# Coordinated Control Using Backstepping of DFIG-Based Wind Turbine for Frequency Regulation in High Wind Energy Penetrated System

Authors: Mohamed Nadour; Ahmed Essadki; Tamou Nasser
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

The expansion of renewable generation has raised some red flags in terms of power system stability, control, and management. For instance, unlike traditional synchronous energy sources, the doubly-fed induction generator- (DFIG-) based wind turbines (WTs) do not instinctively act against frequency deviations. In fact, the power electronics interfacing the generator, merely controlled to warrant maximum wind power conversion, make its output power and mechanical speed immune to the characteristics of the electric network frequency. Moreover, significant wind power penetration (WPP) promotes the retirement of many traditional generation groups, consequently curtailing the power system corresponding inertia and displacing the primary reserves that are essential to retain the frequency within an acceptable range of variation. This paper explores different control approaches, using backstepping, allowing DFIG-based WTs to engage actively in frequency regulation using a coordinated control of the rotor speed and pitch angle to regulate the system during both partial- and full-load operation modes. The first method momentarily discharges part of the kinetic energy stored in the WT spinning masses, and the second method follows a deloaded operation characteristic, so as to keep a specific power reserve that can be automatically activated at the events of frequency excursions. A study case considering an isolated power system that consists of synchronous generators, DFIG-based wind farm, static load, and a sudden frequency disturbance was performed. The simulation result in a Matlab/Simulink environment highlights the robustness and capability of the coordinated control scheme to furnish, under variant operation conditions, active power aid, consequently lifting the frequency nadir up to a superior level than that obtained with 0% wind power penetration in the system.


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## Body

## 1. Introduction

The progression from conventional generation groups to nonconventional cleaner energy sources has pressured the power system to encounter significant changes in terms of its structure, operation, control, and management [1–3]. That is to say, as these renewables continue prospering worldwide, the power network will unavoidably confront multiple stability concerns. For instance, at the occurrence of frequency disruption, which reflects a power imbalance between demand and supply, in contrary to synchronous generation sources (reheat steam turbines, nonreheat steam turbines, hydraulics, etc.), where a natural short-term inertial response represented by an instantaneous absorption or release of the kinetic energy stored in the turbines spinning masses and primary reserve activation both serve the power system in restoring and maintaining the electric network frequency within a tolerable spectrum of variation, the doubly-fed induction generator- (DFIG-) based wind turbine (WT), which is the most prominent structure among the wind energy generation technologies [4], does not acquire this inherited characteristic [5, 6]. As a matter of fact, the power electronics interfacing the DFIG to the electrical network are merely controlled to ensure maximum power point tracking (MPPT) and therefore almost entirely dissociate its output power and mechanical speed from the electric network frequency characteristics.Furthermore, considerable wind power penetration (WPP) promotes the retirement and displacement of many conventional generation groups. Leading to the reduction of the power system’s corresponding inertia, hence lower inertial responses supporting the system (the situation is worse especially in isolated systems since their equivalent inertia is already limited), plus, the curtailment of primary reserves typically needed to compensate for power imbalances between the consumption and the production in order to secure the permanent stability of the power system. Therefore, some transmission system operators (TSOs) and grid planners have early revised their grid code specifications in order to securely fit in the wind power generation in their power system [2, 7]. Among which, for instance, the European Network of Transmission System Operator for Electricity (ENTSO-E) [8] expects that each of the transmission system operators (TSOs) shall obligate their grid-connected WTs to provide extra active power support comparable to that of conventional generation units to assist in the recovery process using the so-called “frequency-sensitive” control methods [9].The industrial and academic proposed solutions that allow variable speed WTs to engage in frequency regulation can be categorized into two main classes. The first class makes use of the naturally inaccessible WT kinetic energy through some appropriate rotor speed control designs. This class mainly contains two methods including, first, an “artificial” inertial reaction, using the kinetic energy stored in WTs spinning masses, retrieved based on the frequency deviation to counteract frequency disruptions for short-term duration [1, 8, 10]. A study by authors in [6, 11] shows that variable speed WT grants more access to the kinetic energy compared to a traditional synchronous generator with equivalent inertia constant, being that the wider the range of speed variation generators can tolerate, the more the kinetic energy can be extracted. However, this method cannot be used alone since it provides assistance only during the transient and has no reaction for quasi-steady state [1]. Then, there is the long-term frequency support where the proposed control strategy expects the WT to shift from MPPT to suboptimal operation mode and a droop controller is used to adapt the WT active power output as a proportion of the frequency deviation [12]. The second class uses the blade pitching to create the power reserve but only when the active power output is higher than the nominal value (full-load operation mode) [13–15].This subject is recognized and fairly discussed over the past years. However, some concerns still require further analysis. For instance, plenty of published papers such as [11, 13, 16, 17] have only considered the full-load operation of WT, whereas this mode represents only a small scale of WT operation time. As an example, the production of Portuguese grid-connected WTs is beyond the half of its nominal power only during 10% of the global operation time [9]. Moreover, few have been the works that have suggested a mix between rotor speed control through power electronics and pitch control for frequency regulation purposes. The authors in [16] have examined a coordinated control scheme, which only incorporates only the short-term inertial response and pitch control comparing the results with existing rotor speed controllers.This paper explores different control approaches used to enhance WT capability to engage in frequency regulation. First rotor speed control methods, namely, the artificial inertial and the primary frequency regulation responses, are developed. The control is done through the DFIG side converter (DSC) using nonlinear backstepping methodology. Then, an innovative pitch angle control method, utilized to protect the WT against overspeeding and to maintain the power reserve even during a full-load operation mode, is presented.A study case considering an isolated power system that contains synchronous generators, DFIG-based wind farm, and static loads was examined to compare the capability of each control scheme individually, in terms of furnishing extra active power assistance at the event of a sudden frequency disruption. Then, the simulation results show that a combination of the three control approaches enhances the performance of the DFIG-based wind farm by bringing the frequency nadir up to a higher level than that where the WPP is of 0% in the power system.


## 2. Modelling and Control of DFIG-Based WT

This section presents some preliminary knowledge, including a brief description of WT and DFIG modelling and control using backstepping. As we shall see in the Results section, compared to the classical control schemes, this control strategy enhances the system stability and robustness especially when parametric variations are registered, which is often the case due to some physical phenomena or modelling uncertainties related to the accuracy of the measuring devices and identification methodologies [4, 18].


### 2.1. Wind Turbine Model

The aerodynamic powerPT captured from the wind power Pw is expressed as follows:(1)PT=Pw⋅Cpλ,β=ρπR2vw32Cpλ,β,where R is the blade radius, ρ is the air density, vw is the wind speed, λ is the tip speed ratio, β is the blade angles, and Cp is the aerodynamic efficiency or the power coefficient approached by the expression given in Appendix [18]. With ΩT being the WT rotor speed, we have(2)λ=R⋅ΩTvw.The gearbox that adapts the mechanical speed Ωm of the DFIG to the rotor speed ΩT of the WT is modelled, neglecting the mechanical energy losses, by a simple gain GT, such that(3)Ωm=GT⋅ΩT,TT=GT⋅Tg,where TT and Tg are the torques at the gearbox input and output, respectively. Then, with Tem being the electromagnetic torque of the generator, Jwt, the system (WT and DFIG) total inertia, and f the friction, according to the fundamental equation of dynamic, we can write(4)JwtdΩmdt=Tg−Tem−f⋅Ωm.


