applied sciences Article
Impacts of Integration of Wind Farms on Power System Transient Stability Shiwei Xia 1 1
2
*
ID
, Qian Zhang 1 , S.T. Hussain 1 , Baodi Hong 2, * and Weiwei Zou 1
State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing 102206, China;
[email protected] (S.X.);
[email protected] (Q.Z.);
[email protected] (S.T.H.);
[email protected] (W.Z.) College of Mechanical and Electrical Engineering, Inner Mongolia Agricultural University, Hohhot 010010, China Correspondence:
[email protected]; Tel.: +86-0471-430-9215
Received: 5 July 2018; Accepted: 31 July 2018; Published: 2 August 2018
Abstract: To compensate for the ever-growing energy gap, renewable resources have undergone fast expansions worldwide in recent years, but they also result in some challenges for power system operation such as the static security and transient stability issues. In particular, as wind power generation accounts for a large share of these renewable energy and reduces the inertia of a power network, the transient stability of power systems with high-level wind generation is decreased and has attracted wide attention recently. Effectively analyzing and evaluating the impact of wind generation on power transient stability is indispensable to improve power system operation security level. In this paper, a Doubly Fed Induction Generator with a two-lumped mass wind turbine model is presented firstly to analyze impacts of wind power generation on power system transient stability. Although the influence of wind power generation on transient stability has been comprehensively studied, many other key factors such as the locations of wind farms and the wind speed driving the wind turbine are also investigated in detail. Furthermore, how to improve the transient stability by installing capacitors is also demonstrated in the paper. The IEEE 14-bus system is used to conduct these investigations by using the Power System Analysis Tool, and the time domain simulation results show that: (1) By increasing the capacity of wind farms, the system instability increases; (2) The wind farm location and wind speed can affect power system transient stability; (3) Installing capacitors will effectively improve system transient stability. Keywords: doubly fed induction generator; wind turbine with two-lumped mass; transient stability; power system
1. Introduction With the growing population, the electrical load is increasing day by day. To compensate the ever-growing energy gap, renewable resources have undergone fast expansion worldwide in recent years [1], but they also result in some challenges for power system operation such as the static security and transient stability issues [2,3]. In particular, as wind power generation accounts for large share of these renewable energy and reduces the inertia of the power network, the transient stability of power systems with high-level wind generation is decreased and has attracted wide attention recently [4,5]. Therefore, it is of great significance to effectively evaluate the influence of wind power generation on power transient stability to improve the safe level of power system operation. In practice, a power system is widely disturbed by small and large disturbances. Since small disturbance is constantly occurring in the form of load changes, the system must be able to accommodate these fast changing conditions and ensure satisfactory operation [6,7]. However, Appl. Sci. 2018, 8, 1289; doi:10.3390/app8081289
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the more important thing is that the system should survive serious disturbances such as the loss of large generators or transmission line faults or short circuits, which is the so-called transient stability problem. Transient stability is the capability of a power system to regain a stable equilibrium operation point when exposed to a severe disturbance, where the dynamic behaviours and interactions of multiple complex dynamic components should be considered [8,9]. If the power system is stable after large disturbance, it will get to new state of balance for maintaining the integrity of the system. Some loads and generators may be isolated from fault components or intentionally tripped to maintain operation continuity of most systems. Interrelated systems can also be intentionally divided into two or more islands for some serious disturbances. The operation of an automatic control device and the system operators eventually restore the system to a normal state. If the system is in the state of instability, it will cause run-down or run-away states [9,10]. For example under a sustained fault, the angle separation of the generator rotor increases gradually, or the bus voltage gradually decreases. Unstable system conditions may lead to cascading outages and turn off the main part of the power system. It is very important to conduct stability analysis when the system is connected to a renewable energy system like wind farms, to avoid system instability [11,12]. There are numerous types of wind turbines in which a doubly fed induction generator (DFIG) has become an advanced development and the mainstream technology because of the high energy efficiency, low power consumption of the electronic converter and the low mechanical stress of the wind turbine [13]. The dynamic response of DFIG depends mainly on the well-coordinated control strategy of the converters in the DFIG excitation system, which is basically different from the old synchronous generator. With the continuous increase in penetration of wind power, it has become an important issue to systematically and effectively evaluate the impact of integrated DFIGs on transient stability [14]. The influence of DFIG integration on power system transient stability has received considerable attention, and the influence of integrated DFIGs on rotor dynamics of synchronous generator can be studied. Some important work about the different network structures, different penetrations of DFIG, and common coupling points to evaluate the impacts of integrated DFIGs was investigated in [15]. To find the equivalent inertia of all power sources, i.e., generators or wind turbines, the use of synchronous pharos measurement can found in [16]. Authors of [17] explored the relationship between wind power generation and the rotor angle stability of conventional synchronous generators from the viewpoint of controlling the reactive power from variable speed wind turbine generators in the system. The authors presented an investigation on wind turbine contribution to the frequency control of non-interconnected island systems in [18], and a novel frequency regulation by DFIG-based wind turbines was presented in terms of coordinating inertial control, rotor speed control and pitch angle control for the low, medium or high wind speed mode [19]. The main contributions of the paper include the following. (1) (2) (3)
A very detailed Doubly Fed Induction Generator with a two-lumped mass Wind Turbine model is presented to analyze the impact of wind power generation on power system transient stability. The factors including wind power generation level, the wind power location and wind speed are comprehensively investigated for system transient stability analysis in the paper. The simulations result of the modified IEEE 14-bus system showed that (a) the system stability decreases with the growing penetration level of wind power generation; (b) The wind farm locations and wind speed can affect power system transient stability; (c) Installing capacitors will improve system transient stability.
The paper is organized as follows. The basic theory of transient stability analysis and the conventional generator dynamic models are introduced in Section 2, and then the very detailed DFIG with wind turbine model is presented in Section 3. In Section 4, the factors possibly affecting the system transient stability level are investigated in detail with a conclusion drawn in the last section.
