# Cascade Control of the Ground Station Module of an Airborne Wind Energy System

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## Abstract

**:**

## 1. Introduction

#### 1.1. Related Work

#### 1.2. Research Gap

#### 1.3. Major Contributions

## 2. Modeling of Ground Station Module

#### 2.1. Mathematical Model of Winch

#### 2.2. Mathematical Model of Induction Machine

#### 2.2.1. $d-q$ Model of an Induction Machine in Synchronously Rotating Reference Frame

#### 2.2.2. $d-q$ Model of an Induction Machine in Stationary Reference Frame

#### 2.3. Coupling of Winch and Induction Machine

## 3. Cascade Control Strategy for Ground Station Module

#### 3.1. Sliding Mode Control Design for Winch System

#### 3.2. Rotor-Based Field-Oriented Control of Induction Machine

#### 3.2.1. Torque and Flux Controller Design

#### 3.2.2. Discrete-time Kalman Filter for Flux Estimation

- The initialization of DKF is carried out as:$$\begin{array}{cc}\hfill \phantom{\rule{1.em}{0ex}}& {\widehat{x}}_{0}^{+}=E\left(\right)open="("\; close=")">{x}_{0},\hfill \end{array}$$
- The main algorithm of DKF comprises the following equations, which are sequentially solved for each time step $k=1,2,\dots $$$\begin{array}{cc}\hfill \phantom{\rule{1.em}{0ex}}& {P}_{k}^{-}={F}_{k-1}{P}_{k-1}^{+}{F}_{k-1}^{T}+{Q}_{k-1},\hfill \\ \hfill \phantom{\rule{1.em}{0ex}}& {K}_{k}^{-}={P}_{k}^{-}{C}_{k}^{T}{\left(\right)}^{C}-1,\hfill \end{array}\hfill \phantom{\rule{1.em}{0ex}}& {P}_{k}^{+}=\left(\right)open="("\; close=")">{I}_{5}-{K}_{k}C{P}_{k}^{-}{\left(\right)}^{{I}_{5}}T\hfill & +{K}_{k}{R}_{k}{K}_{k}^{T},$$

#### 3.2.3. Implementation of RFOC on IM

## 4. Results and Discussions

- A variable step MATLAB solver: Ode23t is used to simulate the AWES in Figure 1. The minimum and maximum step sizes used for simulation are 5 $\mathsf{\mu}$s and 50 $\mathsf{\mu}$s, respectively.
- The minimum height of the tether from where the KM is launched into the cross wind flight is ${L}_{min}=50$ m. Whereas, the power production phase is stopped when the tether length reaches its maximum value: ${L}_{max}=150$ m.
- To evaluate the robustness of the control strategy, it is assumed that the wind gusts generate a constant disturbance torque, i.e., $\zeta \left(t\right)=12.4$ Nm in (1). It is important to mention here that we have not used any specific dynamic model of the wind gust. The constant value for the wind gust used was the maximum value of the disturbance considered, corresponding to the simulation of the worst case scenario.
- The desired angular speed of the winch ${\omega}_{{w}_{r}}=10$ r/s for the traction pahse. Positive angular speed refers to counter-clockwise rotation, whereas, negative angular speed indicates clockwise rotation.
- A 5.5 KW IM with rated line-line voltage ${u}_{LL}=400$ V (${u}_{\varphi}=231$ V), operating at 50 Hz is considered for the simulation study. The rated speed, rated torque, and efficiency of the IM are 1461 rev/min (153 r/s), 780 Nm, and $89.6$%, respectively.
- It is assumed that the gain of voltage fed inverter in Figure 2 is unity.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## Nomenclature

${\omega}_{r}$, ${\omega}_{m}$ | electrical and mechanical speeds of rotor of the induction |

machine (IM), respectively $\left(\right)$ | |

${\theta}_{e}$ | electrical angle required for field oriented control of the IM $\left(\mathrm{r}\right)$ |

${\varphi}_{dr}$, ${\varphi}_{qr}$ | d and q axes rotor fluxes, respectively $\left(\mathrm{Wb}\right)$ |

