Equivalent Model for Calculating Short Circuit Current of Doubly Fed Wind Generator under

Uninterrupted ExcitationZheng-rong Wu, Gang Wang, Hai-feng Li, Xiang Gao

School of Electric Power South China University of Technology

Guangzhou, China

Abstract: The fault ride-through ability of doubly fed wind gene-rators (DFIG) has got more and more attention. New grid codes for interconnection of wind turbines required that wind turbines remain connected to the grid and actively contribute to the sys-tem stability during and after grid faults. Uninterrupted excitation of DFIG can both avoid running over-speed of wind turbines during grid faults and accelerate the recovery of system after clearance of fault. Calculation of DFIG fault current con-tribution will benefit the research on protection for distribution network including DFIG. In this paper, the relations between output of DFIG and exciting current are analysed. Based on the analysis, the fact that the exciting current is increased in order to improve the power output during grid faults and the maximum exciting current is limited by nominal power of converter is demonstrated. According to these conditions, an equivalent model for calculating fault current of DFIG is presented and the no-load exciting potential of equivalent model can be calculated by utilizing the maximum excitation conditions. A comparison between the proposed method and conventional method for cal-culating DFIG fault current is made in this paper. At the end, a DFIG test case is set up in PSCAD/EMTDC and the accuracy of the equivalent model for calculating fault current is verified by simulation.

Keywords-DFIG; fault ride-through; uninterrupted excitation; short circuit; equivalent model

I. INTRODUCTION Recently, wind power has been applied all over the world.

It was reported that the total installed capacity was up to 158GW and the new installed capacity was more than 38GW around the world in 2009. The annual market grew a stagger-ing 41.5% compared to 2008. China doubled its capacity from 12.1GW in 2008 to 25.8GW in 2009. It is said that wind power will go through with fast growth in the future [1].

Among the different alternatives to construct variable speed wind turbines, DFIG are the most commonly used. A DFIG is directly connected to the power network while the rotor is grid-connected through the partial-load converter. Since just used in the exciting circuit, the power converters are sized for a power around 25%–35% of the rated power of the turbine. In addition to the common advantages in cost, size, and weight associated with a small converter, losses are also smaller compared to the system with a full power converter connected to the stator. In contrast to the fixed speed wind tur-bines, DFIG provide the capability of independent control of

active and reactive power [2]. There are many researches concentrating on the dynamic

behavior of DFIG under fault conditions. Transient characte-ristics of DFIG were analyzed when three-phase short circuit occurred in [3-5] and the transient equivalent circuit and con-stant flux linkage theorem were used to calculate the fault current contribution [6-9]. However, all of the works were based on the condition that DFIG was converted to squir-rel-case induction when fault occurred. There were few papers analyzing dynamic behavior of DFIG under the continuous excitation conditions. References [10], [11] analyzed DFIG fault current under constant excitation. Actually, due to fast reaction to grid disturbances, the exciting current cannot be kept constant.

A drawback of DFIG is that it is sensitive to gird distur-bance, especially to voltage dips. The overvoltage and overcurrent caused by abrupt drop of grid voltage could de-stroy the converters. In the past, the solutions to protect the converter were to short-circuit the rotor windings with the crowbar and disconnect the turbine from the grid [7]. New grid codes for interconnection of wind turbines required that wind turbines remain connected to the grid and actively contribute to the system stability during and after grid faults. DFIG under uninterrupted excitation has the advantages of keeping wind mill from running in over-speed mode because of electromag-netic power output during faults. Due to quick adjustment to output, it is helpful for resuming system after clearance of fault. According to the study of equivalent model of uninter-rupted excitation DFIG, it is useful for studying the influence of DFIG on protection setting.

In this paper, the relations between output of DFIG and ex-citing current are analysed. Based on the analysis, the fact that the exciting current is increased in order to improve the power output during grid faults and the maximum exciting current is limited by nominal power of converter is demonstrated. Ac-cording to these conditions, an equivalent model for calculating fault current of DFIG is presented and the no-load exciting potential of equivalent model can be calculated by utilizing the maximum excitation conditions. At the end, a DFIG case is set up in PSCAD/EMTDC to verify the accuracy of the equivalent model for calculating.

The National Basic Research Program of China (973 Program) (2009CB219704). The Crucial Field and Key Breakthrough Project in “Guangdong-Hongkong” (No. 2009498B3201) and the Fundamental Re-search Funds for the Central Universities (No.2009ZM0080).

