Inter national J our nal of Electrical and Computer Engineering (IJECE) V ol. 8, No. 5, October 2018, pp. 3711 – 3721 ISSN: 2088-8708 3711       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w     .    i     a    e    s    j    o    u    r    n    a    l     .    c     o    m     PI and LQR contr ollers f or Fr equency Regulation including W ind Generation Semaria Ruiz 1 , J ulian P ati ˜ no 2,3 , and J air o Espinosa 1 1 Departmento de Ingenier ´ ıa El ´ ectrica y Autom ´ atica, F acultad de Minas, Uni v ersidad Nacional de Colombia, Medell ´ ın, Colombia 2 Departmento de Ingenier ´ ıa El ´ ectrica, F acultad de Ingenier ´ ıa y Arquitectura, Uni v ersidad Nacional de Colombia, Manizales, Colombia 3 Instituci ´ on Uni v ersitaria P ascual Bra v o, Medell ´ ın, Colombia Article Inf o Article history: Recei v ed February 21, 2018 Re vised May 26, 2018 Accepted June 21, 2018 K eyw ord: W ind T urbines Load Frequenc y Control Linear Quadratic Re gulator Proportional Inte gral control Po wer Systems ABSTRA CT The increasing use of rene w able technologies such as wind turbines in po wer systems may require the contrib ution of these ne w sources into grid ancilla ry services, such as Load Frequenc y Control. Hence, this w ork dealt with the performance compar - ison of tw o traditional control structures, PI and LQR, for secondary re gulation of Load Frequenc y Control with the participation of v ariable-speed wind turbines. F or this purpose, the doubly-fed induction generator wind turbine w as modeled with addi- tional control loops for emulation of the inertial response of con v entional machines for frequenc y re gulation tasks. Performance of proposed strate gies w as v erified through simulation in a benchmark adapted from the WSCC 3 machines 9-b us test system. Results s ho wed o v erall superior performance for LQR controller , although requiring more strenuous control ef fort from con v entional units than PI control. Copyright c 2018 Institute of Advanced Engineering and Science . All rights r eserved. Corresponding A uthor: Semaria Ruiz Departmento de Ingenier ´ ıa El ´ ectrica y Autom ´ atica, F acultad de Minas, Uni v ersidad Nacional de Colombia, Medell ´ ın, Colombia Carrera 80 No 65-223 Medell ´ ın, Colombia +57 4 4255092 seruizal@unal.edu.co 1. INTR ODUCTION Electricity production from rene w able ener gy sources (RES) has been continually gro wing. This de v elopment is taking place in a po wer system s tructure designed for con v entional po wer sources, with char - acteristics such as a v ailability , controllability , and reliability utterly dif ferent to those of RES systems [1][2]. Also, the ener getic production of RES may fluctuate significantly o v er time due to some characteristics of natural resources, such as unpredictability , v ariability , and dependenc y on the geographic location [3] [4]. In particular , some issues attracting a lot of interest in the technical community are the acti v e po wer v ariations and frequenc y performance in presence of RES [1][3] [5], for systems including solar photo v oltaic (PV) panels [6] and mostly for wind turbines (WT) [7]. In po wer systems, frequenc y constitutes a parameter indicating the equilibrium between po wer de- manded by load and the ener gy produced by generation systems [8]. When this relationship is unbalanced, control structures are in place to return system frequenc y to the right operat ional v alues. Ho we v er , these frequenc y control strate gies ha v e been de v eloped for a po wer system with almost complete reliance on con v en- tional ener gy sources, and the penetration of RES may require the participation of these ne w units in the control tasks [3]. W ind t urbines, particularly those of v ariable-speed with doubly-fed induction (DFIG), constit ute one of the most used RES around the w orld [9] [10]. Hence, se v eral studies ha v e been proposed about control strate gies for the acti v e inclusion of DFIG WT in Load Frequenc y Control loops, and complete re vie ws can be found in references [7] [11] [12]. J ournal Homepage: http://iaescor e .com/journals/inde x.php/IJECE       I ns t it u t e  o f  A d v a nce d  Eng ine e r i ng  a nd  S cie nce   w     w     w     .    i     a    e    s    j    o    u    r    n    a    l     .    c     o    m     ,  DOI:  10.11591/ijece.v8i5.pp3711-3721 Evaluation Warning : The document was created with Spire.PDF for Python.
