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Improving Stability of a DFIG-Based Wind Power System With Tuned Damping Controller Y. Mishra, Student Member, IEEE, S. Mishra, Senior Member, IEEE, M. Tripathy, N. Senroy, Member, IEEE, and Z. Y. Dong, Senior Member, IEEE
Abstract—This paper focuses on the implementation of a damping controller for the doubly fed induction generator (DFIG) system. Coordinated tuning of the damping controller to enhance the damping of the oscillatory modes is presented using bacterial foraging technique. The effect of the tuned damping controller on converter ratings of the DFIG system is also investigated. The results of both eigenvalue analysis and the time-domain simulation studies are presented to elucidate the effectiveness of the tuned damping controller in the DFIG system. The improvement of the fault ride-through capability of the system is also demonstrated. Index Terms—Bacterial foraging (BF), control, coordinated tuning, damping controller, doubly fed induction generator (DFIG), dynamic system stability, wind turbine (WT).
NOMENCLATURE θtw Ps Lss Lrr Lm Rr Rs Ht Hg ωt ωr ωs ωelb Tsh Tm Tem Ksh eds , eq s ψdr , ψq r ids , iq s vds , vq s idr , iq r
Shaft twist angle (rad). Stator active power per unit (p.u.). Stator self induction (p.u.). Rotor self induction (p.u.). Mutual inductance between rotor and stator (p.u.). Rotor resistance (p.u.). Stator resistance (p.u.). Inertia constant of turbine (s). Inertia constant of the generator (s). Wind turbine angular speed (p.u.). Generator angular speed (p.u.). Synchronous speed (p.u.). Electrical base speed (rad/s). Shaft torque (p.u.). Wind torque (p.u.). Electromagnetic torque (p.u.). Shaft stiffness (p.u./el.rad). d and q axis voltages behind- transient reactance (p.u.). d and q axis rotor fluxes (p.u.). d and q axis stator currents (p.u.). d and q axis stator voltages (p.u.). d and q axis rotor currents (p.u.).
Manuscript received April 15, 2008; revised August 27, 2008. First published June 16, 2009; current version published August 21, 2009. Paper no. TEC-00123-2008. Y. Mishra is with the School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane, QLD-4072, Australia (e-mail:
[email protected]). S. Mishra, M. Tripathy, and N. Senroy are with the Indian Institute of Technology, Delhi 110016, India (e-mail:
[email protected]; nsenroy@ee. iitd.ac.in). Z. Y. Dong is with the Hong Kong Polytechnic University, Kowloon, Hong Kong (e-mail:
[email protected]). Digital Object Identifier 10.1109/TEC.2009.2016034
idg , iq g vdg , vq g vdr , vq r vdc , idc C
d and q axis currents of the grid-side converter (p.u.). d and q axis voltages of the grid-side converter (p.u.). d and q axis rotor voltages (p.u.). Voltage and current of dc capacitor (p.u.). Capacitance of the dc capacitor (µ farad). I. INTRODUCTION
HERE is a great thrust for renewable sources of energy to reduce carbon emissions, minimize the effect on global warming, and cut down the dependence on fossil fuels. In the recent years, there has been a growing amount of interest in wind energy conversion systems (WECS). As power generation from WECS is significantly increasing, it is of paramount importance to study the effect of wind-integrated power systems on overall system stability. The doubly fed induction generator (DFIG) has been popular among various other techniques of wind power generation, because of its higher energy transfer capability, low investment, and flexible control [1]. DFIG is different from the conventional induction generator in a way that it employs a series voltage-source converter to feed the wound rotor. The feedback converters consist of a rotor-side converter (RSC) and a gridside Converter (GSC). The control capability of these converters gives DFIG an additional advantage of flexible control and stability over other induction generators. The dynamic behavior of DFIG has been investigated by several authors in the past. A third-order model for transient stability using PSS/E has been reported in [2]. Furthermore, the detailed model of the grid-connected DFIG has been presented in [3] whereas the modal analysis has been discussed in [4]. The change in modal properties for different operating conditions and system parameters is also discussed in [4]. However, in [4], the real power is considered equal in the RSC and the GSC, and hence, the dc link capacitor voltage oscillations are not considered. However, the power balance cannot be achieved instantaneously, and hence, the inclusion of the dc link capacitor voltage transient is important to complete the DFIG system model. The performance of decoupled control of active and reactive power of DFIG is presented in [5]. Furthermore, the control methods for DFIG to make it work like a synchronous generator and the fault ride-through behavior have been reported in [6] and [7], respectively. The DFIG control strategy is based on conventional proportional integral (PI) technique, which is well accepted in the industry. The decoupled control of DFIG has the following
T
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MISHRA et al.: IMPROVING STABILITY OF A DFIG-BASED WIND POWER SYSTEM WITH TUNED DAMPING CONTROLLER
