# Model predictive control and improved low-pass filtering strategies based on wind power fluctuation mitigation

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## Abstract

The rapid development of renewable energy sources such as wind power has brought great challenges to the power grid. Wind power penetration can be improved by using hybrid energy storage (ES) to mitigate wind power fluctuation. We studied the strategy of smoothing wind power fluctuation and the strategy of hybrid ES power distribution. Firstly, an effective control strategy can be extracted by comparing constant-time low-pass filtering (CLF), variable-time low-pass filtering (VLF), wavelet packet decomposition (WPD), empirical mode decomposition (EMD) and model predictive control algorithms with fluctuation rate constraints of the identical grid-connected wind power. Moreover, the mean frequency of ES as the cut-off frequency can be acquired by the Hilbert Huang transform (HHT), and the time constant of filtering algorithm can be obtained. Then, an improved low-pass filtering algorithm (ILFA) is proposed to achieve the power allocation between lithium battery (LB) and supercapacitor (SC), which can overcome the over-charge and over-discharge of ES in the traditional low-pass filtering algorithm (TLFA). In addition, the optimized LB and SC power are further obtained based on the SC priority control strategy combined with the fuzzy control (FC) method. Finally, simulation results show that wind power fluctuation can be effectively suppressed by LB and SC based on the proposed control strategies, which is beneficial to the development of wind and storage system.

## Keywords

Wind power fluctuation mitigation Control strategies Model predictive control algorithm Hybrid energy storage (ES) Improved low-pass filtering algorithm (ILFA) Fuzzy control (FC) Strategy## 1 Introduction

As energy and environmental issues become increasingly prominent, renewable energy sources such as wind power have been rapidly developed. Large-scale grid-connected renewable energy sources significantly affect the safe and stable operation of the power system owing to their randomness and intermittency [1, 2, 3]. Therefore, in order to enhance the penetration rate of grid-connected renewable energy sources, two methods are always used to improve their controllability. One method is to optimize the control of renewable energy sources and grid-connected interface devices. Reference [4] presents a technique for the control of a modular multilevel converter (MMC)-based distributed generation system in the grid-connected mode. Passivity-based controller, sliding mode method, and reference currents calculator are employed as the outer loop controller, central loop controller, and inner loop controller, respectively, to regulate the operation of an interfaced MMC under steady state operating conditions, and during load and parameter variations. Reference [5] describes a power-based control technique based on a double synchronous controller for an interfaced converter between the renewable energy sources and the power grid, including an active-reactive power-based dynamic equation, so that the stable operation of the power grid can be guaranteed during the integration of large-scale renewable energy sources. Reference [6] proposes a comprehensive dynamic model based on a direct quadrature rotating frame to control a grid-connected single-phase voltage source inverter combined with a capability curve based on active and reactive power. Reference [7] applies a synchronous active proportional resonant-based control technique for interfaced converters to improve the stable operation of the power grid under high penetration of distributed generation sources.

The other method is to size the energy storage (ES) system to reduce the impact of renewable energy power fluctuation on the grid. Reference [8] proposes a new model-driven controller that incorporates a battery ES system (BESS) into a voltage regulation scheme in order to counteract voltage variation caused by photovoltaic (PV) power fluctuations. Reference [9] investigates the effect of wind energy penetration on the frequency response of a multi-machine power network considering the different time constants of a low-pass filter in the direct current (DC) chopper of an energy capacitor system. The results show that a higher time constant of the low-pass filter effectively damps the oscillations of the grid variables and quickly restores the system during network disturbance. Reference [10] proposes the coordinated control strategy of a hybrid ES system (HESS) with complementary features to improve the accommodating ability of PV. Reference [11] illustrates an analytical formulation for assessing the reliability impact of ES supporting distributed generation in the supply restoration of isolated network areas.

Nowadays, using ES to smooth renewable energy power fluctuation has drawn more and more attention, and the corresponding control strategies are becoming more and more diverse. They include constant-time low-pass filtering (CLF), variable-time low-pass filtering (VLF), wavelet packet decomposition (WPD), empirical mode decomposition (EMD) and model predictive control (MPC) algorithms. In [12], because the power generation of PV and the load demand fluctuate frequently, a third-order Butterworth low-pass filter and high-pass filter are adopted to smooth the wind power and allocate power between the battery and supercapacitor (SC), where the time constant does not change. In [13], the aim of integrated HESS is to smooth the variations in wind-solar power production and ensure a more controllable output power based on CLF. CLF has the advantages of simplicity, reliability, and practicality. However, the time constant cannot be flexibly adjusted. Furthermore, renewable energy power is over-suppressed easily, which will increase the cost of ES.

