecasting were performed at each time step (hourly in this paper).
- Step 2:
- Combine the day-ahead forecasting and hour-ahead forecasting. The first entry in day-ahead forecasting is replaced by the hour-ahead forecast.
- Step 3:
- Solve the optimisation problem. Using the corrected forecasting as inputs and the formulated Mixed-integer Linear Programming (MILP) problem, it can be solved by CPLEX with MATLAB API.
- Step 4:
- BESS dispatch. By using the RHC strategy, the first entry in the decision vector which represents BESS dispatch power is adopted as the dispatch command to direct the charge/discharge of the BESS.

## 6. Simulation Results and Discussion

#### 6.1. Simulation Case Setting

#### 6.2. Forecasting Results

#### 6.3. Optimisation Results

- Case NB: ARIMA > ENN > P > WNN
- Case DD: ENN > ARIMA > P > WNN
- Case DR: ENN > P > ARIMA > WNN
- Case MR: ARIMA > ENN > P > WNN

#### 6.4. Impacts of Penalty Rates and Long-term Horizons

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. The Box Chart of the Electricity Prices

## Appendix B. Equations for reformulation

## References

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**Figure 6.**The comparison of optimisation results for one year, including normal and extreme days. (

**a**) The total operation profits; (

**b**) The electricity profits; (

**c**) The cost from undersupply; (

**d**) The cost from oversupply. The red line in each plot indicates the results for perfect forecasting with no battery as a reference.

**Figure 7.**The optimisation results as a function of the penalty rates. (

**a**) The total operation cost of Case DD; (

**b**) The total operation cost of Case DR; (

**c**) The total operation cost of Case MR. The coloured legend on the right side is in AUD.

**Figure 8.**Results of Changing Horizons with ${\rho}_{US}={\rho}_{OS}=1$: (

**a**) for the Whole Year (

**b**) for Normal days.

Forecasting Methods | Day-ahead Forecasting | Hour-ahead Forecasting |
---|---|---|

Persistence | Previous one day data | Previous one hour data |

ENN | Previous 4 days data | Previous 4 hours data |

WNN | Previous 4 days data | Previous 4 hours data |

ARIMA | Previous 20 days data | Previous 20 hours data |

Case | Computational Time for One-year Simulation |
---|---|

Case NB | 0.26 seconds |

Case DD | 20.28 seconds |

Case DR | 211.79 seconds |

Case MR | 235.49 seconds |

Items | Assumptions |
---|---|

System design | PV panels: 15 MW |

Wind turbines: 15 MW | |

BESS: 10 MW of power capacity and 50 MWh of energy capacity | |

Battery technology | It is assumed that the degradation coefficient only changes with respect to the DOD. |

It is assumed that, with similar charge and discharge patterns of battery operation in each day, the battery degradation coefficient is simplified as a constant of 0.005% per day. | |

It is assumed that a lead-acid battery will reach its lifetime when there is a capacity loss of 20%. | |

Market (All cost and profit values in this paper are expressed in Australian dollars (AUD).) | It is assumed that the hybrid power plant will be dispatched as a scheduled power plant. |

It is assumed that the bids from HPP are always accepted by the National Electricity Market (NEM). | |

It is assumed that the penalties for oversupply and undersupply are express by the electricity prices multiplied by the penalty rates. |

Resource | Horizon | Method | MAE | MBE | RMSE | nRMSE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|---|---|

