Indian Institute of Technology 9th symposium on 9th IFAC IFAC symposium on Control Control of of Power Power and and Energy Energy Systems Systems 9th IFAC symposium on Control and Energy Systems December 9-11, 2015. Delhi, Indiaof Power Indian of Available online at www.sciencedirect.com Indian Institute Institute of Technology Technology Indian Institute of Technology December 9-11, 9-11, 2015. 2015. Delhi, Delhi, India India December December 9-11, 2015. Delhi, India
ScienceDirect
IFAC-PapersOnLine 48-30 (2015) 019–024 Investigating the Controller Interactions of Investigating the Interactions of Investigating the Controller Controller Interactions of Distribution Systems with Distributed Generation Distribution Systems with Distributed Generation Distribution Systems with Distributed Generation ∗ ∗∗
N. K. Roy , H. R. Pota ∗∗ N. K. K. Roy ∗∗∗ ,, H. H. R. Pota Pota ∗∗ N. N. K. Roy Roy , H. R. R. Pota ∗∗ ∗ Department of Electrical and Electronic Engineering, Khulna University of ∗∗ Department Engineering & Technology, Khulna 9203, Bangladesh. of Electrical Electrical and Electronic Electronic Engineering, Khulna University University of of and Engineering, Khulna ∗ Department Department of Electrical and
[email protected] Electronic Engineering, Khulna University of of e-mail: Engineering & Technology, Khulna 9203, Bangladesh. Engineering & Technology, Khulna 9203, Bangladesh. & Technology, Khulna 9203, Bangladesh. ∗∗ School ofEngineering Engineeringe-mail: and Information Technology, The University of New
[email protected] e-mail:
[email protected] e-mail:
[email protected] ∗∗ School of Engineering ∗∗ South Wales, ACT 2600, Australia. and Canberra, Information Technology, The University University of New New of Engineering and Information Technology, The ∗∗ School School of Engineering and Canberra, Information Technology, The University of of New e-mail:
[email protected] South Wales, Wales, ACT 2600, Australia. Australia. South Canberra, ACT 2600, South Wales, Canberra, ACT 2600, Australia. e-mail:
[email protected] e-mail: . e-mail:
[email protected] [email protected] .. . Abstract: This paper investigates the interactions among multiple controllers in distribution systems in the presence distributed generation (DG). Twoamong doublymultiple fed induction generator (DFIG) type wind Abstract: This paper investigates the interactions controllers in distribution systems Abstract: This of paper investigates the among multiple controllers in systems Abstract: paper investigates the interactions interactions among multiple controllers in distribution distribution systems turbines areThis connected to a distribution system to investigate their influence in the system. Simulation in the presence of distributed generation (DG). Two doubly fed induction generator (DFIG) type wind in the presence of distributed generation (DG). Two doubly fed induction generator (DFIG) type in the presence of generation (DG). Two doubly induction generator (DFIG) type wind wind results indicate thatdistributed theto parallel operation of DG units and fed their controllers in the the system. same network in a turbines are connected aa distribution system to investigate their influence in Simulation turbines are connected to distribution system to investigate their influence in the system. Simulation turbines are connected to a distribution system to investigate their influence in the system. Simulation relatively smaller geographical area have negative interactions giving rise to control mode oscillations. results indicate that the parallel operation of DG units and their controllers in the same network in a results indicate that the parallel operation of units and controllers in same network in results indicate that the operation of DG DG and their their controllers in the thereduces same network in aa It is also investigated thatparallel the coupling of negative the load units dynamics with DG-controllers the damping relatively smaller geographical area have interactions giving rise to control mode oscillations. relatively smaller geographical area have negative interactions giving rise to control mode oscillations. relatively smaller geographical area have negative interactions giving rise to control mode the oscillations. of thealso system. It is investigated that the coupling of the load dynamics with DG-controllers reduces damping It is also investigated that the coupling of the load dynamics with DG-controllers reduces the damping It is also investigated that the coupling of the load dynamics with DG-controllers reduces the damping of the system. of the system. of the system. © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights Keywords : control modes, composite loads, doubly fed induction generator (DFIG), distributedreserved. generation (DG). :: control Keywords modes, composite loads, doubly fed induction generator (DFIG), distributed generaKeywords control modes, composite loads, doubly fed induction generator (DFIG), distributed generaKeywords tion (DG). : control modes, composite loads, doubly fed induction generator (DFIG), distributed generation (DG). tion (DG). time-varying load demands; see Su et al. (2011). As the con1. INTRODUCTION verters have sophisticated feedback control loops, they mayconintime-varying load demands; see Su et al. (2011). As the 1. INTRODUCTION time-varying load demands; see Su et al. As the con1. INTRODUCTION time-varying load demands; see Sucontrol et power