### 2.2. DFIG Modelling and Control

In this work, we have adopted the field-oriented control, joining the stator flux to thed-axis of the Park reference frame (ψsq = 0 and ψsd = ψs), in order to dissociate the control of active power Ps and reactive power Qs. Neglecting the stator resistance Rs, which is a realistic approximation for high-power generators [4], the state model of the DFIG can be determined by the following equation [19]:(5)P˙s=μVrq+RrIrq+χIrd−η,I˙rq=−σVrq+RrIrq+χIrd−η,z1=Ps,Q˙s=μVrd+RrIrd−χIrq,I˙rd=−σVrq+RrIrd−χIq,z2=Qs,with α=1−M2/LrLs;μ=VsM/αLrLs;χ=gωsαLr;η=gMVs/Ls;σ=1/αLr.The subscriptsd and q denote the two axes of the Park rotating reference frame, and vr, vs, ir, and is are being, respectively, the rotor and the stator voltages (V) and currents (A). ωs and ωr are the angular speeds of the rotating stator and the rotor electromagnetic fields (rad/s). M, Lr, and Ls are the mutual, rotor, and stator inductances (H), and Rr is the rotor resistance.Moreover, withp being the pair of poles, the electromagnetic torque can be determined by the following equation:(6)Tem=pMLsΨsdirq.The benefit of the backstepping control approach relies on its ability to dissociate complex nonlinear systems into multiple simplified design problems (called steps or subsystems) using the so-called virtual control variables (VCVs). In each step, we virtually deal with a simple single-input and single-output subsystem, and each step provides virtual reference for the following one using Lyapunov’s functions to guarantee the stability of the subsystem. In the last step, the actual control variable (ACV) that insures the stability of the overall system can be finally determined [19].The DFIG side converter (DSC) in Figure1 is controlled to regulate the stator active power Ps and the stator reactive power Qs to their references Psr and Qsr, respectively. From equation (4), we have two second-order systems; therefore, the backstepping control design for each is divided into two subsystems as shown in Figure 2.Figure 1
The complete structure of frequency-sensitive DFIG-based WT control.Figure 2
DSC backstepping control.


### 2.3. Subsystem A (Current Reference VCV)

First, we select Lyapunov’s quadratic functionsV1 and V2, and then, we define the error variables such that(7)V1=12e12,V2=12e22,e1=Ps∗−Ps⟶e˙1=P˙s∗−P˙s,e2=Qs∗−Qs⟶e˙2=Q˙s∗−Q˙s.According to backstepping theory, in order to ensure a stable tracking behavior, the derivative of prechosen Lyapunov’s functions must be strictly negative, such that(8)V˙1=e1⋅e˙1=−h1e12,V˙2=e2⋅e˙1=−h2e22,with h1 and h2 being the positive backstepping tuning coefficients. The current reference VCVs can then be mathematically obtained using equations (5), (7), and (8) such that(9)I˙rq∗=1μRrP˙s∗+h1e1−1RrVrq+χIrd−η,I˙rd∗=1μRrQ˙s∗+h2e2−1RrVrd−χIrd.


### 2.4. Subsystem B (Voltage Reference ACV)

Note that the VCVs (Ird∗ and Irq∗) from the previous step (equation (9)) are the desired variables for this step. Therefore, we select Lyapunov’s functions V3 and V4 and define the error variables:(10)V3=12e12+e32,V4=12e22+e42,e3=Ird∗−Irq⟶e˙3=I˙rq∗−I˙rq,e4=Ird∗−Ird⟶e˙4=I˙rd∗−I˙rd.Similarly, in order to secure a stable tracking behavior, according to the backstepping theory, the derivative of Lyapunov’s functions must be strictly negative such that(11)V˙3=e1⋅e˙1e3⋅e˙3=−h1e12−h3e32,V˙4=e2⋅e˙2e4⋅e˙4=−h2e22−h4e42.Using the same steps, the voltage reference ACV can be mathematically determined using equations (5), (10), and (11):(12)Vrq∗=−h3e3−I˙rq∗−μe11σ−RrIrq+χIrd+η,Vrd∗=−h4e4−I˙rd∗−μe21σ−RrIrd−ϕIrd,with h1, h2, h3, and h4 being some strictly positive constants called the backstepping setting coefficients, used on the one hand to guarantee the stability of the system and on the other hand to ensure a quick dynamic response of the group controller system.


## 2.1. Wind Turbine Model

The aerodynamic powerPT captured from the wind power Pw is expressed as follows:(1)PT=Pw⋅Cpλ,β=ρπR2vw32Cpλ,β,where R is the blade radius, ρ is the air density, vw is the wind speed, λ is the tip speed ratio, β is the blade angles, and Cp is the aerodynamic efficiency or the power coefficient approached by the expression given in Appendix [18]. With ΩT being the WT rotor speed, we have(2)λ=R⋅ΩTvw.The gearbox that adapts the mechanical speed Ωm of the DFIG to the rotor speed ΩT of the WT is modelled, neglecting the mechanical energy losses, by a simple gain GT, such that(3)Ωm=GT⋅ΩT,TT=GT⋅Tg,where TT and Tg are the torques at the gearbox input and output, respectively. Then, with Tem being the electromagnetic torque of the generator, Jwt, the system (WT and DFIG) total inertia, and f the friction, according to the fundamental equation of dynamic, we can write(4)JwtdΩmdt=Tg−Tem−f⋅Ωm.


## 2.2. DFIG Modelling and Control

In this work, we have adopted the field-oriented control, joining the stator flux to thed-axis of the Park reference frame (ψsq = 0 and ψsd = ψs), in order to dissociate the control of active power Ps and reactive power Qs. Neglecting the stator resistance Rs, which is a realistic approximation for high-power generators [4], the state model of the DFIG can be determined by the following equation [19]:(5)P˙s=μVrq+RrIrq+χIrd−η,I˙rq=−σVrq+RrIrq+χIrd−η,z1=Ps,Q˙s=μVrd+RrIrd−χIrq,I˙rd=−σVrq+RrIrd−χIq,z2=Qs,with α=1−M2/LrLs;μ=VsM/αLrLs;χ=gωsαLr;η=gMVs/Ls;σ=1/αLr.The subscriptsd and q denote the two axes of the Park rotating reference frame, and vr, vs, ir, and is are being, respectively, the rotor and the stator voltages (V) and currents (A). ωs and ωr are the angular speeds of the rotating stator and the rotor electromagnetic fields (rad/s). M, Lr, and Ls are the mutual, rotor, and stator inductances (H), and Rr is the rotor resistance.Moreover, withp being the pair of poles, the electromagnetic torque can be determined by the following equation:(6)Tem=pMLsΨsdirq.The benefit of the backstepping control approach relies on its ability to dissociate complex nonlinear systems into multiple simplified design problems (called steps or subsystems) using the so-called virtual control variables (VCVs). In each step, we virtually deal with a simple single-input and single-output subsystem, and each step provides virtual reference for the following one using Lyapunov’s functions to guarantee the stability of the subsystem. In the last step, the actual control variable (ACV) that insures the stability of the overall system can be finally determined [19].The DFIG side converter (DSC) in Figure1 is controlled to regulate the stator active power Ps and the stator reactive power Qs to their references Psr and Qsr, respectively. From equation (4), we have two second-order systems; therefore, the backstepping control design for each is divided into two subsystems as shown in Figure 2.Figure 1
The complete structure of frequency-sensitive DFIG-based WT control.Figure 2
DSC backstepping control.