3712 ISSN: 2088-8708 + - - - + + + - + - + - + + + Wind Turb ine Model Figure 1. LF C scheme for a multi-area ( N areas) po wer system, including primary and secondary control loops [1]. The block ”W ind T urbine Model” inte grates WT to LFC. One of the most used strate gies for DFIG contrib ution in frequenc y re gulation, is the so-called syn- thetic inertia method, as e xplained in the studies [13] and [14]. In this technique, additional control loops are de v eloped for the WT with the goal of emulating frequenc y response of con v entional generators. This alter - nati v e w as e xplored in other w orks where controllers based on the dynamic representat ions of the DFIG WT were proposed. In [15] a Linear Quadratic Re gulator type of controller is designed for the WT , taking as model inputs the reference torque and the reference pitch angle of the turbine. The w ork of Mohamed et al. [16] proposes a Model Predicti v e Controller for WT inte gration to frequenc y re gulation, using a simplified model of the DFIG with the quadrature-axis rotor v oltage as the model input. Ho we v er , these studies are not e xploring WT penetration in a multi-area scenario for po wer systems, an increasingly common operational possibility as grid gro ws in size and RES inte gration le v el arises. Also, a performance comparison of some of the proposed strate gies o v er the same scenario w ould be useful to establish the most suitable control structure for WT con- trib ution in frequenc y re gulation tasks. This paper addresses both of the formerly mentioned issues, comparing the performance of PI-based and LQR-based controllers for DFIG WT inte gration into Load Frequenc y Re gu- lation (LFC) structure for a multi-area po wer system. The simulation is performed in a modified v ersion of the 9-b us WSCC po wer system [8]. This w ork is the continuation of the research with preliminary results reported in [17]. The former paper focused on the utilization of the synthetic inertia model for WT inte gration into LFC of po wer systems with PI controllers. Our current article presents a more elaborated description of the non-linear state-space realization emplo yed for the modeling of v ariable speed wind turbines. Moreo v er , DFIG wind turbine operation includes a pitch-angle control loop. Also, additional control structures are e xplored with the consideration of LQR controllers for secondary re gulation, and a performance comparison discussion v ersus PI strate gies. Current paper is di vided as foll o ws: Section 2. describes the LFC structure for po wer systems. Section 3. deals with the WT modeling and the formulation of PI and LQR controllers. Simulation tests and performance comparisons appear in Section 4.. At last, some conclusions are presented in Section 5.. 2. LO AD FREQ UENCY CONTR OL IN MUL TI-AREA PO WER SYSTEMS Frequenc y re gulation can be classified in three main stages according to the nature and timing of the control ef forts: primary actions proportional to the frequenc y de viations, secondary actions allo wing correction of steady-state errors, and tertiary actions related with predefined dispatches and some emer genc y conditions. These three stages constitute the Load Frequenc y Control (LFC) system [8, 1]. Grid eleme nts must be modeled for the design of LFC controllers. First order models are assumed for the go v ernor and turbine of con v entional units, and for the representation of the frequenc y response char - IJECE V ol. 8, No. 5, October 2018: 