al. (2011). (2011). Asand the con1. INTRODUCTION teract with the transients offeedback the electric system result verters have sophisticated loops, they may inverters have sophisticated feedback control loops, they may inWind power is playing a major role in efforts to increase the verters havethe sophisticated feedback control loops, they may inin unintended modes of oscillations while the nonlinear couteract with transients of the electric power system and result teract with the transients of the electric power system and result share of renewable energy in distributed generation (DG). FolWind power is playing a major role in efforts to increase the Wind power is playing a major role in efforts to increase the teract with the transients of the electric power system and result Wind of power is playing a major role in efforts to increase the pling of load dynamics and power electronics converter control in unintended modes of oscillations while the nonlinear couin modes of oscillations while nonlinear coulowing the recent developments in modern power electronics, share renewable energy in distributed generation (DG). Folshare of renewable energy in distributed generation (DG). Folin unintended unintended modes ofand oscillations while the the nonlinear coushare of renewable energy in distributed generation (DG). Folmay complicate this problem; see Meliopoulos and Cokkinides pling of load dynamics power electronics converter control pling of load dynamics and power electronics converter control variable-speed wind turbines equipped with power doublyelectronics, fed induclowing the recent developments in modern lowing the recent developments in modern power electronics, pling of load dynamics and power electronics converter control lowing the recent developments in modern power electronics, (2006). may complicate this problem; see Meliopoulos and Cokkinides may tion generators (DFIGs) have drawn increasing attention in convariable-speed wind turbines equipped with doubly fed inducvariable-speed wind turbines equipped with doubly fed inducmay complicate complicate this this problem; problem; see see Meliopoulos Meliopoulos and and Cokkinides Cokkinides variable-speed wind turbines equipped with doubly fed induc(2006). (2006). trast to the older constant-speed models with attention simple squirreltion generators (DFIGs) have drawn increasing in conIt is investigated that electromechanical dynamics of a DFIG is tion generators (DFIGs) have drawn increasing attention in con(2006). tion generators (DFIGs) have drawn increasing inspeed concage induction generators (SCIGs). Although aattention variable trast to the older constant-speed models with simple squirrelmore sensitive to that the inertia when compared to the of dynamics of trast to the older constant-speed models with simple squirrelIt is investigated electromechanical dynamics aa DFIG is It is investigated that electromechanical dynamics of is trast to the older constant-speed models with simple squirrelIt synchronous is investigated that electromechanical dynamics of a DFIG DFIG is wind turbine hasgenerators several potential benefits; seeaaTsourakis et al. cage induction (SCIGs). Although variable speed a generator and, depending on the operating mode cage induction generators (SCIGs). Although variable speed more sensitive to the inertia when compared to the dynamics of more sensitive to the inertia when compared to the dynamics of cage induction generators (SCIGs). Although a variable speed more sensitive to the inertia when compared to the dynamics of (2009), for its successful integration into existing distribution wind turbine has several potential benefits; see Tsourakis et al. of the DFIG, the networkand, voltage drops significantly that affects wind has several potential benefits; see Tsourakis et aa synchronous generator depending on the operating mode generator and, depending on mode wind turbine turbine has several potential benefits; see Tsourakis et al. al. a synchronous synchronous generator and, depending on the the operating operating mode networks, a its number of technical challenges related to voltage (2009), for successful integration into existing distribution the stability and performance of the system; see de Oliveira (2009), for its successful integration into existing distribution of the DFIG, the network voltage drops significantly that affects of the DFIG, the network voltage drops significantly that affects (2009), for its successful integration into existing distribution of the DFIG, the network voltage drops significantly that affects and poweraahave to be addressed; see Tremblay et al. (2006); networks, number of technical challenges related to voltage et al.stability (2011).and Tsourakis et al. of (2009) reportedsee thatde increased networks, number of technical related to voltage the performance the system; Oliveira the and performance of the system; see de Oliveira networks, ahave number of addressed; technical challenges challenges related to (2006); voltage theal.stability stability and performance of the system; see deincreased Oliveira Pokharel and Gaoto (2010). and power be see Tremblay et al. wind power penetration results in reduced damping or even and power have to be addressed; see Tremblay et al. (2006); et (2011). Tsourakis et al. (2009) reported that et al. (2011). Tsourakis et al. (2009) reported that increased and power have to be addressed; see Tremblay et al. (2006); et al. (2011). Tsourakis et