## 2.3. Subsystem A (Current Reference VCV)

First, we select Lyapunov’s quadratic functionsV1 and V2, and then, we define the error variables such that(7)V1=12e12,V2=12e22,e1=Ps∗−Ps⟶e˙1=P˙s∗−P˙s,e2=Qs∗−Qs⟶e˙2=Q˙s∗−Q˙s.According to backstepping theory, in order to ensure a stable tracking behavior, the derivative of prechosen Lyapunov’s functions must be strictly negative, such that(8)V˙1=e1⋅e˙1=−h1e12,V˙2=e2⋅e˙1=−h2e22,with h1 and h2 being the positive backstepping tuning coefficients. The current reference VCVs can then be mathematically obtained using equations (5), (7), and (8) such that(9)I˙rq∗=1μRrP˙s∗+h1e1−1RrVrq+χIrd−η,I˙rd∗=1μRrQ˙s∗+h2e2−1RrVrd−χIrd.


## 2.4. Subsystem B (Voltage Reference ACV)

Note that the VCVs (Ird∗ and Irq∗) from the previous step (equation (9)) are the desired variables for this step. Therefore, we select Lyapunov’s functions V3 and V4 and define the error variables:(10)V3=12e12+e32,V4=12e22+e42,e3=Ird∗−Irq⟶e˙3=I˙rq∗−I˙rq,e4=Ird∗−Ird⟶e˙4=I˙rd∗−I˙rd.Similarly, in order to secure a stable tracking behavior, according to the backstepping theory, the derivative of Lyapunov’s functions must be strictly negative such that(11)V˙3=e1⋅e˙1e3⋅e˙3=−h1e12−h3e32,V˙4=e2⋅e˙2e4⋅e˙4=−h2e22−h4e42.Using the same steps, the voltage reference ACV can be mathematically determined using equations (5), (10), and (11):(12)Vrq∗=−h3e3−I˙rq∗−μe11σ−RrIrq+χIrd+η,Vrd∗=−h4e4−I˙rd∗−μe21σ−RrIrd−ϕIrd,with h1, h2, h3, and h4 being some strictly positive constants called the backstepping setting coefficients, used on the one hand to guarantee the stability of the system and on the other hand to ensure a quick dynamic response of the group controller system.


## 3. “Electric Network Frequency-Sensitive” Control

Figure1 illustrates the complete DFIG-based WT structure including the network side converter (NSC) used to regulate the DC link voltage Vdc and the reactive power exchanged through the filter Qtr. The DFIG side converter (DSC) used to regulate the stator reactive power Qs to zero in order to get a unity power factor at the point of common coupling (PCC), until the electric network operator demands otherwise, and to adjust almost instantaneously, the stator active power Ps according to the electric network frequency-sensitive control loops. Finally, the pitch angle controller adapts the mechanical power to maintain the frequency regulation capability even under the full-load operation condition. Each controller will be analysed thoroughly in the next subsections.


### 3.1. Artificial Inertial Response

The inertial response permits the DFIG to reproduce synchronous generators behaviour, providing an active power support for the power system during the transient. It consists in customizing the electromagnetic torque referenceTemr, hence the active power reference Psr, as a proportion of the rate of change of the frequency (ROCOF). At the event of frequency disruption, the electromagnetic torque set point rises by ΔTem-IN causing a deceleration of the WT rotor speed Ωm and, as a consequence, discharging a portion of the kinetic energy stored in the WT spinning masses. The mechanism is chosen to be proportionate to that of synchronous generators, and thus, the additional power injected to the network can be expressed as follows:(13)ΔPINpu=2HT⋅fpudfpudt,where fpu is the per-unit system frequency and HT the total inertia constant (DFIG and WT) given by [5](14)HT=HDFIG+HWT=HDFIG+12JTΩrated2Srated.S
rated and Ωrated are, respectively, the rated power and rated mechanical speed. The equation that relates the electromagnetic torque to the frequency can be determined from equation (13) by the following expression:(15)ΔTem−INpu=2HT⋅fpudfpudt1Ωmpu.Furthermore, since the frequency is estimated by means of a phase-locked loop (PLL), a low-pass filter needs to be introduced into the control scheme in order to reduce the impact of the small noises as shown in Figure3, where TIN represents the time constant of the filter and KIN its gain that determines the amount of additional injected wind power in case of a frequency excursion.


### 3.2. Speed Droop Control

The artificial inertial response can only be utilized to assist the system during the transitory phase known as “dynamic frequency variation” [20]. However, in order to enable the WT to provide active power support for an extended period of time, another electric network frequency-sensitive control loop that takes under consideration the quasi-steady-state frequency deviation should be added as shown in Figure 3. The latter obligates the WT to operate following a “deloaded operation characteristic (DL),” as illustrated in Figure 4, creating a specific power reserve that can be automatically activated to support the power system when active power is needed at the event of frequency disruption. The creation of the power reserve is done through the acceleration of mechanical speed Ωm, by acting on the electromagnetic torque reference Temr−DL∗, hence the active power reference Ps∗, moving the operation point from A (which corresponds to the maximum power point tracking (MPPT) operation) to B (which corresponds to the deloaded power point tracking (DL) operation) as shown in Figure 3, such that(16)PB=1−RfPA,ΩB≻ΩA=Ωmppt,where Rf is the reserve factor and PA and ΩA are being, respectively, the active power and the mechanical speed of MPPT operation, given by(17)PA=ρπR2GT2Ωmvw−est3CpmaxΩm⟶MPPT,vw−est=RΩmGTλmppt;λmppt:optimal tip speed ratio.Figure 3
Coordinated frequency-sensitive control scheme.Figure 4
Deloaded operation.Figure 5
Organigram for the tip speed ratio reference computation.Theoretically speaking, the creation of the reserve can also be achieved by decelerating the mechanical speed. However, it is preferred to use the acceleration method to preserve and even increase the amount of kinetic energy stored in the WT. At the event of frequency drop, the controller changes the electromagnetic torque reference, decelerating the WT (moving from the pointB through the point E to the maximum point A) as shown in Figure 4, consequently rising the wind power production by a specific quantity ΔPrsc chosen to be proportionate to the frequency deviation, such that(18)ΔPrsc=K⋅f−fr=K⋅Δf,ΔPrsc−max=Rf∗PA⟶total power reserve,with f and fr being, respectively, the measured and nominal frequency 50 Hz and K is an energy factor determined as a function of the droop parameter δ:(19)K=Pratedδfr,with Prated being the generator’s rated power.The creation and activation (as function ofΔPrsc) of the power reserve are achieved through modifying the power coefficient reference Cp∗ and the tip speed ratio reference λ∗ in equation (17). Therefore, the power coefficient new reference Cp∗ can be determined from equation (1) by the following expression:(20)Cp∗λ∗,β=1−RfCpmax∗ΔPrsc0.5ρπR2vw3,Cp∗λ∗,β=1−RfCpmaxifΔPrsc=0.∗, p∗, p. While the reference of the tip speed ratio λ∗, which depends on the power coefficient reference Cp∗ and fhe angle of orientation of the blades β, can be determined using linear interpolation adopting the algorithm presented in Figure 5.The block diagram of rotor speed control is illustrated in Figure3.Finally, the rotor speed controller along with the inertial response ΔPIN sets the active power reference Psr for the DSC control according to the following expressions:(21)Ps∗=Tem∗⋅Ωm,Tem∗=Tem−DL∗+ΔTem−IN.