978-1-4244-6255-1/11/$26.00 ©2011 IEEE

II. MATHEMATIC MODELS ABOUT DFIG

A. Equations of DFIG Assume stator and rotor windings are symmetrical

three-phase windings around uniform. Consider there are only fundamental current components in the stator and rotor. Ac-cording to synchronous rotating reference frame, the mathematical model of DFIG can be expressed as [12], [13]:

( )

( )

ds s ds ds n qs

qs s qs qs n ds

dr r dr dr n r qr

qr r qr qr n r dr

V R i p

V R i p

V R i p

V R i p

ψ ω ψψ ω ψψ ω ω ψψ ω ω ψ

= + −

= + +

= + − −

= + + −

(1)

ds s ds m dr

qs s qs m qr

dr r dr m ds

qr s qr m qs

L i L iL i L i

L i L iL i L i

ψψψψ

= += +

= += +

(2)

Where, the symbols p , nω , rω , V , ψ , sL , rL ,

mL are respectively differentiation, synchronous angular ve-locity, rotor angular velocity, voltage, flux, inductance of stator and rotor, mutual inductance; The subscripts ds , qs , dr , qr represent d-axis and q-axis components of stator or rotor respectively.

B. Relations between Power Output and Exciting Current Vector control theorem for DFIG has been discussed in

many papers [14-16]. This section mainly analyzes the rela-tions between power output and exciting current. With the d-axis oriented along the stator-flux and the influence of stator resistance on the voltage ignored, the equations can be written as

0ds s

qs

ψ ψψ

==

(3)

0ds ds

qs n ds s

V pV V

ψω ψ

≈ =≈ =

(4)

The power output of DFIG can be expressed as 1.5( ) 1.5

1.5( ) 1.5s ds ds qs qs s qs

s ds qs qs ds s ds

P V i V i V i

Q V i V i V i

= + ≈

= + ≈ (5)

From (2) we have ( ) /ds ds drL Lm si iψ= − (6)

/qs m qr si L i L= − (7) By substituting (6), (7) in (5), the relations between power

output and exciting current is obtained 1.5 /

1.5 ( ) /s s m qr s

s s ds m dr s

P V L i L

Q V L i Lψ= −

= − (8)

According to (8), the d-axis component of exciting current determines the active power Ps and the q-axis component of exciting current determines the reactive power Qs .

III. ANALYSIS OF FAULT CURRENT AND EQUIVALENT MODEL OF DFIG

A. Analysis of fault current In steady state, the rotor of DFIG rotates at the speed of

(1 ) ns ω− and the rotor flux rotates at the speed of nsω rela-tive to rotor, s represents slip. The stator flux rotates at the speed of nω . When system fault occurs, according to the theo-rem of constant flux linkage, DC component will be produced in stator and rotor windings, which is static relative to each winding. DC component induced in rotor windings will induce current with frequency of (1 ) ns ω− in stator windings [6], [7]. Thus, in the early fault, the transient current flowed in the stator windings not only contains steady-state component with frequency of nω , but also contains the decaying DC compo-nent and AC component with frequency of (1 ) ns ω− .

When a crowbar is equipped to protect the converter, fault currents in the DFIG decay with transient time constant. Under uninterrupted excitation conditions, the regulation of excitation control system can accelerate the decay of transient current. Effective measures can be taken to reduce the peak rotor fault current in order to protect the converters [17], [18]. The am-plitude and decay time of transient fault current under uninterrupted condition is lower than that under crowbar pro-tection. The fault current will decay to steady state rapidly.

After a period time of fault, transient over current in rotor circuit attenuates completely, the output of DFIG will be ad-justed with uninterrupted excitation.

By substituting (4) into (8), we get 2 2 2 2 2( -1.5 / ) (1.5 / )Q V X P V X X Irs s s s s m s+ = (9)

Where, X Ls n sω= , X Lm n mω= , 2 2 2I i ir dr qr= + , Ir represents the vector norm from synthesis of three-phase AC exciting current.

In case of faults, the variable 2(1.5 / )V X Xs m s at the right of (9) will reduce under stator voltage dip. In order to enable the output of DFIG to reach reference value, the exciting current will be constantly increased. Under these conditions, exciting current will exceed the nominal current of the rotor-side con-verter. Especially when the output of DFIG is close to the limit of capacity, the converter may be damaged by rapidly in-creased exciting current. So the maximum exciting current is limited by the nominal current of the converter.

During faults, exciting current of DFIG rises rapidly to the maximum value. Under the maximum exciting current, steady-state fault current of DFIG is constant by (6), (7).

B. Equivalent Model for Fault Current Calculation 1) Equivalent Model

When a three-phase fault occurs close to DFIG terminal, due to full voltage dip, the stator flux will stop rotating. Cur-rents in stator windings and rotor windings evolve from its initial value to zero, so the fault current contribution is limited. This section mainly analyzes the fault current calculation when a fault occurs far away from DFIG, under these conditions, the

voltage drops partially. In steady-state operation, stator flux linkage remains un-

changed. Equation (10) can be derived from (1) and (2) ( )

( )ds n s qs m qr

qs n s ds m dr

V L i L i

V L i L i

ωω

= − +

= + (10)

By defining s ds qsV V jV= + , s ds qsI i ji= + ,

s ds qsI i ji= + , the next equation can be obtained

s n s s n m rV j L I j L Iω ω= + (11) When the rotor exciting current remains unchanged,

n m rj L Iω in (11) remains unchanged, which is defined as no-load excitation potential E . The equivalent model of DFIG can be obtained from (11).

sX

sIEsV

Figure 1. Equivalent model for DFIG

The DFIG equivalent circuit reflects the relations between the terminal voltage Vs and the no-load excitation poten-tial E . When short circuit tends to steady state, the value of terminal voltage and no-load excitation potential are steady variables, and then the fault current can be calculated from figure 1.

