Wind Farm Benchmark Model

This paper considers an advanced wind farm simulation benchmark model developed in the EU- FP7 project, AEOLUS [112]. The model allows control designers to develop and investigate farm level control solutions under various operating conditions for an optional quantity and layout of wind turbines installed in a wind farm. In the benchmark model, sensor models are updated as noise-contaminated, uncertain measurement systems. Moreover, different wind fields with

151 arbitrary mean wind speeds and turbulence intensities can be generated and applied in order to facilitate the assessment of the robustness features of any control solution under external disturbances. The default wind farm layout is shown in Figure 5.1.

Figure 5.1 Wind farm layout (D1=600m, D2=500m, D3=300m).

Figure 5.2 Illustration of the overall wind farm structure (This figure is based on [112]).

Figure 5.2 illustrates the overall structure of the wind farm under consideration. As it is shown in Figure 5.2, this benchmark model is composed of four major components:

Network Operator: The network operator determines the active power demand 𝑃_𝐷 required for safe and reliable connection of wind farm to the electrical grid. The baseline model for network operator can function in different modes such as: absolute, delta, and frequency regulation modes. Basically, in the frequency regulation mode used in this paper, the measured grid frequency 𝑓𝑚(𝑘)

is used as a feedback signal to set up active power control in real-time and maintain the necessary balance between power generation and loads, which in turn regulates the grid frequency to its reference value 𝑓𝑟, despite a changing grid load. As presented in the following equations (5.1) and

D2 D1 D1 D2 D1 D3 D3 T5 T1 T2 T3 T4 T6 T7 T8 T9 T10

Wi

nd

Wind Turbines Wind Field

Network Operator Wind Farm

152 (5.2), the baseline model includes a dead-band proportional gain control which employs frequency error 𝑓𝑒(𝑘) in (5.1) to determine the total demanded power 𝑃𝐷(𝑘) at the time step 𝑘 in (5.2). This

simple control scheme regulates the grid frequency to its reference value (e.g., 50 Hz in large areas of the world or any other frequencies).

𝑓𝑒(𝑘) = 𝑓𝑚(𝑘) − 𝑓𝑟 (5.1) 𝑃𝐷(𝑘) = { 0.5(𝑃1) −𝑑 ≤ 𝑓𝑒(𝑘) ≤ 𝑑 0.5(𝑃1− 𝑃2) 𝑓𝑒(𝑘) ≥ 𝑐 0.5(𝑃1+ 𝑃2) 𝑓𝑒(𝑘) ≤ −𝑐 0.5(𝑃₁) − 0.5(𝑃₂) (𝑓𝑒(𝑘) − 𝑑 𝑐 − 𝑑 ) 𝑑 < 𝑓𝑒(𝑘) < 𝑐 0.5(𝑃1) − 0.5(𝑃2) ( 𝑓_𝑒(𝑘) + 𝑑 𝑐 − 𝑑 ) −𝑐 < 𝑓𝑒(𝑘) < −𝑑 (5.2)

In (5.2), the used 𝑐 and 𝑑 are two constants (𝑐 > 𝑑) defined by user to represent control and dead bands, respectively. Moreover, 𝑃₁ and 𝑃₂ are power parameters defined in (5.3) and (5.4), respectively.

𝑃₁ = 𝑃_𝑚𝑎𝑥 + 𝑃_𝑚𝑖𝑛 (5.3)

𝑃₂ = 𝑃_𝑚𝑎𝑥 − 𝑃_𝑚𝑖𝑛 (5.4)

The power range [𝑃_𝑚𝑖𝑛 , 𝑃_𝑚𝑎𝑥] in (5.3) and (5.4) denotes, respectively, the prescribed minimum and maximum limits for the total power generated by the wind farm.

Wind Farm Controller: As can be seen in Figure 5.2, the wind farm controller plays an interface

role which ensures appropriate distribution of total demanded power 𝑃_𝐷 among wind turbines in the farm while providing an estimate of total available power 𝑃𝐴 in the wind farm to the operator

(e.g., in the case of delta mode operator). The baseline wind farm controller in (5.5) carries out operations using a proportional distribution algorithm which sends a set of power demands 𝑃𝑑,𝑞(𝑘)

at the time step 𝑘 (i.e., 𝑃𝑑,𝑞 in Figure 5.2) to each of 𝑁 individual turbines based on a simple

estimate of their currently available powers 𝑃_𝑎,𝑞(𝑘) and the total available 𝑃_𝐴(𝑘) and total demanded 𝑃𝐷(𝑘) powers in the wind farm.

𝑃𝑑,𝑞(𝑘) = 𝑃𝐷(𝑘)

𝑃𝑎,𝑞(𝑘)

153

Wind Turbines: This component simulates the dynamics of the wind turbines installed in the

farm based on the measured nacelle wind speed 𝑉𝑛𝑎𝑐, effective wind speed 𝑉𝑟𝑜𝑡, and power

demands 𝑃𝑑,𝑞 at each individual turbine. Each turbine is represented using a simple model of an

offshore 5 MW baseline turbine proposed by the U.S. National Renewable Energy Laboratory (NREL) (see [70]). As it is shown in Figure 5.3, the baseline control system in each individual wind turbine basically acts upon the power demand 𝑃𝑑,𝑞 in (5.5) specified by the wind farm

controller. To this end, the turbine’s baseline control system employs a blade-pitch controller as well as a torque controller to compute appropriate blade-pitch reference 𝛽𝑟,𝑞 and generator torque

reference 𝜏_𝑟,𝑞, respectively. The blade-pitch controller is basically a PI (proportional-integral) controller to track a constant generator speed called rated generator speed so that the turbine operates at its rated power in the full-load region. The torque controller is designed by varying the generator torque to optimize power capture in the partial-load region, and to improve output power quality in the full-load region. In other words, the torque controller is set to be active for changing the torque in both the below and the above rated wind speeds. A more complete description of the wind turbine benchmark model can be found in [70].

Figure 5.3 The 𝑞th wind turbine in the farm (𝑞 = 1, 2, … , 𝑁). Note that in addition to the generated power 𝑃_𝑔,𝑞, the turbine model provides many other measured variables.

With respect to the outputs, the components of wind turbines in Figure 5.2 generate a set of outputs including a set of measurements 𝑴𝒆𝒔 required for use by the wind farm controller along with a set of coefficients of thrust 𝑪𝑻 for turbines, necessary to calculate the wake effects (i.e., low

speed turbulent air flows behind turbine) by wind field component.

Wind Field: The interactions between the wind turbines installed in a wind farm can be represented

through the wind field model. This model simulates the wind speed throughout the farm based on

Wind Turbine # q Local Wind Profile Baseline Control System 𝛽𝑟.𝑞 𝜏𝑟,𝑞 𝑃𝑔,𝑞 𝑃𝑑,𝑞 ⋮ 𝐶𝑇,𝑞

154 an ambient field model together with a wake model which describes wakes meandering behind turbines and their effects on the ambient wind field.