controllers namely Pref , Vsref , Vdcref and qcref . These controllers are required to maintain maximum power tracking, stator terminal voltage, dc voltage level, and GSC reactive power level, respectively. The coordinated tuning of these controllers by hit and trial method is a cumbersome job. Particle swarm optimization (PSO), an evolutionary computational technique, has been applied for the optimization of the controller for the RSC in time domain [8]. The objective function is to reduce the overcurrent in the rotor circuit. However, as the settling time (proportional to damping ratio) was not considered in the above objective function, the GSC controller was not optimized, and hence, larger oscillations of the dc link voltage was reported in [8]. Eigenvalue approach is adopted in [9] to overcome the problem of larger oscillations in dc link voltage. The objective is to shift all the eigenvalues as far as possible to the left half of the S-plane to improve the damping ratio [9]. It optimizes all controllers in the DFIG system including GSC controllers. However, damping of the low-frequency oscillatory modes were not given due importance. A power system stabilizer (PSS) using an auxiliary speed deviation signal for the DFIG-based wind generation is presented in [10]. It is reported that the presence of the PSS in the DFIG system improves the damping of the oscillations in the network. Nevertheless, it is very important to optimize the controller parameters of the PSS to achieve the best effect. Moreover, according to the present grid code, the wind farm should have enhanced fault ride-through capability [11], [12]. In this paper, the auxiliary signal derived from ωr is added to the rotor phase angle control to enhance the low-frequency damping of the system. This simple PI controller is called damping controller. This is different from [10], where the PSS designed consists of lead–lag blocks and has a different method of implementation. Moreover, all the DFIG controllers namely Pref , Vsref , Vdcref and qcref are implemented in this paper. Hence, the coordinated effect of these controllers on the system damping as well as on the fault ride-through capability is examined. Furthermore, the control philosophy adopted is based on the flux magnitude-angle control (FMAC) and a similar idea can be developed for the alternative DFIG control paradigms. The coordinated tuning of these controllers is necessary to enhance the system stability. Conventional optimization technique such as linear/nonlinear programming are gradient-based algorithms requiring the objective function to be differentiable and often lead to suboptimal solution. However, the populationbased optimization techniques, on the other hand, do not require the differentiable objective function and are known for their capability of locating optimal solution and better convergence speed [13], [14]. It includes genetic algorithm (GA), bacterial foraging (BF), PSO, etc. GA is reported to have trouble in the optimization when dealing with epistatic objective function (i.e., where the parameters to be optimized are highly correlated). Moreover, the premature convergence of GA degrades its performance and reduces its search capability [15]. Among various methods for the optimization, BF is selected because of its better capability of locating optimal solution and higher convergence speed [16].
Fig. 1.
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DFIG system.
The contributions of this paper are as follows: 1) to study the effect of the damping controller on the DFIG system; 2) to tune damping controller to improve the damping of the oscillatory modes; 3) to study the effect of the damping controller on the variation of the dc voltage across capacitor; and 4) to study the efficacy of the damping controller in improving the fault ride-through capability of the system. This paper is structured as follows. Section II presents the modeling of the DFIG system. The detailed control methodology is discussed in Section III with special emphasis on damping controller. Section IV describes the BF algorithm for the optimization of the controllers parameters. Section V discusses simulation and results followed by conclusions in Section VI. II. MODELING OF DFIG The grid-connected single machine infinite bus (SMIB) system shown in Fig. 1 is considered. The stator and rotor voltages of the doubly excited DFIG are supplied by the grid and the power converters, respectively. Simulation of the realistic response of the DFIG system requires the modeling of the controllers in addition to the main electrical and mechanical components. The components considered include turbine, drive train, generator, and the back-to-back converter system. These components are well established in the literature [3], however, for the sake of completeness of the paper, they are introduced in brief later. A. Turbine and Drive Train The mechanical power input to the WT is considered as a constant, i.e., the blade pitch angle does not change during the period of study. In this paper, the two mass drive train model [17] is considered and the dynamics can be expressed by the differential equations [4] dωt = Tm − Tsh dt 1 dθtw = ωt − ω r ωelb dt 2Ht
2Hg where Te =
Ps ωs
dωr = Tsh − Te dt
and Tsh = Ksh θtw .
