TRANSIENT STABILITY ANALYSIS OF PERMANENT
MAGNET SYNCHRONOUS GENERATOR WITH TWO
LEVEL CONVERTER INVERTER
KRISHNA KUMARI.T
AdiShankara Institute Of Engineering and Technology Kalady,Kerala,India
krishnaravi_14@yahoo.com Dr.JAIMOL THOMAS
Saint Gits College of Engineering and Technology Pathamuttom,Kerala,India
thomas.jaimol@yahoo.com Abstract
Wind energy plays a prominent role in the generation of power from renewable sources. Generation by permanent magnet synchronous generator (PMSG) is recently been popular. But the major concern in using this generator is that the voltage and the power generated are variable due to the intermittent nature of wind energy. Because of the wide use of PMSG the study of the transient stability analysis is very important. In this paper the performance study of PMSG is done by using suitable control strategies to develop a constant voltage and power. The transient stability analysis is also carried out by simulating both the symmetrical and the unsymmetrical faults as network disturbances. This is demonstrated using MATLAB simulations.
Keywords: Transient stability analysis; converter; inverter.
1. Introduction
The world-wide concern about the environment and the ever increasing global demands necessitated the search for new alternative renewable energy sources.This search has led to the generation of power from wind which has been expanding due to the large improvement in technology, industrial maturation,competitive cost and emission free. More over wind energy is abundant, and has inexhaustible potential. By the end of 2003, the total installed capacity of the wind turbines has reached as much as 39.234GW andwill exceed 110GW in the near future [11]. Therefore there is huge penetration of wind power into the grid which can negatively affect the stability of the power system. This is evident during start-up of the wind generators which cause oscillations of the system frequency and possible voltage collapse. Thus the operation of wind farm and its response to disturbances is becoming a major concern, especially in areas where wind farms represent a significant portion of the local generation [3].
The two main classification of wind generators commonly used are constant speed and variable speed generators. Till recently constant speed induction generators were widely used due to its superior characteristics such as brushless and rugged construction, low cost, maintenance free and operational simplicity [8]. But due to the advancement of power electronics devices the variable speed generators are becoming very popular. They have increased energy capture, operation at maximum power point, improved efficiency and power quality. The commonly used variable speed generators are the doubly fed induction generators, wound field induction generators and permanent magnet synchronous generators.
These variable speed generators have better fault ride through capabilities as frequency converter is closely connected to the machine. [5,6] – [9, 10].But the constant speedsquirrel cage induction generator needs extra tools to enhance the fault ride through capability because it requires large reactive power to recover the air gap flux when short circuit fault occurs in the power system. Due to the lack of reactive power the electromagnetic torque decreases which causes a large difference between mechanical and electromagnetic torque. This will lead to an increase in the rotor speed and hence the machine becomes unstable and gets disconnected from the power system.
Due to the fluctuating nature of wind the output of the variable speed PMSG varies in amplitude and frequency
which is not suitable for use. In the model system used in this paper a PMSG wind generator is connected to the power system network through a fully controlled power converter. The power convertor consists of generator side AC/DC convertor, DC link capacitor and grid side DC/AC invertor. The generator side convertor controls the electromagnetic torque and therefore the extracted power while the grid side convertor controls both the DC link voltage and the power factor. The simulation analysis is performed by using MATLAB, Simpower system. By suitably controlling the power converters of PMSG in proper way, the transient stability of VSWT-PMSG can be enhanced.
2. System Overview
The system used is a variable speed wind turbine with a multi pole. The proposed wind energy system is designed for a 50kW wind turbine system (Fig.1). This is equipped with (1) a direct driven permanent magnet synchronous generator (PMSG), (2) an AC/DC converter which consists of uncontrolled three phase diode
rectifiers for tracking the maximum power from the available wind resources (3) an internal DC-Link modeled as
a capacitor(4) an inverter (5) a resistive load and (6) step up transformer.
Studies have been performed for transient stability of WTGS by using two-mass shaft model. The parameters of the PMSG used are given in Table 1
Table 1. Parameters of PMSG.
PMSG
No. of poles 10
Rated Speed 500 rad/sec
Rated Current 12 A
Armature Resistance, Rs 0.425 Ω
Magnetic Flux Linkage 0.433 Wb
Stator inductance Ls 8.4mH
Rated Torque 80Nm
Rated power 50kW
Figure 1. Schematic diagram of a PMSG connected to grid.
3. Transient Stability Analysis
A fault in the system will lead to instability and the machine will fall out of synchronism. If the system can’t sustain till the fault is cleared, then the whole system will be instabilised.During the instability not only the
oscillation in rotor angle around the final position goes on increasing but also the change in angular speed. In such a situation the system will never come to its final position. The unbalanced condition or transient condition may
leads to instability where the machines in the power system fall out of synchronism.
