# Output Power Smoothing Control for a Wind Farm Based on the Allocation of Wind Turbines

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Wind Energy Conversion System Description

#### 2.1. Wind Turbine Model

_{p}is power coefficient which is a function of the tip speed ratio (TSR) λ and blade pitch angle β. λ is defined as:

_{o}indicates the rotational speed in rad/s.

_{opt}and then maximize the power coefficient as C

_{pmax}. The wind turbine aerodynamic efficiency C

_{p}(λ, β) is given by the following Equation [21]:

_{p}by using λ and β. The curves of the power coefficient C

_{p}and the TSR λ with different blade pitch angles are shown in Figure 1. It can be seen that the maximum power coefficient is decreasing by increasing the pitch angle. Therefore, the output power of the wind turbine can be limited to the rated value through the variable pitch angle control.

_{opt}is the coefficient associated with the wind turbine characteristics.

#### 2.2. PMSG Model

_{ds}, u

_{qs}are the stator winding voltages in dq-axes. i

_{ds}, i

_{qs}are the stator winding currents in dq-axes. ψ

_{ds}, ψ

_{qs}are the stator winding magnet fluxes in dq-axes. ω

_{e}is the rotor speed, R

_{s}is the resistance of the stator windings.

_{f}is the permanent magnet flux. L

_{d}, L

_{q}are the stator winding inductances in dq-axes.

_{p}is the pole pairs of the PMSG.

_{L}is the input load torque, F is friction coefficient, J is the moment of inertia, ω is the mechanical rotor speed.

#### 2.3. Configuration of the Wind Farm

#### 2.4. Wake Effect Model of the Wind Farm

_{x}is the downstream wind speed, V

_{in}is the free stream wind speed, d is the diameter of the WT rotor, x is the distance between the WTs, k is the wake expansion coefficient which represents the effects of atmospheric stability, and d

_{x}= d + 2kx. In general, k is set as 0.075 for onshore wind farms and 0.05 for offshore wind farms. In this paper, k was set as 0.075. C

_{t}is the thrust coefficient which is usually given by the wind turbine manufacturer or can be calculated according to the simulation software by giving the required data. In this paper, C

_{t}was set as 0.8 when the wind speed was between 3 and 12 m/s by consulting the Vestas V80 type [24].

_{s}is the shade area caused by the other upstream WTs, and A is area of the downstream WT. Most wind farms consist of a large number of WTs, thus the cumulative shade effect of each WT should be considered. Thus, the Equation (13) is modified as

_{si}is the shade area caused by upstream WT i. The method for calculating the shade area is introduced in [24].

## 3. Power Smoothing Control Strategy

#### 3.1. Power Allocation of the PWTs, CWTs and the BESS

_{given}exceeded the maximum capability of the WTs P

_{∑_max}. At this time, the demand power cannot be reached and the BESS will work in the discharging state as shown in the gray box of Figure 4. The discharge power of the BESS was obtained by P

_{given}subtracting the output power of the all WTs. When the maximum output power of the wind farm was more than the demand power, the judgment will be continued.

_{given}subtracting the output power of PWTs. Otherwise, the CWTs were controlled to output the minimum power and the process will continue by comparing the state of charge (SOC) of the BESS with the specified maximum value SOC

_{max}.

_{max}, as shown in the yellow box of Figure 4. At this time the control target of the PWTs should be changed as the reference power of the PWTs were given by P

_{given}subtracting the minimum output power of CWTs. Otherwise, the BESS will be in the charging state, as shown in the blue box of Figure 4 and the main judgment process will continue. The calculated charging power should be compared with the maximum charging power capability of the BESS P

_{ess_max}.

_{ess_max}, the reference charging power was set to the value P

_{ess_max}. Then the reference power of PWTs will be obtained according to P

_{given}, P

_{ess}and P

_{control_min}. If the calculated charging power was less than P

_{ess_max}, the PWTs will be controlled to output the maximum power and the extra power was stored in the BESS. The red digital markers (1)–(3) in Figure 4 are referring to the general power allocation of CWTs and PWTs. The detailed reference power for each CWT and PWT can be obtained according to the wind speed relationship between each WT. Though the Jensen wake effect model is widely used in engineering due to its simplicity, it is not accurate enough in prediction over short-term period, as well as for wind farm application. Thus, the wind speed of each WT needed in the control process was not calculated according to the wake effect model. It can be achieved through the anemoscope simply. Alternatively, short-term wind speed forecasting can be utilized to get the wind speed, which will be studied by authors next.