al. (2009) reported that increased Pokharel and Gao (2010). instability of either the oscillatory control or electromechanical Pokharel and Gao (2010). wind power penetration results in reduced damping or even wind power penetration results in reduced damping or The statorand of Gao a DFIG is directly connected to the power grid Pokharel (2010). wind power penetration results incontrol reduced damping or even even mode. Usually, highthe concentration of loads and production in instability of either oscillatory or electromechanical instability of either the oscillatory control or electromechanical while its rotor uses converters which limit the electric current The stator of a DFIG is directly connected to the power grid The stator of a DFIG is directly connected to the power grid instability of either the oscillatory control or electromechanical The stator of a DFIG is directly connected to the power grid a small area can lead to poorly damped oscillations in a distrimode. Usually, high concentration of loads and production in mode. Usually, high concentration of and in during faults and transients; seewhich Meliopoulos and Cokkinides while its rotor uses converters limit the electric current while its rotor uses converters which limit the electric current mode. Usually, high concentration of loads loads and production production in while its rotor uses converters which limit the electric current bution network; see Roy (2013). Although interactions among a small area can lead to poorly damped oscillations in a distriaa small area can lead to poorly damped oscillations in a distri(2006). A low-inertia of a wind generator mayand result in larger during faults and transients; see Meliopoulos Cokkinides during faults and transients; see Meliopoulos and Cokkinides small area can lead to poorly damped oscillations in a distriduring faults and transients; see generator Meliopoulos and Cokkinides power system controls for high-voltage transmission systems bution network; see Roy (2013). Although interactions among bution network; see Roy (2013). Although interactions among and faster deviations in aavoltage and power after occurrence (2006). A low-inertia of wind may result in larger (2006). A low-inertia of wind may result in larger butionbeen network; see Royfor (2013). interactions among (2006). A variations low-inertia of avoltage wind generator generator mayafter result in larger have widely investigated; seeAlthough EPRI transmission (1998); Martins et al. power system controls high-voltage systems power system controls for high-voltage transmission systems of abrupt in generation and system load. Another and faster deviations in and power occurrence and faster deviations in voltage and power after occurrence power system controls for high-voltage transmission systems and faster deviations in voltage and power after occurrence (Status Report of ClGRE Task Force 38.02.16, Brochure have been widely investigated; see EPRI (1998); Martins etNo. al. have been widely investigated; see EPRI (1998); Martins al. issue is that the converter model ofand a DFIG is load. a multi-input of abrupt variations in generation system Another of abrupt variations in generation and system load. Another have 2000), been widely investigated; see EPRI (1998); Martins et etNo. al. of abrupt variations in generation and system load. Another 166, very little attention has been paid to analyzing the (Status Report of ClGRE Task Force 38.02.16, Brochure (Status Report of ClGRE Task Force 38.02.16, Brochure No. multi-output nonlinear model and of theaadifficulty of controlling issue is that the converter model DFIG is aa multi-input issue is that the converter model of DFIG is multi-input (Status Report of ClGRE Task Force 38.02.16, Brochure No. issue is that due the to converter model of adifficulty DFIG is of a multi-input interactions among multiple DGhas controllers within distribution 166, 2000), very little attention been paid to analyzing the 166, very little attention has been to analyzing the it is mainly its model nonlinear behavior. Conventionally, PI multi-output nonlinear and the controlling multi-output nonlinear model and the difficulty of 166, 2000), 2000), little attention been paid paid to analyzing the multi-output nonlinear model andbehavior. the difficulty of controlling controlling systems. In very the near future, itDG ishas expected that small-scale DG interactions among multiple controllers within distribution interactions among multiple DG controllers within distribution controllers are used for converter control but their response it is mainly due to its nonlinear Conventionally, PI it is mainly due to its nonlinear behavior. Conventionally, PI interactions among multiple DG controllers within distribution it is mainly dueused toslow itsfornonlinear Conventionally, PI units withIn sophisticated inverters will be permitted to control systems. the near future, it is expected that small-scale DG systems. In the future, it that small-scale DG times are usually and it is behavior. difficult to find appropriate controllers are converter control but their response controllers are used for converter control but their response systems. Insophisticated thethenear near future, it is is expected expected that small-scale DG controllers are used for converter control but their response the voltage at point of common coupling (PCC). A massive units with inverters will be permitted to control units with