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2. Basic Theory of Transient Stability Analysis Transient stability is the capability of a power system to regain a stable equilibrium operation point when subjected to a large disturbance such as a three-phase ground fault, and the dynamic behaviours of multiple complex dynamic components should be considered. 2.1. Introduction of Transient Stability Power system transient stability analysis could be generally described with high dimensional differential algebraic, such as Equations (1) [20]. (
X 0 = F ( X, Y, t) 0 = G ( X, Y, t)
(1)
where X and Y are the state and algebraic variables, respectively. The upper part of Equation (1) describes the state variables of dynamic components during the transient period, while the lower part of Equation (1) is the power network coupling in terms of nodal voltages and currents. The most important dynamic component for transient stability is for generators, including the conventional generator as detailed in the following and the wind power generator which will be elaborately presented in Section 3. 2.2. Dynamic Model of Conventional Generators A four-order differential model is introduced to describe the dynamics of conventional generators for transient stability analysis in this paper, and each generator is equipped with one IEEE type I voltage regulator. The differential equations for the four-order dynamic model are as follows. dδi = ωi dt Mi 0 Tdi
0 dEqi
dt Tqi0
dωi = Pmi − Pei − Dωi dt
0 0 = − Eqi + ( Xdi − Xdi ) Idi + E f di
0 dEdi 0 0 = − Edi + ( Xqi − Xqi ) Iqi dt
(2) (3) (4) (5)
where M is the generator time constant; δi is the ith generator angles while ω i its speed per unit (p.u.); Pmi and Pei are the mechanical and electromagnetic power of the ith generator; D is the ith generator 0 and T 0 are the d and q transient time damping ratio; Idi and Iqi are stator currents on the d and q axis; Tdi qi 0 , X 0 , X and X are transient and synchronous reactances on the d and q axis; E0 and constants;Xdi qi di qi di 0 are transient potential voltages on the d and q axis. Eqi For a generator equipped with the IEEE type I voltage regulator as shown in Figure 1 for regulating its potential voltage, its dynamics could be described by Equations (6) and (7).
(1)
Xi
Iqi −1 = Tmi Ami Idi + vi (i = 1, 2, . . . n) Xi
(6)
Mi
Tdi'
dEqi' dt
d ωi = Pmi − Pei − Dωi dt
(3)
= − Eqi' + ( X di' − X di ) I di + E fdi
(4)
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Tqi' 0 , E0 , R , E , V ) T , ( Eqi fi f di ri di
' di
dE = − E di' + ( X qi − X qi' ) I qi dt
(5)
0 , T 0 , T , T , T ), diag( Tdi qi Fi Ei Ai
where Xi = Tmi = and where M is the generator time constant; δi is the ith generator angles while ωi its speed per unit (p.u.); and electromagnetic Pmi and Pei are the mechanical power0of the0 ith generator; 0 −X 0 Xdi 1 0D is the ith generator di −1 ' ' damping ratio; Idi and Iqi are currents on d and q transient 0 stator 0 the d and 0 q−axis; 1 T0di and 0T q i are0the Xqi − Xqi ' ' and X are transient and synchronous reactances onthe d and q axis; time constants; X di ,AXmi (7) 0 qi 0 0 0 −1 K Fi /TFi 0 di qi ,=X ' ' 0 0 0 0 0 − K 1 Edi and Eqi are transient potential voltages on the d and q axis. Ei K Ai K Fi 0 0 0 0 K − −1 Ai For a generator equipped with the IEEE type I voltage regulatorT as shown in Figure 1 for Fi
regulating its potential voltage, its dynamics could be described by Equations (6) and (7). and vi = K Ai (Vre f i − Vti ) − SEi E f di . Vti
Vrefi
S Ei = Ae i
Vr max
K Ai 1 + sTAi
Bi E fdi
1 K Ei + sTEi
E fdi
Vr min
sK Fi 1 + sTFi Figure Figure1.1.Block Blockfunction functionofofthe theIEEE IEEEtype typeI Iexcitation excitationsystem. system.
2.3. Power Network Couples Between Nodal Voltage and Current The network equations G ( X, Y, t) in Equation (1) are used to describe the relationships between nodal voltages and currents as Equation (8) YV = I
(8)
where Y is the power network admittance matrix, V and I are nodal voltages and injected currents, respectively. The transient stability of a large-scale power system is usually related to a large number of nodes and directly solving Equation (8) is very complicated, and therefore Equation (8) is usually rewritten in a more concise form. If we denote the nodal current vector in two parts, one is for the generator bus and the other is for the non-generator bus, then the nodal current could be rewritten as I=[
Im ] 0
(9)
Then Equation (8) will be rearranged as (10) "
Im 0
#
"
=
Ymm Yrm
Ymr Yrr
#"
Vm Vr
# (10)
where Yrr and Ymm denote the self-admittance matrix for non-generator nodes and generator nodes, respectively. Ymr and Yrm denote the mutual admittance matrix between non-generator and generator nodes. If we rewrite Equation (10) in two equations, we have Im = Ymm Vm + Ymr Vr
(11)
0 = Yrm Vm + Yrr Vr
(12)
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If expressed in terms of Vm and afterward be substituted in (11) to eliminate Vr , then we have the form as (13) Im = Ymm − Ymr Yrr−1 Yrn Vm (13) This matrix (Ymm − Ymr Yrr−1 Yrm ) is the required reduced YBus matrix. It is an (m × m) matrix where m denotes the number of generators. 3. Dynamic Model of DFIG and Wind Turbine The completed dynamic model of wind power generation can be expressed by the equations of sub systems which actually include the model for the wind turbine with drive train, the induction generator and the control system. The detailed descriptions of these dynamic models are presented as follows, with the general configurations given in Figure 2. 3.1. Model of Drive Train and Wind Turbine Generally, the rotor is considered to be two concentrated masses, one is the mass of generator and the other is mass of the turbine. Both are connected together with a specific damping and stiffness system value, which could be as described in (14) and (15) [21]. dθtw = ωb ( ωt − ωr ) dt 1 Pm dωt = − Ktw θtw − Dtw (ωt − ωr ) dt 2Ht ωt
(14) (15)
where ω t , ω r and ω b are the turbine speed, rotor speed and system base speed, respectively; θ tw (rad) is the shaft twist angle; Ktw (p.u./rad) and Dtw are the shaft stiffness and mechanical damping coefficients; Ht (s) is wind turbine inertia constant; and Pm is the mechanical power extracted from the wind. 3.2. Model of DFIG Generator Figure 2 shows the widely used structure of the DFIG generator for stability analysis with the following assumptions: (1) (2) (3)
the dynamics of the DC capacitor are neglected; the active powers of the rotor side converter (RSC) and grid side converter (GSC) are considered as equal; GSC is assumed to be ideal in that there is no reactive power exchanged with the grid during the transient and the total reactive power is supported only by the stator [22].