### 3.3. Pitch Control

The contribution of a WT to the global power reserve can be achieved either by accelerating the rotor speed or by the orientation of the pitch angle. During partial-load operation mode (wind speed below rated), the first method could be used alone in case of a tolerable power reserve. However, it becomes incapable if a larger reserve is requested, since the rotor speed should not exceed its maximum value (pointB in Figure 4). In that case, the second method is then called to take over. The pitch controller calculates the appropriate pitch angle βref that prevents the generator speed from surpassing the maximum value 1.2 pu, and βref is then transferred to the pitch system, which will either direct the fluid to the cylinders or the power to the motors, depending on the actuator, to increase the angle of the blades, consequently adjusting their lift for further mechanical power curtailment.For high wind speeds, the WT is at full-load operation mode, and the pitch system is already activated to keep the rotor speed at its maximum value (pointC in Figure 4). Note that, contrary to the classical WT control, the regulation using pitch angle control could be activated for all wind conditions. The dynamic of the pitch actuator can be modelled using the following transfer function, with Tp being the time constant of the pitch system [21]:(22)β=11+Tpsβref.As previously mentioned, the pitch angleβ is used to regulate the rotor speed Ωm. The process is highly nonlinear, and there is no direct relationship between these two variables. Traditionally, a gain scheduling control method is implemented to make up for the existent nonlinear aerodynamic behaviour [21]. However, the deloaded operation of the WT, used for frequency regulation purposes, complicates the control since the adjustment of the process gain now depends on not only the wind speed but also the power set point [21]. Accordingly, a simpler and more efficient approach is presented in this paper. It is based on Cp (λ, β) table inversion since the nonlinear characteristic is essentially brought by its curve. The architecture of the control approach is depicted in Figure 6.Figure 6
Block diagram of the rotor speed control.The reference of the pitch angleβref is determined using the reference of the power coefficient Cp∗, an estimation of tip speed ratio λ∗, and an inversion of the Cp (λ, β) table. Moreover, λ∗ is determined using the rotor speed measurement and Cp∗ is obtained from the aerodynamic torque reference TT∗, after inverting each element of the WT model (equation (1) to equation (4)) (note that in the steady state, Tem = Tg). As a consequence, the process view by the controller becomes linear, and electromagnetic torque reference Tem∗ could be provided using a simple constant gain PI controller. A dynamic saturation is used to limit Cp∗ reference to Cp−up∗λ,β=30° and Cp−down∗λ,β=0,1°.The inversion of theCp (λ, β) table could be applied to any mathematical approximation. It is based on 1- and 2-dimensional linear interpolations, and it can be depicted in the organigram (Figure 7)Figure 7
Organigram of theCp table inversion.


## 3.1. Artificial Inertial Response

The inertial response permits the DFIG to reproduce synchronous generators behaviour, providing an active power support for the power system during the transient. It consists in customizing the electromagnetic torque referenceTemr, hence the active power reference Psr, as a proportion of the rate of change of the frequency (ROCOF). At the event of frequency disruption, the electromagnetic torque set point rises by ΔTem-IN causing a deceleration of the WT rotor speed Ωm and, as a consequence, discharging a portion of the kinetic energy stored in the WT spinning masses. The mechanism is chosen to be proportionate to that of synchronous generators, and thus, the additional power injected to the network can be expressed as follows:(13)ΔPINpu=2HT⋅fpudfpudt,where fpu is the per-unit system frequency and HT the total inertia constant (DFIG and WT) given by [5](14)HT=HDFIG+HWT=HDFIG+12JTΩrated2Srated.S
rated and Ωrated are, respectively, the rated power and rated mechanical speed. The equation that relates the electromagnetic torque to the frequency can be determined from equation (13) by the following expression:(15)ΔTem−INpu=2HT⋅fpudfpudt1Ωmpu.Furthermore, since the frequency is estimated by means of a phase-locked loop (PLL), a low-pass filter needs to be introduced into the control scheme in order to reduce the impact of the small noises as shown in Figure3, where TIN represents the time constant of the filter and KIN its gain that determines the amount of additional injected wind power in case of a frequency excursion.


## 3.2. Speed Droop Control

The artificial inertial response can only be utilized to assist the system during the transitory phase known as “dynamic frequency variation” [20]. However, in order to enable the WT to provide active power support for an extended period of time, another electric network frequency-sensitive control loop that takes under consideration the quasi-steady-state frequency deviation should be added as shown in Figure 3. The latter obligates the WT to operate following a “deloaded operation characteristic (DL),” as illustrated in Figure 4, creating a specific power reserve that can be automatically activated to support the power system when active power is needed at the event of frequency disruption. The creation of the power reserve is done through the acceleration of mechanical speed Ωm, by acting on the electromagnetic torque reference Temr−DL∗, hence the active power reference Ps∗, moving the operation point from A (which corresponds to the maximum power point tracking (MPPT) operation) to B (which corresponds to the deloaded power point tracking (DL) operation) as shown in Figure 3, such that(16)PB=1−RfPA,ΩB≻ΩA=Ωmppt,where Rf is the reserve factor and PA and ΩA are being, respectively, the active power and the mechanical speed of MPPT operation, given by(17)PA=ρπR2GT2Ωmvw−est3CpmaxΩm⟶MPPT,vw−est=RΩmGTλmppt;λmppt:optimal tip speed ratio.Figure 3
Coordinated frequency-sensitive control scheme.Figure 4
Deloaded operation.Figure 5
Organigram for the tip speed ratio reference computation.Theoretically speaking, the creation of the reserve can also be achieved by decelerating the mechanical speed. However, it is preferred to use the acceleration method to preserve and even increase the amount of kinetic energy stored in the WT. At the event of frequency drop, the controller changes the electromagnetic torque reference, decelerating the WT (moving from the pointB through the point E to the maximum point A) as shown in Figure 4, consequently rising the wind power production by a specific quantity ΔPrsc chosen to be proportionate to the frequency deviation, such that(18)ΔPrsc=K⋅f−fr=K⋅Δf,ΔPrsc−max=Rf∗PA⟶total power reserve,with f and fr being, respectively, the measured and nominal frequency 50 Hz and K is an energy factor determined as a function of the droop parameter δ:(19)K=Pratedδfr,with Prated being the generator’s rated power.The creation and activation (as function ofΔPrsc) of the power reserve are achieved through modifying the power coefficient reference Cp∗ and the tip speed ratio reference λ∗ in equation (17). Therefore, the power coefficient new reference Cp∗ can be determined from equation (1) by the following expression:(20)Cp∗λ∗,β=1−RfCpmax∗ΔPrsc0.5ρπR2vw3,Cp∗λ∗,β=1−RfCpmaxifΔPrsc=0.∗, p∗, p. While the reference of the tip speed ratio λ∗, which depends on the power coefficient reference Cp∗ and fhe angle of orientation of the blades β, can be determined using linear interpolation adopting the algorithm presented in Figure 5.The block diagram of rotor speed control is illustrated in Figure3.Finally, the rotor speed controller along with the inertial response ΔPIN sets the active power reference Psr for the DSC control according to the following expressions:(21)Ps∗=Tem∗⋅Ωm,Tem∗=Tem−DL∗+ΔTem−IN.