sophisticated inverters will be permitted to control PI parameters in a slow systematic way for nonlinear systems with times are usually and it is difficult to find appropriate times are usually slow and it is difficult to find appropriate units with sophisticated inverters will be permitted to control times are usually slow and it is difficult to find appropriate deployment ofthe converter-interfaced DERs in (PCC). a distribution systhe voltage at point of common coupling A the at point common coupling (PCC). A massive massive switching devices. PI parameters in a systematic way for nonlinear systems with PI in the voltage voltage atofthe the point of of dynamic common interactions coupling (PCC). PI parameters parameters in aa systematic systematic way way for for nonlinear nonlinear systems systems with with tem generates additional with A themassive utility deployment converter-interfaced DERs in aa distribution sysdeployment of converter-interfaced DERs in distribution sysswitching devices. switching devices. deployment of additional converter-interfaced DERs sysWith the increasing switching devices. penetration of wind energy, its impact on system. Therefore, the aim of thisinteractions paper in is atodistribution investigate the tem generates dynamic with the utility tem generates additional dynamic interactions with the utility tem generates additional dynamic interactions with the utility aWith system depends heavily upon of thewind effectiveness ofimpact converter the increasing penetration energy, its on interactions of multiple converter connected distributed gensystem. Therefore, the aim of this paper is to investigate the With the increasing penetration of wind energy, its impact on system. Therefore, the aim of this paper is to investigate the the increasing penetration of wind energy, its impact on system. in Therefore, the aim of this connected paperlinear is todistributed investigate the control with multiple distributed energy resources (DERs) since aWith depends heavily upon the effectiveness of converter erators a of distribution network. Both and nonlinear interactions multiple converter genaa system system depends heavily upon the effectiveness of converter interactions of multiple converter connected distributed gensystem depends heavily upon the effectiveness of converter interactions of multiple converter connected distributed gendistribution networks are dividedenergy into subsystems of radial or control with multiple distributed resources (DERs) since simulations carried outnetwork. to gatherBoth a complete understanding erators in a are distribution linear and nonlinear control with multiple distributed energy resources (DERs) since erators in distribution network. Both linear nonlinear control with networks multiple distributed energy resources since erators in aa are distribution network. Both linear and and nonlinear loop feeders with a number of switches to which(DERs) commercial, distribution are divided into subsystems of radial or of the problem. simulations carried out to gather a complete understanding distribution networks are divided into subsystems of radial or simulations are carried out to gather a complete understanding distribution networks are divided into subsystems of radial or simulations are carried out to gather a complete understanding industrial, and residential end-users are connected and impose loop feeders with aa number of switches to which commercial, of the problem. loop with of to of loop feeders feeders with a number number of switches switches to which which commercial, commercial, of the the problem. problem. industrial, and residential end-users are connected and impose industrial, and residential end-users are connected and impose industrial, and residential end-users are connected and impose
Copyright © 2015 IFAC 19 2405-8963 © 2015, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. Copyright ©under 2015 responsibility IFAC 19 Control. Copyright 2015 IFAC 19 Peer review© of International Federation of Automatic Copyright © 2015 IFAC 19 10.1016/j.ifacol.2015.12.347
IFAC CPES 2015 20 December 9-11, 2015. Delhi, India
N. K. Roy et al. / IFAC-PapersOnLine 48-30 (2015) 019–024
The rest of the paper is organized as follows. In Section 2, the mathematical model of the system is presented. Both linear and nonlinear analyzes are given in Section 3. The impacts of variations in controller parameters are demonstrated in Section 4. Finally, concluding remarks are given in Section 5.
2.1 Generator Model The nonlinear model of DFIG is based on a static model of the aerodynamics, a two mass model of the drive train, a third order model of the generator, the GSC with DC-link capacitor, the pitch controller and the RSC. The rotor of the wind turbine, with radius Ri , converts the energy from the wind to the rotor shaft, rotating at the speed ω mi . The power from the wind depends on the wind speed, Vwi , the air density, ρ i , and the swept area, Awti . From the available power in the swept area, the power on the rotor is given based on the power coefficient c pi (λri , θi ), which depends on the pitch angle of the blade, θ i , and the ratio between the speed of the blade tip and the wind ωm R speed ratio, λri = Vwi i . The aerodynamic torque applied to the i rotor by the effective wind passing through the rotor is given as: ρi Awt c p (λr , θ )Vw3i (1) Taei = 2ωmi i i i
v�rdi =
vrdi Xmi (Xmi +Xri ) ,
and v�rqi =
CiVdci
vrqi Xmi (Xmi +Xri ) .