3711 – 3721 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 3713 + + + + - + - + - + - + - + - P i t c h a ngl e c o nt r o l l er s LF C LF C pr i ma r y l o o p LF C s ec o nda r y l o o p R o t o r s peed vs t o r que c ur v es Figure 2. W ind turbine model with frequenc y response and v ariable wind speed (based on [19]). acteristic of an y control area in the po wer system. Figure 1 sho ws the LFC for a N -area po wer system, where parameters for the i -th area are: P mk i the change in mechanical po wer of the generator k , P g k i the change in the acti v e po wer output of generator k , P L the load perturbation, f i the frequenc y change, D i the damp- ing coef ficient. H i the equi v alent inertia, P ck i the control action of the LFC for the k -th generator , T ij the po wer e xchange coef ficient between area i and area j , P tiei the total change in the po wer e xchanged between area i and other areas and f j the change in the frequenc y of area j connected to area i . Also, B i denotes the bias f actor for modulation of the error signal in secondary re gulation, K i ( s ) is the transfer function of the secondary controller and i the participation f actor of each generator in secondary control. 3. INCLUSION OF V ARIABLE SPEED WT IN LFC This w ork only considered v ariable-speed DFIG WT , as the y are the best-suit ed WT f or acti v e part ici- pation in grid ancillary services [18]. Ho we v er , WT units with DFIG do not present a natural inertial response to frequenc y changes [1]. F or enabling frequenc y response capabilities to the DFIG WT , synthetic inertia control strate gy [14] w as emplo yed. This technique proposes operation of the DFIG WT belo w the point of maximum po wer e xtraction to maintain a reserv e of kinetic ener gy to be used for frequenc y compensat ion. The operating point P o depends on the DFIG angular speed w r and the so-called operational torque T o [ N m ] , calculated as indicated in equation 1 for dif ferent v alues of wind speed v . Gain K op is adjusted for the operation of the WT under the curv e formed by the points of maximum withdra w able po wer from wind at each speed. T op = K op v 2 : (1) F or the electromagnetic component of the DFIG, the simplified model proposed in [13] [19] is used and included in the LFC as the wind-turbine model block in Figure 1. This representation, denominated as synthetic-inertia model , is a reduced induction-machine model of fourth order and only uses the quantities in q -axis, as the d -axis is selected as the reference frame. Figure 2 presents both models. In the scheme of Figure 2, P base is the nominal po wer of t he area, w r is the angular speed of rotor , n is the quantity of WTs, v q r is the rotor quadrature v oltage, i q r is the rotor quadrature current, iq r ;r is the reference quadrature current for rotor , P I v q r is the PI controller for v q r , T e is the electromagnetic torque, T m is the mechanical torque, is the bla d e pitch angle, r is the blade pitch angle reference, denotes the time delay of pitch angle actuator , w r ;r is the rotor angular speed reference, P I v q r is the PI controller for w r , v r is the rated wind speed of WT , K 1 is the proportional action of primary control, K 2 is the proportional action of secondary control, K w and T w are the g ain and time delay of secondary control loop, J is the inertia moment of WT , and X 1 X 2 , X 3 , and T 1 are approximately constant v alues representing some combinations among DFIG internal generator parameters (see [13] and [20] for detailed e xplanation). As seen from Figure 2, se v eral control loops are added to the simplified turbine model to emulate the beha vior of the dif ferent control stages of the LFC struct ure and to k eep the stable operation of the DFIG WT after contrib ution to frequenc y re gulation. These loops are described as follo ws: 1. A primary response loop for the DFIG labeled as LFC primary loop in Figure 2. Proportional g ain K 1 is PI and LQR contr oller s for F r equency Re gulation including W ind Gener ation (Semaria Ruiz) Evaluation Warning : The document was created with Spire.PDF for Python.
