Evaluation of different APC operating strategies considering turbine loading and power dynamics for grid support

This work focuses on the design, implementation, and implications of different operational strategies for wind turbines when providing active power control (APC). APC is a necessary functionality for contributing to the stabilization of the electrical grid. Specifically, two different operational strategies are used as the foundation for a model-based control design that allows the turbine to follow a given power demand. The first relies on keeping a constant rotational speed while varying the generator torque to match the power demand. The second approach varies both, the generator torque and rotational speed of the 5 turbine to yield the desired power output. In the power reduction mode, both operational strategies employ the pitch to maintain the desired rotational speed of the turbine and therefore desired power output. The attainable power dynamics of the two closedloop systems to varying power demands are analyzed and compared. Reduced-order models formulated as transfer functions and suitable for the integration into an upper-level control design are proposed. It is found that the first strategy involving only the generator torque while keeping a constant rotational speed provides significantly faster power control authority. Further, 10 the resulting fatigue loading in turbulent wind conditions is briefly discussed for the two operational strategies, where constant operational storage is emulated to enable a bidirectional variation of the power output. Without any additional load reducing control loops, the results also suggest that this operational strategy is more favorable with regard to the resulting loading of the turbine structure. The simulation studies are conducted for the 5 MW reference turbine using FAST.

To achieve the desired grid stabilizing functionality, power system studies usually consider the turbine as a variable and 25 adjustable power source (Margaris et al., 2012). For participation in grid stabilization, local control loops may be designed on the turbine level resulting in a variation of the power output depending on the measured states of the electrical grid, see e.g., the droop-based approaches in (Margaris et al., 2012;Van de Vyver et al., 2016;Abouzeid et al., 2019) or the comparison of different approaches in Jain et al. (2020). Moreover, wind turbines may be clustered with other distributed power generators into a virtual power plant aiming for a coordinated response governed by a central control scheme. For the design and 30 implementation of these control loops, however, knowledge about the attainable dynamics of the energy conversion system are necessary (Xin et al., 2013;Björk et al., 2021). As a result, simple models are needed capable of portraying the relevant dynamics emerging from power tracking operation of wind turbines.
On the wind turbine level, APC results in an enlarged operational range that needs to be coped by the wind turbine controller compared to the usual strategy that aims for a maximization of the power output in partial-load region and a limitation of power 35 above rated wind speed (Aho et al., 2016;Pöschke et al., 2020;Jain et al., 2020). The operating trajectory that results in the desired power output, however, is not unique and therefore depends on the choice of the operational scheme encoded in the control strategy. This can be illustrated by considering the generator power given as where ω g and T g are the rotational speed and generator torque, respectively, and v represents the current effective wind speed.

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From (1), it is apparent that a variation of power output to the demand can be achieved by an adjustment of either the rotational speed, the generator torque, or both. Consequently, there is a need to study the implications of different operating strategies for power tracking with regard to the structural loading and the attainable dynamics seen by the electrical grid. An insightful comparison addressing the loading using two different operational schemes to follow a variable power demand is given by Aho et al. (2016). By additionally proposing reduced order models obtained from the simulation data, this paper aims to feed 45 the discussion on the integration of dynamical turbine models for control design and simulation studies of large-scale power systems. The employed model-based control framework allows to enforce similar turbine dynamics with respect to the wind in both investigated schemes, such that fundamental properties only influenced by the operating strategy and subject to varying power demands may be revealed and discussed.
2 Operating strategies 50 For this study, two different operating strategies are chosen and compared. In the first strategy, termed OS1 in the following, the demanded power is achieved by a variation of the generator torque only while keeping the rotational speed at its nominal value at the current wind speed. Contrarily, in OS2 the controller enforces a variation of both, the generator torque and rotational speed to meet the power demand. Compared to other strategies involving the limited extraction of rotational energy to support frequency events, the control strategies presented here are conceptualized to enable a permanent operation at the desired power 55 level. With ω opt (v) and T opt (v) being the optimal (or limited above rated power) rotational speed and generator torque depending on the current effective wind speed v, and p d is normalized desired power output of the turbine, the two strategies used for turbine operation are formalized as follows OS1 : (2) 60 OS1 employs the generator to produce the desired power by a reduction of the torque directly proportional to the demand p d . In this strategy, the controller is set to enforce the same rotational speed irrespective of the power output demand p d by an adjustment of the pitch. Contrarily, in OS2 a reduction of both, the rotational speed and the generator torque setpoints proportional to √ p d are designed also incorporating regulation by pitching. The minimum rotational speed was limited to ω min = 0.75 (or 9.1 rpm for the 5 MW reference turbine) to avoid hitting the first tower eigenfrequency with the 3P excitation of the rotation; see the Campbell diagram for the reference turbine in Jonkman and Jonkman (2016). To achieve this, the operating point depending factor l ω (v,

