Optimal and suboptimal controller design for wind power system
- Reshma Ehtesham^{1}Email author,
- Shahida Khatoon^{1} and
- Ibraheem Naseeruddin^{2}
DOI: 10.1186/s40807-015-0020-2
© Ehtesham et al. 2015
Received: 23 July 2015
Accepted: 13 November 2015
Published: 4 January 2016
Abstract
Wind power is a cost-effective renewable source and can be smoothly integrated into power grid by incorporating adequate control strategies. The wind turbine prime mover, wind, is uncontrollable which makes it different from conventional generation. Therefore, it becomes very important to carry out investigations on the dynamic behavior of wind power-generating systems. In this paper, the state space model of the system is developed, optimal controllers using full-state feedback control strategy and suboptimal controllers using strip eigenvalue assignment method are designed to study the dynamic behavior of the system. Also, the optimal controllers are designed for various operating conditions using pole placement technique. Following the controller designs, the closed-loop system eigenvalues and dynamic response plots are obtained for various system states considering various operating conditions. The investigations of these reveal that the implementation of optimal controllers offers not only good dynamic performance, but also ensures system dynamic stability.
Keywords
Optimal controller Pole placement technique Suboptimal controller Wind power Strip eigenvalue assignment methodBackground
The power system dynamics is essential to be understood for stable system operation. The optimization of the existing resources is necessary for the long term stable operation of the power system. Therefore, the dynamic performance of the wind turbine generator is of concern as it affects the dynamic stability of the system to which it is connected (Al-Duwaish et al. 1999). Focus of power system engineers is currently directed to the impact of wind power on variation in frequency of system. Research efforts concentrate on the ability of wind farms to contribute in the frequency droop events by injecting active power to the grid (Khatoon et al. 2015; Attya and Hartkopf 2012; Chamorro et al. 2013). In George (2011), the impacts of wind power in the electricity grid are analyzed and a technique is presented for planning future electricity grids. In Esteban (2012), wind power uncertainty and its effects on power system adequacy are discussed. Nonlinear characteristics of wind turbine structure and generator operational behavior demand for high-quality optimal controller to ensure both stability and safe performance (Aghdam and Allahbakhsh 2014). In Jackson et al. (2015) it is shown that the optimal state estimation can be effectively used to reconstruct unknown states of a plant influenced by both system and measurement noises. In David et al. (2013) a novel scheme is presented to give dynamic wind speed estimation by measuring rotor angular velocity for small wind turbines. A compromise can be achieved between loads and variation in power without any information of the damping of wind turbine (Yolanda et al. 2012). In Epa (2011), a nonlinear controller is developed for a wind turbine generator based on nonlinear, H_{2} optimal control theory. Therefore, optimal controllers maximize the delivered electrical power thus maximizing the global efficiency of the energy conversion system (Munteanu et al. 2008). The wind turbine generator used is a synchronous generator (Mellow and Concordia 1969a) with a static excitation system. The transient stability signals derived from speed, terminal frequency, or power are superposed on the normal voltage signal of voltage regulator, which provides additional damping to the oscillations (Rabelo et al. 2004; Thomas et al. 1975). A wind turbine generator exhibits an unsteady input behavior mainly because of unsteady wind speeds. This unsteady behavior causes severe oscillations. The transient stability signals derived from speed and terminal frequency are superposed on the normal voltage error signal of automatic voltage regulator, thus providing damping to these oscillations (Padiyar 2006). Also, the damping can be provided using an output feedback and strip eigenvalue assignment technique. The eigenvalues location affects the dynamics of the system. Therefore, it is necessary to locate the eigenvalues at some desired positions. The exact location of all eigenvalues at each operating point is difficult to attain. But a satisfactory response for both transient and steady state can be obtained by placing all eigen values within a suitable region in complex s-plane (Kirk 1970; Sheih et al. 1986).
Wind power system under investigation
Methods
The classical control theory expressed in frequency domain leads to a stable system and satisfies a set of more or less arbitrary requirements. Optimal control recognizes the random behavior of the system and attempts to optimize response or stability on an average rather than with assured precision. The optimal control theory provides a comprehensive, consistent, and flexible design approach. The classical response criteria such as step response are helpful in determining what values to use in quadratic cost function weighting matrices. These weighting factors have a powerful and direct effect on achieving desired response (Lewis and Syrmos 1995; Lee and Wu 1995).
Optimal controller design using full-state feedback control strategy
Suboptimal controller design using strip eigenvalue assignment method
The linear systems are influenced by the locations of eigenvalues. Therefore, for a system to get good response, both in transient and steady states, it is necessary to locate all eigenvalues in desired positions. Due to approximations, it is difficult to attain the exact locations of all eigenvalues. Hence it is sufficient that all eigenvalues are placed within a suitable region in complex s-plane, using strip eigenvalue assignment method.