_{power_max}and P

_{control_max}indicate the maximum output power of the power wind turbines and control wind turbines, respectively. The maximum output power was based on the equation ${P}_{w}=\rho \pi {R}^{2}{C}_{p}(\lambda ,\beta ){v}^{3}/2$ while C

_{p}is the maximum value (0.48 in the manuscript). In the practical application, the efficiency of the wind turbine η should be considered and then ${P}_{power\_\mathrm{max}}=\eta \rho \pi {R}^{2}{C}_{p\mathrm{max}}{v}_{power}^{3}/2$, ${P}_{control\_\mathrm{max}}=\eta \rho \pi {R}^{2}{C}_{p\mathrm{max}}{v}_{control}^{3}/2$. In the simulation, many losses, such as iron loss and mechanical loss, are not considered. Then the efficiency of the wind turbines were relatively high and the efficiency was set as 0.95 in this paper. The minimum output power of CWTs P

_{control_min}can be changed according to the wind speed condition and wind farm or grid demand.

#### 3.2. Control Strategy for the PWTs

_{filter}is the maximum power after low-pass filtering. The rotor inertial power smoothing based MPPT control by adopting the low-pass filter is shown in Figure 5. The cut-off frequency of the low-pass filter is set according to the power smoothing demand of the grid. The lower the cut-off frequency is, the smoother the output power is. T

_{s}is the sampling time of the kinetic energy.

^{*}, the actual speed ω is compared with ω

^{*}and the difference was imported to a Proportional Integral (PI) controller. For realizing the vector control of the PMSG, the real three phase currents (i

_{a}, i

_{b}, i

_{c}) were transformed into direct axis (d-axis) current i

_{ds}and quadrature axis (q-axis) current i

_{qs}through the combination of the Clark transformation and Park transformation (abc/dq) using the rotor position θ. The reference q-axis current i

^{*}

_{qs}was obtained from the speed PI loop. i

_{d}= 0 control was adopted widely due to its simplicity and practicality [28]. Thus, the reference d-axis current i

^{*}

_{ds}was set to zero to simplify the control. The reference current was compared with the actual current and the difference is input to the current PI loop, as shown in Figure 6. Then the reference d-axis voltage U

^{*}

_{ds}and q-axis voltage U

^{*}

_{qs}were achieved from the current PI loops. The reference α-axis voltage U

^{*}

_{αs}and β-axis voltage U

^{*}

_{βs}in the two-phase static frame were obtained according to the inverse Park transformation. The space vector pulse width modulation (SVPWM) method [29] was adopted here to generate the PWM signal of the generator-side converter (S

_{a}, S

_{b}, S

_{c}). The complete control diagram of the PWTs is presented in Figure 6.

#### 3.3. Control Strategy for the CWTs

#### 3.4. Control Strategy for the BESS

_{1}and S

_{2}. The duty ratios of switches S

_{1}and S

_{2}were controlled to regulate the power flow between output power of the nine WTs and grid demand power. The reference power of the BESS was obtained according to Figure 4.

_{1}was controlled to be activated and the BESS was charged, while the DC/DC converter operated in the buck mode. On the contrary, when the output power of the nine WTs was lower than the grid demand power, S

_{2}will be in the turn-on operation and the BESS was discharged while the DC/DC converter operated in the boost mode.

#### 3.5. Evaluation of the Power Efficiency

^{*}

_{level}and maximum energy function P

^{*}

_{max}, which are expressed as [5]:

_{o}(t) is the output power at the time t.

^{*}

_{level}is small, the fluctuation of the output power is small. In other words, the performance of the power smoothing is great. The output power efficiency is also an important factor to power smoothing control method. The efficiency cannot be sacrificed too much for realizing the power smoothing. The larger the maximum energy function P

^{*}

_{max}is, the higher the output power efficiency is. Thus, the two factors will be calculated in the simulation to evaluate the effectiveness of proposed power smoothing control strategy.