${\varphi}_{opt}$ | optimal rotor flux $\left(\mathrm{Wb}\right)$ |

${i}_{ds}$, ${i}_{qs}$ | d and q axes stator currents, respectively $\left(\mathrm{A}\right)$ |

${R}_{s}$, ${R}_{r}$ | stator and rotor resistances, respectively $\left(\Omega \right)$ |

${L}_{s}$, ${L}_{r}$ | stator and rotor leakage inductances, respectively $\left(\mathrm{mH}\right)$ |

${L}_{m}$ | magnetizing inductance $\left(\mathrm{mH}\right)$ |

${N}_{P}$ | number of pole pairs $\left(\right)$ |

f | frequency of $3-\varphi $ stator |

J | inertia of the IM rotor $\left(\right)$ |

b | damping coefficient of the IM rotor $\left(\right)$ |

${F}_{T}$ | tether tension $\left(\mathrm{N}\right)$ |

${\omega}_{{w}_{r}}$, ${\omega}_{w}$ | desired and measured speeds of the winch $\left(\right)$ |

${T}_{{w}_{c}}$ | torque generated by winch speed controller $\left(\mathrm{Nm}\right)$ |

${T}_{r},{T}_{e}$ | desired and actual induced torques of the IM, respectively $\left(\mathrm{Nm}\right)$ |

${T}_{{w}_{i}}$ | input torque to the winch system $\left(\mathrm{Nm}\right)$ |

${J}_{w}$ | winch inertia $\left(\right)$ |

${b}_{w}$ | damping coefficient of winch $\left(\right)$ |

${r}_{w}$ | winch radius $\left(\mathrm{m}\right)$ |

${N}_{w}$, ${N}_{{}_{IM}}$ | Number of teeth of winch and IM gears, respectively $\left(\right)$ |