3714 ISSN: 2088-8708 modulating the frequenc y change rate d! dt . 2. A secondary response loop mark ed as LFC secondary loop in Figure 2 operating in the same w ay as t he secondary control of LFC. The po wer deli v ered by WT is restored to the nominal operating point after a control of frequenc y disturbances. 3. The pitc h-angle contr oller loop in Figure 2, task ed with maintaini ng the angular speed of the WT at nominal operating v alue for wind speeds equal or o v er the rated ones. Under the action of pitch control, in case of a frequenc y disturbance occurring, an additional control loop is required for modulating pitch angle with a g ain R proportional to frequenc y de viation. The area de viation frequenc y signal is filtered (through a filter with g ain K a and time delay T a , see Figure 2) before being applied to primary and secondary control loops. This w ork performs a comparison of the mentioned loops for tw o dif ferent secondary controllers in frequenc y re gulation. The follo wing subsections describe the PI and LQR secondary controllers (see K i ( s ) block i n Figure 1) and their interaction with the WT control scheme. 3.1. Considerations f or system with secondary PI contr oller Proportional Inte gral (PI) control constitutes the most used v ariation of the Proportional Inte gral Deri v ati v e (PID) structure [21]. Starting from a simple Single-Input Single-Output (SISO) loop [21], the trans- fer function C P I ( s ) of the PI controller is C P I ( s ) = K p (1 + ( T r s ) ( 1) . The term K p is the Proportional g ain, T r is kno wn as the reset time [21], and the relationship K p ( T r ) ( 1) is called the inte gral g ain. PI controllers constitute the traditional strate gy for secondary re gulation in LFC system. In this w ork, additional PI controllers re gulate quadrature rotor current ( P I i q r ) and the pitch angle ( P I w r ), as sho wn in Figure 2. 3.2. Considerations f or LFC system with secondary LQR contr oller Criterion-based synthesis of controllers is a design technique dri v en by the comple xity of multi- v ariable systems. A commonly emplo yed set of criteria is formed by cost functions related to quadratic forms of control ef fort and error signals [21]. F or linear case, the so-called Linear Quadratic Re gulator e xpresses the problem as the feasible solving of the dynamic Riccati equation in continuous time, leading to a time-v ariable state feedback [21]. F or this configuration, secondary controller K i ( s ) requires a state-space representation of the whole LFC. Equations (2) to (11) describe the complete non-linear state-space model for a multi-area po wer system with inte gration of WT to the LFC scheme, adapted from [16]. This representation includes the transferred po wer between areas P tie as a state, with an additional state equation for WT pitch-angle (see eq. (8)) as a parameter with high influence in the contrib ution of WT to LFC [15]. _ f = P m D f P L 2 H P tie 2 + X 3 w r iq r n P r ef P base f 2 H (2) _ P tie = 2 N X j =1 T i;j f + P c T g 2 v i (3) _ P m = P m T P g T g (4) _ P g = f R T g P g T g + P c T g (5) _ i q r = i q r T 1 + v q r T 1 (6) _ w r = X 3 i q r J + T m J (7) IJECE V ol. 8, No. 5, October 2018: 3711 – 3721 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 3715 Gen2 Gen3 Gen1 1 2 3 4 5 6 7 8 9 Lo a d5 Lo a d6 Lo a d8 Ar ea I Ar ea I I Ar ea I I I Figure 3. WSCC 9-b us system multi-area partitioning. System parameters can be found in [8]. _ = + r ef + R f (8) Mechanical torque T m is calculated from parameters such as air density , length of turbine blades and WT po wer coef ficient C p (fraction of a v ailable wind po wer being e xtracted). Dif ferences with [16] in v olv e the consideration of pitch angle reference r ef as an