2 Vdc dVdci i − Pri (t) − Pgi (t) =− dt Rlossi
(10)
where, Vdci and Ci are the dc-link voltage and capacitance, respectively. Resistor Rlossi represents the total conduction and switching loss of the converter. Also, Pri (t) is the instantaneous input rotor power and Pgi (t) is the instantaneous output power of the GSC, which are given by: Pri = vrdi irdi + vrqi irqi (11) Pgi = vgdi igdi + vgqi igqi (12) 2.2 Load Model The proper representation of load is important in power system stability studies, but it is a difficult problem because power system loads are composed of different devices; see Morison et al. (2003). A composite load model is used in this paper to represent the dynamic behavior of an aggregate group of small motors, electronic loads and static loads, as shown in Figure 1. HV
LV Distribution feeder impedance
The induction generator gets the power from the gear box through the stiff shaft. The relationship between the mechanical torque and torsional angle is given by: Tmi = Ksi λi (5)
Induction motor
Discharge lighting
Static load
Fig. 1. Example of composite load
The mechanical torque depends on torsion stiffness (K si ), torsion angle (λ i ), rotor speed (ω gi ), etc.
Static load: Static load models are relevant to load flow studies as they express active and reactive steady-state powers as functions of the bus voltages (at a given fixed frequency). Common static load models for active and reactive power are expressed in polynomial or exponential forms and can include, if necessary, a frequency dependence term. In this paper, the exponential form is used to represent static load as:
The transient model of a DFIG can be described by the following algebraic-differential equations;; see Ackermann (2005), Nandigam and Chowdhury (2004):
1 (Tmi − Tei ) 2Hgi
X X
The DC link dynamic is given by:
A two-mass drive train model of a wind turbine generator system (WTGS) is used in this paper. The drive train attached to the wind turbine converts the aerodynamic torque T aei on the rotor into the torque on the low speed-shaft, which is scaled down through the gearbox to the torque on the high-speed shaft. The first mass term stands for the blades, hub and low-speed shaft, while the second mass term stands for the high speed shaft having the inertia constants, H mi and Hgi . The shafts are interconnected by the gear ratio, N gi , combined with torsion stiffness, Ksi , and torsion damping, D mi and Dgi resulting in torsion angle, λ i . The normal grid frequency is f . The dynamics of the shaft can be represented as follows; see Ackermann (2005): 1 ω˙ mi = [Taei − Ksi λi − Dmi ωmi ] (2) 2Hmi 1 ω˙ gi = [Ksi λi − Taei − Dgi ωgi ] (3) 2Hgi 1 (4) λ˙i = 2π f ωmi − ωg i Ngi
s˙i =
(9)
i ri here, Xi� = Xsi + Xmm+X is the transient reactance, R si is the stari i tor resistance, Xri is the rotor reactance, Xmi is the magnetizing reactance, Xi = Xsi + Xmi is the rotor open circuit reactance, To�i is transient open circuit time constant, Tmi is the mechanical � � torque, si is the slip, Tei = Erd i + Erq i is the electrical i sqi i sdi � � torque, Erdi and Erqi are the direct and quadrature axis transient voltages respectively, i sdi and isqi are the direct and quadrature axis currents respectively, ω si is the synchronous speed,
2. SYSTEM MODEL
1 � � − ωsi v�rdi − (Xi − Xi� )isdi + si ωsi To�i Erd E˙ � rqi = − � Erq i i Toi 1 � � E˙ � rdi = − � Erd + ωsi v�rqi + (Xi − Xi� )isqi − si ωsi To�i Erq i i Toi
� � − jErd vsdi + jvsqi = Rsi + jXi� isdi + jisqi + j Erq i i
(6)
P(V ) = P0
(7) (8)
Q(V ) = Q0
20
V V0 V V0
a
b
,
(13a)
,
(13b)
IFAC CPES 2015 December 9-11, 2015. Delhi, India
N. K. Roy et al. / IFAC-PapersOnLine 48-30 (2015) 019–024
Utility grid
DFIG1
1
2
5 c
11
14
Vgi
c
15
12
Fig. 3. Schematic diagram of DFIG
16 c
Fig. 2. 16-bus distribution test system
Pi
where P and Q are active and reactive components of the load, respectively, and V is the bus voltage magnitude. The subscript 0 identifies the values of the respective variables at the initial operating condition. The parameters of this model are the exponents a and b. With these exponents equal to 0, 1, or 2, the model represents the constant power, constant current, or constant impedance characteristics of load components, respectively.