Control design
The continuous description of the desired operational strategies encoded in (2) is discretized at 280 operating points each. The steady-state inputs of the wind turbine are derived for the corresponding operating points, and subsequently, a linearization resents the nominal operating strategy used in wind turbine control for energy maximization. Fig. 1 shows that the introduction of reduced power modes enlarges the range of possible operating points and consequently dynamics that the controller needs to cope with appropriately.
The identified linear model dynamics gained by the linearization procedure are then interconnected to form an overall nonlinear description in a so-called Takagi-Sugeno structure. The framework is based on the definition of convex membership functions spanning across the entire operational range, which blend the individual linear submodels in operation depending on the current power output demand, operational strategy, and wind speed.
The control design procedure yields a disturbance observer-based control scheme. Therein, the observer estimates the current effective wind speed by a measurement of the rotational speed. This estimate is used in the calculation of the current operating conditions influencing the membership functions in the nonlinear modeling framework. Further, the estimate determines the 85 calculation of a feedforward term in the control input of the turbine. Details about the applied control scheme and its design process are discussed in (Pöschke et al., 2020). Whereas in (Pöschke et al., 2020) several degrees of freedom including tower or drivetrain dynamics are considered, the applied controller in this work uses the rotational dynamics as only degree of freedom and measured quantity. The control design here follows the lines of the procedure for the rotational dynamics in (Pöschke et al., 2020). It embeds the feedback gain design into a linear matrix inequalities-based optimization problem involving the 90 stability of the closed-loop dynamics. Additional constraints may be introduced to account for performance criteria like decay rates or active damping supplied by the control system in a wide operational range aiming for load reduction at specific turbine components. The model-based design process can be applied to widespread linearization points determined by the control engineer's choice of operational strategy.
Whereas in (Pöschke et al., 2020) OS1 is applied for the simulation studies involving power tracking and load analysis, 95 within this work OS2 is added into the operational spectrum. Effectively, this is achieved by introducing an additional variable as the premise in the Takagi-Sugeno framework used for the nonlinear modeling of the turbine dynamics. This has no effect on the general control approach but introduces an additional dimension in the operating space coped by the premise variables.
Even though we present the two operational strategies separately to underline the comparison of resulting loading and power tracking dynamics for the electrical grid, essentially the turbine is operated by one controller that is capable of blending and 100 switching between the different operational strategies.
Application of the described control scheme to the FAST (Jonkman and Buhl, 2005) implementation of NREL's 5 MW reference turbine (Jonkman et al., 2009) allows studying the impact of the two operational strategies on the loading and the response time for changes in the power output. The pitch speed is limited to 8 deg/s in all considered scenarios. In the following two 105 sections, the discussed operational strategies are compared from two different perspectives. First, the loading of the turbine structure in some components is briefly analyzed in turbulent wind as this influences the possible choice of operating trajectories with regard to the overall cost of energy. Second, the response time of the power output to instantaneous changes in the power demand is compared for the two operational concepts. Due to the possibly fast dynamics needed in the range of milliseconds to hours (Machowski et al., 2008), the attainable power dynamics of wind turbines is a crucial metric for a successful 110 contribution to grid stabilizing services.
Essentially, the same controller is used for turbine operation in the two strategies. It is capable of blending between the operational strategies as shown in Fig. 2 (a). Therein, it is illustrated how the operational strategy is varied from OS1 at 160 s to OS2 within 15 s, which results in a reduction of the rotational speed until matching the trajectory for the operation of the turbine in OS2 only with the same wind excitation. Subsequently, the opposite change of operational strategy is conducted 115 from 195 s to 210 s. While a small delay in the reduction and increase of rotational speed due to the rotor inertia is visible, the controller is capable of altering the operational strategy online and the turbine trajectories smoothly follow the demand. In Fig. 2 (b) and (c) the resulting generator torque and power output of the turbine are visualized. It can be observed that the two operational strategies OS1 and OS2 result in approximately the same power production, which in this case was set to demand 70% of the available power (or p d = 0.7). When transitioning from OS1 to OS2, an increase of output power is apparent in 120 a time range from 160 s to approx. 175 s, which stems from the energy released due to the decline in rotational speed being previously stored in the turbine rotation. Consequently, the opposite effect is visible when returning to nominal rotational speed by blending from OS2 to OS1 in the time range of 195 s to 210 s.