(1) (2) (3)
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B. Generator The most common way of representing DFIG for the purpose of simulation and control is in terms of direct and quadrature axes (dq axes) quantities, which form a reference frame that rotates synchronously with the stator flux vector [3]. The various variables are defined as: eq s = Km r r ωs ψdr , eds = −Km r r ωs ψq r , Ls = Lss − L2m /Lr r , Tr = Lr r /Rr , Km r r = Lm /Lr r , and ωe = ωelb ωs . For balanced and unsaturated conditions, the corresponding p.u. DFIG model can be expressed as [3] ωr 1 ωs Ls diq s = −R1 iq s + ωs Ls ids + e − e ... ωe dt ωs q s Tr ωs ds . . . − vq s + K m r r v q r ωs Ls ωe
Fig. 2.
(4)
dids ωr 1 = −R1 ids − ωs Ls iq s + e + e ... dt ωs ds Tr ωs q s
(5) . . . − vds + Km r r vdr 1 ωr 1 = R2 ids − eq s + 1 − eds −Km r r vdr ωe dt Tr ωs ωs deq s
deds
1 1 ωr = −R2 iq s − e − 1− ωe dt Tr ωs ds ωs
(6) eq s +Km r r vq r (7)
where 2 R 2 = Km r r Rr
R1 = Rs + R2 . C. Converter Model The converter model in DFIG system comprises of two pulsewidth modulation invertors connected back-to-back via a dc link. The RSC is a controlled voltage source as it injects an ac voltage at slip frequency to the rotor. The GSC acts as a controlled voltage source, by generating an ac voltage at power frequency and maintains the dc link voltage constant. The power balance equation for the converter model can be written as Pr = Pg + Pdc
(8)
where Pr , Pg , Pdc are the active power at RSC, GSC, and dc link, respectively, which can be expressed as Pr = vdr idr + vq r iq r
(9)
Pg = vdg idg + vq g iq g
(10)
dvdc . (11) dt The details of converter controllers are elaborated in the following section. Pdc = vdc idc = Cvdc
III. CONTROLLERS FOR DFIG This section describes the controllers used for the DFIG system. As mentioned earlier, there are two back-to-back converters hence we need to control these two converter sides. Primarily,
Phasor diagram illustrating the operation of DFIG system [10].
these controller are known as RSC and GSC controllers. This section also introduces a new auxiliary control signal that is added to the angle control in the RSC to enhance the damping. This is known as damping control. A. RSC Controllers The phasor diagram in Fig. 2 describes the control scheme (based on FMAC), for the RSC controller. The magnitude of the eig , internally generated voltage vector in the stator, depends on the magnitude of the rotor flux vector ψr . This flux can be controlled by Vr , the rotor voltage. The angle δig , between the voltage vectors eig and Vs (stator terminal voltage, and hence, q-axis of the reference frame), is determined by the power output of the DFIG. Since vector eig is orthogonal to ψr , the angle between d-axis and ψr is also given by δig . The adjustment of the magnitude of the rotor voltage vector |Vr | and its phase angle δr is employed for the control of terminal voltage and electrical power, respectively [10]. The configuration of the feedback controllers for the DFIG system is as shown in the Fig. 3. The RSC controller is as shown in the Fig. 3(a). First part aims at controlling the active power so as to track the Pref while the second part is to maintain the terminal voltage. The Pref is determined by the wind turbine (WT) power speed characteristic (Cp (λ, β) curve) for maximum power extraction [17]. Under normal operating condition, the active power set-point, Pref for the RSC is defined by the maximum power tracking point, which is a function of optimal generation speed. Mathematically, the aforementioned concept can be expressed by the set of differential equations as du1 = Pref − P (12) dt (13) u2 = Kp1 (Pref − P ) + KI 1 u1 du3 = (δe i g ref + u2 − δe i g ) dt u4 = Kp3 (Vsref − Vs ) + KI 3 u5 du5 = Vsref − Vs dt du6 = (|eig |ref + u4 − |eig |) dt ∆ |Vr | = Kp4 (|eig |ref + u4 − |eig |) + KI 4 u6
(14) (15) (16) (17) (18)
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to the grid by DFIG is only through the stator du10 = Qcref − Qc dt u11 = Kp6 (Qcref − Qc ) + KI 6 u10 .
(25) (26)
The reactive power setpoint Qcref is set to zero to reduce the GSC power rating. This implies that GSC only exchanges active power with the grid, and hence, the reactive power transmission to the grid by DFIG is only through the stator. The inphase and quadrature component of the GSC voltage is modified by (27) and (28) vginphase = vginphaseref + u11 xtg − ∆Vs vgquad = vgquadref − u9 xtg
(27) (28)
where vginphaseref = Vs + icgquadref × xtg and vgquadref = icginphaseref × xtg . And xtg is the three-winding transformer reactance between GSC and the stator terminal. icginphaseref and icgquadref are the inphase and quadrature component of GSC current to the stator terminal voltage defined as icginphaseref = Pr /Vs and icgquadref = (vds × iq g − vq s × idg )/Vs . ∆Vs is equal to (Vsref − Vs ). C. Damping Controller
Fig. 3. Control scheme for the DFIG system. (a) RSC. (b) GSC. (c) Damping controller.
