# Modelling a Wind Turbine in Dymola

Wind turbines are machines designed to harness the kinetic energy of the wind and convert it into electrical energy. They are a form of renewable energy technology, as wind is an abundant and naturally occurring resource. Wind turbines are typically installed in areas with consistent and sufficient wind speeds to generate electricity efficiently. Moreover, wind turbines have played a significant role in the UK’s energy landscape. The UK has been one of the global leaders in the deployment of wind energy, both onshore and offshore. The usage of the turbines in the UK and all over the world has steadily increased over the years due to various factors, including government support, advancements in technology, and a strong commitment to renewable energy.

The system modelling of wind turbines in Dymola is a great option as it provides a comprehensive and dynamic representation of the entire wind turbine system. By integrating the mechanical, electrical, and control components, Dymola allows engineers to analyse the turbine’s performance under various conditions, optimise design parameters, and assess control strategies. In this blog post I will be explaining how to build a basic Wind Turbine System model and I will be integrating the model into a larger system model of the Water Pumping from the Well that I talked about in my previous blog post.

The Model

The wind turbine system is a sophisticated integration of mechanical, electrical, and control components, purpose-built to harness the power of the wind and convert it into eco-friendly and sustainable electrical energy. In this blog post, I will provide a step-by-step demonstration of how to model each component, showcasing the intricacies of their interactions and functionality within the overall system.

Figure 1: The Model of the System of Wind Turbine

List of Components

Mechanical Componets

• Wind Source
• Turbine (Including Inertia)
• Tip Speed Ratio (TSR)
• Pressure Coefficient (Cp)

Electrical Components

• DC Generator
• Battery

Control Components

• Pitch Angle
• Maximum Power Tracking Point by optimal torque (MPPT_OT)

The wind source refers to the incoming wind that interacts with the turbine. The energy available in the wind depends on its speed and density, with higher wind speeds containing more kinetic energy. In our model, we have included four different wind speed levels to represent real-world variations. The turbine is the main component of the wind energy system, consisting of blades mounted on a hub. When the wind blows, it transfers its energy to the blades, making them rotate. In our model, we have simplified the turbine’s behaviour using empirical power calculations. This allows us to analyse how it performs under different wind conditions and optimise its design for better efficiency.

The mechanical power is calculated as

Pm= 0.5ρπR2v3cp(λ, β) (1)

where ρ is density of air, R is turbine radius, v is the speed of wind and cp is power coefficient which is function of λ (Tip speed ratio) and β (blade pinch angle).

The turbine model calculates power by using equation (1) and converts it into torque.

Turbine Torque is obtained as

T = Pmr (2)

where T is torque generated by the turbine model and ωr is angular speed of the turbine shaft.

To calculate the mechanical power generated by the turbine over time using equation (1), the power coefficient cp is required. The power coefficient is a dimensionless parameter that indicates the efficiency of the wind turbine in converting the wind’s kinetic energy into mechanical power. In our model, we determine the power coefficient using an empirical polynomial as described below and this calculated power coefficient is then fed into the turbine model at different time intervals, enabling us to study the turbine’s efficiency and performance under various wind conditions.

Cp = 0.5(λ-0.022β2-5.6)e(-0.17λ) (3)

where λ is the Tip-speed ratio and β is pitch angle.

The empirical polynomial Cp requires variation of pitch angle and tip speed ratio of the turbine in time. The component TSR calculates the tip speed ratio as follows:

λ= ωrR/v (4)

where ωr is angular rotor speed of the turbine, R is the radius of the turbine and v is the wind speed.

Pitch control is a mechanism that adjusts the angle of the turbine blades in response to varying wind conditions. By changing the blade pitch, the turbine can regulate its rotational speed and power output. During high wind speeds, the pitch can be adjusted to reduce the turbine’s rotational speed and avoid mechanical stress excursions or damage. Conversely, during low wind speeds, the pitch can be adjusted to maximize power generation. The component in the model Pitch Control provides pitch angle value in the time domain for the equation (3).