Loading in turbulent wind
To compare the structural loading, the turbine was simulated in a turbulent wind field for 40 min, where the power output can 125 be seen in Fig. 2 (d). The wind time series was synthesized using TurbSim (Jonkman and Buhl, 2006) and configuring a normal turbulence model at a mean wind speed of 12 m/s. The rotational speed and power output of the turbine in a time range from 150 s to 260 s are given in Fig. 2 (a) and (c), respectively. The power demand is set to p d = 0.7 to emulate an operational power storage of 30% that can be released into the electrical grid by a variation of the power demand (and of course the opposite way). This flexibility for a reaction to changes in the electrical grid comes at the expense of a 30% reduced energy yield, in 130 this synthesized case.
In Fig. 3 (a), the resulting damage equivalent loads (DELs) of different turbine components are visualized. Therein, the DELs for operational strategy OS2 are normalized to the results when operating the turbine in strategy OS1. An increase in both, tower fore-aft (TwrBsMyt) and tower side-to-side (TwrBsMxt) loading of 14.4% and 21.6% can be observed, respectively.   compared to OS1. The pitch activity is greatly affected by the employed operational concept, as can be seen by the 37.8% increase in actuator duty cycle (ADC) (Riboldi, 2016).

Discussion: Loading in turbulent wind
Surprisingly, the fatigue loading of the tower is not reduced in OS2, despite of the fewer blade-tower interactions due to the reduced rotational speed, as can be seen in Fig. 3 (a). The simulation results suggest that the greater pitch magnitudes for reacting to the varying wind speed in OS2 compared to OS1, along with the strong coupling of the tower to the pitch movement (Bossanyi, 2003), is responsible for this effect. These results differ from the findings in (Aho et al., 2016), where a reduction in tower loading was predominantly observed in comparable operating scenarios as discussed here. The greater pitch magnitudes 145 needed for balancing the rotational speed to the desired value are also visible in the increased ADC for OS2 shown in Fig. 3 (a), which aligns well with the findings in (Aho et al., 2016). The blade loading is positively affected when operated at a lower rotational speed in OS2 as also reported in (Aho et al., 2016), especially in flapwise direction.
While we have designed a basic controller that only operates based on the rotational speed measurement, the resulting load profiles may be influenced by the introduction of additional performance shaping control architectures. To achieve this, addi-150 tional degrees of freedom may be introduced into the modeling and design process, yielding feedback loops actively shaping the closed-loop dynamics of components like the drivetrain or the tower movement, as discussed in e.g., (Bossanyi, 2003) or specifically for the applied disturbance observer-based approach used here in (Pöschke et al., 2020). From this perspective, the discussed results within this work constitute a fundamental confrontation of operational strategies without any further load reducing measures. This is supported by our approach to yield similar closed-loop dynamics for both operational strategies by 155 an identical definition of performance constraints formulated in the model-based design process, which results in the similar evolution of the power output that can be seen in Fig. 2 (d).