## References

- Archer, C.L.; Caldeira, K. Global Assessment of High-Altitude Wind Power. Energies
**2009**, 2, 307–319. [Google Scholar] [CrossRef] [Green Version] - Loyd, M.L. Crosswind kite power (for large-scale wind power production). J. Energy
**1980**, 4, 106–111. [Google Scholar] [CrossRef] - Licitra, G.; Koenemann, J.; Bürger, A.; Williams, P.; Ruiterkamp, R.; Diehl, M. Performance assessment of a rigid wing Airborne Wind Energy pumping system. Energy
**2019**, 173, 569–585. [Google Scholar] [CrossRef] - Cherubini, A.; Papini, A.; Vertechy, R.; Fontana, M. Airborne Wind Energy Systems: A review of the technologies. Renew. Sustain. Energy Rev.
**2015**, 51, 1461–1476. [Google Scholar] [CrossRef] [Green Version] - Weiss, P. Airborne Wind Energy Prepares for Take Off. Engineering
**2020**, 6, 107–109. [Google Scholar] [CrossRef] - Todeschini, D.; Fagiano, L.; Micheli, C.; Cattano, A. Control of a rigid wing pumping Airborne Wind Energy system in all operational phases. Control Eng. Pract.
**2021**, 111, 104794. [Google Scholar] [CrossRef] - Vermillion, C.; Cobb, M.; Fagiano, L.; Leuthold, R.; Diehl, M.; Smith, R.S.; Wood, T.A.; Rapp, S.; Schmehl, R.; Olinger, D.; et al. Electricity in the air: Insights from two decades of advanced control research and experimental flight testing of airborne wind energy systems. Annu. Rev. Control
**2021**, in press. [Google Scholar] [CrossRef] - Salma, V.; Friedl, F.; Schmehl, R. Improving reliability and safety of airborne wind energy systems. Wind Energy
**2020**, 23, 340–356. [Google Scholar] [CrossRef] [Green Version] - Rapp, S.; Schmehl, R.; Oland, E.; Haas, T. Cascaded Pumping Cycle Control for Rigid Wing Airborne Wind Energy Systems. J. Guid. Control Dyn.
**2019**, 42, 2456–2473. [Google Scholar] [CrossRef] - Jehle, C.; Schmehl, R. Applied Tracking Control for Kite Power Systems. J. Guid. Control Dyn.
**2014**, 37, 1211–1222. [Google Scholar] [CrossRef] [Green Version] - Rapp, S.; Schmehl, R.; Oland, E.; Smidt, S.; Haas, T.; Meyers, J. A Modular Control Architecture for Airborne Wind Energy Systems. In Proceedings of the AIAA Scitech 2019 Forum, San Diego, CA, USA, 7–11 January 2019. [Google Scholar] [CrossRef] [Green Version]
- Wood, T.A.; Hesse, H.; Smith, R.S. Predictive Control of Autonomous Kites in Tow Test Experiments. IEEE Control Syst. Lett.
**2017**, 1, 110–115. [Google Scholar] [CrossRef] - Ruiterkamp, R.; Sieberling, S. Description and Preliminary Test Results of a Six Degrees of Freedom Rigid Wing Pumping System. In Airborne Wind Energy; Ahrens, U., Diehl, M., Schmehl, R., Eds.; Springer: Berlin/Heidelberg, Germany, 2013; pp. 443–458. [Google Scholar] [CrossRef]
- Wood, T.A.; Hesse, H.; Zgraggen, A.U.; Smith, R.S. Model-based flight path planning and tracking for tethered wings. In Proceedings of the 2015 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, 15–18 December 2015; pp. 6712–6717. [Google Scholar] [CrossRef]
- Fechner, U.; Schmehl, R. Flight path control of kite power systems in a turbulent wind environment. In Proceedings of the 2016 American Control Conference (ACC), Boston, MA, USA, 6–8 July 2016; pp. 4083–4088. [Google Scholar] [CrossRef]
- Fagiano, L.; Schnez, S. On the take-off of airborne wind energy systems based on rigid wings. Renew. Energy
**2017**, 107, 473–488. [Google Scholar] [CrossRef] [Green Version] - Bontekoe, E. Up! How to Launch and Retrieve a Tethered Aircraft. Master’s Thesis, Delft University of Technology, Delft, The Netherlands, 2010. [Google Scholar]
- Fagiano, L.; Nguyen-Van, E.; Rager, F.; Schnez, S.; Ohler, C. Autonomous Takeoff and Flight of a Tethered Aircraft for Airborne Wind Energy. IEEE Trans. Control Syst. Technol.
**2018**, 26, 151–166. [Google Scholar] [CrossRef] [Green Version] - Rapp, S.; Schmehl, R. Vertical Takeoff and Landing of Flexible Wing Kite Power Systems. J. Guid. Control Dyn.
**2018**, 41, 2386–2400. [Google Scholar] [CrossRef] - Fagiano, L.; Huynh, K.; Bamieh, B.; Khammash, M. On Sensor Fusion for Airborne Wind Energy Systems. IEEE Trans. Control Syst. Technol.
**2014**, 22, 930–943. [Google Scholar] [CrossRef] [Green Version] - Girrbach, F.; Hol, J.D.; Bellusci, G.; Diehl, M. Optimization-Based Sensor Fusion of GNSS and IMU Using a Moving Horizon Approach. Sensors
**2017**, 17, 1159. [Google Scholar] [CrossRef] [PubMed] - Malz, E.C.; Walter, V.; Göransson, L.; Gros, S. The value of airborne wind energy to the electricity system. Wind Energy
**2021**. [Google Scholar] [CrossRef] - Fernandes, M.C.R.M.; Paiva, L.T.; Fontes, F.A.C.C. Optimal Path and Path-Following Control in Airborne Wind Energy Systems. In Advances in Evolutionary and Deterministic Methods for Design, Optimization and Control in Engineering and Sciences; Gaspar-Cunha, A., Periaux, J., Giannakoglou, K.C., Gauger, N.R., Quagliarella, D., Greiner, D., Eds.; Computational Methods in Applied Sciences; Springer International Publishing: Cham, Switzerland, 2021; pp. 409–421. [Google Scholar] [CrossRef]
- Paiva, L.T.; Fontes, F.A.C.C. Optimal electric power generation with underwater kite systems. Computing