input, and wind speed v and frequenc y de viation of neighboring areas f j as outputs. Complete v ectors of system inputs U and disturbances W are sho wn belo w , with P L the de viations in demanded-load: Mechanical torque is calculated di viding equation (9) by the angular rotor speed: P m = 1 2  R 2 v 3 C p : (9) where represents air density , R is the length of the turbine blades and the po wer coef ficient C p denotes the fraction of a v ailable po wer in the wind that is being harv ested. This parameter is a function of the T ip-Speed Ratio (TSR) denoted by = R w r v , and the collecti v e blade pitch . U T = v q r P c r ef , W T = P L f j v (10) Finally , v ector Y presents system outputs in equation (11). The first output is the rotor quadrature current i q r , whose reference is gi v en by i q r ;r . The second output is the system Area Control Error (A CE), reference signal for the LFC secondary controller ( AC E = f + P tie ). The last output is the rotor angular speed, whose reference is defined for a gi v en mechanical torque. y T = iq r f + P tie w r : (11) 4. RESUL TS 4.1. Description of case of study A slightly modified v ersion of the WSCC 9-b us po wer system [8] w as emplo yed for simulation of the DFIG participation in the LFC for a multi-area po wer . The modified sys tem parameters are summarized in T able 1. This system w as partitioned into three areas, as illustrated in Figure 3. Consider Generator 1 as h ydraulic and Generators 2 and 3 as g as units. F or the sak e of this w ork, 50% of con v entional generation in Area III w as replaced by a wind f arm. The wind f arm w as formed by 32 DFIG WT of 2 M W each, whose model parameters are sho wn in T able 2. W ind speed w as simulated from a normally distrib uted random signal with a period of 50 seconds, mean v alue of 12 : 5 m=s and v ariance of 2 : 8 m=s . Finally , load disturbances were applied as follo ws: an increment of 0.06 [ p:u ] at 30 seconds of operation in area III; a v ariation of magnitude 0.08 [ p:u ] at 60 seconds in area II; and another disturbance of 0.01 [ p:u ] at 90 seconds for area I. The Po wer Base is set at 100 M V A . PI and LQR contr oller s for F r equency Re gulation including W ind Gener ation (Semaria Ruiz) Evaluation Warning : The document was created with Spire.PDF for Python.
3716 ISSN: 2088-8708 T able 1. WSCC 9 b us system parameters [8]. P arameter V alue P arameter V alue P arameter V alue H 1 23.64 s T 12 2.064 p.u. R 1 2 p.u. H 2 6.4 s T 13 6.1191 p.u. R 2 10 p.u. H 3 1.505 s T 23 14.4353 p.u. R 3 7.5019 p.u. M V A nom 1 247.5 D 1 ; D 2 ; D 3 0.8 B 1 2.8 s M V A nom 2 192 T g 1 ; T g 2 ; T g 3 0.2 B 2 10.8 s M V A nom 3 128 T 1 ; T 2 ; T 3 0.3 B 3 8.3 s T able 2. W ind-turbine model simulation parameters [14]. P arameter V alue P arameter V alue P nom 2 M W R s 0.00491 p.u. V nom 966 V X l s 0.09273 p.u. K 1 5000 N m X m 3.96545 p.u. K 2 2000 N m R r 0.00552 p.u T w 1 X l r 0.1 p.u. K a 500 H 4.5 s T a 20 J 506.6059 K g m 2 . 4.2. T uning of PI contr ollers PI controllers for secondary frequenc y re gulation in each area were tuned using the Gradient Descent method, along with P I controllers of rotor angular speed w r and rotor quadrature v oltage v q r . T able 3 presents the parameters for all of them. T able 3. P arameter v alues for the dif ferent PI controllers in simulation for the case of study . Contr oller Pr oportional Gain k P Integral Gain k I PI Area I 0 -0.05 PI Area II 0 -0.05 PI Area III 0 -0.28 PI v q r 0 2.70 PI w r 7.19 0.53 4.3. T uning of LQR contr oller T o calculate the g ains of LQR controller with reference tracking, a linearization must be performed in the non-linear state-space model described by equations (2) to (8). This process results in the operating point v ectors U T op = [27 : 97 0 : 08 9] for the inputs and W T op = [0 : 2 0 12] for disturbance signals. Design of LQR controllers for secondary LFC implies the tuning of the positi v e definite matrices Q ar ea and R