Power tracking dynamics
To provide flexible, fast, and predictable control authority to grid stabilizing services and the control loops therein, the response characteristic to changes in the power demand is crucial. To assess the dynamics involved, the turbine is faced with instan-  The different operating strategies yield varying amounts of ultimate loading depending on the considered structural turbine component, wind speed and magnitude of the power demand step, which is shown in Fig. 4. The greatest absolute increase in ultimate loading for all considered components is found for a wind speed of 12 m/s, which is an information shadowed by the 180 normalization in Fig. 4 The results reveal the dependency of the response characteristic on the employed operational strategy. For OS1, very fast responses to the step demand are possible. This aligns with (Aho et al., 2016), where an increased power tracking performance is found when keeping the rotational speed constant and varying the power with the torque only. The response illustrated in Figure 5. Comparison of step response to the synthetic transfer functions G OS1/OS2 (s) designed for control design and simulation studies on a power system level. Fig. 3 (b) reveals a first-order dynamic behavior in OS1 that can be accounted to the generator torque dynamics used in the simulation model. It is observed that the first-order dynamics is present irrespective of the current wind speed, step magnitude, 190 or direction of step. In the frequency domain, this transfer function can be given as with timescale T OS1 governed by the generator torque loop. It is found sufficient for describing the power demand dynamics of the wind turbine if a strategy like (or very similar to) OS1 is chosen by the turbine control engineer. The step response of the transfer function with T OS1 = 20 m/s is shown in Fig. 5. 195 If, however, acceleration and deceleration of the turbine is involved in meeting the desired power demand as defined for OS2, the attainable power dynamics depends on the current operating point and direction of the step demand as illustrated in Fig. 4 (c). As a result, an adequate model of the active power dynamics for this strategy depends on the current operating point and step magnitude, revealing the nonlinearities inherited in the system. From Fig. 5 it can be observed that especially an increase in power, i.e., ∆p d > 0 results in varying response dynamics due to the varying levels of excess power when 200 increasing the power demand 1 . Further, it can be observed that the resulting power dynamics is governed by the applied control scheme, which is the cause for the non-minimum phase behavior seen at some operating trajectories. Essentially, this behavior is observed when operating the turbine in partial-load region (i.e., in the simulated cases for a wind speed of v = 8 m/s), where the generator torque is employed to control the rotational speed. When the power command increases, the altered rotational speed setpoint results in a reduction of the generator torque by the controller to allow turbine acceleration. This effect necessitates an 205 extension of the transfer function assigned to OS1 to account for this kind of non-minimum phase behavior that usually is also an important aspect in the modeling of hydro-power for grid studies and control design (Kishor et al., 2007;Björk et al., 2021).
Following the conception of OS2, the response characteristic is governed by two processes consisting of generator torque actuation in parallel to a variation of the rotational speed. The rotation is determined by a combination of excess power for (de-)acceleration and the wind turbine inertia. Following this reasoning, a simple transfer function for OS2 consisting of two  The upper bound parametrization corresponds to the highest simulated wind speed of v = 16 m/s and consists of two parallel first-order functions, i.e., G I/II (s) = k I/II 1 c I/II s+1 . The two parallel processes consist of torque and rotational speed setpoint variation, and therefore, c I/II describe the dynamics of closed-loop torque and inertia-based rotational speed evolution, respec-220 tively. As the concept in OS2 relies on an equal setpoint sharing among torque and rotational speed (established by √ p d in (2)), setting k I/II = 0.5 is an intuitive choice. On the other hand, in the lower bound parametrization corresponding to partial-load operation at v = 8 m/s, the discussed controller interaction from the rotational speed to the torque actuation plays a dominant role and decays when the desired rotational speed is reached. Therefore, the two parallel process are I: the torque actuated rotation as first-order transfer function G I = 1 cIs+1 and II: a negative derivative transfer function G II = − aIIs s+dII . The influence 225 of G II (s) vanishes as s → 0 to account for the non-minimum phase behavior stemming from the control interaction. Note that c I represents the inertia in combination with the available power in both upper and lower bound, but due to the varying power levels substantially depend on the current wind speed, see the parameters in Tab. 1.
From consideration of the ultimate loading, it was found that OS1 by remaining at constant rotational speeds tends to be superior to OS2 in avoiding additional ultimate loading of the components. As concluded for fatigue loading in turbulent wind, 230 the lower pitch magnitudes in OS1 compared to OS2 cause smaller excitation of the turbine structure, and consequently result in lower or similar ultimate loading when instantaneously adjusting the current power demand. Only at the lower wind speed (8 m/s) and a demanded increase of power, OS2 significantly outperformed OS1 in ultimate loading. Especially those scenarios, however, showed unsatisfactory response dynamics to the power changes in OS2, as discussed for the power output trajectories in Fig. 3 (c). The comparatively low power that is solely available for an acceleration of the turbine has positive effects on the 235 ultimate loading experienced by the turbine in these cases.