Optimal controller design using pole placement technique
Most of the conventional design approaches specify only dominant closed-loop poles, while the pole placement design approach specifies all closed-loop poles. The pole placement technique places the poles at any desired locations by means of an appropriate state feedback gain matrix. The MATLAB software is used for placing the poles at desired locations.
Results and discussion
Closed-loop system eigenvalues using optimal controllers
P _{o} = 0.35 | P _{o} = 0.65 | P _{o} = 0.8 | P _{o} = 1.0 |
---|---|---|---|
−20,020 | −20,020 | −20,020 | −20,020 |
−3 + 8i | −2 + 9i | −2 + 9i | −1 + 8i |
−3 − 8i | −2 − 9i | −2 − 9i | −1 − 8i |
−21 | −21 | −21 | −21 |
−17 | −17 | −17 | −17 |
−2 | −2 | −3 | −4 |
−1 | −1 | −2 | −2 |
−1 | −1 | −1 | −1 |
Closed-loop system eigenvalues using suboptimal controllers
P _{o} = 0.35 | P _{o} = 0.65 | P _{o} = 0.8 | P _{o} = 1.0 |
---|---|---|---|
−325.63 + 32.47i | −325.63 + 32.45i | −325.63 + 32.45i | −325.63 + 32.45i |
−325.63 − 32.47i | −325.63 − 32.45i | −325.63 − 32.45i | −325.63 − 32.45i |
−20.61 | −20.61 | −20.61 | −20.62 |
−2.53 + 9.44i | −2.33 + 9.44i | −1.61 + 8.73i | −0.84 + 7.89i |
−2.53 − 9.44i | −2.33 − 9.44i | −1.61 − 8.73i | −0.84 − 7.89i |
−2.19 | −2.19 | −2.91 | −4.42 |
−1.39 | −1.39 | −2.12 | −2.14 |
−1 | −1 | −1 | −1 |
Closed-loop system eigenvalues using optimal controllers based on pole placement technique
P _{o} = 0.35 | P _{o} = 0.65 | P _{o} = 0.8 | P _{o} = 1.0 |
---|---|---|---|
−20,020 | −20,020 | −20,020 | −20,020 |
−21 | −21 | −21 | −21 |
−17 | −17 | −17 | −17 |
−3 + 8i | −2 − 9i | −2 + 9i | −1 + 8i |
−3 − 8i | −2 + 9i | −2 − 9i | −1 − 8i |
−2 | −2 | −3 | −4 |
−1 | −1 | −2 | −2 |
−1 | −1 | −1 | −1 |
Rising and settling time pattern for optimal controller, suboptimal controller and optimal controller using pole placement technique for ω
Point | Rising time (s) | Settling time (s) | ||||
---|---|---|---|---|---|---|
Optimal controller using full-state feedback | Suboptimal controller using output feedback | Optimal controller using pole placement technique | Optimal controller using full-state feedback | Suboptimal controller using output feedback | Optimal controller using pole placement technique | |
0.35 | 1.3e−018 | 1.3e−018 | 1.3e−018 | 3.49 | 3.29 | 2.48 |
0.65 | 0 | 1.3e−018 | 0 | 2.33 | 2.32 | 2.37 |
0.8 | 8.67e−019 | 8.67e−019 | 0 | 2.43 | 2.43 | 1.74 |
1.0 | 0 | 0 | 0 | 4.66 | 4.66 | 3.83 |
Conclusions
In the present work, optimal and suboptimal controllers are designed to study the dynamic performance of the wind turbine generator model at different operating conditions. As the system dynamic model is not stable, pole placement technique is applied to place the poles of the system in stable region. The dynamic response plots and closed-loop eigenvalues are obtained. The designed controllers ensured the closed-loop system stability in the study. Furthermore, the impact of wind power on frequency of the system is seen visible. The various controllers designed in the work are found to exhibit their effect under various operating conditions.
To study the impacts on power generated with the variation in wind speed and hence power, the system is investigated at different operating conditions corresponding to different real power values, keeping the reactive power as constant. The investigations show that with all controllers, the settling time is reduced as the P _{o} is increased. However, it is interesting to note that the settling time has reverse trend at P _{o} = 1 p.u. The trend of the peak shows a considerable improvement, when the dynamic responses obtained using optimal controller and suboptimal controller are compared with pole placement technique.
Declarations
Authors’ contributions
IN gives the original idea of research problem formulation, design methodology and overall supervision of the study and analysis and interpretation of data. SK carried out co-ordination in implementing the work for conception, design, analysis and drafting of the manuscript. RE carried out experimental and simulation work of the problem and performance evaluation of the outcome of the study on the basis of experimental/ simulation results obtained. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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