ar ea for each area. The adjusted matrix elements are listed in T able 4. T able 4. P arameter v alues for the dif ferent PI controllers in simulation for the case of study . Matrix dimensions for area III are dif ferent due to the presence of wind generation. P arameter V alue Q ar ea 1 diag ([1 ; 1 ; 10 1 ; 10 1 ; 10 3 ]) Q ar ea 2 diag ([1 ; 1 ; 10 1 ; 10 1 ; 10 3 ]) Q ar ea 3 diag ([10 2 ; 10 2 ; 5 ; 5 ; 10 2 ; 10 2 ; 10 2 ; 1 ; 10 6 ; 10 2 ]) R ar ea 1 10 7 R ar ea 2 10 2 R ar ea 3 diag ([10 2 ; 10 6 ; 10 9 ]) IJECE V ol. 8, No. 5, October 2018: 3711 – 3721 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 3717 0 25 50 75 100 125 150 175 200 Time [s] 49.2 49.6 50 50.4 50.7 Frequency [Hz] PI LQR Figure 4. Frequenc y de viation in area II. LQR achie v ed a reduction of 0.32 H z o v er PI response in maximum v alue. 0 25 50 75 100 125 150 175 200 Time [s] 49 49.5 50 50.5 51 Frequency [Hz] PI LQR Figure 5. Frequenc y de viation in area III. Peak de viation v alue for PI w as 0.17 H z bigger than LQR. 4.4. Comparison between PI and LQR contr olled LFC with WT participation Simulations were performed on the selected benchmark with models and conditions pre viously de- scribed. Figures 4 and 5 depict frequenc y de viations for areas II and III respecti v ely , as the y present more significant v ariations than area I. Load disturbance in area I II at 30 seconds causes the most notorious ef fects, not only in the local frequenc y de viation b ut also in the other areas as well. This beha vior could be attrib uted to the inertia reduction in re gion 3 and some latenc y in the operation of WT control loops: po wer transferred to area I II increases as WT contrib utions in frequenc y re gulation start. On the other hand, the o v erall magnitude of the frequenc y de viations o v er the total simulation time is smaller for the LQR controller in each area. Fe wer v ariations w ould mean less stress in the re gulation systems, a k e y f actor as RES penetration increases. Also, longer reco v ery and settling times can be seen for PI controllers at each area, gi ving the LQR a better o v erall performance for secondary control design in the studied case. Figure 6 sho ws the e xchanged po wers between area III and the other areas. In this case, LQR reduces the po wer e xchanged with other areas when compared with PI response. Ho we v er , a continued oscillation in po wer is observ ed, due to wind v ariability causing fluctuations in WT generation. This v ariation mak es area III more sensiti v e to sudden changes in load, as confirmed when the most significant po wer de viations appear at the same time as the load disturbances occur . W ith a load disturbance in area III at 30 seconds, LFC system requires an increase in po wer transference from the other areas to mitig ate frequenc y fluctuations. Ho we v er , the e xchanged po wer in area III stabilizes as WT start contrib uting to frequenc y re gulation. Figure 7 sho ws the po wer generated by the wind f arm in area III. F ocusing on DFIG WT performance, analysis of the control ef forts for both LQR and PI strate gies in area III is required. Control actions for the pitch-angle r ef are smaller for LQR than for PI controller , as seen in figure 8. This beha vior seems to indicate that WT’ s are less stressed with LQR controller . Ho we v er , the total control ef fort of the secondary control P c is higher for the LQR than the PI scheme, as sho wn in Figure 9. LQR is imposing an aggressi v e control action in the con v entional unit of area III, diminishing the stress in WT contrib utions to frequenc y re gulation. This, i n turn, reduces frequenc y fluctuations due to wind v ari ability for PI and LQR contr oller s for F r equency Re gulation including W ind Gener ation (Semaria Ruiz) Evaluation Warning : The document was created with Spire.PDF for Python.