To protect the power electronic converters and rotor circuit from high transient current in the rotor, a protection device named as a crowbar is used. A crowbar is the external rotor impedance that is coupled with the sliding ring of the generator rotor. This device is triggered and blocks the RSC when the current in the rotor exceeds the rated current of the crowbar. By ignoring the dynamics of the stator current, the DFIG model could be described as 1 ded 1 Lm =− e − X − X 0 iqs + sωs eq − ωs vqr ωb dt T0 d Lr + Lm
(16)
1 Lm 1 deq =− eq + X − X 0 ids − sωs ed + ωs v ωb dt T0 Lr + Lm dr
(17)
1 dωr = Ktw θtw + Dtw (ωt − ωr ) − (ed ids + eq iqs ) dt 2Hg
(18)
vds = −rs ids + X 0 iqs + ed
(19)
=
dt
− K twθ tw − Dtw (ωt − ωr ) 2H t ωt
(15)
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where ωt, ωr and ωb are the turbine speed, rotor speed and system base speed, respectively; θtw (rad) is the shaft twist angle; Ktw (p.u./rad) and Dtw are the shaft stiffness and mechanical damping ignoring the dynamics of the stator current, the DFIG model could be described coefficients; Ht (s) is wind turbine inertia constant; and Pm is the mechanical power extracted from the wind.
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as
Lm 1 de 1 vqr = − ed − ( X − X ′) iqs + sωs eq − ωs dt the widely T0 used structure of the DFIG Lr + Lanalysis Figureω 2 bshows generator for stability with the m 0
3.2. Model of DFIG Generator d
(16)
vqs = −rs iqs − X ids + eq
following assumptions:
(20)
(1) the dynamics of the DC capacitor are neglected; Pw = v side idsconverter + vqs i(RSC) vdrgrid idr side − vconverter qs −and qr iqr (GSC) are considered (2) the active powers of the rotor ds as equal;1 de 1 q m = ids iqs exchangedLwith (3) GSC is assumed to that isXno the ′ reactive vdspower = be − idealeinqQ +w there X −vqs i− vdrgrid during ds − s s ed + s the transient and the total reactive power is supported only by the stator [22]. d T t L + Lm r b 0
(
ω
)
ω
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(21)
ω
(22) (17)
where ed and eq are d and q components of internal voltage; Pw and Qw are active and reactive power To protect the power electronic converters and rotor circuit from high transient current in the of DFIG absorbed bya protection network; X and Xas0 are open-circuit and short-circuit reactance; T0 is the transient rotor, device named a crowbar is used. A crowbar is the external rotor impedance that dωsliding 1 is coupled with the ring of the generator rotor.constant. This device is triggered and blocks the RSC r open-circuit time constant; Hg is=the generator K twθ tw +inertia ω ω ( ) D e i + e i − − ) d ds q qs (18) tw ( tof thercrowbar. when the current in the rated current dtthe rotor 2Hexceeds g is
vds + jvqs
Pw
vds = −rs ids + X ′iqs + ed
(19)
ir
vdr + jvqr
vqs = −rs iqs − X ′ids + eq
(20)
C
Pw = vds ids +vqs iqs − vdr idr − vqr iqr
(21)
Qw = vqs ids − vds iqs
(22)
where ed and eq are d and q components of internal voltage; Pw and Qw are active and reactive power of DFIG absorbed by network; X Figure and X' are open-circuit and short-circuit reactance; T0 is the transient 2. Structure of Doubly Fed Induction Generators. Figure 2. Structure of Doubly Fed Induction Generators. open-circuit time constant; Hg is the generator inertia constant. 3.3. Model of 3.3. Model of Control Control System System When When the the rotor rotor speed speed exceeds exceeds the the stability stability of of the the power power system, system, the the mechanical mechanical power power of of the the wind turbine is reduced by decreasing the value of P . In order to control the reactive power on the m wind turbine is reduced by decreasing the value of . In order to control the reactive power on the grid for the RSC and GSC are grid terminals terminals and and the the DC DC voltage voltageof ofcapacitors, capacitors,voltage voltagesignals signalsVVdrdr and and V Vqr qr for the RSC and GSC are generated by the control system. generated by the control system. In In this this paper, paper, the the FMAC FMAC structure structure with with two two control control loops loops is is used used as as the the control control strategy strategy for for DFIG DFIG as shown in Figure 3, one for the terminal voltage and the other for the power output of DFIG [22]. as shown in Figure 3, one for the terminal voltage and the other for the power output of DFIG [22]. It It controls the generator terminal voltage and power by adjusting the magnitude and angle of the rotor controls the generator terminal voltage and power by adjusting the magnitude and angle of the rotor flux flux vector, vector, and and has has the the advantage advantage of of (1) providing low low interaction interaction between between the the power power and and voltage voltage control control loop, (1) providing loop, and and (2) enhancing voltage recovery after faults (2) enhancing voltage recovery after faults
vs
vsref
ωr
+
−
k kpv + iv s Peref
+
Pe
Eg
gv (s)
− kpp +
kip
E ref
+
δg
s
ref
−
kim s
kpa +
kia s
δ
−
+
kpm +
g v ( s ) vr
vdr
gv (s) δ r
vqr
Figure 3. Block diagram of FMAC controller. controller.