du12 = ωrref − ωr dt u13 = Kp7 (ωrref − ωr ) + KI 7 u12
(19) (20)
∆δr = (Kp2 (δe i g ref + u2 − δe i g ) + KI 2 u3 ) − u13
(21)
where Kpi and KI i are the proportional and integral gain constant, respectively for ith PIcontroller. The internal generated
voltage vector eig is |eig | = as δe i g = tan
−1
e2 ds
+
e2 qs
and the angle is defined
(eds /eq s )
B. GSC Controllers The GSC control scheme is represented in Fig. 3(b). The reference signal for the dc voltage,Vdcref , is set to a constant value independent of the wind speed. And Vdc is regulated by the following equation: dVdc 1 = (vdr idr + vq r iq r − vdg idg − vq g iq g ) (22) dt Vdc C du8 = Vdcref − Vdc dt u9 = Kp5 (Vdcref − Vdc ) + KI 5 u8 .
(23) (24)
The reactive power setpoint qcref is set to zero to reduce the GSC power rating. This implies that GSC only exchanges active power with the grid, and hence, the reactive power transmission
Damping controller is employed in the RSC by (20), as shown in Fig. 3(c). The auxiliary signal u13 is added to the angle control of the RSC controller to enhance the damping of low-frequency angular oscillations. The auxiliary signal helps in increasing the damping torque by controlling the angular position of the rotor flux vector with respect to the stator flux vector. Thus, in summary, the state equations of the DFIG are (1)–(7), while RSC and GSC controller state equations are (12), (14), (16), (17), (22), (23), and (25). The damping controller state equation is (19). Hence, there are total 15 states of the DFIG system including the damping controller. IV. BF FOR THE OPTIMAL CONTROL OF DFIG SYSTEM The idea of BF is based on the fact that natural selection tends to eliminate animals with poor foraging strategies and favor the propagation of genes of those animals that have successful foraging strategies since they are more likely to enjoy reproductive success. After many generations, poor foraging strategies are either eliminated or reshaped into good ones. The E. coli bacteria that are present in our intestines also undergo a foraging strategy. The control of these bacteria is basically governed by four processes namely chemotaxis, swarming, reproduction, and elimination and dispersal [13]. A. Chemotaxis This process is achieved through swimming and tumbling. Depending upon the rotation of the flagella in each bacterium, it decides whether it should move in a predefined direction (swimming) or an altogether different direction (tumbling) in the entire lifetime of the bacterium. To represent a tumble, a unit length random direction, say φ(j), is generated; this will be used to define the direction of movement after a tumble. In
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particular θi (j + 1, k, l) = θi (j, k, l) + Cl(i)φ(j)
(29)
where θi (j, k, l) represents the ith bacterium at jth chemotactic, kth reproductive, and lth elimination and dispersal step. Cl(i) is the size of the step taken in the random direction specified by the tumble (run length unit). B. Swarming During the process of reaching toward the best food location, it is always desired that the bacteriumthat has searched optimum path should try to attract other bacteria so that they reach the desired place quickly. Swarming makes the bacteria congregate into groups, and hence, move as concentric patterns of groups with high bacterial density. Mathematically, swarming can be represented by Jcc (θ, P (j, k, l)) =
S i=1
=
S
i i θ, θ (j, k, l) Jcc
−dattract exp −ωattract
i=1
+
S
p m =1
hrep ellent exp −ωrep ellent
i=1
i 2 (θm −θm )
p
i 2 (θm −θm )
m =1
(30) where Jcc (θ, P (j, k, l)) is the cost function value to be added to the actual cost function to be minimized to present a timevarying cost function “S” is the total number of bacteria. “p ’ is the number of parameters to be optimized that are present in each bacterium. dattract , ωattract , hrep ellent , and ωrep ellent are different coefficients that are to be chosen judiciously. dattract is the depth of the attractant released by the cell and sets the magnitude of secretion of attractant by a cell. ωattract is the width of the attractant signal and determines the chemical cohesion signal diffusion (smaller value makes it diffuse more). Whereas, hrep ellent is the height of the repellent effect, and ωrep ellent is the measure of the width of the repellent that controls the tendency to repel other cells. The magnitude of dattract and hrep ellent should be same [18]. It is so that there is no penalty added to the cost function when the bacterial population converges, i.e., Jcc of (30) will be 0. Their numerical value should be decided based on the required variation in the magnitude of the actual cost function J to obtain a satisfactory result. The value of ωattract and ωrep ellent should be such that if the Euclidian distance between bacteria is large, the penalty Jcc is large. C. Reproduction The weakest bacteria die and the healthiest bacteria split into two, which are placed in the same location. This makes the population of bacteria constant. Instead of taking the average value of all the chemotactic cost functions, the minimum value
