# Tip Speed Ratio Optimization: More Energy Production with Reduced Rotor Speed

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## Abstract

**:**

## 1. Introduction

#### 1.1. The Wake Loss Problem and Its Significance

^{2}, below natural gas (~482 W/m

^{2}), nuclear (~241 W/m

^{2}), oil (~195 W/m

^{2}), coal (~135 W/m

^{2}), solar (6–7 W/m

^{2}), and even geothermal (2–3 W/m

^{2}) [5]. This is one of the main reasons that wind energy amounts to only about 7% of the world’s electricity generation after all the progress made in recent decades [6]. Expanding wind farms’ power density and wind energy’s contribution to global electricity generation requires viable solutions for reducing wake losses. This paper presents a potential solution to address this problem partially.

#### 1.2. Existing Solutions: Wind Farm Layout Optimization and Active Control Strategies

#### 1.3. The Proposed Solution: TSR Optimization

**What is this article’s proposed solution and its rationale?**The proposed solution is to deviate from the TSR that maximizes an individual turbine’s efficiency in the interest of the entire farm as a whole. Such deviation would decrease the adjusted turbine’s production; however, it weakens its wake, increasing its downstream counterparts’ output. Figure 1 presents a small sample of the data generated in this research to provide a better demonstration of the proposed solution. The figure illustrates the solution for a three-turbine section of a column within a wind farm for one wind direction aligned with the column. Figure 1a shows the case of maximizing every turbine’s efficiency. The maximum achievable power coefficient for the studied turbines (SWT-2.3-93) is 0.4454, which one can achieve by setting the TSR at 9.2. Turbine manufacturers provide such data. The first turbine produced 77.9 MWh per year in this wind direction. The overall amount of energy reaching the second turbine was 69.6 MWh, leading to its production of 69.6 MWh × 0.4454 = 31.0 MWh. The energy received by the third turbine throughout the year in this wind direction was 49.6 MWh, resulting in the production of 49.6 MWh × 0.4454 = 22.1 MWh. Hence, these three turbines’ total annual energy production in this one direction was 131 MWh. Figure 1b shows the production of these turbines after adjusting the TSRs. The efficiency of all three turbines decreased to 0.3911, 0.3423, and 0.3638, respectively. Hence, the production of the first turbine decreased to 68.4 MWh. This increased the energy received by the next two turbines so that their production increased to 33.8 MWh and 32.9 MWh, although their efficiency had decreased. The total annual energy production in this wind direction increased to 135.1 MWh, 4.1 MWh (~3.13%) more than the baseline case.

**What is the novelty and significance of this research?**This study proves that optimizing each individual turbine’s efficiency would not maximize the farm’s AEP. The study demonstrates that a real-time optimization and control of TSR for every turbine and wind direction can save a significant amount of AEP while reducing the blades’ rotational speed on average, which offers several environmental and structural improvements, including reduced noise, bird/bat accidents, and leading-edge erosion. In addition, this solution does not require any significant additional hardware upgrade and does not add to the load that blades experience.

**What is this article’s approach to examining the effectiveness of TSR optimization?**This research utilized the Jensen wake model and the Particle Swarm Optimization to find the optimal TSR of the turbines of a utility-scale wind farm for every wind direction with a 5-degree increment. The analysis shows a 4% increase in AEP and an 8% reduction in the farm’s average TSR. These are both significant improvements. A detailed description of the investigated wind farm follows this section. Section 3 explains the employed methodologies. Furthermore, finally, detailed results are presented and discussed in Section 4.

## 2. Case Study

## 3. Methodology

#### 3.1. Optimizing TSR

**Figure 5.**Wind data recorded at the hub height level ($h=$ 63 m). Weibull parameters of the illustrated speed distribution are ${c}_{w}=9.42$ and ${k}_{w}=2.41$ [2].

#### 3.2. The Jensen Model

#### 3.2.1. The Formulation

#### 3.2.2. The Validation

#### 3.3. Modeling the TSR Effect

## 4. Results and Discussion

#### 4.1. Annual Energy Production

#### 4.2. Other Advantages

- First, altering the TSR does not lead to any additional loading on the blades since the rotor still operates under normal conditions and is not misaligned in any direction. One only needs to increase the load applied to the generator to make it harder or easier to rotate. This can be achieved via electronics and does not require any mechanical modification.
- The proposed strategy appears to decrease the TSR overall. For the case of Lillgrund investigated in this article, the farm-averaged TSR decreased by more than 8%. A reduced TSR is equivalent to a slower rotor, and a slower rotor generates less noise since turbines’ noise is primarily created by the giant blades cutting through the air, which is a serious environmental issue surrounding the wind energy industry [34,35]. So, an active TSR optimization not only enhances AEP, it reduces noise pollution.
- Slowing down the rotor helps reduce bird and bat collisions, which is a serious issue that needs to be addressed. Recently, an energy company was given five-year probation and ordered to pay approximately $8 million in fines as their wind turbines caused the death of 150 bald and golden eagles [36]. Decreasing a wind farm’s overall TSR can help with such accidents.
- The proposed strategy enhances the performance of wind turbines by relaxing the leading-edge erosion (LEE) phenomenon. LEE is the deterioration of a wind turbine blade’s leading edge by airborne particles such as sand, dust, rain, and insects [37]. Such erosion decreases the blade’s lifespan and aerodynamic efficiency, which eventually reduces the farm’s AEP. Slowing down the blades via TSR optimization contributes to addressing such LEE-induced issues.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Detailed Power and Energy Production Data

**Figure A1.**Blue line shows each turbine’s relative power production in every wind direction without applying a TSR optimization. Red line shows the relative power production after applying a TSR optimization.

**Figure A2.**Blue line shows each turbine’s AEP in every wind direction in GWh without applying a TSR optimization. Red line shows the AEP after applying a TSR optimization.

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**Figure 1.**Solution: (

**a**) optimizing TSR to maximize every individual turbine’s efficiency, leading to a total energy production of 131 MWh, (

**b**) optimizing TSR to maximize the total AEP, leading to 135.1 MWh.

**Figure 3.**Power curve of SWT-2.3-93 turbine [2].

**Figure 6.**Comparing results obtained from our Jensen implementation and those of CFD [31].

**Figure 7.**Optimizing TSR in 150°: (

**a**) Optimal TSR values, (

**b**) Changes in power production, (

**c**) Changes in AEP.

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**MDPI and ACS Style**

Hosseini, A.; Cannon, D.T.; Vasel-Be-Hagh, A.
Tip Speed Ratio Optimization: More Energy Production with Reduced Rotor Speed. *Wind* **2022**, *2*, 691-710.
https://doi.org/10.3390/wind2040036

**AMA Style**

Hosseini A, Cannon DT, Vasel-Be-Hagh A.
Tip Speed Ratio Optimization: More Energy Production with Reduced Rotor Speed. *Wind*. 2022; 2(4):691-710.
https://doi.org/10.3390/wind2040036

**Chicago/Turabian Style**

Hosseini, Amir, Daniel Trevor Cannon, and Ahmad Vasel-Be-Hagh.
2022. "Tip Speed Ratio Optimization: More Energy Production with Reduced Rotor Speed" *Wind* 2, no. 4: 691-710.
https://doi.org/10.3390/wind2040036