4. Case Studies, Results Results and and Discussion Discussion 4. Case Studies, As shown is is used asas thethe benchmark to As shown in in Figure Figure 4, 4,the themodified modified4-generator 4-generator14-bus 14-busIEEE IEEEsystem system used benchmark investigate the impacts of adding wind farms (WFs) or capacitors on system transient stability. In this to investigate the impacts of adding wind farms (WFs) or capacitors on system transient stability. system, the dynamic models of four conventional generators areare 4th4thorder In this system, the dynamic models of four conventional generators orderfor fortransient transient stability stability analysis, while each generator is equipped with a IEEE Type 1 exciter. For wind farms, an aggregated model is used to investigate wind generation impact on the system transient stability [23], the DFIG
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analysis, while each generator is equipped with a IEEE Type 1 exciter. For wind farms, an aggregated model is used to investigate wind generation impact on the system transient stability [23], the DFIG parameters with wind wind turbine turbineparameters: parameters:KK = 0.6 p.u./rad, =70.45 parameters with twtw = 0.6 p.u./rad, DtwD =tw 0.45 and Ht = Appl. Sci. are 2018, cited 8, x FORfrom PEER [22] REVIEW of 16 and H = 3.8 s. In this paper, the power system analysis toolbox (PSAT) developed by Dr. Federico Milano 3.8 s. In this paper, the power system analysis toolbox (PSAT) developed by Dr. Federico Milano is t analysis, while each generator is equipped with a IEEE Type 1 exciter. For wind farms, an aggregated is used conduct the transient stabilityanalysis analysisininthis thispaper paper[20]. [20]. used toto conduct the transient stability model is used to investigate wind generation impact on the system transient stability [23], the DFIG parameters are cited from [22] with wind turbine parameters: Ktw = 0.6 p.u./rad, Dtw = 0.45 and Ht = 3.8 s. In this paper, the power system analysis toolbox (PSAT) developed by Dr. Federico Milano is used to conduct the transient stability analysis in this paper [20].
Figure 4. 4. Modified Modified IEEE-14 IEEE-14 bus bus system system with with wind wind farms. farms. Figure Figure 4. Modified IEEE-14 bus system with wind farms. 4.1. Effect Effect of of Wind Wind Power Power Generation Generation on Transient Transient Stability 4.1. on Stability
4.1.this Effect of Wind Power on Transient Stability In this subsection, weGeneration will investigate investigate the effect effect of wind wind power power generation generation penetration penetration level level on on In subsection, we will the of transient stability of the IEEE 14-bus system, and comparisons are made by observing generator In this subsection, we14-bus will investigate the effect of wind power generation penetration level on transient stability of the IEEE system, and comparisons are made by observing generator angles angles and generator speeds in time domain as below. shown below. are made by observing generator transient stability of time the IEEE 14-bus and comparisons and generator speeds in domain as system, shown angles and generator speeds in time domain as shown below.
4.1.1. For For System System with with One One WF WF at at Bus Bus 11 4.1.1. 4.1.1. For System with One WF at Bus 1
Generator speed(p.u.)
Generator speed(p.u.)
In this this case, case, itit can can be seen clearly clearly from from the the results results for for generator generator speeds speeds in in Figure Figure 55 that that the the system system In In thisacase, it can be period seen clearly from the results for generator speeds inshow Figurethat 5 that thefirst system is stable stable after after short time of transients. transients. the peak of of is a short time period of The results in Figure 5 show that the first peak is stable after a short time period of transients. The results in Figure 5 show that the first peak of generator speeds during the disturbance almost approaches 1.01 p.u. and settles down in 8 s. Now, generator speeds during disturbance generator speeds during the disturbance almost approaches 1.01 p.u. and settles down in 8 s. Now, welook lookatatthe thegenerator generator angle response in Figure 6, generator 2 the hasmaximal the maximal positive angle ifif we angle response in Figure 6, generator 2 has if we look at the generator angle response in Figure 6, generator 2 has the maximalpositive positiveangle anglepeak peak at 0.6 radian and generator 4 has the minimal negative angle peak at −1 radian, and all at 0.6peak radian andradian generator 4 has the 4minimal negativenegative angle peak at peak −1 radian, and alland theall generator at 0.6 and generator has the minimal angle at −1 radian, the the generator angles static at at 2020 s. s. angles are static atare 20are s. static generator angles
Figure 5. Generator speeds for WF at bus 1.
Figure 5. Generator speeds for WF at bus 1. Figure 5. Generator speeds for WF at bus 1.
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Generator angel(rad)
0.5
syn1
syn2
syn3
syn4
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0.5
syn1
syn2
syn3
syn4
Generator angel(rad)
-0.5
0
-1
-0.5
0
5
10
15
20
Time(s) -1
Figure6.6.Generator Generator angles bus 1. 1. Figure anglesfor forWF WFatat bus
0
5
4.1.2. For System with Two Wind Farms
4.1.2. For System with Two Wind Farms
10
15
20
Time(s)
In this scenario, two wind farms are toangles this system, Figure 6. added Generator for WF atone bus is 1. at bus 1 and the other is at bus 4.