Vti
Vdci
Vrq
i
Vrdi
Vtrefi
GSC controller
Vg
i
Vdcrefi
Fig. 4. DFIG converter control 3. INTERACTIONS AMONG DFIG CONTROLLERS
Induction motor model: A large amount of power is consumed by induction motors in residential, commercial, and industrial areas, commonly for the compressor loads of air conditioning, pumps, fans, and refrigeration; see Kundur (1994).
Control interactions of distribution systems are complex phenomena due to the growing use of converter-connected DG. To investigate the controller interaction, the 16-bus distribution test system shown in Figure 2 is used. The numerical values of its parameters are given in Appendix.
In power system stability studies, the transients in stator voltage can be neglected; see Taylor (1994), which corresponds to ignoring the DC components in stator transient currents, thereby permitting representation of only the fundamental frequency components. The transient model of a squirrel-cage induction motor (SCIM) is described by the following DAEs written in a synchronously-rotating reference frame; see Taylor (1994): 1 [Te − TL ] , 2Hm � � e˙�qm = −e�qm + (X − X �)idm − Tdom sωs e�dm , Tdom
RSC controller
Prefi
Fluorescent lighting: About one-third of commercial load is lighting–mainly fluorescent; see EPRI (1989); Taylor (1994). Fluorescent and other discharged lighting have voltage sensitivities of a in the range from 1 to 1.3 and b from 3 to 4.5 in equation (13). In this paper, an exponential load model is used for fluorescent lighting with the exponents a and b equal to 1 and 3, respectively; see Taylor (1994).
In this paper, two DFIG type wind turbines, one at bus 2 and one at bus 3 are connected, each of which provides a nominal output of 4 MW. The total load on the system is 28.7 MW and 17.3 MVAr. The additional load is supported by the grid through the substation located at bus 1. The total load on the system is modeled as a composite load composed of (i) 50% induction motor load; see Taylor (1994), (ii) 20% fluorescent light; see Taylor (1994), and (iii) 30% static load. The machine parameters are given in Appendix.
(14) (15)
� = −e�dm − (X − X �)iqm + Tdom sωs e�qm , (16) � � � jvqs ) = (Rs + jX )(idm + jiqm ) + j(eqm − jedm ),(17)
� Tdom e˙�dm
(vds +
≈
Controller
c
s˙ =
= =
c
7
Grid
Pgi , Qgi
GSC
DC-link
≈
V ri
9 c
RSC
13 10
c
6
Pi , Vt i DFIG
3
8
4
Gear box
DFIG2
21
The DFIG schematic, in which the stator winding is connected directly to the network while the rotor winding is connected to the network through two back-to-back voltage source converters (VSCs) is shown in Figure 3. Variable speed operation is achieved by injecting a variable voltage into the rotor at a slip frequency. This voltage is obtained using two AC/DC insulated gate bipolar transistor (IGBT)-based VSCs linked by a DC bus. PI controllers are used for controlling the DFIG converters. The controllers for both the RSC and GSC of DFIGs are shown in Figure 4 in which Pi represents the real power output and Vti represents the voltage at the PCC. In this chapter, Pi and Vti are controlled from RSC whereas Vdci is regulated using GSC. It is assumed that Vsd i = 0 and thus, Vgi = Vsqi = ki mdci Vdci , where ki is a constant and mdci is the modulation index.