## 3.3. Pitch Control

The contribution of a WT to the global power reserve can be achieved either by accelerating the rotor speed or by the orientation of the pitch angle. During partial-load operation mode (wind speed below rated), the first method could be used alone in case of a tolerable power reserve. However, it becomes incapable if a larger reserve is requested, since the rotor speed should not exceed its maximum value (pointB in Figure 4). In that case, the second method is then called to take over. The pitch controller calculates the appropriate pitch angle βref that prevents the generator speed from surpassing the maximum value 1.2 pu, and βref is then transferred to the pitch system, which will either direct the fluid to the cylinders or the power to the motors, depending on the actuator, to increase the angle of the blades, consequently adjusting their lift for further mechanical power curtailment.For high wind speeds, the WT is at full-load operation mode, and the pitch system is already activated to keep the rotor speed at its maximum value (pointC in Figure 4). Note that, contrary to the classical WT control, the regulation using pitch angle control could be activated for all wind conditions. The dynamic of the pitch actuator can be modelled using the following transfer function, with Tp being the time constant of the pitch system [21]:(22)β=11+Tpsβref.As previously mentioned, the pitch angleβ is used to regulate the rotor speed Ωm. The process is highly nonlinear, and there is no direct relationship between these two variables. Traditionally, a gain scheduling control method is implemented to make up for the existent nonlinear aerodynamic behaviour [21]. However, the deloaded operation of the WT, used for frequency regulation purposes, complicates the control since the adjustment of the process gain now depends on not only the wind speed but also the power set point [21]. Accordingly, a simpler and more efficient approach is presented in this paper. It is based on Cp (λ, β) table inversion since the nonlinear characteristic is essentially brought by its curve. The architecture of the control approach is depicted in Figure 6.Figure 6
Block diagram of the rotor speed control.The reference of the pitch angleβref is determined using the reference of the power coefficient Cp∗, an estimation of tip speed ratio λ∗, and an inversion of the Cp (λ, β) table. Moreover, λ∗ is determined using the rotor speed measurement and Cp∗ is obtained from the aerodynamic torque reference TT∗, after inverting each element of the WT model (equation (1) to equation (4)) (note that in the steady state, Tem = Tg). As a consequence, the process view by the controller becomes linear, and electromagnetic torque reference Tem∗ could be provided using a simple constant gain PI controller. A dynamic saturation is used to limit Cp∗ reference to Cp−up∗λ,β=30° and Cp−down∗λ,β=0,1°.The inversion of theCp (λ, β) table could be applied to any mathematical approximation. It is based on 1- and 2-dimensional linear interpolations, and it can be depicted in the organigram (Figure 7)Figure 7
Organigram of theCp table inversion.


## 4. Results and Discussions

### 4.1. General Discussion

The power system is exposed to many forms of disturbances. A load change results in variation of the electrical torqueTe output of all generators, and a change in the production results in variation of the mechanical torque Tm of all generators. The frequency deviations reflect the mismatches between the electrical Te and mechanical Tm torques, as represented by the following equation of motion [22]:(23)Tm−Te=2Hdωdt=2Hdfdt,where H is the power system’s corresponding inertia constant and ω and f are the (per unit) rotational speed and the ENF, respectively [23]. Equation (20) can be expressed in terms of the electrical Pe and mechanical Pm powers, such that(24)Pm1−Pe1+ΔPm−ΔPe=ω1−ΔωTm1−Te1+ΔTm−ΔTe,where we denote the deviations by the prefix (Δ) and the steady-state values by the subscript (1). with ω1(pu) = 1 and by ignoring the higher order terms and adopting the realistic assumption of Pm1=Pe1 and Tm1=Te1 in the steady state. Equation (24) can further be adjusted into [22](25)ΔPm−ΔPe=ΔTm−ΔTe.Replacing into equation (23), we can write(26)ΔPm−ΔPe=2HdΔωdt=2HdΔfdt.In this work, we have considered the load sensitivity to frequency deviations. Being that practically an abrupt change in frequency will cause a variation of the power demand [22]. The overall network frequency-dependent characteristic of loads can be represented by the following equation:(27)ΔPe=ΔPl+DΔf,with ΔPl being the non-frequency-sensitive load variation and DΔω is frequency-sensitive load variation. The coefficient D represents the self-regulation of loads, and it is expressed as a percent change in load for 1% deviation in frequency [22]. Substituting into equation (26), we can write(28)ΔPm−ΔPl=2HdΔfdt+DΔf.


### 4.2. Power System Modelling

To investigate the performances of the proposed control strategies, a model of a small power system, based on the scheme illustrated in Figure8, was designed in Matlab/Simulink environment. It consists of four identical conventional generating units (n = 4 medium power hydroelectric generators) [2, 22]; each has a power rating of Si = 100 MVA, an inertia constant of Hi = 5.0 s on 100 MVA base, and a droop for the speed governor δi = 0.2, feeding a total load of 220 MW. For the analysis of frequency regulation capability, we are concerned with the collective behaviour of all generators in the power system. Therefore, in this study, all conventional synchronous generators are represented by a single equivalent machine driven by the mechanical outputs of each turbine [22]. The power rating of the equivalent generator is of Seq = nSi, and the equivalent droop δeq and the corresponding inertia constant of the power system Heq can be determined using the following equations:(29)Heq=nHiSiSeq;δeq=δin.Figure 8
Electric network frequency regulation control scheme of a power system.Note that the synchronous generators are operating without automatic generation control (AGC), and only primary frequency regulation is considered in this study, which is practically sufficient for the research objectives.


### 4.3. Artificial Inertial Response Evaluation

In order to examine the implemented artificial inertial control behaviour, we have compared three simulation scenarios as summarized in Table1.Table 1
Simulation scenarios.
Scenarios
S1
S2
S3
Generation units 1, 2, and 3
C
C
C
Generation unit 4
C
no PFC
NC
NC
Wind farm
NC
C
no IC
C
only IC
C: connected; NC: nonconnected; PFC: primary frequency control; IC: inertial control.The first scenario S1 represents the reference case where the first, second, and third synchronous generation units provide both inertial response and primary frequency control (PFC), while the fourth synchronous generation unit is providing only its inherited inertial reaction without primary frequency response (no PFC). Thus, according to equation (29), the system equivalent inertia remains constant Heq = 5.0 s, but the equivalent droop coefficient is now δeq = 0.066. The remaining scenarios represent the case where the fourth synchronous generation unit is replaced with a wind farm (WF) with an equivalent power rating, where S2 and S3 are, respectively, the wind farm cases without and with inertial control implemented. In this case, the wind power penetration rises up to LP = 25%; therefore, the equivalent inertia constant is decreased to H’eq = Heq (1−Lp) = 3.75, while the equivalent droop remains constant δ’eq = 0.066. A sudden rise in load by 20 MW (0.05 pu system base) is introduced to the system at t = 300 s.Figure9 portrays the dynamic reaction of the electric network frequency for the three simulation scenarios. With scenario S1 being the reference case, it can be observed that the deepest frequency nadir, the worst case, is obtained with scenario S2 where the artificial inertial response of WTs is disabled. That is mainly due to the reduction of the system equivalent inertia caused by the increase of the wind power penetration Lp to 25% in the system. Meanwhile, the narrow frequency nadir, the finest case, is obtained with scenario S3 where the inertial response is enabled, and with an appropriate gain KIN choice, the inertial support from the WTs could be even greater than that obtained from the synchronous generation unit. Since the wider the range of speed variation, the bigger the amount of kinetic energy can be extracted.Figure 9
Electric network frequency deviation for different scenarios.Figures10–12 show the dynamic behaviour of a single WT for different operation conditions. Initially (before the disturbance), the rotor speed and the active power output are maintained to their optimal values corresponding to MPPT. At the event of frequency drop t = 120 s, and when the wind speed is below rated vw = 6.5 m/s (partial-load operation mode), the sequence of events that occur can be summarized as follows:(i)
The controller adjusts the electromagnetic torque reference causing a deceleration of the rotor speed (Figure10(a)).(ii)
The rotor speed is below its maximum value (>1.2 pu); therefore, the pitch angle is kept at zero (Figure11(a)).(iii)
The reduction of the rotor speed causes the extraction of a portion of the kinetic energy stored in the spinning masses (Figure12(a)). This extra active power will be used to support the power system in recovering the frequency to 50 Hz.(iv)
The countering spike of the output power (Figure12(a)) at roughly t = 310 s can be explained as follows: let us consider that the WT was operating at point A (Figure 4), with the rotor speed reduction, the WT will move to a suboptimal power extraction operation point at the end of the inertial reaction. Therefore, less power will be delivered until full recovery of the WT.Figure 10
Rotor speed evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 11
Pitch angle evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 12
Active power evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)For a high wind speedvw = 15 m/s (full-load operation mode), the sequence of events that occur can be summarized as follows:(i)
The pitch controller (Figure11(b)) maintains the rotor speed at its maximum value (≈1.2 pu) (Figure 10(b)).(ii)
The controller tries to adjust rotor speed, but since the pitch controller is activated in this mode, it counteracts the action by reducing the pitch angle, thus indirectly exploiting the mechanical power that was already curtailed by the positive pitch angle to create the power surge (Figure12(b)). Not that the power response at this mode requires no recovery process since the pitching system is the one responsible for the contribution.In order to highlight the merits of using a backstepping control algorithm instead of classical controllers, it is particularly important to analyse the system performance under some kind of disturbances. Therefore, since the machine parameters are usually exposed to many forms of inaccuracies especially due to the measuring devices, identification methodology, or several natural phenomena, a robustness test was carried out to compare the performance of the proposed control strategy versus classical PI controllers when parametric variations are registered. The test consists in purposefully modifying the rotor resistanceRr of the DFIG by 50% and the stator inductance Ls by 10% from their normal values.Figures12 and 13 show, respectively, the evolution of the DFIG stator active and reactive powers, and Figures 14 and 15, respectively, show the evolution of d and q components of the rotor currents. The test highlights the high sensitivity of classical PI controllers towards parametric variation, which is notably observed due to the appearance of a significant static error in all simulation results, whereas the proposed backstepping control algorithm demonstrates an exquisite disturbance rejection, being that all the outputs converge correctly to their designated references. Moreover, the three-phased stator current sinusoidal waveform is shown in Figure 16.Figure 13
Reactive power evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 14
Active currentIrq evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 15
Reactive currentIrd evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 16
Stator current evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)