Fig. 4. Flowchart summarizing the bacteria foraging algorithm for the optimization of controller parameters. TABLE I SELECTED EIGENVALUES OF THE WT SYSTEM WITHOUT ANY CONTROLLERS AT WIND SPEED: 8.5 m/s
is selected for deciding the health of the bacteria [19]. Mathematically, for particular kth and lth, the health of the ith bacteria i = min {Jsw (i, j, k, l)}, where would be given by, Jhealth j ε{1,2...N c } Jsw = J + Jcc . D. Elimination and Dispersal It is possible that in the local environment the life of a population of bacteria changes either gradually (e.g., via consumption of nutrients) or suddenly due to some other influence. Events can occur such that all the bacteria in a region are killed or a group is dispersed into a new part of the environment. They have the effect of possibly destroying the chemotactic progress, but they also have the effect of assisting in chemotaxis, since dispersal may place bacteria near good food sources. From a broad perspective, elimination and dispersal are parts of the population-level long-distance motile behavior. It helps in reducing the behavior of stagnation, (i.e., being trapped in a premature solution point or local optima) often seen in such parallel search algorithms. This section is based on the work in [14]. The
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TABLE II SELECTED EIGENVALUES OF THE WT SYSTEM
detailed mathematical derivations as well as theoretical aspect of this new concept are presented in [13], [14], [16], [19], and [20]. In this paper, optimization using BF scheme is carried out to find the optimal controller parameters of the DFIG system. The algorithm is presented in the flow chart as shown in Fig. 4.
B. DFIG System Without Damping Controller
V. SIMULATION AND RESULTS The aforementioned optimization technique is applied to a SMIB DFIG system. The DFIG system with controllers can be represented by the set of differential and algebraic equations (DAEs) as . x = f (x, y, u) 0 = g(x, y, u)
(31)
where x, y, and u are the vectors of DFIG state, algebraic, and control variables, respectively. The state vector is defined by x = [iq s , ids , eq s , eds , ωr , θw t , . . . . . . ωt , vdc , u1 , u3 , u5 , u6 , u8 , u10 , u12 ]T . (32) Linearizing the above DAE about an operating point (x0 , y0 , u0 ) (which is obtained by the load flow at a particular wind speed), the system matrix Asys can be calculated as .
∆ x = Asys ∆x.
(33)
The parameters of the DFIG system are given in the Appendix. A. Objective Function The parameters of DFIG controllers are selected so as to minimize the following objective function: J = 1/(min ζi ) ∀i
where ζi is the damping ratio of the ith eigenvalue of the system. This objective function makes sure that the minimum damped eigenvalue is heavily damped and the system small signal stability is ensured.
(34)
Eigenvalues of the WT system without any control scheme at wind speed of 8.5 m/s is shown in Table I. There are only seven differential equations corresponding to the DFIG system without any control. The first mode is stator or electrical mode and the second is electromechanical mode, which can be identified by looking at the participation factors. As electrical state (eds ) and mechanical state (ωr ) participate in the second mode, hence this mode is electromechanical mode. The stator mode has the lowest damping ratio but its frequency is high, and hence, out of the range of interest. The low frequency mode, i.e., mechanical mode (0.60 Hz) is well damped. However, the application of controllers (necessary to enhance the performance of the DFIG system) deteriorates its damping from 28.38% (Table I) to 13.4% (Table II). Having said this, it is easy to suspect that the damping might reduce or even may become negative under changed operating conditions, and hence, the damping of this mode should be investigated thoroughly. Initially, the DFIG system has four controllers [as presented in Fig. 3(a) and (b)]. The coordinated tuning of the parameters of the these controllers is performed by BF at wind speed of 8.5 m/s. With the optimized parameters (listed in the Appendix), the eigenvalues of the DFIG system is presented in left-half of Table II. As there are total 14 differential equations (including seven equations for the WT system, one for dc capacitor, and six equations for the different controllers), there are 14 eigenvalues. The damping of the third mode (0.95 Hz) is 13.4%. It is observed that the state associated with 0.95 Hz mode are primarily
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Dynamic response of the DFIG system under small perturbation With wind speed as 8.5 m/s.