where X � = Xs + Xm Xr / (Xm + Xr ) is the transient reactance, � X = Xs + Xm is the rotor open-circuit reactance, Tdom = (Xr + Xm ) /ωs Rr is the transient open-circuit time constant, Te = e�qm iqm + e�dm idm is the electrical torque, s is the slip, e �dm is the direct-axis transient voltage, e �qm is the quadrature-axis transient voltage, TL is the load torque, Xs is the stator reactance, Xm is the magnetizing reactance, R s is the stator resistance, Rr is the rotor resistance, Hm is the inertia constant of the motor, vds is the direc-axis stator voltage, v qs is the quadrature-axis stator voltage, and i dm and iqm are the direct- and quadratureaxis components of the stator current, respectively. 21
IFAC CPES 2015 22 December 9-11, 2015. Delhi, India
N. K. Roy et al. / IFAC-PapersOnLine 48-30 (2015) 019–024
Bode Diagram
Magnitude (dB)
60 40 20 0 −20
Phase (deg)
−40 90 0 −90 −180 −1 10
0
10
1
2
10 10 Frequency (rad/sec)
3
10
4
10
Fig. 7. Real power output of DFIG1 (as a result of three-phase short-circuit fault at bus 12)
Fig. 5. Closed-loop system with PI controllers
Table 1. PI controller parameters Active power Terminal voltage DC-voltage regulator regulator regulator KP1 = 1.2,KI1 = 10.5 KP1 = 2.25,KI1 = 20.60 KP1 = 0.3,KI1 = 0.5 KP2 = 1.0,KI2 = 12.8 KP2 = 2.65,KI2 = 20.35 KP2 = 0.2,KI2 = 0.8
Fig. 6. Voltage at bus 2 (as a result of three-phase short-circuit fault at bus 12) From the modal analysis, it is seen that the closed-loop system with PI controllers has critical modes corresponding to eigenvalues at −0.2248 ± 28.707 which are control modes with low damping ratios (0.78%). The frequency response of the closedloop system with PI controllers is shown in Figure 5. It can be seen from Figure 5 that there is a resonant peak at 28.707 rad/s and also a sharp drop in the phase angle.
Fig. 8. Proportional gain of power regulator of DFIG1
A nonlinear simulation is performed to confirm the results from the small-signal stability analysis and investigate the impact of nonlinearities on damping. Figures 6 and 7 show the voltage at bus 2 and real power output of DFIG1, respectively in which it can be observed that both voltage and power have oscillations and the frequency of the oscillation is 4.56 Hz in this particular case. For comparative purposes, responses of the system with constant impedance loads are also plotted which signify that composite loads have an adverse effect compared to constant impedance loads on the damping of control modes. The electrical proximity of the generator controllers is the main reason for these oscillations. Interactions are also strongly linked with nonlinear coupling of the system with dynamic loads. It has to be mentioned that the PI controllers are tuned using Ziegler-Nichols tuning method; see Xue et al. (2007) to obtain the best performance. The gains of PI controllers are given in Table 1.
Fig. 9. Integral gain of voltage regulator of DFIG2 22
IFAC CPES 2015 December 9-11, 2015. Delhi, India
N. K. Roy et al. / IFAC-PapersOnLine 48-30 (2015) 019–024
23
Two-mass model parameters: Inertia constant, Hm = 4.3 s, Hg = 0.9 s, torsion damping, D m = 1.5 pu, Dg = 0.3 pu, torsion stiffness, Ks = 2.0 pu, gearbox ratio = 90. Induction motor parameters: Stator resistance, Rs = 0.031 pu, stator reactance, X s = 0.10 pu, magnetizing reactance, X m = 3.2 pu, rotor resistance, R r = 0.018 pu, rotor reactance, X r = 0.18 pu, inertia constant, H = 0.7 s. Table 2. Line and load data of 16-bus distribution system SE 1 8 8 9 9 2 4 4 6 3 13 13 15 5 10
Fig. 10. Integral gain of voltage regulator of DFIG1 4. IMPACTS OF CONTROLLER PARAMETERS The sensitivity of the critical modes to the control system parameters is also investigated. The proportional gain of the active power regulator of DFIG1, which determines the power delivered into the grid, is increased from 0.2 to 1.6 and the corresponding damping ratio is depicted in Figure 8. It can be seen that the damping ratio increases as the gain increases from 0.2 to 1.2 and then decreases for further gain increases. The integral gain of the voltage regulator of DFIG2 is varied from 1 to 35 and effects on system damping are shown in Figure 9 from which it can be seen that a high value of integral gain causes a poor damping performance of the system. The variations in the DC-voltage regulator gains do not have a significant impact on damping of the critical modes, as depicted in Figure 10 which shows the damping performance for variations in the integral gain from 0.2 to 1.2.