The system is subjected to a large variety of disturbances. The switching on and off of an appliance in the house is also a disturbance depending upon the size and capability of the interconnected system. Large disturbances such as lightning strokes, loss of transmission line carrying bulk power do occur in the system. Therefore transient
stability is defined as the ability of the power system to survive the transition following the large disturbance and
to reach an acceptable operating condition.
result will be the loss of synchronism of the generator and the machine will be disconnected from the system.This phenomenon is referred to as a generator going out of step.
4. Modeling Of Wind Turbine
By varying the pitch angle, the wind turbine which is connected to the grid, operates at constant speed and generates power. A variable speed wind generation system generates variable frequency, variable voltage and power that are converted to constant frequency and constant voltage before connecting to the grid.
The main function of a wind power system is to transform kinetic energy in the wind into electric energy. Wind energy forces an aerodynamic rotor to turn and thus the wind energy is transformed into mechanical energy. Mechanical energy, in a slow turning rotor shaft of wind blade, is geared up to a high-speed shaft which is connected to a generator. Inside the generator, the rotational mechanical energy is transformed into electrical energy. The electric power output is then connected to the grid.[4]
The power extracted from the wind
Pw = Cp*ρ *A*Vw3/2 (1)
Where Pw; is the power extracted from the windCp the power coefficient, ρ is the density of the air in kg/m3,
A is the exposed area in m2, and V is the velocity in m/s. The density is a function of pressure, temperature, and
relative humidity.
The amount of aerodynamic torque (τw)in Nm is given by the ratio between the power extracted from the wind
(Pw) in W, and the turbine rotor speed (ωw), in rad/s.
τw= Pw/ ωw (2)
Since there is no gear box the gearbox ratio ng= 1.Therefore mechanical torque (τw_g) transmitted to the generator is the same as the aerodynamic torque.
τw= τw_g. (3)
The power coefficient Cpreaches a maximum value equal to Cp= 0.593 [4]. That means, the power extracted
from the wind is always less than 59.3% (Betz’s limit), because various aerodynamic losses depend on the rotor construction (number and shape of blades, weight, stiffness, etc.). Because of this, the generation of power from
wind has very low efficiency. The tip-speed ratio λis defined as
TSR (λ) = ωw*R/Vw (4)
Where ωwis the angular velocity of rotor [rad/s], R is the rotor radius [m] and Vwis the wind speed upstream of
the rotor [m/s].
Figure 2. Turbine characteristic with maximum power point tracking (used in VSWT).
5. Modeling Of PMSG
The PMSG is used here for the generation of electrical power. The two phase synchronous reference frame is used to derive the dynamic model of the PMSG. The q-axis is 90° ahead of the d-axis with respect to the direction of rotation. A phase locked loop (PLL) is used for the synchronization between the d-qrotating reference frame
and the abc threephase frame. Fig. 3 shows the d-qreference frame used in a PMSG, where θis the mechanical
Figure 3. d-qand 𝛼-𝛽axis of a typical salient-pole synchronous machine
The mathematical model of the PMSG in the synchronous reference frame is
di
dt L L R i L L i u
d
ds ls
s d e qs ls q d
=
+ − +
(
+)
+1
( ω (5)
di
dt L L R i L L i u
q
qs ls
s q e ds ls d f q
=
+ − +
(
+)
+ +1
( ω ψ (6)
where d and q refer to the physical quantities that have been transformed into the d-q synchronous rotating reference frame, Rs, is the stator resistance [Ω], Ldand Lqare the inductances of the generator on the d and q axis, Lldand Llqare the leakage inductances of the generator on the d and q axis respectively, Ψfis the permanent
magnetic flux and ωeis the electrical rotating speed and
ωe= pωg (7)
Where p is the no of pole pairs of the generator.
The electromagnetic torque equation τe is given by
τe =1.5p (Lds-Lls)idiq+iqΨ (8) The equivalent circuit of the PMSG in d-q synchronous rotating reference frame is shown in Fig 4.
Figure 4. Equivalent circuit of the PMSG in the synchronous frame.
6. Modeling Of Mass drive unit
In this study the two mass drive unit is considered. The mathematical equation is represented as
2H
d
dt T T
t t
m sh
ω
= − (9)
1
ω θ
ω ω
elb tw
t r
d
dt
2H d dt T T g r sh g ω
= − (11)
Where Htand Hg are the inertia constants of the turbine and the PMSG. θtw is the shaft twist angle, ωt is the
angular speed of the turbine in p.u, ωtis the rotor speed of the PMSG in p.u, is the base speed in electrical,
and Tsh the shaft torque
T K D d
dt
sh sh tw t
tw
= θ + θ (12)
Where Tsh is the shaft stiffness and Dt is the damping coefficient.