In scenario, two wind farms are added to this system, one is at the busdisturbance 1 and thealmost other is at As this can be seen in generator speed responses in Figure 7, the first peak during 4.1.2. For System with Two Wind Farms bus 4.approaches As can be1.008 seenp.u. in generator Figure the first peak during and settlesspeed down responses in 15 s still in with some7,disturbances. Now, if wethe lookdisturbance at the theta angle in two Figure 8,farms though the in positive andwith negative first peaks at generator and almost approaches p.u. and down s system, still disturbances. Now, look at In response this 1.008 scenario, windsettles are added to15 this one some is at bus 1 and the other is at busif4.2we As can be seen in generator speed responses in Figure 7, the first peak during the disturbance almost generator 4 occur at value i.e., +0.5 radian and −0.9 radian respectively, all the generator angles are the theta angle response in Figure 8, though the positive and negative first peaks at generator 2 and approaches and settles down in 15 s still with some disturbances. Now, if we look at the fluctuating even at 20 p.u. s. i.e., generator 4 occur at1.008 value +0.5 radian and −0.9 radian respectively, all the generator angles are theta angle to response in Figure 8, though the positive negative that first peaks at generator 2 and According the observation in Figures 5–8, it and is obvious the stability of the system fluctuatinggenerator even at420 s. occur at value i.e., +0.5 radian and −0.9 radian respectively, all the generator angles are deteriorates dramatically by integrating more wind farms into the existing power grid. This is According to even the at observation in Figures 5–8, it is obvious that the stability of the system fluctuating 20 s. because with more integration of wind farms, the inertia of the original simultaneous system is According to by theintegrating observation in Figures 5–8, it is obvious the stability the system deteriorates dramatically more wind farms into thethat existing powerofgrid. This is because reduced and therefore the system is more sensitive to the external disturbance. deteriorates dramatically by integrating more wind farms into the existing power grid. This is with more integration of wind farms, the inertia of the original simultaneous system is reduced and because with more integration of wind farms, the inertia of the original simultaneous system is therefore the system is more the sensitive the sensitive externalto disturbance. reduced and therefore system istomore the external disturbance.
Figure 7. Generator WFsatatbus bus1 and 1 and Figure 7. Generatorspeeds speeds for for WFs busbus 4. 4.
Figure 7. Generator speeds for WFs at bus 1 and bus 4.
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Figure Generatorangles angles for for WFs bus 4. 4. Figure 8. 8. Generator WFsatatbus bus1 1and and bus Figure 8. Generator angles for WFs at bus 1 and bus 4. 4.2. Impact of Wind Farm Location on System Transient Stability
Figure Generator angles forStability WFs at bus 1 and bus 4. 4.2. Impact of Wind Farm Location on8.System Transient
In this of scenario, an experiment performed by changing 4.2. Impact Wind Farm Location onisSystem Transient Stability the location of the wind generator from
In scenario, experiment isSystem performed by changing the location of the wind generator 4.2.this Impact Wind Location on Transient Stability the bus 1 toofbus 4 an ofFarm IEEE 14-bus system. The results show that instability is changed by changing the from In this scenario, an 14-bus experiment is performed by changing the location of theiswind generator from the bus 1 to bus 4 of IEEE system. The results show that instability changed by changing location of WFs. As can be seen in is the omega angle response in location Figure 9, the duringfrom the In this an experiment performed by changing thefirst windpeak generator the bus 1 toscenario, bus 4 of IEEE 14-bus system. The results show thatthe instability of is changed by changing the the location of WFs. As can be seen in the omega angle response in Figure 9, the first peak during disturbance almost approaches 1.01 p.u. and it settles down in 3 s to 4 s. Now, if we look at the theta the bus 1 of to WFs. bus 4 As of IEEE 14-bus The results that instability changing location can be seensystem. in the omega angleshow response in Figure is 9, changed the first by peak during the the angle response inAs Figure the in positive and negative peaks endinat3different values forwe different the disturbance almost approaches 1.01 p.u. and it settles down s 9, tothe 4 s.first Now, if look location of WFs. can be10,seen theat the disturbance almost approaches 1.01the p.u.omega and it angle settlesresponse down in in 3 sFigure to 4 s. Now, if wepeak look during at the theta at 0.8 s, but the system could regain the transient stability within 4 s. theta generators angle response in Figure 10, the positive and negative peaks end at different values for different disturbance almost approaches 1.01 p.u. and it settles down in 3end s to at 4 s.different Now, if we lookfor at the theta angle response in Figure 10, the positive and negative peaks values different generators at 0.8ats,0.8 but the the system regain stability within 4 values s. angle response ins,Figure 10, thecould positive andthe negative peaks end atwithin different for different generators but system could regain thetransient transient stability 4 s. generators at 0.8 s, but the system could regain the transient stability within 4 s.
Figure 9. Generator speeds for WFs at bus 4. 0.2
Figure 9. Generator speeds for WFs at bus 4.
Figure 9. 9.Generator forWFs WFsatatbus bus Figure Generator speeds speeds for 4. 4. syn1
0.2 0 0.2
syn2
syn1 syn1
0 -0.20
syn2 syn2
syn3 syn3 syn3
syn4 syn4 syn4
-0.2 -0.4 -0.2 -0.4 -0.6 -0.4 -0.6 -0.8 -0.6 0 -0.8 -0.8 0 0
5
10
15
20
5 10 15 Figure 510. Generator angles 4. 10 for WFs at bus15 Time(s)
20 20
Time(s)
Time(s)
Figure 10. Generator angles for WFs at bus 4. Figure 10. Generator angles for WFs at bus 4.
Figure 10. Generator angles for WFs at bus 4.