The low-pass filter passes the lower components of the frequency of wind power. It shows that the wind power fluctuation decreases as the time constant of low-pass filter increases [14]. In order to improve the ability of power systems for integrating wind power, wind farm power output fluctuation is mitigated by an ES system with the control strategy of a flexible first-order low-pass filter control strategy. And the wind power is flat after smoothing [15]. A flexible first-order low-pass filter with an optimization of the time constant is developed to limit wind power fluctuation under restriction with smaller BESS capacity [16]. However, VLF has the defect in time delay due to its filtering properties, which is not conducive to online real-time control.

An HESS power allocation control including an online wavelet filter and a new power allocation optimization algorithm is adopted to meet the technical requirements of the grid for smoothing wind power. The online wavelet filtering method is established to minimize the phase lag in decomposing frequency components [17]. A new smoothing method based on self-adaptive WPD in HESS is proposed. It can adjust the wavelet decomposition level based on the change range of PV output power, so that the low frequency component of PV power can be accurately extracted [18]. A wind power filtering approach is presented to mitigate short- and long-term fluctuations using an HESS, and a new wavelet-based capacity configuration algorithm to properly size the HESS [19]. The power allocation between multi-type ES can be online achieved with WPD or wavelet decomposition. However, a large amount of historical data must be analyzed to select the wavelet function.

Wind power smoothing is achieved by regulating the output power of SCs and batteries to negate the high and low frequency fluctuating power components based on EMD [20]. The EMD is used to analyze the wind power fluctuations and the power distribution of the ES system. Different types of power commands can be obtained according to the reconstructed frequency characteristics, which are suitable for different types of ES systems [21]. EMD is used to smooth wind power fluctuation with a BESS. After describing the wind power, the low-frequency parts are used as the wind power grid-connected value, and the high-frequency parts are stored in the BESS [22]. Unfortunately, the decomposition results sometimes vary greatly owing to its broad cut-off conditions.

MPC is suitable for online optimization control with the advantage of high-precision model prediction and receding horizon optimization. In [23], a new coordinated control strategy based on MPC is proposed for wind power fluctuation suppression, which employs MPC for the total power required for the entire ES system.

- 1)
Firstly, the impact of different smoothing strategies on wind power are analyzed. The optimal control strategy is selected for comparison with CLF, VLF, WPD, EMD and MPC. Then the reason is interpreted by the cut-off frequency analysis.

- 2)
In addition, an ILFA is applied to achieve power allocation and to overcome the over-charge and over-discharge of hybrid ES compared with conventional low-pass filtering algorithm, whose time constant is flexibly obtained by Hilbert Huang transform (HHT). The optimized LB and SC power are further acquired, and the operation of hybrid energy is improved by the proposed SC priority FC-based control strategy.

This paper is organized as follows. The introduction is provided in Section 1. In Section 2, wind power fluctuation smoothing strategies are discussed in detail. In Section 3, the achievement of power allocation in hybrid ES based on an ILFA is described. In Section 4, conclusions are drawn.

## 2 Wind power fluctuation smoothing strategies

- 1)
According to grid-connected fluctuation rate constraints, wind power fluctuation is mitigated by a smoothing strategy, such as CLF, VLF, WPD, EMD, and MPC. ES power and grid-connected wind power can be obtained.

- 2)
LB and SC power can be obtained by an improved low-pass filtering algorithm, whose time constant is calculated by HHT.

- 3)
The SC power optimization is realized by FC based on the SC state of charge (SOC). Then, the optimized LB power can also be acquired.

### 2.1 Low-pass filtering algorithm

*R*is the equivalent resistor;

*C*is the equivalent capacitor;

*X*denotes the original wind power is the input variable;

*Y*denotes the smoothed wind power is the output variable.

*k*and

*k −*1; \(X_{k}\) is the original wind power at time

*k*.

