# A Power Smoothing Control Strategy and Optimized Allocation of Battery Capacity Based on Hybrid Storage Energy Technology

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## Abstract

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## 1. Introduction

## 2. Power Smoothing Control Method Based on an Inertial Filter and PID Control Algorithm

#### 2.1. Simplified Diagrams of the Power Smoothing Control Model

_{w}is the active power of wind farm output; P

_{out}is the grid-connected power; P

_{b}is the target signal for BESS, T is the time constant of first-order low-pass filter, it adopts 0 s~1800 s. When P

_{out}is higher than P

_{w}, the surplus energy will be stored in BESS. When P

_{out}is less than P

_{w}, the energy stored in BESS will be released to supply it to the power grid. The fluctuations of the output power for wind farm can be effectively restrained in this way and the active power output of the wind farm gets more smoothing.

#### 2.2. The Relationship between Inertia Filtering Time Constant and BESS Capacity

_{out}(s) is derived from P

_{w}(s) after first-order low-pass filter according to Figure 2, that is:

_{b}(s) is described by:

_{w}(s) is a step signal and equal to 1.5 MWh, Figure 3 shows the relationship of the output power of BESS and time constant T of the low-pass filter. It can be seen from it that time constant T is smaller, the speed of the grid-connected power tracking the active power from wind farm is faster.

**Figure 5.**The relationship of the allocated capacity and power variation of BESS with the time constant T.

#### 2.3. Simulation Example of Power Smoothing Based on an Inertial Filter

#### 2.4. Power Smoothing Control Based on Inertial Filter and PID Control Algorithm

_{s}is 0.1.

**Figure 7.**The curve of power smoothing control combining an Inertial Filter with a PID control algorithm.

_{b}(s) and actual output power H(s) of the energy storage system there is a certain deviation which is related to the parameters of the PID control algorithm and the characteristics of the energy storage battery leading to the power C(s) of wind power into grid being obviously different from the expected power P

_{out}(s), so the smoothness of the actual output power received by the PID is less than the expected output power compared with Figure 6. The lags caused by the Inertial Filter cannot be eliminated even using PID control in the control process, because the battery is charged and discharged frequently, the power control curve in Figure 6 is not very smooth and some burrs exist.

## 3. The Construction of a Power Smoothing Model Based on a Hybrid Energy Storage System

#### 3.1. The Fluctuating Characteristics of Wind Power

^{−4}Hz), the energy of the high frequency part is low and relatively average.

#### 3.2. Multi-Scale Decomposition of Wind Power Signals Based on Multi-Resolution Analysis Theory

**Figure 9.**The tree structure of a three layers wavelet decomposition based on multi-resolution Analysis.

^{−4}Hz, calculated by 1/(60 × 2

^{7})).

**Figure 10.**The power curves of wavelet multi-scale decomposition. (

**a**) The power curves of low frequency A7 and high frequency D7; (

**b**) the power curves from high frequency D4 to D6; (

**c**) the power curve from high frequency D1 to D3.

#### 3.3. The Structure of the Power Smoothing Model Based on Hybrid Energy Storage Technology

#### 3.4. Comparison of Smoothed Power Based on Wavelet Theory and Inertial Filter

**Figure 12.**The comparison of power smoothing curve based on Inertia Filtering and Wavelet Transform in some wind farm about 50 h.

**Figure 13.**The power variation smoothed by the Inertial Filter and Wavelet Transform in 1 min and 10 min.

## 4. The Realization of Power Smoothing Control Strategy Based on Model Algorithmic Control (MAC)

#### 4.1. Principles of Model Algorithmic Control (MAC)

#### 4.2. Simulation Examples of Power Smoothing Control Strategy Combining MAC Control and Wavelet Transform

**Figure 15.**The power control curves of a hybrid energy storage system based on PID control and MAC control in the period of 300 s.

_{b}(s), if the integral time is too big, it will cause overshoot; if the integral time is too small, it needs longer time to become stable. It can be seen that MAC control method can track the target power quicker than the PID control method to ensure the computational speed in a practical application for the real-time processing requirements. Due to the influence of the inertia and the response speed of BESS, its actual output is not completely equal to the target value which mainly reflects in the high-frequency part, SC is used to compensate the difference part and makes the output of battery and SC closer to the target value in the end. The mean error between the combined output power C(s) and the target power P

_{b}(s) obtained by PID control and MAC is equal to 134.4 kW and 28.35 kW, respectively. In order to further compare, the use of the combination of Inertial Filtering and PID as well as the combination of Wavelet Transform and MAC to achieve power smoothing control, the contrast curve is as shown in Figure 16.

**Figure 16.**The power smoothing control curves combining Inertial Filtering with PID and combining Wavelet Transform with MAC.

_{out}(s) filtered by Wavelet Transform does not have the lags caused by the Inertial Filter which has been proven in Section 2. The control effect of MAC on the target power filtered by Wavelet Transform is so ideal that the maximum error is only about 10 kWh, so it has no difference from Figure 11 without any burrs after MAC control.