θtw and eq s . The damping is sufficient, as the controller parameters are optimized using BF technique for this operating condition. However, this electromechanical mode might bring the system to instability under changed operating conditions, e.g., wind speed. This is depicted in Table II. When the wind speed (which is highly uncertain) is changed to 8.9 m/s, the third mode becomes unstable with negative damping. Therefore, it is essential to improve the damping of this eigenmode. The aim of this paper is to develop the damping controller to improve the damping of the oscillatory modes. Hence, only the oscillatory modes and their corresponding states are listed in Table II. C. DFIG System With Damping Controller This section proposes the need of an additional control to improve the damping of the DFIG system. The auxiliary signal generated from (ωrref − ωr ) is used to improve the damping of electromechanical mode that is associated with the variable θtw . This signal is indirectly associated with θtw and ωt states. The reason for selecting ωr signal instead of θtw or ωt , for the damping controller is its relative ease of sensing and measuring for control applications. The damping controller, as shown in Fig. 3(c), is used and its parameters are optimized using BF algorithm. The parameters of the damping controller Kp7 and KI 7 are optimized for the wind speed of 8.5 m/s, keeping all other controllers’ parameters at their optimum value. The objective is to improve the damping of electromechanical mode associated
Fig. 6. Performance of the damping controller on the dc link capacitor voltage under small perturbation with wind speed as 8.9 m/s.
with θtw . This objective function is formulated as in (34), where ζ corresponds to the damping of the mode associated with highest participation of the state θtw . In this case, there are total of 15 differential equations. The additional differential equation corresponds to the damping controller as mentioned in section III-C. The damping of mode 3 has increased from 13.4% to 36.7% as shown in Table II.
MISHRA et al.: IMPROVING STABILITY OF A DFIG-BASED WIND POWER SYSTEM WITH TUNED DAMPING CONTROLLER
Fig. 7. 1.04 s.
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Response of the DFIG system under three-phase fault for 30 ms with crowbar protection. The fault inception is at 1 s and the crow bar is removed at
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D. Performance of Damping Controller Under Changed Wind Speed, i.e., 8.9 m/s The wind speed is unpredictable, and hence, the aim of the controllers should be to keep the system well under stability limits even under variable wind speed. Under different wind speed, system has a negative damping corresponding to the electromechanical mode (i.e., mode 3). However, the system is stable (positive damping) in the presence of the damping controller (Table II). This confirms the need of the damping controller in the system. It not only improves the damping of the critical mode under normal operating conditions, but also under changed operating condition.
E. Dynamic Simulations The nonlinear simulation of the DFIG system is observed to validate the efficacy of the damping controller. The optimized controller parameters are used and the system is simulated in MATLAB using ODE15s. The efficacy of the optimization procedure is observed and the fault ride-through capability is also studied. 1) Small Perturbation: The system is subjected to a small perturbation by a small change in the wind speed at 1.0 s. It amounts to 5% decrease in electrical torque. The system torque returns to its original value after 200 ms. The response of the DFIG system with and without damping controller is shown in Fig. 5. The system is very well behaved if the optimized damping controller is used. 2) Oscillations in dc Capacitor Voltage Vdc : It is important to study the oscillations in the dc capacitor voltage as it decides the converter rating in the DFIG. The RSC and GSC should be rated to have enough margin for safe and reliable operation of the system. Larger the variation in the voltage, larger should be the rating of the converters, so that in the event of any perturbation system remains operational. Under small perturbations, the oscillations of Vdc with damping controller is improved as shown in Fig. 5. The improvement in the damping is clearly observed. The performance of the system under changed operating conditions is also performed and only the dc link capacitor voltage variation is presented in Fig. 6. The dc voltage becomes unstable (with growing oscillations) when the wind speed is changed to 8.9 m/s from 8.5 m/s. However, in the presence of the damping controller, the dc link voltage settles down in around 6 s. This confirms the result obtained by the eigenvalue analysis in Table II. Hence, the damping of the dc voltage variation is automatically achieved by the implementation of damping controller. It reduces the stress on the converter rating of the DFIG system. 3) Fault Ride-Through Capability: The effect of damping controller on the DFIG wind generator under fault inception is observed by a three-phase fault created near to the infinite bus for 30 ms. The system returns to its normal condition very quickly because of the damping controller. The response of the DFIG system under fault is presented in Fig. 7. Crowbar protection scheme has been considered. The RSC is disconnected and the rotor of the DFIG is shorted with the crowbar resistance
Fig. 8. Fault ride capability of DFIG system under three-phase fault for 33 ms with Wind speed is 8.5 m/s. System is able to ride through the fault with damping controller.
of 0.1 p.u. [21]. Crowbar is removed after 10 ms of the fault clearance. The GSC and RSC graphs are also elaborated. The fault ride through capability of the DFIG-based wind system with the damping controller is observed by increasing the duration of fault from 30 to 33 ms. It is observed that, without damping controller, the simulation stopped as system becomes unstable after 2.4 s of fault inception as depicted in Fig. 8. However, the system is stable with the damping controller in operation. Hence, the tuned damping controller has improved the fault ride-through capability of the DFIG system.