#### 2.1.1 CLF algorithm

#### 2.1.2 VLF algorithm

### 2.2 WPD algorithm

^{j}wavelet package subspace. Then a complete binary tree structure is formed. The WPD frame diagram is shown in Fig. 10, where W is the wind power signal.

*t*

_{s}is the sampling time; and

*n*is the number of layers in WPD. The first band frequency range is 0–

*f*

_{0}, and the second one is

*f*

_{0}–2

*f*

_{0}, etc.

### 2.3 EMD algorithm

- 1)
EMD application

- 2)
HHT application

_{11}, c

_{10}, …, c

_{1}are arranged in ascending order of frequency. Lower frequency IMFs combined with the residual component are usually selected as grid-connected wind power to meet the grid-connected fluctuation rate constraint. The 1-min max fluctuation rate of c

_{11}–c

_{7}IMFs combined with the residual component is 0.0261, which is greater than 0.02, while that of c

_{11}–c

_{8}IMFs combined with the residual component is 0.0141, which is significantly lower than the smoothing requirements, as displayed in Fig. 13. Therefore, the c

_{11}–c

_{8}IMFs combined with the residual component are used as the grid-connected wind power, as shown in Fig. 14.

### 2.4 MDC algorithm

- 1)
Receding horizon strategy

*k*+ 1,

*k*+ 2, …, and

*k*

*+ M*can be acquired based on the current time

*k*and state

*x*(

*k*) by solving the optimization problem; ② the first control instruction is applied to the control system, thus the state is updated to

*x*(

*k*

*+*1) at time

*k*

*+*1; and ③ the above steps are repeated until the operation requirements are met.

- 2)
State space model

*k*can be expressed as

*(*

**x***k*),

*(*

**u***k*),

*(*

**r***k*), and

*(*

**y***k*), respectively. Then the state space equation can be established as follows.

*,*

**A**

**B**_{1},

**B**_{2},

*,*

**C**

**D**_{1}, and

**D**_{2}are the coefficient matrices.

*k*+

*M*can be predicted by iteration of (13). The specific equation is:

- 3)
MPC application

*k*are expressed as \(P_{w} (k)\), \(P_{es} (k)\), and \(SOC(k)\). In addition, the relationships between grid-connected wind power, wind power, and ES power are characterized as:

*k*

*+*1.

Equations (18) and (19) reflect the power and fluctuation rate constraints of grid-connected wind power, respectively. Equations (20) and (21) reflect the power and SOC constraints of ES, respectively.

Wind power fluctuation rate with different control strategies

Method | Max fluctuation rate before smoothing | Max fluctuation rate after smoothing |
---|---|---|

CLF | 0.0630 | 0.0180 |

VLF | 0.0630 | 0.0199 |

WPD | 0.0630 | 0.0154 |

EMD | 0.0630 | 0.0141 |

MPC | 0.0630 | 0.0200 |

### 2.5 ES sizes with different control strategies

ES sizes with different control strategies

Methods | Max charge and discharge power (MW) | Capacity (MWh) |
---|---|---|

CLF | 5.4371 | 0.4286 |

VLF | 5.2688 | 0.3790 |

WPD | 4.7085 | 0.3160 |

EMD | 8.9724 | 0.8662 |

MPC | 4.2978 | 0.2662 |

*E*is the change in energy, and it can be obtained by the integrating power with respect to time.

In addition, the reasons for different ES sizes under different control strategies are analyzed from the viewpoint of smoothed cut-off frequency. The time constant in CLF is 130 s, and the cut-off frequency of 1.22 × 10^{−3} Hz can be calculated according to \(\tau = 1/(2\pi f)\). The time constant range in VLF is from 90 s to 119.1 s, and the calculated cut-off frequency is from 1.34 × 10^{−3} to 1.77×10^{−3} Hz. The cut-off frequency of 1.56 × 10^{−3} Hz in WPD can be obtained by (4). The max instantaneous frequency of 0.97 × 10^{−3} Hz in EMD can be acquired by the decomposition and HHT of grid-connected wind power. Similarly, the max instantaneous frequency of 8.65 × 10^{−3} Hz in MPC can also be acquired.

