Article Transactions of the Institute of Measurement and Control 1–11 Ó The Author(s) 2019 Article reuse guidelines: sagepub.com/journals-permissions DOI: 10.1177/0142331219834605 journals.sagepub.com/home/tim Gain-phase margins-based delay-dependent stability analysis of pitch control system of large wind turbines Omer Turksoy 1 , Saffet Ayasun 2 , Yakup Hames 1 and Sahin Sonmez 2 Abstract This paper investigates the effect of gain and phase margins (GPMs) on the delay-dependent stability analysis of the pitch control system (PCS) of large wind turbines (LWTs) with time delays. A frequency-domain based exact method that takes into account both GPMs is utilized to determine stability delay margins in terms of system and controller parameters. A gain-phase margin tester (GPMT) is introduced to the PCS to take into GPMs in delay margin computation. For a wide range of proportional–integral controller gains, time delay values at which the PCS is both stable and have desired sta- bility margin measured by GPMs are computed. The accuracy of stability delay margins is verified by an independent algorithm, Quasi-Polynomial Mapping Based Rootfinder (QPmR) and time-domain simulations. The time-domain simulation studies also indicate that delay margins must be deter- mined considering GPMs to have a better dynamic performance in term of fast damping of oscillations, less overshoot and settling time. Keywords Delay margin, direct method, gain-phase margins, large wind turbines, pitch control system, QPmR algorithm, stability Introduction When the wind speed is below the nominal speed, the system behaves like a variable speed wind turbine system and oper- ates at maximum energy conversion conditions. When the wind speed is above the nominal speed, the system changes the blade angle so that the output power remains at nominal value (Anjun et al., 2013; Jafarnejadsani et al., 2013; Li et al., 2016). According to these changes in wind speed, the blade angles of the turbine are controlled by the pitch control unit (Anjun et al., 2011; Geng and Yang, 2010; Liao et al., 2014; Schuler et al., 2013). The pitch control of LWT is realized by two types of drive models, hydraulic pressure model and elec- tric drive model. The hydraulic pressure unit model is more commonly used in large power wind turbine systems than the electric drive model because it provides more torque. However, this hydraulic pressure unit introduces a time delay, which may cause instabilities (Gao and Gao, 2016). Time delays are often a source of adverse effects in dynami- cal systems of the LWT, such as oscillations and poor dynamic performance (Choi and Hammer, 2018; Firouzbahrami and Nobakhti, 2017; Novella et al., 2017). It is also well-known that such time delays may reduce the control system damping performance and even could cause instability if they exceed the upper bound or delay margin for stability. Therefore, time delays should be taken into account in the stability analysis and control design of large wind turbines (LWTs). There are several studies in the literature that focus on the adverse effect of time delays on the pitch controller of LWTs (Ren et al., 2016; Van and Lee, 2012; Wang et al., 2011). In their approach, they consider stability as the only design cri- terion and the boundary of the stability region represents proportional–integral (PI) controller gains for which the pitch control system (PCS) is marginally stable. Even though the approaches all possible PI controller gains that ensure the sta- bility of PCS, they have the following two main drawbacks. First, from a practical point of view, time delays that occur in PCS are not known in advance and thus they are usually ignored in tuning PI controller gains. However, time delays reduce the dynamic performance of the controller. For this reason, it is vital to determine the value of the maximum time delay defined as the delay margin for fixed PI controller gains such that the pitch controller will be not only stable but also satisfies desired gain and phase margins (GPMs). For a given PI controller gains, delay margin computation is not reported in the previous studies. Second, in the PI-based pitch controller design, the asymp- totic stability or marginal stability is a necessary condition to 1 Department of Electrical and Electronics Engineering, Iskenderun Technical University, Turkey 2 Department of Electrical and Electronics Engineering, Nigde O ¨ mer Halisdemir University, Turkey Corresponding author: Yakup Hames x, Department of Electrical and Electronics Engineering, Iskenderun Technical University, 31200 Iskenderun/Hatay, Turkey. Email: yakup.hames@iste.edu.tr