VI. CONCLUSION A damping controller using the auxiliary signal of speed deviation is used in the angle control of the RSC controller in the DFIG system. It gives promising results in damping out the low frequency oscillations, and hence, improves the system stability of the grid-connected DFIG system. The coordinated tuning of the damping controller with the other DFIG controllers is also reported in this paper. It is observed that this tuning is helpful in not only improving the damping of the oscillatory modes but also in enhancing the fault ride-through capability of the DFIG system. Hence, tuned damping controller is necessary for enhancing the stability of the DFIG system connected to the grids. With the increasing penetration of DFIG-based wind farms into the grid, it is important to study the implications of largescale DFIG systems on grid stability. As this study is based on SMIB DFIG system, conclusions of this paper should not be extended to multimachine DFIG-based WT system. Nevertheless, this paper does provide a good initial study of the DFIG system with controller. Computations with multimachine DFIG system will be required to confirm the obtained results and determine if its possible to quantify the impact of DFIGs on power system stability.
MISHRA et al.: IMPROVING STABILITY OF A DFIG-BASED WIND POWER SYSTEM WITH TUNED DAMPING CONTROLLER
APPENDIX A. Parameters of the SMIB DFIG System (p.u.) Ht = 4; Hg = 0.4; Xm = 4; Lm = 4; xtg = 0.55; C = 0.01; xe = 0.06; Lss = 4.04; Lr r = 4.0602; Rs = (Xm /800); Rr = 1.1 × Rs B. Parameters Used for the Optimization (BF Algorithm) S = 4; Cl = 0.07; dattract = 1.9; ωattract = 0.1; hrep elant = dattract ; ωrep elant = 10; C. Optimized Controller Parameters With the Damping Controller
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[15] M. A. Abido, “Optimal design of power system stabilizers using particle swarm optimization,” IEEE Trans. Energy Convers., vol. 17, no. 3, pp. 406–413, Sep. 2002. [16] S. Mishra, M. Tripathy, and J. Nanda, “Multimachine power system stabilizer design by rule based bacteria foraging,” Electr. Power Syst. Res., vol. 77, no. 12, pp. 1595–1607, Oct. 2006. [17] S. K. Salman and A. L. J. Teo, “Windmill modeling consideration and factors influencing the stability of a grid-connected wind power based embedded generator,” IEEE Trans. Power Syst., vol. 18, no. 2, pp. 793– 802, May 2003. [18] S. Mishra, “Hybrid least-square adaptive bacteria foraging strategy for harmonic estimation,” Inst. Elect. Eng. Proc. Gener. Transm. Distrib., vol. 152, no. 3, pp. 379–389, May 2005. [19] M. Tripathy and S. Mishra, “Bacteria foraging-based solution to optimize both real power loss and voltage stability limit,” IEEE Trans. Power Syst., vol. 22, no. 1, pp. 240–248, Feb. 2007. [20] M. Hunjan and G. K. Venayagamoorthy, “Adaptive power system stabilizers using artificial immune system,” in Proc. IEEE Symp. Artif. Life, Apr. 2007, pp. 440–447. [21] A. D. Hansen and G. Michalke, “Fault ride through capability of DFIG wind turbines,” Renewable Energy, vol. 32, pp. 1594–1610, 2007.
Kp1 = 0.4340; KI 1 = 0.2613; Kp2 = 0.4952; KI 2 = 0.4632; Kp3 = 0.0225; KI 3 = 0.1713; Kp4 = 0.0062; KI 4 = 0.1590; Kp5 = 0.0116; KI 5 = 0.2360; Kp6 = 0.2495; KI 6 = 0.1238; Kp7 = 16.1174; KI 7 = 42.3049; REFERENCES [1] P. B. Eriksen, T. Ackermann, H. Abildgaard, P. Smith, W. Winter, and J. M. Rodriguez Garcia, “System operation with high wind penetration,” IEEE Power Energy Manag., vol. 3, no. 6, pp. 65–74, Nov./Dec. 2005. [2] Y. Lei, A. Mullane, G. Lightbody, and R. Yacamini, “Modeling of the wind turbine with a doubly fed induction generator for grid integration studies,” IEEE Trans. Energy Convers., vol. 21, no. 1, pp. 257–264, Mar. 2006. [3] F. Mei and B. C. Pal, “Modeling SND small signal analysis of a grid connected doubly fed induction generator,” in Proc. IEEE PES Gen. Meeting, San Francisco, CA, 2005, pp. 358–367. [4] F. Mei and B. C. Pal, “Modal analysis of grid connected doubly fed induction generator,” IEEE Trans. Energy Convers., vol. 22, no. 3, pp. 728–736, Sep. 2007. [5] M. Yamamoto and O. Motoyoshi, “Active and reactive power control for doubly-fed wound rotor induction generator,” IEEE Trans. Power Electron., vol. 6, no. 4, pp. 624–629, Oct. 1991. [6] F. M. Hughes, O. Anaya-Lara, N. Jenkins, and G. Strbac, “Control of DFIG-based wind generation for power network support,” IEEE Trans. Power Syst., vol. 