2) Calculation of E When coming to steady state after fault, DFIG runs with

maximum exciting current. At this point the short circuit cur-rent in amplitude is the same as the point that short circuit fault occurs during DFIG runs under maximum exciting current, which is called maximum operation mode. In maximum opera-tion mode, the active power output of DFIG reaches rated value and the exciting current reaches maximum value. In maximum operation mode, the no-load excitation potential E can be calculated. The vector graphics for calculating no-load excitation potential E is showed in figure2.

E

sVθ

s sjX I

sI

Figure 2. Vector space of voltage Where, Vs , Is , θ means respectively terminal voltage,

current and power factor angle in maximum operation mode.

IV. VALIDATION In this section a case is built in PSCAD/EMTDC for veri-

fying the result of calculation by the equivalent model. In the case, the aerodynamic part is simplified and the mechanical torque produced by wind is supposed unchanged. The case data are showed in table 1.

TABLE I. Generator and System Data

parameter value Rated power (MW) 0.9

Stator resistance (pu) 0.0054 Stator leakage reactance (pu) 0.1 Mutual leakage reactance (pu) 6.75

Rotor resistance (pu) 0.00607 Rotor leakage reactance (pu) 0.11

Nominal current of converter (kA) 0.30 Transformer reactance (ohm) 6j

Equivalent impedance of system (ohm) 1.1+3.76j Line1 impedance (ohm) 0.51+1.88j Line2 impedance (ohm) 0.51+1.88j

The wiring diagram of simulation system is showed Fig-ure3.

1Zl 2ZlGI

Zs

Figure 3. Simulation system wiring diagram

After the system runs steadily for a while, a three-phase fault occurs at the site of f as showed in figure 3. The DFIG fault current from simulation is 33.3A.

The equivalent circuit for simulation system can be simpli-fied as figure4 by making use of equivalent model of DFIG.

GIVs

Zs

1Zl

EX

TX

s

Figure 4. Equivalent circuit for simulation system

Where, the system voltage Vs is 21kV, the calculated value of no-load excitation potential E is 3.86kV. According to figure 4, the fault current of DFIG by calculating is 29.4A.

The error between calculation and simulation result is 11.7%. The reason for error is that the fault current of rotor circuit is neglected and the phase between system voltage and no-load excitation potential is supposed equal during calculat-ing. Actually, the ratio of resistance to reactance in distribution network is high. There is a certain phase angle difference be-tween head and tail of line when fault current flows through the line. The phase angle difference may cause the error. Ac-tually, the first factor is the major reason for the error.

V. DISCUSSION This paper presents an equivalent model for calculating

the DFIG fault current. The dynamic process of DFIG is considered in the model, which is different from the con-ventional model. This section will give a discussion on the difference between proposed model and the conventional model.

Generally, the subtransient equivalent circuit is used to calculate the fault current of generators. The subtransient circuit is showed in Figure 5, Z means the equivalent impedance of the external system [8].

''X

''EZ

Figure 5. The subtransient circuit for calculating fault current

mL

rL σ sL σ

''L

Figure 6. The equivalent circuit for ''L ( '' ''nX j Lω= ) calculation

With the same case and given conditions, the DFIG fault current calculated by the conventional method is 75.9A. The error between calculation and simulation result is 128%. The error is bigger than that in proposed method.

The change of DFIG exciting current is considered in the proposed equivalent model, which is helpful to the calculating result. However, the forced exciting current is assumed con-stant in conventional model, which is contrary to the facts. So the bigger error is got.

A number of approximation and simplification had to be made to determine the equivalent model. It should be noted the equivalent model in this paper only give an approximation. In the future, more efforts should be made to study the fault cur-rent of rotor circuit, which is neglected in the proposed model. Only all these factors are considered, the fault current calcu-lated by equivalent model is closer to the fact.

VI. CONCLUSIONS This paper analysed the relations between output of DFIG

and exciting current. The equivalent model is presented for calculating the fault current after considering the changes of exciting current during grid faults. The no-load exciting poten-tial can be calculated in maximum operation model. It is proved that equivalent circuit provides a simplified method for analysis of DFIG fault current. Calculation of fault current by equivalent model provides a basis for protection setting and equipment selection.

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