### 4.4. Speed Droop Control Evaluation

The performance of the proposed speed droop control will be evaluated for the following simulation cases.Case 1: partial-load operation mode (wind speedvw = 6.5 m/s)Case 1: Full-load operation mode (wind speedvw = 15 m/s)The set of results shown in the following figures demonstrates the capability of the proposed control strategy to respond to a sudden active power call att = 150 s. Before the arrival of the frequency drop, the WT is running at a rotational speed higher than the optimum (Ω > Ωmppt), in order to lower the aerodynamic conversion efficiency represented by Cp and, therefore, to operate following a deloaded operation characteristic with the power reserve being created. For the research objectives, this work presumes that the WT is operating with a reserve factor Rf = 10%, while on the practical level the power margins are generally specified by the grid codes.At the arrival of frequency excursion (t = 150 s), the sequence of events that occur, under partial-load operation mode, can be summarized as follows:(i)
The step in the output power reference (byΔPrsc, Figure 3) modifies the electromagnetic torque reference Tem∗ causing the rotor speed reduction as shown in Figure 17(a)(ii)
The rotor speed is below its maximum value, the pitch control is not required in this case, and therefore, the pitch angle is maintained at zero (Figure18(a))(iii)
The rotor speed deceleration rises the power coefficientCp to its maximum value (Figure 4) as shown in Figure 19(a) allowing, consequently, the WT to activate its full power reserve(iv)
The power reserve activation rises the output power of the WT byΔPrsc (Figure 20(a)), therefore allowing it to participate in the frequency recovery process(v)
The power peaks induced as shown in Figure20(a) demonstrate the benefit from creating the power reserve by acceleration of the rotor speed, the left side of the power curve Figure 4, since now more kinetic energy is at our disposal, and it can be used whenever the WT is decelerating(vi)
When the frequency recovers att = 400 s, the control strategy reaccelerates the WT (Figure 17(a)), lowering the power coefficient (Figure 19(a)), in order to recreate the power reserve (Figure 20(a)) for the next useFigure 17
Rotor speed evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 18
Pitch angle evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 19
Power coefficient evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 20
WR output power evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)At the arrival of frequency excursion (t = 150 s), the sequence of events that occur, under full-load operation mode, can be summarized as follows:(i)
The pitch control is now activated as shown in Figure18(b), to keep the rotor speed at its maximum value (Figure 17(b)) and to create the power reserve (Figure 19(b)) since the rotor speed can no longer be accelerated(ii)
The active power call (ΔPrsc, Figure 4) reduced the pitch angle to make use of the mechanical power curtailed by the positive β(iii)
β reduction increases the power coefficient CP as shown in Figure 19(b),consequently rising the output according to the amount of power specified by ΔPrsc (Figure 20(b))(iv)
When the frequency recovers att = 400 s, the pitch control strategy rises the pitch angle (Figure 18(b)), lowering the power coefficient (Figure 19(b)), in order to recreate the power reserve (Figure 20(b)) for the next use


### 4.5. Coordinated Control

The artificial inertial reaction, the speed droop control, and the pitch control could be used altogether, to further enhance the frequency regulation capability of WTs. In this subsection, we compared the simulation scenarios summarized in Table2, with S1 being the reference case where the wind power penetration is Lp = 0%. For the other simulation scenarios, the fourth generation synchronous is replaced with a WF with an equivalent power rating, and the wind power penetration rises to Lp = 25%, with S2, S3, S3, and S4 being, respectively, the cases without any frequency control, the inertial reaction only, speed droop control only, and all controllers.Table 2
Simulation scenarios.
Scenarios
S1
S2
S3
S3
S4
Generation units 1, 2, and 3
C
C
C
C
C
Generation unit 4
C
NC
NC
NC
NC
Wind farm
NC
C no control
C only IC
C only PFC
C IC and PFC
C: connected; NC: nonconnected; PFC: primary frequency control; IC: inertial control.Figure21 portrays the dynamic reaction of the frequency for each scenario. All simulations were performed for a medium wind speed of vw = 9 m/s, and a sudden rise in load by 0.05 pu system base is introduced to the system at t = 200 s.Figure 21
Deviation of the frequency for each simulation scenario.The results show that the severest case is obtained with the simulation scenario S2, the case where the WF is connected with no frequency regulation ability. Compared to the reference case S1, where the wind power penetrationLp = 0%, the frequency curve for the second simulation scenario S2 falls to a deeper nadir due to the reduction of the system’s equivalent inertia caused by increasing the wind power penetration Lp = 25%. On the other hand, in the case where the inertial control is implemented S3, the WT decelerates to release a portion of its kinetic energy transiently improving the frequency deviation. Consequently, the frequency nadir is lifted up to the level of the reference case S1. However, the quasi-steady-state frequency does not get any better with only the inertial control being enabled, since it provides only short-term frequency support. With the speed droop controller being enabled, simulation scenario S4, it can be observed that the WT contribution is higher since the maximum transient and the quasi-steady-state frequency deviations are both optimised. Finally, with both controllers being simultaneously enabled, simulation scenario S5, the frequency curve will further be improved for both short- and long-term durations.As mentioned previously, with only the inertial control being activated, at the event of frequency excursion, the rotor speed deceleration will impose a suboptimal power extraction, and then less power will be delivered until the full recovery of the WT to its optimum speed (Figure10(c)). This recovery phase that generally lasts tens of seconds could be avoided when both controllers are simultaneously activated, given that the droop speed controller forces the WT to operate at a higher rotational speed (Ω > Ωmppt), left side of the curve (Figure 4). Therefore, when the WT decelerates, the operating point will climb toward the optimum point, and as a result, there will be no need for the WT to recover at the end of the inertial response.