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Comparing the the Figures 55 and and 6 with the Figures 99 and and 10, 10, these these figures figures clearly clearly indicated that by Comparing Comparing the Figures Figures 5 and 66 with the Figures Figures figures clearly indicated that by changing the location of the turbine from bus 4 to bus 1, the transient instability of this this IEEE 14-bus 14-bus changing changing the location of the turbine turbine from bus bus 44 to to bus bus 1, 1, the the transient transient instability instability of of this IEEE IEEE 14-bus system increases. increases. Therefore, the location location of wind wind turbine integration integration into the the power system system is one one of system system increases. Therefore, the the location of of wind turbine turbine integration into into the power power system is is one of of the key factors affecting the transient stability margin of a system with wind farms, and the wind the stability margin of aofsystem withwith windwind farms, and the farm the key keyfactors factorsaffecting affectingthe thetransient transient stability margin a system farms, andwind the wind farm should be carefully determined the planning considering transient stability. should be carefully determined in thein planning stage stage considering transient stability. farm should be carefully determined in the planning stage considering transient stability. 4.3. Impact of Varied Varied Wind Speed Speed on System System TransientStability Stability 4.3. 4.3. Impact Impact of of Varied Wind Wind Speed on on System Transient Transient Stability In this this experiment, the the wind speed speed drivingthe the windturbine turbine decreasesfrom from 20 m/sto to 10m/s m/s to In In this experiment, experiment, thewind wind speeddriving driving thewind wind turbinedecreases decreases from2020m/s m/s to10 10 m/s to to see what changes could happen to the system. see see what what changes changes could could happen happen to to the the system. system. 4.3.1. For Wind Speed at 20 m/s m/s 4.3.1. For Wind Speed at 20 m/s The wind speed of wind wind turbine turbine is is set set to to 20 20 m/s m/s to see the possible effect on power system system The wind speed of wind turbine is set to 20 m/s to see the possible effect on power system transient Figure 11,11, thethe speed magnitudes of allofgenerators fluctuate with transient stability. stability.As Asdemonstrated demonstratedinin Figure speed magnitudes all generators fluctuate transient stability. As demonstrated in Figure 11, the speed magnitudes of all generators fluctuate the valuevalue 1.0081.008 p.u. and settlesettle down in 9 in s. 9Now, if we at the generator angle response in withpeak the peak p.u. and down s. Now, if look we look at the generator angle response with the peak value 1.008 p.u. and settle down in 9 s. Now, if we look at the generator angle response Figure 12, 12, thethe firstfirst positive andand negative peaks are at different levelslevels for different generators, and all of in Figure positive negative peaks are at different for different generators, and in Figure 12, the first positive and negative peaks are at different levels for different generators, and them synchronism after 9after s. 9 s. all of regain them regain synchronism all of them regain synchronism after 9 s. 1.01 1.01
syn1 syn1
syn2 syn2
syn3 syn3
syn4 syn4
1.005 1.005 1 1 0.995 0.995 0.99 0.99 0.985 0.9850 0
5 5
10 10
15 15
Time(s) Time(s)
20 20
Figure 11. Generator speeds for wind speed at 20 m/s. Figure Figure11. 11.Generator Generatorspeeds speedsfor forwind windspeed speedat at20 20m/s. m/s.
1 1
syn1 syn1
syn2 syn2
syn3 syn3
syn4 syn4
0.5 0.5 0 0 -0.5 -0.5 -1 -1 -1.5 -1.50 0
5 5
10
10 Time(s) Time(s)
15 15
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Figure 12. Generator angles for wind speed at 20 m/s. Figure 12. Generator angles for wind speed at 20 m/s. Figure 12. Generator angles for wind speed at 20 m/s.
4.3.2. For Wind Speed at 15 m/s 4.3.2. For Wind Speed at 15 m/s In this case, wind speed of the turbine is set to 15 m/s. As shown by the omega curve in Figure 13, In this case, wind speed of the turbine is set to 15 m/s. As shown by the omega curve in Figure 13, the first peak approaches the same value 1.008 p.u. during the disturbance and settles down in 8 s. the first peak approaches the same value 1.008 p.u. during the disturbance and settles down in 8 s.
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4.3.2. For Wind Speed at 15 m/s Appl. In Sci.this 2018,case, 8, x FOR PEER REVIEW wind speed of the turbine is set to 15 m/s. Appl. Sci. 2018, 8, x FOR PEER REVIEW
11 of13, 16 As shown by the omega curve in Figure 11 of 16 the first peak approaches the same value 1.008 p.u. during the disturbance and settles down in 8 s. Now considering considering generator generator angle angle curves curves in in Figure Figure 14, 14, itit can can be be noticed noticed that that the the first positive positive and Now Now considering generator angle curves in Figure 14, it can be noticed that the first first positive and and negative peaks are very similar to those in Figure 12 and all generator angles finally settle down after negative peaks are very similar to those in Figure 12 and all generator angles finally settle down negative peaks are very similar to those in Figure 12 and all generator angles finally settle down after 9 s. 9 s. 9after s.
1.01 1.01
syn1 syn1
syn2 syn2
syn3 syn3
syn4 syn4
1.005 1.005 1 1 0.995 0.995 0.99 0.99 0.985 0.985 0 0
5 5
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Time(s) Time(s)
15 15
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Figure 13.Generator Generatorspeeds speeds forwind wind speedatat15 15 m/s. Figure Figure 13. 13. speeds for for wind speed speed at 15 m/s. m/s.