7. Modeling Of PWM Frequency Converter
The pulse width modulation (PWM) frequency converter consists of generator side ac/dc converter, dc-link capacitor, and grid side dc/ac inverter. The output ac voltage is controlled in terms of amplitude and frequency. Power from the PMSG-based wind turbine is fed to ac–dc–ac converters to maintain the output ac voltage at
specified amplitude and frequency.
The variations in the wind speed as well as the load, affect the dc link voltage between rectifier and inverter.
Therefore, if Vdc is maintained constant at its reference value and keeping the modulation index of load side inverter at 1, the amplitude of output ac voltage can be controlled and maintained at the rated voltage.
The relation between dc voltage and output ac voltage of three-phase pulse width modulation (PWM) inverter is given by
V kV
LL = dc
3
2 2 (13)
Where
VLL =Fundamental phase-phase root-mean-square (rms) voltage on the ac side;
k = Modulation index of the PWM inverter; and Vdcthe dc link voltage.
From Eq. (13), it is seen that the ac voltage can be maintained at rated value by maintaining Vdc at its reference value and with k=1.
The frequency of the output ac is maintained at a specified value by choosing the frequency of sinusoidal
reference signal while generating the PWM pulses. [2]
8. Control Of Load Side Inverter
The main objective of the converter at the supply end is to regulate the voltage and frequency. This is achieved with the help of an output voltage controller which controls the output voltage during load transients or wind variation. .
The dynamic model of the grid connection when selecting a reference frame rotating synchronously with the grid voltage space vector is
V V R i L di
dt L i
d di f d f d
f q
= −. − +ω (14)
V V R i L
di
dt L i
q qi f q f
q
f d
= . .− − +ω (15)
where Lf and Rfare the grid inductance and resistance respectively, and vdi and vqi are the inverter voltage components.
The instantaneous power in a three phase system is given by
P(t)=vaia +vbib+vcic
P t V i V i V i
v
i i i
a a b b c c
a b c a b c
( )
= + +[
]
Using d-q transformation the active and reactive power is given by
P=
(
V id d +V iq q)
3
2 (17)
Q=
(
V id q+V iq d)
3
2 (18)
If the reference frame is as vq = 0 and vd=V2, the active and reactive power will be
P=
(
V id d)
=(
V id)
3 2
3
2 (19)
Q=
(
V id q)
=(
V iq)
3 2
3
2 (20)
Therefore the active and reactive power can be controlled by controlling the direct and quadrature current component. [12]
9. Simulation Results
The simulation model of a PMSG is developed on a 50kW and this runs at a speed of 500rpm. This machine is connected to a grid as shown in Fig 5. The subsystem used in the wind turbine is shown in Fig. 6.The fault is simulated for a time period of 1.2 to 1.4 secs. A load of 40 kW is connected to the system. Under normal operating condition the PMSG is supplying the active power. For detailed transient stability analysis the simulations are done for Symmetrical fault (3LL), and Unsymmetrical fault (LG), (LLG). All the simulations are carried out using the MATLAB/SimPower Systems simulation software.
9.1Transient stability analysis during a symmetrical fault condition
A balanced three phase fault is considered to occur on the transmission line during a time period of 1.2 to 1.4 secs. The simulation time period is 2 sec. During the transient disturbance the grid side inverter provides the necessary reactive power so that the terminal voltage returns back to the prefault value itself. The Reactive power on the grid side is shown in Fig. 7 and the variation in terminal voltage in Fig 8. This is maintained by changing the rotor speed which is shown in Fig. 9. The variation in electromagnetic torque and the electrical
Figure 5. Simulink model of PMSG connected to grid
torque is shown in Fig 10. During the disturbance also there is not much difference between the mechanical and electromagnetic torque. The real power response is shown in Fig. 11. From the simulation results, it is clearly understood that the proposed system enhance the transient stability of variable speed permanent magnet under symmetrical fault condition.
9.2 Transient stability analysis during an unsymmetrical fault condition (LG)
electromagnetic torque and the real power on the inverter side are shown in the Fig.12, Fig. 13, Fig 14, Fig 15, and Fig. 16. From the simulations it is seen that the disturbances are not severe as in the case of symmetrical fault. It is evident from the diagrams that the proposed control system can enhance the transient stability of VSWT-PMSG, when an LG fault occurs.