3718 ISSN: 2088-8708 0 25 50 75 100 125 150 175 200 Time [s] -0.2 -0.1 0 0.1 0.2 0.3 Power exchanged [p.u.] PI LQR Figure 6. Inter -area po wer e xchange de viation for area III. 0 25 50 75 100 125 150 175 200 Time [s] 0 0.03 0.06 0.09 0.12 0.15 Wind-turbine power change [p.u.] PI LQR Figure 7. V ariations in po wer generated by the wind f arm in area III. IJECE V ol. 8, No. 5, October 2018: 3711 – 3721 Evaluation Warning : The document was created with Spire.PDF for Python.
IJECE ISSN: 2088-8708 3719 0 25 50 75 100 125 150 175 200 Time [s] 0 5 10 15 20 25 30 Pitch angle [Degree] PI LQR Figure 8. Magnitude of control action for v ariable r ef in area III 0 25 50 75 100 125 150 175 200 Time [s] 0 0.02 0.04 0.06 0.08 0.1 ACE signal PI LQR Figure 9. Magnitude of control action for v ariable P c in area III. the LQR in this area. 5. CONCLUSIONS This w ork studied the performance of v ariable-speed wind turbines in LFC structure of po wer syst ems. W ith inertial response emulation methodology , DFIG WT were included in the primary re gulation stage of the LFC. T w o controllers were compared for secondary re gulation in the test system, and Linear Quadratic Re gulator presented a better o v erall performance than the Proportional Inte gral controller . F or e v ery e xplored case, frequenc y de viations under LQR strate gy were smaller and the settling times of the output v ariables were also lo wer than the PI-controlled results. Furthermore, LQR operation diminishe d control ef forts of WT . LQR controller based on the system model and it achie v ed acceptable performances despite the mandatory requirement for linearization of the state-space representation. An unw anted o v ershoot in area III frequenc y appears for both strate gies with sudden wind v ariations. This reaction occurs because the operating point of the system is changing with e v ery v alue of wind speed. This ef fect w as more notorious for LQR configuration, as the model implemented included wind speed as a disturbance. When the operating point changed, linearization might ha v e lead to the inadequate representation of the nonlinear system. Neither PI nor LQR presented a total disturbance rejection, and wind v ariability may require the pairing of WT with ”continuous” generation to reduce operational uncertainty . Consideration of additional control s chemes for the participation of v ariable-speed WT in LFC enabl es the contrib ution of WT to ancillary tasks. Ho we v er , the increment of WT in po wer systems may lead to inertia reduction with the decreasing operation of con v entional generation systems. More adv ancements and studies are needed to get a better performance of the wind units in frequenc y re gulation tasks or e xpanding their role into secondary control. Finally , the implementation of a transition-band control loop between torque and pitch controllers of WT is suggested. This additional loop w ould help to a v oid o v ershoots in WT generated po wer when wind v aries from nominal speed. PI and LQR contr oller s for F r equency Re gulation including W ind Gener ation (Semaria Ruiz) Evaluation Warning : The document was created with Spire.PDF for Python.
3720 ISSN: 2088-8708 A CKNO WLEDGEMENT Colciencias supported contrib utions of S. Ruiz and J. P atino through the programs ”J ´ ov enes in v es- tig adores - Con v ocatoria N.645 of 2014” and ”Con v ocatoria 528 - Con v ocatoria Nacional para Estudios de Doctorados en Colombia 2011”, respecti v ely . REFERENCES [1] H. Be vrani, Rob ust P ower System F r equency Contr ol , 2nd ed., ser . Po wer Electronics and Po wer Systems. Springer , 2014. [2] E. Duque, J. P atino, and L. V el ´ ez, “Implementation of the A CM0002 methodology in small h ydropo wer plants in Colombia under the Clean De v elopment Mechanism, ” International J ournal of Rene wable Ener gy Resear c h , v ol. 6, no. 1, pp. 21–33, 2016. [Online]. A v ailable: www .scopus.com [3] C. L. DeMarco and C. A. Baone, “Chapter 29 - Control of Po wer Systems with High Penetration V ariable Generation, ” in Rene wable Ener gy