Conclusions
Within this contribution, it is discussed how different operational strategies can be designed for wind turbines using a modelbased control design. The influence on the attainable power dynamics for supporting the electrical grid and the resulting loading are analyzed for synthetically designed scenarios. The presented simulation studies reveal the dependency of the power 240 dynamics on the operational strategy, where it is found that OS1 (keeping the rotational speed constant) provides significantly faster control authority in the power dynamics compared to OS2, where a de-or acceleration of the turbine's rotor is performed.
While for OS1 the fast generator dynamics are governing, the response in OS2 is mainly determined by the turbine's inertia.
This underlines the additional flexibility in following a power demand in favor of the electrical grid when using OS1, where the amount of injected power can be controlled by the generator torque at a fast scale.

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While faster power dynamics in OS1 could be expected, the results from a loading perspective are surprising, which holds for both, the fatigue loading during turbulent wind and the ultimate loading at power demand steps. Except for the decreased blade fatigue loading, it was found that OS1 in the considered turbulent wind scenario and turbine setup showed smaller fatigue loading of the tower despite the greater rotational speed compared to power reduction at OS2. OS1 also tends to decrease the ultimate loads when following a power demand step compared to OS2.

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While the presented results suggest an application of OS1 from both considered perspectives, i.e., loading and power dynamics, the considered scenarios within this work are limited, where a variety of different aspects that are not subject of this work can determine the choice of the operational strategy applied to the turbine (also e.g., bird fatalities (Baerwald et al., 2009) or noise emission (Leloudas et al., 2007) decrease with lower rotational speed). It is shown how model-based control introduces flexibility in the choice of operational strategies for wind turbines at comparable dynamical properties. Further, a 255 dedicated control design allows for an online variation of the operational strategy, such that wind turbines can flexibly adjust the operational strategy subject to varying conditions.
For studying stability of the power system with a high share of decentralized generation, the participating power units and their relevant dynamical behavior must be considered and combined with models of the electrical grid. Therefore, modeling approaches are needed capable of portraying relevant dynamical properties, while satisfying complexity constraints to be 260 suitable for the large-scale integration in both advanced control design on a power system level, and the required simulations studies. The results obtained from the simulation studies suggest that the model for portraying the relevant dynamics depends on the chosen operating strategy. When aiming for constant rotational speed in a reduced power mode, a first-order transfer function governed by the closed-loop generator dynamics is seen to provide a reasonable model description. If a simultaneous rotational speed variation is assigned in the control scheme, the inertial response of the turbine rotor in conjunction with the 265