## 5. The Capacity Allocations of BESS Based on Wavelet Transform

_{w}(s) from wind farm and grid-connected power P

_{out}(s) in 1 min, shown in Figure 11.

**Figure 17.**The comparison of energy storage capacity in a wind farm over 50 h based on Inertial Filtering and Wavelet Transform, respectively.

Time | Inertial Filter | Wavelet Filter | ||||||
---|---|---|---|---|---|---|---|---|

T = 600 s | T = 1200 s | T = 1800 s | ||||||

Capacity | Fluctuation rate | Capacity | Fluctuation rate | Capacity | Fluctuation rate | Capacity | Fluctuation rate | |

10 min | 0.1175 | 0.22% | 0.1324 | 0.12% | 0.1381 | 0.08% | 0.3605 | 0.05% |

30 min | 0.4402 | 0.36% | 0.5619 | 0.18% | 0.6258 | 0.13% | 0.34 | 0.05% |

1 h | 0.5751 | 0.36% | 0.9073 | 0.18% | 1.1406 | 0.13% | 1.2406 | 0.16% |

6 h | 12.3531 | 1.07% | 23.6910 | 0.8% | 34.7048 | 0.68% | 4.2565 | 0.47% |

12 h | 12.7734 | 1.36% | 24.4047 | 1.05% | 35.8569 | 0.89% | 10.4147 | 0.47% |

24 h | 12.7734 | 1.36% | 24.4047 | 1.05% | 35.8569 | 0.89% | 11.5506 | 0.47% |

7 day | 12.0890 | 6.27% | 27.3457 | 3.17% | 40.5777 | 2.07% | 21.0206 | 0.57% |

14 day | 14.0891 | 6.27% | 27.3483 | 3.17% | 40.5902 | 2.07% | 35.2689 | 0.58% |

30 day | 14.4780 | 6.27% | 28.1508 | 3.17% | 41.6251 | 2.07% | 35.2689 | 0.58% |

Month | Inertial Filter | Wavelet Filter | ||||||
---|---|---|---|---|---|---|---|---|

T = 600 s | T = 1200 s | T = 1800 s | ||||||

Capacity | Fluctuation rate | Capacity | Fluctuation rate | Capacity | Fluctuation rate | Capacity | Fluctuation rate | |

1 | 13.5525 | 5.69% | 26.3605 | 3.07% | 39.2466 | 2.11% | 32.0343 | 0.68% |

2 | 12.0408 | 4.91% | 23.3865 | 2.78% | 34.9313 | 1.93% | 25.9837 | 0.58% |

3 | 11.5335 | 6.01% | 22.4609 | 3.07% | 33.3663 | 2.04% | 26.9449 | 0.57% |

4 | 14.4780 | 6.27% | 28.1508 | 3.17% | 41.6251 | 2.07% | 35.2689 | 0.58% |

5 | 14.4155 | 7.02% | 28.1101 | 3.74% | 41.8126 | 2.55% | 41.9205 | 0.75% |

6 | 13.4053 | 3.12% | 25.9378 | 1.71% | 38.3804 | 1.28% | 26.3218 | 0.48% |

7 | 13.4397 | 5.29% | 25.9693 | 2.53% | 38.2902 | 1.81% | 26.8048 | 0.46% |

8 | 11.78881 | 3.22% | 22.4104 | 1.57% | 32.3637 | 1.19% | 19.6621 | 0.39% |

9 | 14.0477 | 2.98% | 27.2093 | 1.66% | 40.0676 | 1.21% | 23.4834 | 0.54% |

10 | 14.6336 | 3.61% | 28.3331 | 2.20% | 41.7807 | 1.56% | 26.6868 | 0.54% |

11 | 15.2521 | 5.63% | 29.4935 | 3.12% | 43.7327 | 2.14% | 29.0139 | 0.75% |

12 | 15.0642 | 6.47% | 29.3345 | 3.36% | 43.5619 | 2.29% | 38.0849 | 0.79% |

## 6. Conclusions

## Acknowledgments

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**MDPI and ACS Style**

Han, X.; Chen, F.; Cui, X.; Li, Y.; Li, X.
A Power Smoothing Control Strategy and Optimized Allocation of Battery Capacity Based on Hybrid Storage Energy Technology. *Energies* **2012**, *5*, 1593-1612.
https://doi.org/10.3390/en5051593

**AMA Style**

Han X, Chen F, Cui X, Li Y, Li X.
A Power Smoothing Control Strategy and Optimized Allocation of Battery Capacity Based on Hybrid Storage Energy Technology. *Energies*. 2012; 5(5):1593-1612.
https://doi.org/10.3390/en5051593

**Chicago/Turabian Style**

Han, Xiaojuan, Fang Chen, Xiwang Cui, Yong Li, and Xiangjun Li.
2012. "A Power Smoothing Control Strategy and Optimized Allocation of Battery Capacity Based on Hybrid Storage Energy Technology" *Energies* 5, no. 5: 1593-1612.
https://doi.org/10.3390/en5051593