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In this paper, an active frequency control strategy of wind turbines based on model predictive control is proposed by using the power margin of wind turbines operating in load shedding mode. The frequency response model of the microgrid system with the load shedding of the wind turbines is used to predict the output power and system frequency deviation of the wind turbine. According to the prediction information, the output power control signal of the model predictive controller in the wind turbine can be optimized. On this basis, a wind turbine active participation frequency control strategy based on model predictive control is designed by rolling prediction and optimization. The wind turbine power control signal after the strategy is used to adjust the output power of the wind turbine and balance the change of the active power of the system to reduce the frequency deviation.

With the large-scale development and access of domestic wind turbines, some wind turbines already have frequency modulation (FM) capacity, so that they can actively participate in the FM control [

As wind power retains a significant proportion of generation mix in the electric system, it may impact the system's frequency security due to the lack of frequency support from units. To make up for such a system change, wind turbines should actively provide frequency response upon request. Hence, the variable speed wind turbine generators, such as doubly-fed induction generator (DFIG) [

Therefore, considering both the load shedding and the prediction of wind turbines, this paper proposes a novel active frequency control strategy of the wind power based on model predictive control (MPC). The contributions of this paper can be summarized as follows:

The load shedding operation model of the wind turbine is established in this paper, in which a certain amount of mechanical power reserve for frequency modulation is obtained by reducing load and maintaining wind turbines worked at a suboptimal operating point.

An MPC-based active frequency control strategy is proposed for wind turbines in the paper by utilizing the power margin of wind turbines operating in load shedding mode, which is able to regulate the frequency deviations to be within the safe operation range and has the excellent dynamic performance of the system frequency.

The proposed control strategy in the paper can make full use of the advantages of model predictive control. Specifically, the proposed strategy is feasible without wind speed prediction due to the power output delay caused by the inertia link of the wind turbine.

The remainder of this paper is organized as follows. Section

Traditional wind turbines operate in the maximum power tracking mode, in which there is no power reserve for continuous frequency adjustment. In order to obtain a certain amount of mechanical power reserve for frequency modulation, wind turbines need to reduce load and maintain it at a suboptimal operating point, i.e., the load shedding operation model of the wind turbine. Specifically, this section describes the load reduction operation of the wind turbine to obtain the power reserve for frequency modulation.

The mechanical characteristic _{m}(_{r}) of the wind turbine is shown in Figure

Power tracking curve of the fan under load reduction operation.

As shown in Figure _{p}(_{opt}) is multiplied by a load reduction coefficient _{del}:

The active power of the wind turbine under load shedding mode is as follows:

Under the load-shedding operation mode, the tip speed ratio can be deduced as follows:_{del} is expressed as

The load shedding suboptimal power tracking curve shown in the red line in Figure

The model predictive control system is introduced in Section

The traditional active power control strategy of the wind turbine is based on the maximum power tracking curve generation success rate, so the frequency change and active power injection can be decoupled subtly. The objective of the auxiliary frequency controller in the wind turbine is to support the system frequency by associating its active power output with the system frequency. Therefore, the frequency deviation signal is introduced into the auxiliary frequency control strategy based on model predictive control.

The wind turbine has frequency modulation capability under load shedding mode, and its frequency response model structure is shown in Figure

Structural block diagram of the fan frequency response model based on model predictive control.

Frequency response model block diagram of wind turbine active participation in microgrid frequency control.

In Figure

As shown in Figure

Due to the active participation of wind turbines in frequency control, wind turbines need to operate in load shedding mode to obtain a frequency modulation power margin. In this section, the wind turbine model and the frequency response model of multiarea microgrid under load shedding operation are described and derived. The frequency response model is the basis of the predictive model in the subsequent model predictive control strategy.

According to the mathematical model of wind turbine and microgrid frequency control system under load shedding operation described above, the frequency response model of wind turbine active frequency control is established. The mechanical torque and electromagnetic torque models of the wind turbine are expanded according to Taylor series, and the following mathematical models are obtained:

The mathematical model of the elemental block drive model of the wind turbine under the download operation mode is expressed as an incremental form:

Taking into account the dynamic relation formula of generator load in the microgrid frequency control model, the following relation between frequency and power can be deduced according to the block diagram of the microgrid frequency response model in which the fan actively participates in the control:

By combining (

By combining formula (

The regional frequency deviation

The output vector

In the frequency response model formula (

In the frequency response model proposed in formula (

Firstly, the frequency response model is discretized. The frequency response model of microgrid with wind turbine actively participating in frequency control, namely, the discrete linear state-space model of formula (

According to the principle of the model predictive control algorithm, the system response

The matrix form of formula (

In the formula,

Formula (

The function of active frequency control of wind turbines based on model predictive control is to predict the system output and adjust the power control signal to change the fan output power, so as to obtain the better dynamic frequency response of the system. Therefore, model predictive control needs to determine appropriate control objectives and constraints and also needs to take into account the special dynamic characteristics of wind turbine under load shedding operation.

Figure

Flow chart of the model predictive control method for active frequency control of wind turbine.

For microgrid systems with wind turbines actively participating in frequency control under load shedding operation, the goal of model predictive control is to optimize the output power of wind turbines based on the system frequency standard and the actual frequency of the system. Therefore, for each control area containing wind turbines, the control objective function of model predictive control design should not only take into account the dynamic performance of wind turbines, but also consider the minimization of the frequency deviation of the microgrid. By optimizing the target, the proposed strategy can achieve maximum security and economic profits at the same time. The objective function of area

The optimal control problem at time

Its constraint condition is the discretization equation of the system frequency response model, namely, the equality constraint:

The inequality constraint is the limitation of the frequency modulation capacity margin of the wind generator:

Optimization objective formula (

Flow chart of the fan active frequency control strategy for MPC.