## 4.1. General Discussion

The power system is exposed to many forms of disturbances. A load change results in variation of the electrical torqueTe output of all generators, and a change in the production results in variation of the mechanical torque Tm of all generators. The frequency deviations reflect the mismatches between the electrical Te and mechanical Tm torques, as represented by the following equation of motion [22]:(23)Tm−Te=2Hdωdt=2Hdfdt,where H is the power system’s corresponding inertia constant and ω and f are the (per unit) rotational speed and the ENF, respectively [23]. Equation (20) can be expressed in terms of the electrical Pe and mechanical Pm powers, such that(24)Pm1−Pe1+ΔPm−ΔPe=ω1−ΔωTm1−Te1+ΔTm−ΔTe,where we denote the deviations by the prefix (Δ) and the steady-state values by the subscript (1). with ω1(pu) = 1 and by ignoring the higher order terms and adopting the realistic assumption of Pm1=Pe1 and Tm1=Te1 in the steady state. Equation (24) can further be adjusted into [22](25)ΔPm−ΔPe=ΔTm−ΔTe.Replacing into equation (23), we can write(26)ΔPm−ΔPe=2HdΔωdt=2HdΔfdt.In this work, we have considered the load sensitivity to frequency deviations. Being that practically an abrupt change in frequency will cause a variation of the power demand [22]. The overall network frequency-dependent characteristic of loads can be represented by the following equation:(27)ΔPe=ΔPl+DΔf,with ΔPl being the non-frequency-sensitive load variation and DΔω is frequency-sensitive load variation. The coefficient D represents the self-regulation of loads, and it is expressed as a percent change in load for 1% deviation in frequency [22]. Substituting into equation (26), we can write(28)ΔPm−ΔPl=2HdΔfdt+DΔf.


## 4.2. Power System Modelling

To investigate the performances of the proposed control strategies, a model of a small power system, based on the scheme illustrated in Figure8, was designed in Matlab/Simulink environment. It consists of four identical conventional generating units (n = 4 medium power hydroelectric generators) [2, 22]; each has a power rating of Si = 100 MVA, an inertia constant of Hi = 5.0 s on 100 MVA base, and a droop for the speed governor δi = 0.2, feeding a total load of 220 MW. For the analysis of frequency regulation capability, we are concerned with the collective behaviour of all generators in the power system. Therefore, in this study, all conventional synchronous generators are represented by a single equivalent machine driven by the mechanical outputs of each turbine [22]. The power rating of the equivalent generator is of Seq = nSi, and the equivalent droop δeq and the corresponding inertia constant of the power system Heq can be determined using the following equations:(29)Heq=nHiSiSeq;δeq=δin.Figure 8
Electric network frequency regulation control scheme of a power system.Note that the synchronous generators are operating without automatic generation control (AGC), and only primary frequency regulation is considered in this study, which is practically sufficient for the research objectives.


## 4.3. Artificial Inertial Response Evaluation

In order to examine the implemented artificial inertial control behaviour, we have compared three simulation scenarios as summarized in Table1.Table 1
Simulation scenarios.
Scenarios
S1
S2
S3
Generation units 1, 2, and 3
C
C
C
Generation unit 4
C
no PFC
NC
NC
Wind farm
NC
C
no IC
C
only IC
C: connected; NC: nonconnected; PFC: primary frequency control; IC: inertial control.The first scenario S1 represents the reference case where the first, second, and third synchronous generation units provide both inertial response and primary frequency control (PFC), while the fourth synchronous generation unit is providing only its inherited inertial reaction without primary frequency response (no PFC). Thus, according to equation (29), the system equivalent inertia remains constant Heq = 5.0 s, but the equivalent droop coefficient is now δeq = 0.066. The remaining scenarios represent the case where the fourth synchronous generation unit is replaced with a wind farm (WF) with an equivalent power rating, where S2 and S3 are, respectively, the wind farm cases without and with inertial control implemented. In this case, the wind power penetration rises up to LP = 25%; therefore, the equivalent inertia constant is decreased to H’eq = Heq (1−Lp) = 3.75, while the equivalent droop remains constant δ’eq = 0.066. A sudden rise in load by 20 MW (0.05 pu system base) is introduced to the system at t = 300 s.Figure9 portrays the dynamic reaction of the electric network frequency for the three simulation scenarios. With scenario S1 being the reference case, it can be observed that the deepest frequency nadir, the worst case, is obtained with scenario S2 where the artificial inertial response of WTs is disabled. That is mainly due to the reduction of the system equivalent inertia caused by the increase of the wind power penetration Lp to 25% in the system. Meanwhile, the narrow frequency nadir, the finest case, is obtained with scenario S3 where the inertial response is enabled, and with an appropriate gain KIN choice, the inertial support from the WTs could be even greater than that obtained from the synchronous generation unit. Since the wider the range of speed variation, the bigger the amount of kinetic energy can be extracted.Figure 9
Electric network frequency deviation for different scenarios.Figures10–12 show the dynamic behaviour of a single WT for different operation conditions. Initially (before the disturbance), the rotor speed and the active power output are maintained to their optimal values corresponding to MPPT. At the event of frequency drop t = 120 s, and when the wind speed is below rated vw = 6.5 m/s (partial-load operation mode), the sequence of events that occur can be summarized as follows:(i)
The controller adjusts the electromagnetic torque reference causing a deceleration of the rotor speed (Figure10(a)).(ii)
The rotor speed is below its maximum value (>1.2 pu); therefore, the pitch angle is kept at zero (Figure11(a)).(iii)
The reduction of the rotor speed causes the extraction of a portion of the kinetic energy stored in the spinning masses (Figure12(a)). This extra active power will be used to support the power system in recovering the frequency to 50 Hz.(iv)
The countering spike of the output power (Figure12(a)) at roughly t = 310 s can be explained as follows: let us consider that the WT was operating at point A (Figure 4), with the rotor speed reduction, the WT will move to a suboptimal power extraction operation point at the end of the inertial reaction. Therefore, less power will be delivered until full recovery of the WT.Figure 10
Rotor speed evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 11
Pitch angle evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 12
Active power evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)For a high wind speedvw = 15 m/s (full-load operation mode), the sequence of events that occur can be summarized as follows:(i)
The pitch controller (Figure11(b)) maintains the rotor speed at its maximum value (≈1.2 pu) (Figure 10(b)).(ii)
The controller tries to adjust rotor speed, but since the pitch controller is activated in this mode, it counteracts the action by reducing the pitch angle, thus indirectly exploiting the mechanical power that was already curtailed by the positive pitch angle to create the power surge (Figure12(b)). Not that the power response at this mode requires no recovery process since the pitching system is the one responsible for the contribution.In order to highlight the merits of using a backstepping control algorithm instead of classical controllers, it is particularly important to analyse the system performance under some kind of disturbances. Therefore, since the machine parameters are usually exposed to many forms of inaccuracies especially due to the measuring devices, identification methodology, or several natural phenomena, a robustness test was carried out to compare the performance of the proposed control strategy versus classical PI controllers when parametric variations are registered. The test consists in purposefully modifying the rotor resistanceRr of the DFIG by 50% and the stator inductance Ls by 10% from their normal values.Figures12 and 13 show, respectively, the evolution of the DFIG stator active and reactive powers, and Figures 14 and 15, respectively, show the evolution of d and q components of the rotor currents. The test highlights the high sensitivity of classical PI controllers towards parametric variation, which is notably observed due to the appearance of a significant static error in all simulation results, whereas the proposed backstepping control algorithm demonstrates an exquisite disturbance rejection, being that all the outputs converge correctly to their designated references. Moreover, the three-phased stator current sinusoidal waveform is shown in Figure 16.Figure 13
Reactive power evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 14
Active currentIrq evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 15
Reactive currentIrd evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 16
Stator current evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)