9.3 Transient stability analysis during an unsymmetrical fault condition (LLG)
A LLG fault is considered on the transmission line and the simulations were carried out. The response of the grid side inverter reactive power, terminal voltage, rotor speed, torque and the real power on the inverter side are shown in the Fig. 17. Fig. 18, Fig. 19.Fig. 20.Fig. 21.
ind speed 3 C 2 B 1 A Ws Te Tm Wm A B C wind generation subsysten 2 Discrete, Ts = 2e-005 s.
genertaor terminal2 1 Vref (pu) Vabc (pu) Vd_ref (pu) Vabc_inv m Voltage Regulator v + -Vdc v + -Vab_load v + -Vab_inv z 1
Va b c I a b c A B C a b c Three-Phase V-I Measurem ent1
Vabc Iabc A B C a b c Three-Phase V-I Measurement T Speed3 Scope4 Scope1 A B C + -Rectifier g A B C + -PWM IGBT Inverter Vabc A B C a b c Measure Manual Switch A B C A B C LC Filter L1 Uref Pulses Discrete PWM Generator 12 C1
Va b c I a b cPQ
modulation index Vdc
Vab Load Vab inverter
Figure 6. Subsystem used in the Simulink
Figure 7. Reactive power inverter side (Symmetrical fault)
0 0.5 1 1.5 2 2.5 3 3.5 4 0 200 400 600 800 1000 1200 Time V ol ta ge i n ve rt er s ide
Figure 9. Rotor speed (Symmetrical fault)
Figure 10. Variation of electromagnetic torque and mechanical torque (symmetrical fault)
Figure 12. Reactive power inverter side (LG)
Figure 13. Voltage inverter side (LG)
Figure 15. Variation of electromagnetic torque and mechanical torque (LG)
Figure 16. Real power inverter side (LG)
Figure 18. Voltage inverter side (LLG)
Figure 19. Rotor speed (LLG)
Figure 21. Real power inverter side (LLG)
10. Conclusion
In this paper a detailed study on the transient stability of the variable speed permanent magnet synchronous generator is carried out during the symmetrical and unsymmetrical fault condition. Detailed modeling of the wind turbine PMSG and the converters are done in each section. A two level converter inverter is used for the AC- DC - AC conversion. Suitable control strategies provide maximum power to the grid and it also supplies the reactive power to maintain the terminal voltage of the grid to the pre fault value during the transient disturbance.During the simulation it has been found that the system is stable for both the symmetrical and unsymmetrical fault. Hence it can be concluded that the control system can well be used for enhancing the transient stability of the variable speed PMSG during the symmetrical and unsymmetrical fault.
11. References
[1] BertlingL.M; Ribrant .J.(2007):Survey of failures in wind power systems with focus on Swedish wind power plants during 1997– 2005, IEEE Trans. Energy Convers., vol. 22, no. 1, pp. 167–173.
[2] BhendeC.N;Mishra.S; Siva Ganesh Malla . (2001) :Permanent Magnet Synchronous Generator-Based Standalone Wind Energy Supply System.IEEE transations on sustainable energy, pp. 361-373.
[3] Fengquan Zhou, et al(2004) Use of Large Capacity SMES to Improve the Power Quality and Stability of Wind Farms,Proc. IEEE Power Engineering Society General Meeting, vol. 2, pp. 2025–2030.
[4] FangYao, et al:Wind Energy Resources: -Theory, Design and Applications. Handbook of renewable energy technology, World
Sci-entific Publishing Co. Pvt. Ltd.
[5] La SetaP;SchegnerP.(2005):Comparison of stabilizing methods for doubly-fed induction generators for wind turbines,Proc. Int. Conf.Future Power System.
[6] LedesmaP; UsaolaJ.(2005):Doubly fed induction generator model for transient stability analysis,IEEE Trans. Energy Convers., vol. 20, no. 2, pp. 388–397.
[7] Md. EnamulHaque;Kashem M. Muttaqi; Michael Negnevitsky.(2010): A novel control strategy for a variable speed wind turbine with a permanent-magnet synchronous generator, IEEE transations on Industry applications, vol 46 No 1, pp. 331-339 .
[8] Muyeen,S.M, et.al.(2010):A Variable Speed Wind Turbine Control Strategy to Meet Wind Farm Grid Code Requirements, IEEE transactions on power systems, vol.25, no.1.
[9] Muyeen.S.M,et al.(2007):Transient stability analysis of permanent magnet variable speed synchronous wind generator,Int. Conf. Electrical Machines and Systems.
[10] Sun.T;Chen.Z;Blaabjerg.T:(2005). Transient stability of DFIG windTurbines at an external short-circuit fault,Wind Energy, vol. 8, no. 3, pp. 345–360,