RE 8 9 10 11 12 4 5 6 7 13 14 15 16 11 14
R (pu) 0.110 0.080 0.110 0.110 0.080 0.075 0.080 0.090 0.040 0.110 0.090 0.080 0.040 0.040 0.040
X (pu) 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.180 0.040 0.110 0.120 0.110 0.040 0.040 0.040
Pl (pu) 0.040 0.050 0.010 0.006 0.045 0.020 0.030 0.020 0.015 0.010 0.010 0.010 0.021 0.000 0.000
Ql (pu) 0.027 0.030 0.009 0.001 0.020 0.016 0.015 0.008 0.012 0.009 0.007 0.009 0.010 0.000 0.000
C (pu) 0.000 0.012 0.000 0.006 0.037 0.000 0.011 0.012 0.000 0.000 0.018 0.000 0.018 0.000 0.000
(Base power is 100 MVA and base voltage is 23 kV, SE and RE are the sending and receiving end nodes, respectively)
REFERENCES Ackermann, T. (2005). Wind power in power systems. John Wiley & Sons, Ltd, England. de Oliveira, R.V., Zamadei, J.A., and Hossi, C.H. (2011). Impact of distributed synchronous and doubly-fed induction generators on small-signal stability of a distribution network. In IEEE PES General Meeting, 1–8. Detroit, USA. EPRI (1989). Lighting the commercial world. EPRI Journal, 14(8), 4–15. EPRI (1998). Analysis of control interactions on FACTSassisted power systems. EPRI Final Report TR-I09969. Kundur, P. (1994). Power system stability and control. McGraw-Hill, New York. Martins, N., Corsi, S., Andersson, G., Gibbard, M.J., SanchezGasca, J.J., Silva, A., and Taranto, G.N. (Status Report of ClGRE Task Force 38.02.16, Brochure No. 166, 2000). Impact of the interaction among power system controls, 1– 16. Meliopoulos, A.P.S. and Cokkinides, G.J. (2006). Dynamic ˝ modelinteractions between the power system and DERs - U ing and case studies. In Power Engineering Society General Meeting, 1–7. Montreal, Quebec. Morison, K., Hamadani, H., and Wang, L. (2003). Practical issues in load modeling for voltage stability studies. In IEEE Power Engineering Society General Meeting, volume 3, 1392–1397. Nandigam, K. and Chowdhury, B.H. (2004). Power flow and stability models for induction generators used in wind turbines. In IEEE Power Engineering Society General Meeting, volume 2, 2012–2016.
5. CONCLUSION In this paper, it is investigated that control interactions among the converter connected generators and loads can limit the DG integration. The performance of a DFIG type wind turbine is critically dependent on its control systems as the nonlinear interactions among its converter controllers lead to control mode oscillations. Interactions are also influenced by nonlinear coupling of the system with dynamic loads. Composite loads have an adverse effect compared to constant impedance loads on the damping of control modes. The tuning of a PI controller for different operating conditions is a difficult task for a multiinput multi-output converters. Therefore, the design of a new controller considering the effect of interconnections among subsystems in a geographically dispersed distribution network is essential in order to avoid controller interactions which is the future aim of this work. APPENDIX DFIG parameters: Power = 2 MW, voltage = 690 V, frequency, f = 50 Hz, rated slip = 0.02, rated DC-link voltage = 1200 V, stator resistance, Rs = 0.013 pu, stator reactance, X s = 0.077 pu, magnetizing reactance, Xm = 2.98 pu, rotor resistance, R r = 0.0162 pu, rotor reactance, Xr = 0.077 pu. 23
IFAC CPES 2015 24 December 9-11, 2015. Delhi, India
N. K. Roy et al. / IFAC-PapersOnLine 48-30 (2015) 019–024
Pokharel, B. and Gao, W. (2010). Mitigation of disturbances in DFIG-based wind farm connected to weak distribution system using STATCOM. In North American Power Symposium, 1–7. Arlington, TX, USA. Roy, N.K. (2013). Voltage stability enhancement of distribution systems with renewable energy. PhD Dissertation, The University of New South Wales, Australia. Su, S.Y., Lu, C.N., Chang, R.F., and Gutiérrez-Alcaraz, G. (2011). Distributed generation interconnection planning: a wind power case study. IEEE Trans. on Smart Grid, 2(1), 181–189. Taylor, C.W. (1994). Power system voltage stability. McGrawHill, New York. Tremblay, E., Chandra, A., and Lagacé, P.J. (2006). Gridside converter control of DFIG wind turbines to enhance power quality of distribution network. In Power Engineering Society General Meeting, 1–6. Montreal, Quebec, Canada. Tsourakis, G., Nomikos, B.M., and Vournas, C.D. (2009). Effect of wind parks with doubly fed asynchronous generators on small-signal stability. Electric Power Systems Research, 79, 190–200. Xue, D., Chen, Y., and Atherton, D.P. (2007). Linear feedback control: analysis and design with MATLAB. Society for Industrial and Applied Mathematics (SIAM), Philadelphia.
24