**2018**, 100, 1137–1153. [Google Scholar] [CrossRef] - Paiva, L.T.; Fontes, F.A.C.C. Optimal Control Algorithms with Adaptive Time-Mesh Refinement for Kite Power Systems. Energies
**2018**, 11, 475. [Google Scholar] [CrossRef] [Green Version] - Canale, M.; Fagiano, L.; Milanese, M. High Altitude Wind Energy Generation Using Controlled Power Kites. IEEE Trans. Control Syst. Technol.
**2010**, 18, 279–293. [Google Scholar] [CrossRef] - Zanon, M.; Gros, S.; Andersson, J.; Diehl, M. Airborne Wind Energy Based on Dual Airfoils. IEEE Trans. Control Syst. Technol.
**2013**, 21, 1215–1222. [Google Scholar] [CrossRef] [Green Version] - Karg, B.; Lucia, S. Learning-based approximation of robust nonlinear predictive control with state estimation applied to a towing kite. In Proceedings of the 2019 18th European Control Conference (ECC), Naples, Italy, 25–28 June 2019; pp. 16–22. [Google Scholar] [CrossRef]
- Bafandeh, A.; Vermillion, C. Altitude Optimization of Airborne Wind Energy Systems via Switched Extremum Seeking—Design, Analysis, and Economic Assessment. IEEE Trans. Control Syst. Technol.
**2017**, 25, 2022–2033. [Google Scholar] [CrossRef] - Zgraggen, A.U.; Fagiano, L.; Morari, M. Real-Time Optimization and Adaptation of the Crosswind Flight of Tethered Wings for Airborne Wind Energy. IEEE Trans. Control Syst. Technol.
**2015**, 23, 434–448. [Google Scholar] [CrossRef] [Green Version] - Magdy Gamal Eldeeb, H. Modelling, Control and Post-Fault Operation of Dual Three-phase Drives for Airborne Wind Energy. Ph.D. Dissertation, Technische Universität München, München, Germany, 2019. [Google Scholar]
- Eldeeb, H.; Abdel-Khalik, A.S.; Hackl, C.M. Highly efficient fault-tolerant elelctrical drives for airborne wind energy systems. In Book of Abstracts of the International Airborne Wind Energy Conference (AWEC 2017); Diehl, M., Leuthold, R., Schmehl, R., Eds.; University of Freiburg|Delft University of Technology: Freiburg, Germany, 2017; pp. 75–77. [Google Scholar]
- Ebrahimi Salari, M.; Coleman, J.; Toal, D. Power Control of Direct Interconnection Technique for Airborne Wind Energy Systems. Energies
**2018**, 11, 3134. [Google Scholar] [CrossRef] [Green Version] - Silva, G.B.; Paiva, L.T.; Fontes, F.A. A Path-following Guidance Method for Airborne Wind Energy Systems with Large Domain of Attraction. In Proceedings of the 2019 American Control Conference (ACC), Philadelphia, PA, USA, 10–12 July 2019; pp. 2771–2776. [Google Scholar] [CrossRef]
- Fernandes, M.C.R.M.; Vinha, S.; Paiva, L.T.; Fontes, F.A.C.C. L0 and L1 Guidance and Path–following Control for Airborne Wind Energy Systems. Energies
**2021**. submitted. [Google Scholar] - Utkin, V. Variable structure systems with sliding modes. IEEE Trans. Autom. Control
**1977**, 22, 212–222. [Google Scholar] [CrossRef] - Bose, B.K. AC Machines for Drivers. In Modern Power Electronics and AC Drives; Prentice-Hall Inc.: Hoboken, NJ, USA, 2002. [Google Scholar]
- Kim, S.H. Modeling of alternating current motors and reference frame theory. In Electric Motor Control; Kim, S.H., Ed.; Elsevier: Amsterdam, The Netherlands, 2017; Chapter 4; pp. 153–202. [Google Scholar] [CrossRef]
- Kim, S.H. Vector control of alternating current motors. In Electric Motor Control; Kim, S.H., Ed.; Elsevier: Amsterdam, The Netherlands, 2017; Chapter 5; pp. 203–246. [Google Scholar] [CrossRef]
- Teixeira, M.C.M.; Zak, S.H. Stabilizing controller design for uncertain nonlinear systems using fuzzy models. IEEE Trans. Fuzzy Syst.
**1999**, 7, 133–142. [Google Scholar] [CrossRef] - Bose, B.K. Control and Estimation of Induction Motor Drive. In Modern Power Electronics and AC Drives; Prentice-Hall Inc.: Hoboken, NJ, USA, 2002; Chapter 8; pp. 29–97. [Google Scholar]
- Hanif, A. Electric Machine Control Design for Hybrid Electric Vehicles. Ph.D. Thesis, Capital Universiyt of Science and Technology, Islamabad, Pakistan, 2018. [Google Scholar]
- Utkin, V.; Guldner, J.; Shi, J. Introduction. In Sliding Mode Control in Electro-Mechanical Systems, 2nd ed.; CRC Press: Boca Raton, FL, USA, 2009. [Google Scholar]
- Edwards, C.; Spurgeon, S. Sliding Mode Control: Theory And Applications; CRC Press: Londo, UK, 1998. [Google Scholar] [CrossRef]
- Uppal, A.A.; Butt, S.S.; Khan, Q.; Aschemann, H. Robust tracking of the heating value in an underground coal gasification process using dynamic integral sliding mode control and a gain-scheduled modified Utkin observer. J. Process Control
**2019**, 73, 113–122. [Google Scholar] [CrossRef] - Simon, D. The discrete-time Kalman filter. In Optimal State Estimation; John Wiley & Sons Ltd.: Hoboken, NJ, USA, 2006; Section 5; pp. 121–148. [Google Scholar] [CrossRef]
- Hanif, A.; Ahmed, Q.; Bhatti, A.I.; Rizzoni, G. A Unified Control Framework for Traction Machine Drive Using Linear Parameters Varying-Based Field-Oriented Control. J. Dyn. Syst. Meas. Control
**2020**, 142, 101006. [Google Scholar] [CrossRef]