## 4. Simulation Results

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**The wake effect model. (

**a**) Jensen model principle; (

**b**) wind turbine distribution structure.

**Figure 9.**Time histories of the wind speed and rotor speed in the wind farm under the maximum power point tracking (MPPT) control. (

**a**) Wind speed of the first group WTs (1–3). (

**b**) Wind speed of the second group WTs (4–6). (

**c**) Wind speed of the third group WTs (7–9). (

**d**) Rotor speed of the first group WTs (1–3). (

**e**) Rotor speed of the second group WTs (4–6). (

**f**) Rotor speed of the third group WTs (7–9).

**Figure 10.**Time histories of the torque, power of WTs in the wind farm under the maximum power point tracking (MPPT) operation mode. (

**a**) Torque of the first group WTs (1–3). (

**b**) Torque of the second group WTs (4–6). (

**c**) Torque of the third group WTs (7–9). (

**d**) Output power of the first group WTs (1–3). (

**e**) Output power of the second group WTs (4–6). (

**f**) Output power of the third group WTs (7–9). (

**g**) Total output power. (

**h**) DC link voltage. (

**i**) Power of the BESS.

**Figure 11.**Time histories of the PWTs in the wind farm under the power smoothing operation mode. (

**a**) Rotor speed of PWTs (1–3). (

**b**) Torque of PWTs (1–3). (

**c**) Output power of PWTs (1–3). (

**d**) Rotor speed of PWTs (4–6). (

**e**) Torque of PWTs (4–6). (

**f**) Output power of PWTs (4–6).

**Figure 12.**Time histories of the CWTs and the wind farm under the power smoothing operation mode. (

**a**) Output power of CWT (WT7). (

**b**) Output power of CWT (WT8). (

**c**) Output power of CWT (WT9). (

**d**) Power of the BESS. (

**e**) Total output power of the wind farm. (

**f**) DC link voltage. (

**g**) Maximum energy function. (

**h**) Power smoothing function.

**Figure 13.**Time histories of the wind farm under the specified power given operation mode. (

**a**) Output power of CWT (WT7). (

**b**) Output power of CWT (WT8). (

**c**) Output power of CWT (WT9). (

**d**) Total output power of the wind farm. (

**e**) Power of the BESS; (

**f**) DC link voltage.

**Figure 14.**Time histories of the wind farm when the wind speed condition of CWTs is changed. (

**a**) wind speed of CWTs. (

**b**) Rotor torque of CWTs. (

**c**) Output power of CWT (WT7). (

**d**) Output power of CWT (WT8). (

**e**) Output power of CWT (WT9). (

**f**) Total output power of the wind farm.

Wind Turbine | PMSG | ||
---|---|---|---|

Blade radius (m) | 35 | Stator resistant (Ω) | 0.01 |

Air density (kg/m^{3}) | 1.225 | Inductance (mH) | 0.835 |

Optimum TSR | 8.1 | Rotor inertia (kg·m^{2}) | 8500 |

Optimum power coefficient | 0.48 | PM linkage (Wb) | 8.76 |

Rated wind speed (m/s) | 12 | Pole pairs | 32 |

Rated power (MW) | 2 | Rated power (MW) | 2 |

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## Share and Cite

**MDPI and ACS Style**

Zhu, Y.; Zang, H.; Cheng, L.; Gao, S.
Output Power Smoothing Control for a Wind Farm Based on the Allocation of Wind Turbines. *Appl. Sci.* **2018**, *8*, 980.
https://doi.org/10.3390/app8060980

**AMA Style**

Zhu Y, Zang H, Cheng L, Gao S.
Output Power Smoothing Control for a Wind Farm Based on the Allocation of Wind Turbines. *Applied Sciences*. 2018; 8(6):980.
https://doi.org/10.3390/app8060980

**Chicago/Turabian Style**

Zhu, Ying, Haixiang Zang, Lexiang Cheng, and Shengyu Gao.
2018. "Output Power Smoothing Control for a Wind Farm Based on the Allocation of Wind Turbines" *Applied Sciences* 8, no. 6: 980.
https://doi.org/10.3390/app8060980