1 1
syn1 syn1
syn2 syn2
syn3 syn3
syn4 syn4
0.5 0.5 0 0 -0.5 -0.5 -1 -1 -1.5 -1.5 0 0
5 5
10 10
Time(s) Time(s)
15 15
20 20
Figure 14. Generator angles for wind speed at 15 m/s. Figure 14. 14. Generator Generator angles angles for for wind wind speed speed at at 15 15 m/s. m/s. Figure
4.3.3. For Wind Speed at 10 m/s 4.3.3. Speed at at 10 10 m/s m/s 4.3.3. For For Wind Wind Speed In this case, the wind speed was further reduced to 10 m/s. Based on the generator speed curves In case, the wind wind speed speed was was further further reduced reduced to to 10 10 m/s. m/s. Based on the speed curves In this this case, the Basedthe on disturbance the generator generator speed in Figure 15, the first peak also approaches the value 1.008 p.u. during and thencurves settles in Figure 15, the first peak also approaches the value 1.008 p.u. during the disturbance and then settles in Figure 15, the first peak also approaches the value 1.008 p.u. during the disturbance and then settles down in 9 s. The generator angle responses in Figure 16 clearly show that all generators undergo a down in 99s.s.The Thegenerator generatorangle angle responses Figure 16 clearly show all generators undergo a down in in Figure 16 clearly show that that all within generators short short in time period of transientresponses fluctuation, and they all synchronize 9 s.undergo Based aon the short time period of transient fluctuation, and they all synchronize within 9 s. Based on the time period of fluctuation, and they synchronize within s. Based on the comparison comparison oftransient Figures 13–16, it is shown thatall when the speed of the9 wind turbine decreases fromofa comparison of it Figures 13–16, itwhen is shown that when the speed of thedecreases wind turbine decreases from a Figures 13–16, is shown that the speed of the wind turbine from a nominal value, nominal value, the system instability does not change much. nominal value, the system instability does not change much. the system instability does not change much.
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1.01 1.01
syn1 syn1
syn2 syn2
syn3 syn3
syn4 syn4
1.005 1.005 1 1 0.995 0.995 0.99 0.99 0.985 0.985 0 0
5 5
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Time(s) Time(s)
20 20
Figure 15. Generator speeds for wind speed at 10m/s. Figure m/s. Figure15. 15.Generator Generatorspeeds speedsfor forwind windspeed speedatat10 10m/s.
0.5 0.5
syn1 syn1
syn2 syn2
syn3 syn3
syn4 syn4
0 0 -0.5 -0.5 -1 -1 -1.5 -1.5 0 0
5 5
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Time(s) Time(s)
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Figure 16. Generator speeds for wind speed at 10m/s. Figure 16. Generator speeds for wind speed at 10m/s. Figure 16. Generator speeds for wind speed at 10 m/s.
4.4. Effect of Installing Static Capacitors on System Transient Stability 4.4. Effect of Installing Static Capacitors on System Transient Stability 4.4. Effect of Installing Static Capacitors on System Transient Stability The transient stability of a system can be controlled by installing capacitor banks at the The transient stability of a system can be controlled by installing capacitor banks at the The transient stability of a system can be controlled by installing capacitor banks at the generation bus. generation bus. generation bus. 4.4.1. Result of installing 3 capacitors along with generation buses 4.4.1. Result of installing 3 capacitors along with generation buses 4.4.1. Result of installing 3 capacitors along with generation buses As seen from the generator speed curves in Figure 17, the first peak during the disturbance As seen from the generator speed curves in Figure 17, the first peak during the disturbance As from the1.01 generator speed curves in Figure first peak during thethe disturbance almost seen approaches p.u. and settles down after17, 12the s. Now, considering generatoralmost angle almost approaches 1.01 p.u. and settles down after 12 s. Now, considering the generator angle approaches p.u. down after 12 s.angle Now, considering the generator angle response in response in 1.01 Figure 18,and the settles positive and negative peaks for generator 2 and generator 4 appeared response in Figure 18, the positive and negative angle peaks for generator 2 and generator 4 appeared Figure 18, the positive and negative angle peaks for generator 2 and generator 4 appeared near 1 s, near 1 s, and the angle fluctuations completely disappear after 12 s. near 1 s, and the angle fluctuations completely disappear after 12 s. and the angle fluctuations completely disappear after 12 s.
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1.015 1.015 syn1 syn1
1.01 1.01
syn2 syn2
syn3 syn3
syn4 syn4
1.005 1.005 1 1 0.995 0.995 0.99 0.99 0.985 0.9850 0
5 5
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Time(s) Time(s)
20 20
Figure Generator speeds Figure 17. 17. Generator Generator speeds for for aa system system with with 33 capacitors. capacitors.
1 1 syn1 syn1
syn2 syn2
syn3 syn3
syn4 syn4
0.5 0.5 0 0 -0.5 -0.5 -1 -1 -1.5 -1.50 0
5 5
10 10
Time(s) Time(s)
15 15
20 20
Figure Figure 18. 18. Generator Generator angles angles for for aa system system with with 33 capacitors. capacitors. Figure 18. Generator angles for a system with 3 capacitors.
4.4.2. 4.4.2. Result Result of of Installing Installing 44 Capacitors Capacitors Along Along with with Generation Generation Buses Buses 4.4.2. Result of Installing 4 Capacitors Along with Generation Buses As As shown shown by by the the figure figure below below by by installing installing one one more more capacitor capacitor to to generation generation bus bus 2, 2, the the stability stability Assystem shown increases. by the figure below by installingspeed one more capacitor to generation bus positive 2, the stability of of the From the generator curves in Figure 19, the first of the system increases. From the generator speed curves in Figure 19, the first positive peak peak is is the system increases. From the generator speed curves in Figure 19, the first positive peak is delayed delayed to 1.2 s compared with 0.8 s for Figure 17 with a magnitude of 1.007 p.u. during the delayed to 1.2 s compared with 0.8 s for Figure 17 with a magnitude of 1.007 p.u. during the to 1.2 s compared with 0.8 s fordown Figure 17 with a magnitude of 1.007 p.u. during the in disturbance and disturbance disturbance and and finally finally settles settles down after after 88 s. s. With With regard regard to to the the generator generator angles angles in Figure Figure 20, 20, the the finally settles down afterpeaks 8 s. With regardat to the sgenerator angles in Figure 20, the positive and negative positive positive and and negative negative peaks appeared appeared at 1.2 1.2 s with with maximal maximal value value as as 0.35 0.35 radian radian which which is is much much peaks appeared at 1.2 s in with maximal value as 0.35 radian which is much smaller than 0.5 radian in smaller smaller than than 0.5 0.5 radian radian in Figure Figure 18, 18, and and all all the the generators generators are are finally finally synchronized synchronized after after 88 s. s. These These Figure 18, and all the generators are finally synchronized after 8 s. These comparisons show that by comparisons comparisons show show that that by by increasing increasing the the capacitor capacitor capacity, capacity, the the system system transient transient stability stability can can be be increasing the capacitor capacity, the systemcan transient stability can be improved. This is the because more improved. This is because more capacitors provide more reactive power to assist system improved. This is because more capacitors can provide more reactive power to assist the system to to capacitors can provide more reactive power to assist the system to endure the fault disturbances. endure endure the the fault fault disturbances. disturbances.