Inte gr ation , L. E. Jones, Ed. Boston: Academic Press, 2014, pp. 369 – 379. [4] S. Ruiz, J. P atino, A. Marquez, and J. Espinosa, “Optimal Design for an Electrical Hybrid Microgrid in Colombia Under Fuel Price V ariation, ” International J ournal of Rene wable Ener gy Resear c h , v ol. 7, no. 24, pp. 1535–1545, 2017. [5] J. P atino, F . V alencia, and J. Espinosa, “Sensiti vity analysis for frequenc y re gulation in a tw o-area po wer system, ” International J ournal of Rene wable Ener gy Resear c h , v ol. 7, no. 2, pp. 700–706, 2017. [6] C. Rahmann and A. Castillo, “F ast Frequenc y Response Capability of Photo v oltaic Po wer Plants: The Necessity of Ne w Grid Requirements and Definitions, ” Ener gies , v ol. 7, no. 10, p. 6306, 2014. [7] F . D ´ ıaz-Gonz ´ alez, M. Hau, A. Sumper , and O. Gomis-Bellmunt, “P artici pation of wind po wer plants in system frequenc y control: Re vie w of grid code requirements and control methods, ” Rene wable and Sustainable Ener gy Re vie ws , v ol. 34, pp. 551 – 564, 2014. [8] P . M. Anderson and A. A. F ouad, P ower System Contr ol and Stability (IEEE Pr ess P o w er Engineering Series) . W ile y-IEEE Press, 2002. [9] A. Boulahia, M. Adel, and B. Hocine, “Predicti v e Po wer Control of Grid a n d Rotor Side con v erters in Doubly Fed Induction Generators Based W ind T urbine, ” International J ournal of Electrical and Computer Engineering (IJECE) , v ol. 3, no. 3, Jun. 2013. [Online]. A v ailable: http://www .iaesjournal.com/online/inde x.php/IJECE/article/vie w/3474 [10] T . Benamimour , A. Bentounsi, and H. Dje ghloud, “Study of W ind T urbine based V ariable Reluctance Generator using Hybrid FEMM-MA TLAB Modeling, ” International J ournal of Electrical and Computer Engineering (IJECE) , v ol. 7, no. 1, pp. 1–11, 2017. [11] K. V . V i d ya n a nd a n and N. Senro y , “Primary frequenc y re gulation by deloaded wind t urbines using v ari- able droop, ” IEEE T r ansactions on P ower Systems , v ol. 28, no. 2, pp. 837–846, May 2013. [12] M. Dreidy , H. Mokhlis, and S. Mekhilef, “Inertia response a nd frequenc y contr ol techniques for rene w able ener gy sources: A re vie w , ” Rene wable and Sustainable Ener gy Re vie ws , v ol. 69, pp. 144 – 155, 2017. [13] G. Ramtharan, J. Ekanayak e, and N. Jenkins, “Frequenc y support from doubly fed induction generator wind turbines, ” IET Rene wable P ower Gener ation , v ol. 1, no. 1, pp. 3–9, Mar . 2007. [14] I. F . Moore, “Inertial Response from W ind T urbines, ” Ph.D. thesis, Cardif f Uni v ersity , Cardif f, 2012. [15] H. Camblong, I. V echiu, X. Guillaud, A. Etx eberria, and S. Kreck elber gh, “W ind turbine controller com- parison on an island grid in terms of frequenc y control and mechanical stress, ” Rene wable Ener gy , v ol. 63, pp. 37–45, Mar . 2014. [16] T . H. Mohamed, J. Morel, H. Be vrani, and T . Hiyama, “Model predicti v e based load frequenc y con- trol design concerning wind turbines, ” International J ournal of Electrical P ower & Ener gy Systems , v ol. 43, no. 1, pp. 859 – 867, 2012. [17] S. Ruiz, J. P ati ˜ no, and J. Espinosa, “Load Frequenc y Control of a Multi-area Po wer System Incorporating V ariable-speed W ind T urbines, ” in Confer ence Pr oceedings of XVII LA TIN AMERICAN CONFERENCE IN A UT OMA TIC CONTR OL , Medell ´ ın, Colombia, 2016, pp. 447–452. [18] A. Mullane and M. O’Malle y , “The Inertial Response of Induction-Machine-Based W i nd T urbines, ” P ower Systems, IEEE T r ansactions on , v ol. 20, no. 3, pp. 1496–1503, Aug. 2005. [19] J. B. Ekanayak e, N. Jenkins, and G. Str bac, “Frequenc y response from wind turbines, ” W ind Engineering , v ol. 32, no. 6, pp. 573–586, 2008. [20] G. Ramtharan, N. Jenkins, and O. Anaya-Lara, “Modelling and control of synchronous generators for wide-range v ariable-speed wind turbines, ” W ind Ener gy , v ol. 10, no. 3, pp. 231–246, 2007. IJECE V ol. 8, No. 5, October 2018: 3711 – 3721 Evaluation Warning : The document was created with Spire.PDF for Python.