GHI | D | Persistence | 0.0367 | 1.29×10^{−18} | 0.0854 | 0.2537 | 0.9026 |

GHI | D | ENN | 0.0394 | 5.8×10^{−4} | 0.0735 | 0.2184 | 0.9278 |

GHI | D | WNN | 0.0520 | 0.0154 | 0.1000 | 0.2972 | 0.8663 |

GHI | D | ARIMA | 0.0361 | 0.0016 | 0.0733 | 0.2177 | 0.9283 |

GHI | H | Persistence | 0.0562 | −2.78×10^{−6} | 0.0899 | 0.2671 | 0.8920 |

GHI | H | ENN | 0.0237 | −0.004 | 0.0441 | 0.1311 | 0.9740 |

GHI | H | WNN | 0.0214 | 3.7×10^{−4} | 0.0394 | 0.1171 | 0.9792 |

GHI | H | ARIMA | 0.0168 | 5.6×10^{−4} | 0.0365 | 0.1084 | 0.9822 |

Wind speed | D | Persistence | 0.1283 | −2.6×10^{−18} | 0.1708 | 0.5819 | 0.0719 |

Wind speed | D | ENN | 0.1156 | −0.0044 | 0.1493 | 0.5088 | 0.2903 |

Wind speed | D | WNN | 0.1337 | −0.0179 | 0.1748 | 0.5956 | 0.0278 |

Wind speed | D | ARIMA | 0.1145 | 0.0039 | 0.1521 | 0.5184 | 0.2633 |

Wind speed | H | Persistence | 0.0638 | −1.27×10^{−19} | 0.0876 | 0.2985 | 0.7557 |

Wind speed | H | ENN | 0.0651 | 1.7×10^{−4} | 0.0852 | 0.2903 | 0.7691 |

Wind speed | H | WNN | 0.0677 | −0.0160 | 0.0886 | 0.3020 | 0.7501 |

Wind speed | H | ARIMA | 0.0657 | 0.00148 | 0.0886 | 0.2951 | 0.7614 |

Horizon | Method | MAE | MBE | RMSE | nRMSE | ${\mathit{R}}^{2}$ |
---|---|---|---|---|---|---|

D | Persistence | 3.296 | 0.00091 | 5.125 | 0.5134 | 0.5241 |

D | ENN | 3.147 | −0.7202 | 4.811 | 0.4820 | 0.5806 |

D | WNN | 3.817 | −0.6341 | 5.760 | 0.5770 | 0.3988 |

D | ARIMA | 3.186 | −0.0413 | 4.937 | 0.4946 | 0.5583 |

H | Persistence | 1.974 | −0.1588 | 3.092 | 0.3097 | 0.8268 |

H | ENN | 1.630 | −0.3909 | 2.696 | 0.2701 | 0.8683 |

H | WNN | 1.666 | −0.7499 | 2.800 | 0.2805 | 0.8580 |

H | ARIMA | 1.580 | −0.1194 | 2.635 | 0.2640 | 0.8742 |

Case | Method | Total Profit | Electricity Profit | Undersupply Cost | Oversupply Cost | O&M Cost |
---|---|---|---|---|---|---|