The first step (initialization): set the initial time _{p}, the control signal _{i}(_{i}(

The second step (prediction): the system state xi(

The third step (optimization): by solving the optimization objective formula (_{i}(

The fourth step (judgment): if the optimal control action of time

The fifth step (prediction): predict the system state and output response in the next prediction time domain;

The sixth step (implementation): apply the control action _{i}(

Through the above steps, the control action sequence can be solved by the model predictive controller designed in this section, and then the control signal adjusts the output power of the wind turbine with frequency modulation capacity according to the fluctuation of wind speed, so as to balance the fluctuation of system load and stabilize the system frequency.

In order to verify the effectiveness of the proposed model predictive control based wind turbine active participation frequency control strategy in improving the system frequency performance, this section carries out simulation experiments on the four-zone microgrid frequency control model shown in Figure

Structure of the studied four-zone power system.

In the single-area microgrid system of an airport island in reference [_{p} = 0.3s, and control time _{c} = 0.1s were set to simulate the proposed control strategy.

Parameters of single-zone microgrid system with non-reheat generators.

_{t} | |||
---|---|---|---|

0.4 | 0.08 | 0.08335 | 0.015 |

Parameters of wind turbine.

Fan parameters | Symbol | Value & units |
---|---|---|

Radius of rotor | 38.5 m | |

Air density | Ρ | 1.901 × 10^{−3}(m/s)^{−3} |

Number of pole pairs | 2 | |

Generator inertia constant | _{DFIG} | 5.28 s |

Nominal frequency | _{nom} | 50 Hz |

Based power | _{base} | 1.5 MW |

Load shedding factor | _{del} | 0.85 |

Input the 50-second wind speed sequence as shown in Figure

Simulation results of fan active frequency control strategy based on model predictive control. (a) A 50-second wind speed sequence. (b) Wind power output of wind turbine. (c) System frequency deviation. (d) Fan output power command, i.e., control signal.

Comparison of single region simulation results.

PID control strategy | Proposed control strategy | |
---|---|---|

|∆_{max}| | 0.173 Hz | 0.032 Hz |

ITAE | 2.114 | 0.440 |

In Figures

In the microgrid system of an airport in reference [_{p} = 0.3s, and the control time domain is _{c} = 0.1s, the proposed scheme is simulated.

Simulation rated parameters of four-zone microgrid with non-reheat prime mover.

_{t} | ||||
---|---|---|---|---|

Area 1 | 0.4 | 0.08 | 0.08335 | 0.015 |

Area 2 | 0.33 | 0.072 | 0.111 | 0.04 |

Area 3 | 0.35 | 0.07 | 0.08 | 0.05 |

Area 4 | 0.375 | 0.085 | 0.065 | 0.0667 |

Wind speed series curve. (a) 50 s wind speed sequence input in zone 1. (b) 50 s wind speed sequence input in zone 4.

Similarly, the proposed wind turbine active participation in the microgrid frequency control strategy is compared with the traditional PID microgrid frequency control strategy in this section. The frequency deviation of zone 1 to zone 4 is shown in Figure

Frequency deviation of four regions.

The maximum frequency deviation of each region.

Section number | PID control strategy | Proposed control strategy |
---|---|---|

Area 1 | 0.213 Hz | 0.024 Hz |

Area 2 | 0.186 Hz | 0.018 Hz |

Area 3 | 0.186 Hz | 0.018 Hz |

Area 4 | 0.303 Hz | 1.47 Hz |

Frequency deviation ITAE index values in each region.

Section number | PID control strategy | Proposed control strategy |
---|---|---|

Area 1 | 3.7 | 0.5 |

Area 2 | 3.2 | 0.4 |

Area 3 | 3.2 | 0.4 |

Area 4 | 4.5 | 0.8 |

As shown in Figure

In this paper, an active frequency control strategy of the wind turbine is proposed based on model predictive control by using the power margin of wind turbines operating in load shedding mode. Specifically, the frequency response model of the microgrid system with the load shedding of the wind turbine is utilized to predict the output power and system frequency deviation of the wind turbine. According to the prediction information, the output power control signal of the model predictive controller in the wind turbine can be optimized. On this basis, an MPC-based active frequency control strategy is designed for the wind turbine by rolling prediction and optimization. The wind turbine power control signal after the strategy is used to adjust the output power of the wind turbine and balance the change of the active power of the system to reduce the frequency deviation. Besides, controlled by the proposed strategy, the frequency regulation capacity of the load shedding fan can be fully utilized when the wind speed changes, the frequency deviation can be controlled within the safe operation range, and the dynamic performance of the system frequency can be adjusted to the expected results.

Moreover, due to the power output delay caused by the inertia link of the wind turbine, the proposed strategy is feasible without wind speed prediction, so the strategy can make full use of the advantages of MPC. In order to verify the effectiveness of the strategy, the traditional PID frequency control strategy and the strategy proposed in this paper are simulated and analyzed in a single-area and four-area microgrid.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This study is financially supported by the National Natural Science Foundation of China (No. 71804177) and the Natural Science Foundation of Hunan Province (No. 2019JJ50455).