**Figure 2.**Rotor flux-oriented control of IM. (

**a**) Alignment of rotor flux. (

**b**) Rotor flux angle calculation.

Parameter | Value | Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|---|---|

${N}_{p}$ | 2 | ${R}_{s}$ | 0.295 | ${R}_{r}$ | 0.379 | ${L}_{r}$ | 0.0608 |

${L}_{s}$ | 0.0608 | ${L}_{m}$ | 0.059 | J | 0.62 | b | 0.1 |

${b}_{w}$ | 0.01 | ${J}_{w}$ | 0.124 | ${r}_{w}$ | 0.25 | ${N}_{w}/{N}_{IM}$ | 12 |

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## Share and Cite

**MDPI and ACS Style**

Uppal, A.A.; Fernandes, M.C.R.M.; Vinha, S.; Fontes, F.A.C.C.
Cascade Control of the Ground Station Module of an Airborne Wind Energy System. *Energies* **2021**, *14*, 8337.
https://doi.org/10.3390/en14248337

**AMA Style**

Uppal AA, Fernandes MCRM, Vinha S, Fontes FACC.
Cascade Control of the Ground Station Module of an Airborne Wind Energy System. *Energies*. 2021; 14(24):8337.
https://doi.org/10.3390/en14248337

**Chicago/Turabian Style**

Uppal, Ali Arshad, Manuel C. R. M. Fernandes, Sérgio Vinha, and Fernando A. C. C. Fontes.
2021. "Cascade Control of the Ground Station Module of an Airborne Wind Energy System" *Energies* 14, no. 24: 8337.
https://doi.org/10.3390/en14248337