Maximum Power Point Tracking (MPPT) via Optimal Torque (OT) is another control component that is used to maximise the power output of the wind turbine by continuously adjusting the rotor speed. It involves dynamically adjusting the tip speed ratio of the turbine to maintain it at an optimal value corresponding to the current wind conditions. This means that it will produce the most power possible for any given wind condition, resulting in higher energy capture and increased overall performance. The component model MPPT_OT calculates the optimum torque required for the specific wind speed and demands that optimum torque from the generator.

The Optimum torque is calculated as follows

Topt = Koptωr2 (5)

where Kopt is the optimum torque curve gain and defined as

Kopt = (0.5ρπR5 Cpmax )/λopt3 (6)

where Cpmax is the maximum available pressure coefficient and λopt is the optimum tip speed ratio.

The component Generator generates electricity which charges the battery and also generates required reverse torque in the system to maintain the optimum tip speed ratio of the turbine.

RESULTS

The Wind Power model was tested using four different wind sources, and the results are illustrated in figure 2. (Please note that the wind sources are not constant; they fluctuate around the expected wind speed). As evident from the figures, the mechanical power generated by the turbines increased exponentially as the wind speed rose from 5 m/s to 10 m/s. Once the turbine reaches its nominal speed, which can be controlled through the pitch angle controller, both the MPPT and pitch angle controller maintain a constant angular speed, resulting in a consistent power output of approximately 2100 kW for wind speeds of 15 m/s and 20 m/s.

Figure 2: Mechanical Power generated by the turbine and Power coefficients with 4 different wind speed 5m/s, 10 m/s 15 m/s 20 m/s

In Figure 2, it is evident that the Cp values for wind speeds of 5 m/s and 10 m/s are close to the expected maximum value (0.44). However, as the wind speed increases to 15 m/s and 20 m/s, the Cp values decrease significantly to approximately 0.20 and 0.08, respectively. These variations in Cp are attributed to the changes in the pitch angle of the turbine blades, which are clearly depicted in Figure 3. The pitch control mechanism plays a crucial role in adjusting the blade angles to optimise power generation under different wind conditions, thus influencing the overall efficiency of the wind turbine system.

Figure 3: Pitch Angle variation for 4 different wind speed 5 m/s, 10 m/s 15 m/s and 20 m/s

Figure 4: Changes in State of the Charge (SOC) of the Batteries.

As observed from Figure 4, the generator integrated into the model efficiently charges the battery at different time intervals, corresponding to the four different wind speeds tested.

Figure 5: Implementation of the Wind Power into the System of Water Pumping from the Well

As previously mentioned, the wind power model has been successfully integrated into the system model of water pumping from the well. Figure 5 demonstrates the seamless operation of the system, where the 18 water pumps efficiently provide the expected mass flow rate, ensuring a steady water supply. Additionally, the batteries integrated into the system exhibit periodic charging and discharging patterns as anticipated, showcasing the effective energy management capabilities of the combined wind and water pumping system. This integration highlights the potential of renewable energy sources to drive crucial applications like water pumping, offering a sustainable and reliable solution for meeting water demands while reducing dependence on conventional power sources and mitigating environmental impacts.

CONCLUSION

In this blog post, we presented a basic model of a wind turbine system using Dymola, which integrates mechanical, electrical, and control components. The model showcased how the turbine harnesses wind energy and converts it into clean and sustainable electrical power. By analysing the performance under different wind conditions, optimising design parameters, and implementing control strategies, engineers can gain valuable insights into the system’s behaviour.

The results demonstrated that as the wind speed increases, the mechanical power generated by the turbine increases exponentially. However, once the turbine reaches its nominal speed, the control components, such as MPPT and pitch angle controller, maintain the turbine’s angular speed and keep the power output relatively constant. This results in a stable and consistent power generation, even with varying wind speeds.

Finally, if a more detailed wind turbine is required, the Wind Power Library is available for Dymola.

Written by: Kadir Sahin – Project Engineer

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