Cut-off frequency with different control strategies

Method | Cut-off frequency (Hz) |
---|---|

CLF | 1.22 × 10 |

VLF | 1.34 × 10 |

WPD | 1.56 × 10 |

EMD | 0.97 × 10 |

MPC | 8.65 × 10 |

## 3 Power allocation between hybrid ES

### 3.1 Allocation strategies

Recently, the low-pass filtering algorithm has been used to achieve the power allocationin between hybrid ES [23, 24, 25]. However, the determination of the filter time constant is less studied. In addition, when the traditional low-pass filtering algorithm (TLFA) is used to achieve power distribution in hybrid ES, the opposite charge and discharge statuses for LB and SC will appear. When LB charges, SC discharges. Conversely, when LB discharges, SC charges. This will lead to power flow between the LB and SC, and the energy loss will increase. Therefore, an ILFA is proposed to improve the operation efficiency of hybrid ES.

Firstly, the mean frequency of the ES, as the cut-off frequency of the low-pass filtering algorithm, is obtained by HHT in this section. Furthermore, the filter time constant can also be calculated.

Furthermore, as the SC has a longer cycle life and a more rapid response, the preferred SC charging and discharging strategy based on the FC method is used to optimize the operation of hybrid ES. Therefore, the efficiency and cycle life of the hybrid ES will be improved greatly through the proposed control strategies.

### 3.2 Case study

- 1)
ILFA

As shown in Fig. 22a, when ES power is 0, the output power values of LB and SC are contradictory. In this case, the usages of the LB and SC are increased, and their cycle lives are reduced.

- 2)
SC preferred FC-based method

- 1)
When SOC is moderate, the SC charges or discharges according to the instructions.

- 2)
When the SC is ready to discharge with a smaller SOC or charge with a larger SOC, the SOC will be modified based on FC and the correction factor

*k*can be obtained. The corrected SC power is calculated by \(P_{sc,fc} = kP_{sc,r}\). The difference between \(P_{sc,fc}\) and \(P_{sc,r}\) will be compensated by the LB.

*k*is described as the output variable. The input and output variable subordinating degree functions are introduced in Fig. 23. The fuzzy set of the input variable SOC is {VS, S, M, B, VB}, and the domain is [0, 1]. The fuzzy set of input variable \(\Delta SOC\) is {NB, NM, NS, PS, PM, PB}, and the domain is [− 1, 1]. The fuzzy set of the output variable

*k*is {VS, S, MS, MB, B, VB}, and the domain is [0, 1]. The fuzzy rules are displayed in Table 4.

Rule of FC

Fuzzy set of SOC | \(\Delta SOC\) | |||||
---|---|---|---|---|---|---|

NB | NM | NS | PS | PM | PB | |

VS | VS | VS | VS | VB | VB | VB |

S | S | MB | B | VB | VB | MB |

M | MS | B | VB | VB | MB | MS |

B | MB | VB | VB | B | MB | S |

VB | VB | VB | VB | VS | VS | VS |

## 4 Conclusion

- 1)
CLF, VLF, WPD, EMD, and MPC are used to mitigate wind power fluctuation under the same constrains. MPC has the advantages of early prediction and timely control. The smoothed cut-off frequency of MPC is the widest, and the over-suppressed wind power will not appear. Then the max charge and discharge power, and the capacity of ES can be saved.

- 2)
The average frequency of ES power as the time constant in ILFA is obtained by HHT. Then ILFA is applied to achieve the power allocation between the LB and SC to overcome the overuse and internal energy consumption of hybrid ES. Furthermore, preferential use control strategy of the SC based on FC is established considering its SOC, and optimized LB and SC power can be obtained.

Therefore, hybrid ES is used to stabilize wind power fluctuation, which can greatly promote the large-scale development of renewable energy sources, and the popularization of ES in renewable energy sources. In the future, the application of ES in a demand side response will be studied, whose technical economy will be analyzed and the potential profit will be explored.

## Notes

### Acknowledgements

This work was supported by National Key Research and Development Program of China (No. 2016YFB0900400), Foundation of Director of Institute of Electrical Engineering, Chinese Academy of Sciences (No. Y760141CSA), and Jiangsu Province 2016 Innovation Ability Construction Special Funds (No. BM2016027).

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