## 4.4. Speed Droop Control Evaluation

The performance of the proposed speed droop control will be evaluated for the following simulation cases.Case 1: partial-load operation mode (wind speedvw = 6.5 m/s)Case 1: Full-load operation mode (wind speedvw = 15 m/s)The set of results shown in the following figures demonstrates the capability of the proposed control strategy to respond to a sudden active power call att = 150 s. Before the arrival of the frequency drop, the WT is running at a rotational speed higher than the optimum (Ω > Ωmppt), in order to lower the aerodynamic conversion efficiency represented by Cp and, therefore, to operate following a deloaded operation characteristic with the power reserve being created. For the research objectives, this work presumes that the WT is operating with a reserve factor Rf = 10%, while on the practical level the power margins are generally specified by the grid codes.At the arrival of frequency excursion (t = 150 s), the sequence of events that occur, under partial-load operation mode, can be summarized as follows:(i)
The step in the output power reference (byΔPrsc, Figure 3) modifies the electromagnetic torque reference Tem∗ causing the rotor speed reduction as shown in Figure 17(a)(ii)
The rotor speed is below its maximum value, the pitch control is not required in this case, and therefore, the pitch angle is maintained at zero (Figure18(a))(iii)
The rotor speed deceleration rises the power coefficientCp to its maximum value (Figure 4) as shown in Figure 19(a) allowing, consequently, the WT to activate its full power reserve(iv)
The power reserve activation rises the output power of the WT byΔPrsc (Figure 20(a)), therefore allowing it to participate in the frequency recovery process(v)
The power peaks induced as shown in Figure20(a) demonstrate the benefit from creating the power reserve by acceleration of the rotor speed, the left side of the power curve Figure 4, since now more kinetic energy is at our disposal, and it can be used whenever the WT is decelerating(vi)
When the frequency recovers att = 400 s, the control strategy reaccelerates the WT (Figure 17(a)), lowering the power coefficient (Figure 19(a)), in order to recreate the power reserve (Figure 20(a)) for the next useFigure 17
Rotor speed evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 18
Pitch angle evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 19
Power coefficient evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)Figure 20
WR output power evolution for partial-load (a) and full-load (b) operation modes.
(a)
(b)At the arrival of frequency excursion (t = 150 s), the sequence of events that occur, under full-load operation mode, can be summarized as follows:(i)
The pitch control is now activated as shown in Figure18(b), to keep the rotor speed at its maximum value (Figure 17(b)) and to create the power reserve (Figure 19(b)) since the rotor speed can no longer be accelerated(ii)
The active power call (ΔPrsc, Figure 4) reduced the pitch angle to make use of the mechanical power curtailed by the positive β(iii)
β reduction increases the power coefficient CP as shown in Figure 19(b),consequently rising the output according to the amount of power specified by ΔPrsc (Figure 20(b))(iv)
When the frequency recovers att = 400 s, the pitch control strategy rises the pitch angle (Figure 18(b)), lowering the power coefficient (Figure 19(b)), in order to recreate the power reserve (Figure 20(b)) for the next use


## 4.5. Coordinated Control

The artificial inertial reaction, the speed droop control, and the pitch control could be used altogether, to further enhance the frequency regulation capability of WTs. In this subsection, we compared the simulation scenarios summarized in Table2, with S1 being the reference case where the wind power penetration is Lp = 0%. For the other simulation scenarios, the fourth generation synchronous is replaced with a WF with an equivalent power rating, and the wind power penetration rises to Lp = 25%, with S2, S3, S3, and S4 being, respectively, the cases without any frequency control, the inertial reaction only, speed droop control only, and all controllers.Table 2
Simulation scenarios.
Scenarios
S1
S2
S3
S3
S4
Generation units 1, 2, and 3
C
C
C
C
C
Generation unit 4
C
NC
NC
NC
NC
Wind farm
NC
C no control
C only IC
C only PFC
C IC and PFC
C: connected; NC: nonconnected; PFC: primary frequency control; IC: inertial control.Figure21 portrays the dynamic reaction of the frequency for each scenario. All simulations were performed for a medium wind speed of vw = 9 m/s, and a sudden rise in load by 0.05 pu system base is introduced to the system at t = 200 s.Figure 21
Deviation of the frequency for each simulation scenario.The results show that the severest case is obtained with the simulation scenario S2, the case where the WF is connected with no frequency regulation ability. Compared to the reference case S1, where the wind power penetrationLp = 0%, the frequency curve for the second simulation scenario S2 falls to a deeper nadir due to the reduction of the system’s equivalent inertia caused by increasing the wind power penetration Lp = 25%. On the other hand, in the case where the inertial control is implemented S3, the WT decelerates to release a portion of its kinetic energy transiently improving the frequency deviation. Consequently, the frequency nadir is lifted up to the level of the reference case S1. However, the quasi-steady-state frequency does not get any better with only the inertial control being enabled, since it provides only short-term frequency support. With the speed droop controller being enabled, simulation scenario S4, it can be observed that the WT contribution is higher since the maximum transient and the quasi-steady-state frequency deviations are both optimised. Finally, with both controllers being simultaneously enabled, simulation scenario S5, the frequency curve will further be improved for both short- and long-term durations.As mentioned previously, with only the inertial control being activated, at the event of frequency excursion, the rotor speed deceleration will impose a suboptimal power extraction, and then less power will be delivered until the full recovery of the WT to its optimum speed (Figure10(c)). This recovery phase that generally lasts tens of seconds could be avoided when both controllers are simultaneously activated, given that the droop speed controller forces the WT to operate at a higher rotational speed (Ω > Ωmppt), left side of the curve (Figure 4). Therefore, when the WT decelerates, the operating point will climb toward the optimum point, and as a result, there will be no need for the WT to recover at the end of the inertial response.


## 5. Conclusion

This paper explores different control approaches that allow DFIG-based WTs to engage actively in frequency regulation, via coordinating the rotor speed and the pitch angle controllers. In a short-term duration, the inertial control permits the WT to emulate the synchronous generator natural behaviour. Accordingly, at the event of frequency excursion, the controller decelerates the WT in order to extract a portion of its kinetic energy, shortly providing extra active power support for the power system. However, the inertial reaction alone is heavily dependent on the initial point of operation and a good tuning of the controller gain is required since, for instance, at low wind speeds, the rotor speed should not exceed its minimum value 0.6 pu for the stable operation of the WT. The speed droop controller enables the WT to provide active power assistance over an extended period improving the robustness of the system. It forces the WT to operate following a deloaded characteristic, creating a certain power reserve that can be automatically triggered at the event of frequency deviations. Moreover, an innovative pitch angle control is utilized to protect the WT against over speeding and to maintain the frequency regulation capability under various operation conditions.Finally, a study case considering an isolated power system that consists of synchronous generators, DFIG-based wind farm, and static loads was examined to compare the performance of each controller. These simulation results show that the coordination of the controllers improves both the dynamic and the quasi-steady-state frequency deviation and brings the frequency nadir up to a far superior level than that obtained with the wind farm being disconnected (0% wind power penetration).



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*Source: 8287949-2020-04-29.xml*