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1.01 1.01 1.005 1.005
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syn2
syn3
syn4
syn1
syn2
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1 1 0.995 0.995 0.99 0.99 0.985 0.985 0 0
5 5
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15
10 15 Time(s) Time(s) Figure 19. Generator speeds for systems with 4 capacitors. Figure for systems systemswith with44capacitors. capacitors. Figure19. 19.Generator Generator speeds speeds for
1 1
syn1 syn1
0.5 0.5
syn2 syn2
syn3 syn3
20 20
syn4 syn4
0 0 -0.5 -0.5 -1 -1 -1.5 -1.5 0 0
5 5
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15 15
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Figure 20. Generator angles for systems with 4 capacitors. Figure20. 20.Generator Generator angles angles for Figure for systems systemswith with44capacitors. capacitors.
5. Conclusions 5. Conclusions 5. Conclusions Since DFIGs are greatly influenced by the oscillation in the shaft of rotating mass, over-speed of Since DFIGs arepeak greatly influenced by the oscillation in the shaft of rotating mass, over-speed of rotor, and transient currents during a very detailed with two-lumped mass Since DFIGs are greatly influenced byfault, the oscillation in theDFIG shaft model of rotating mass, over-speed of rotor, and transient peak currents during fault, a very detailed DFIG model with two-lumped mass based wind turbinepeak is firstly introduced investigating the dynamics windwith farms. By using PSAT rotor, and transient currents duringfor fault, a very detailed DFIG of model two-lumped mass based wind turbine is firstly introduced for investigating the dynamics wind farms. usingsystem PSAT software, this research work has analyzed the impacts of wind powerofof generation onBy power based wind this turbine is firstly introduced for investigating the dynamics wind farms. By using PSAT software, research work has analyzed the impacts of wind power generation on power system transient stability from different points of view, i.e., what will be the impact on the system response software, this research has analyzed the impacts ofwill wind power generation on power system transient fromwork different pointsitsoflocation? view, i.e.,And what on theifsystem response of addingstability wind farms and changing what be willthe beimpact the impact the wind speed transient stability from different points of view, i.e., what will be the impact on the system response of of adding The wind farms andresults changing location? whatrelationship will be the between impact ifcapacity the windofspeed changes? simulation showitsthat there isAnd a direct wind adding wind farms and changing its location? And what will be the impact if the wind speed changes? changes? simulation show that there a direct relationship between capacity of wind farms andThe power system results transient stability. With isthe increased integration of wind generation, the The simulation results show that there is a direct relationship between capacity ofgeneration, wind farmsthe and farms and power system transient stability. With the increased integration of wind transient instability of the power system increases. Moreover, the wind farm locations and wind power system transient stability. With theincreases. increasedMoreover, integration ofwind windfarm generation, the transient transient instability of the power system the locations and wind speed could also affect power system stability, but the negative impacts on the system transient instability of the power Moreover, wind farm locations wind speed could speed could also affectsystem powerincreases. system stability, but the the negative impacts onasand the system transient stability can be greatly alleviated by adding capacitors at the generator buses demonstrated in the stability can be greatly alleviated by adding capacitors at the generator buses as demonstrated in the be also affect power system stability, but the negative impacts on the system transient stability can case studies. case studies. greatly alleviated by adding capacitors at the generator buses as demonstrated in the case studies. Author Contributions: S.X. and Q.Z. designed the study and mainly wrote the paper; S.T.H. and W.Z. Author Contributions: S.X.S.X. and Q.Z. designed the study andpaper. mainly wrote wrote the paper; S.T.H. and W.Z. performed Author Contributions: and Q.Z. designed the study and mainly the paper; S.T.H. and W.Z. performed the experiments; B.H. revised and proofread the theperformed experiments; B.H. revised B.H. and proofread paper. the paper. the experiments; revised andthe proofread Funding: This research received no external funding. Funding: This research Funding: This researchreceived receivedno noexternal externalfunding. funding. Acknowledgments: This work was supported in part by Beijing Natural Science Foundation (3174057), Support Acknowledgments: This work was supported in part by Beijing BeijingNatural NaturalScience ScienceFoundation Foundation (3174057), Support Acknowledgments: This work was supported in (2016000020124G079), part by (3174057), Support Program Excellent Talents BeijingCity City Funds forfor thethe Program forfor thethe Excellent Talents ininBeijing (2016000020124G079),the theFundamental FundamentalResearch Research Funds Program for the Excellent Talents in Beijing City (2016000020124G079), the Fundamental Research Funds for the Central Universities (2016MS14), and the Science and Technology Program of State Grid Corporation of China Central Universities (2016MS14), and the Science and Technology Program of State Grid Corporation of China Central Universities (2016MS14), and the Science and Technology Program of State Grid Corporation of China (SGHE 0000KXJS1700086). (SGHE 0000KXJS1700086). (SGHE 0000KXJS1700086). Conflicts of Interest: The authors declare no conflict of interest.
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