20, no. 4, pp. 1958–1966, Nov. 2005. [7] J. Morren and S. W. H. de Haan, “Ridethrough of wind turbines with doubly-fed induction generator during a voltage dip,” IEEE Trans. Energy Convers., vol. 20, no. 2, pp. 435–441, Jun. 2005. [8] W. Qiao, G. K. Venayagamoorthy, and R. G. Harley, “Design of optimal PI controllers for doubly fed induction generators driven by wind turbines using particle swarm optimization,” in Proc. Int. Joint Conf. Neural Netw., Canada, Jul. 2006, pp. 1982–1987. [9] F. Wu, X. P. Zhang, K. Godfrey, and P. Ju, “Small signal stability analysis and optimal control of a wind turbine with doubly fed induction generator,” Inst. Elect. Eng. Proc. Gener., Transm. Distrib., vol. 1, no. 5, pp. 751–760, 2007. [10] F. M. Hughes, O. A. Lara, N. Jenkins, and G. Strbac, “A power system stabilizer for DFIG-based wind generation,” IEEE Trans. Power Syst., vol. 21, no. 2, pp. 763–772, May 2006. [11] W. P. F. T. Requirements, “Alberta electric system operator technical report,” No: 2004-10803-2.R01.4. [12] “Grid Code: High and Extra High Voltage, E.O.N Netzanschlussregeln Hoch-und Hoechstspannung,” Rep. ENENARHS2006, pp. 46, Apr. 2006. [13] K. M. Passino, “Biomimicry of bacterial foraging for distributed optimization and control,” IEEE Control Syst. Mag., vol. 22, no. 3, pp. 52–67, Jun. 2002. [14] S. Mishra, “A hybrid least square-fuzzy bacteria foraging strategy for harmonic estimation,” IEEE Trans. Evol. Comput., vol. 9, no. 1, pp. 61– 73, Feb. 2005.
Y. Mishra (S’06) received the B.E and M.Tech degrees from the Birla Institue of Technology (BIT), Ranchi, India and the Indian Institue of Technology (IIT), New Delhi, India, in 2003 and 2005, respectively. He is currently working toward the Ph.D. degree at the University of Queensland, Australia. His current research interests include distributed generation, DFIG-based wind generation systems, and power system stability and control.
S. Mishra (SM’04) received the B.E. degree from the University College of Engineering, Burla, India, in 1990, and the M.E. and Ph.D. degrees from the Regional Engineering College, Rourkela, India, in 1992 and 2000, respectively. In 1992, he joined the Department of Electrical Engineering, University College of Engineering as a Lecturer, where he became a Reader in 2001. Currently, he is an Associate Professor at the Department of Electrical Engineering, Indian Institute of Technology, New Delhi, India. Dr. Mishra is a Fellow of the Indian Academy of Engineers. He was the recipient of many prestigious awards such as the Indian National Science Academy (INSA) Young Scientist Medal in 2002, Indian National Academy of Engineering (INAE) Young Engineer’s Award in 2002, recognition as Department of Science and Technology (DST) Young Scientist in 2001–2002, etc. His current research interests include fuzzy logic and artificial neural network (ANN) applications to power system control and power quality.
M. Tripathy is currently working toward the Ph.D. degree in the Department of Electrical Engineering, Indian Institute of Technology, Delhi, India. He is a Lecturer in the Department of Electrical Engineering, University College of Engineering, Burla. His current research interests include intelligent control application to power system dynamics.
N. Senroy (M’06) received the Ph.D. degree from Arizona State University, Tempe. He also has postdoctoral experience at the Center for Advanced Power Systems, Florida State University, Tallahassee. He is currently an Assistant Professor in the Department of Electrical Engineering, Indian Institute of Technology, New Delhi, India. His current research interests include power system stability and signal processing applications in power systems.
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Z. Y. Dong (M’99–SM’06) received the Ph.D. degree from the University of Sydney, Sydney, Australia in 1999. He is with the Hong Kong Polytechnic University, Hong Kong. Previously, he held various academic positions with the University of Queensland, Australia and National University of Singapore. He also held industrial positions with Powerlink Queensland, and Transend Networks, Tasmania, Australia (both are transmission network services providers). His research interest includes power system planning, power system security, stability and control, load modeling, electricity market, and computational intelligence and its application in power engineering.