NB | Perfect | 1,601,728 | 2,078,128 | 0 | 0 | 476,400 |

NB | Persistence | 613,223 | 2,078,128 | 515,389 | 473,116 | 476,400 |

NB | ENN | 666,601 | 2,078,128 | 470,079 | 465,048 | 476,400 |

NB | WNN | 418,454 | 2,078,128 | 692,953 | 490,321 | 476,400 |

NB | ARIMA | 675,513 | 2,078,128 | 482,102 | 444,113 | 476,400 |

DD | Persistence | 891,222 | 2,042,082 | 264,589 | 186,270 | 700,000 |

DD | ENN | 1,007,830 | 2,141,019 | 187,664 | 245,525 | 700,000 |

DD | WNN | 970,804 | 2,287,803 | 304,977 | 312,022 | 700,000 |

DD | ARIMA | 900,133 | 2,050,986 | 257,992 | 192,861 | 70,000 |

DR | Persistence | 900,891 | 2,045,274 | 259,754 | 184,628 | 700,000 |

DR | ENN | 1,014,593 | 2,143,558 | 184,283 | 244,683 | 700,000 |

DR | WNN | 987,397 | 2,294,338 | 296,680 | 310,260 | 700,000 |

DR | ARIMA | 905,935 | 2,053,697 | 255,091 | 192,671 | 70,000 |

MR | Persistence | 1,118,056 | 2,077,182 | 117,459 | 141,667 | 700,000 |

MR | ENN | 1,160,506 | 2,040,701 | 62,098 | 118,097 | 700,000 |

MR | WNN | 1,174,790 | 2,099,715 | 45,016 | 179,910 | 700,000 |

MR | ARIMA | 1,168,070 | 2,045,471 | 89,187 | 88,214 | 700,000 |

**Table 7.**The number of days when the case in the row outperforms that in the column using different forecasting methods.

Forecasting Methods | Cases | NB | DD | DR | MR |
---|---|---|---|---|---|

Persistence | NB | - | 0 | 10 | 15 |

Persistence | DD | 363 | - | 222 | 111 |

Persistence | DR | 355 | 142 | - | 107 |

Persistence | MR | 350 | 254 | 258 | - |

ENN | NB | - | 0 | 8 | 2 |

ENN | DD | 363 | - | 239 | 102 |

ENN | DR | 357 | 126 | - | 97 |

ENN | MR | 363 | 263 | 268 | - |

WNN | NB | - | 1 | 8 | 3 |

WNN | DD | 362 | - | 229 | 90 |

WNN | DR | 357 | 135 | - | 84 |

WNN | MR | 362 | 275 | 281 | - |

ARIMA | NB | - | 1 | 6 | 4 |

ARIMA | DD | 363 | - | 232 | 83 |

ARIMA | DR | 359 | 133 | - | 82 |

ARIMA | MR | 361 | 282 | 283 | - |

**Table 8.**The number of days when the method in the row outperforms that in the column in different cases.

Cases | Forecasting Methods | Persistence | ENN | WNN | ARIMA |
---|---|---|---|---|---|

NB | Persistence | - | 170 | 223 | 174 |

NB | ENN | 195 | - | 252 | 179 |

NB | WNN | 142 | 113 | - | 140 |

NB | ARIMA | 191 | 186 | 225 | - |

DD | Persistence | - | 181 | 223 | 181 |

DD | ENN | 184 | - | 248 | 195 |

DD | WNN | 142 | 117 | - | 147 |

DD | ARIMA | 184 | 170 | 218 | - |

DR | Persistence | - | 173 | 225 | 184 |

DR | ENN | 192 | - | 251 | 192 |

DR | WNN | 140 | 114 | - | 144 |

DR | ARIMA | 181 | 173 | 221 | - |

MR | Persistence | - | 152 | 203 | 146 |

MR | ENN | 213 | - | 240 | 177 |

MR | WNN | 162 | 125 | - | 128 |

MR | ARIMA | 219 | 188 | 237 | - |

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## Share and Cite

**MDPI and ACS Style**

Yang, Y.; Bremner, S.; Menictas, C.; Kay, M.
A Mixed Receding Horizon Control Strategy for Battery Energy Storage System Scheduling in a Hybrid PV and Wind Power Plant with Different Forecast Techniques. *Energies* **2019**, *12*, 2326.
https://doi.org/10.3390/en12122326

**AMA Style**

Yang Y, Bremner S, Menictas C, Kay M.
A Mixed Receding Horizon Control Strategy for Battery Energy Storage System Scheduling in a Hybrid PV and Wind Power Plant with Different Forecast Techniques. *Energies*. 2019; 12(12):2326.
https://doi.org/10.3390/en12122326

**Chicago/Turabian Style**

Yang, Yuqing, Stephen Bremner, Chris Menictas, and Merlinde Kay.
2019. "A Mixed Receding Horizon Control Strategy for Battery Energy Storage System Scheduling in a Hybrid PV and Wind Power Plant with Different Forecast Techniques" *Energies* 12, no. 12: 2326.
https://doi.org/10.3390/en12122326