Page 1 of 11 2013-PSEC-270

Modeling Variable Frequency Drive and Motor Systems in Power Systems Dynamic Studies

Xiaodong Liang Senior Member, IEEE Schlumberger

Wilsun Xu Fellow, IEEE University of Alberta

Edmonton Technology Center Edmonton, AB, Canada

Department of Electrical and Computer Engineering Edmonton, AB, Canada

E-mail: xiaodongliang@yahoo.ca E-mail: wxu@ualberta.ca

Abstract - Variable frequency drives (VFD) are widely used

in industrial facilities, however, dynamic models for VFD-motor

systems suitable for power system dynamic studies are not

available. In this paper, a generic VFD-motor system modeling

technique is proposed for the ca se that VFDs are able to ride

through the fault. To illustrate the proposed technique, a

dynamic model for a low voltage 6-pulse voltage source inverter

(VSI) based drive and induction motor system with voltage per

Hz control is created. To verify the accuracy of the developed

dynamic model, a case study is conducted using a sam pie VFD­

motor system, both derived dynamic model and detailed

switching model for the same system are simulated using

Matlab/Simulink, and their dynamic responses are compared. It

is found that there are good agreements between the two models,

and thus the accuracy of the developed dynamic model is

verified. For the case that VFDs will trip out of lines, a VFD trip

characteristic curve is proposed, and a simple screening

procedure is recommended for evaluating whether the VFD­

motor system shall remain in service or trip out of lines in power

systems dynamic studies.

Index Terms - Dynamic Load Model, Transfer Functions,

Variable Frequency Drives, Voltage and Frequency

Dependence, VFD Trip Characteristic Curve

I. INTRODUCTION

Variable frequency drives (VFD) can control the speed of an induction or synchronous motor by converting fixed frequency and fixed voltage magnitude to variable frequency and variable voltage magnitude at motor terminals, and thus, provide significantly improved process control, energy saving, and soft motor starting. The common VFD structure comprises of an AC/DC rectifier, a dc link, a DCI AC inverter, additional control and protection circuits. The dominant type of VFDs is the pulse-width-modulation (PWM)-controlled voltage source inverter (V SI) type [1].

Power system dynamic studies investigate the system responses after the occurrence of one or multiple disturbances. Typical disturbances are short circuit faults and subsequent line trips. Such disturbances first appear as voltage sags at various buses of the system. It is, therefore, very important to understand how VFDs respond to voltage sags. As complex non-linear power electronics equipment, VFDs are more sensitive to voltage sags than older mechanical systems. The control and protection circuits in

VFDs could disconnect the drives to protect their components during large voltage sags [1]. The sensitivity of VFDs to voltage sags are affected by many factors such as voltage sag types, loading and operating condition of the drives, threshold settings in the protection of the drives, and the control method etc [2].

Most drives will trip when voltage sags are below certain values [1, 2], in this case they should not be included in power systems dynamic studies. However, when the drives are able to ride-through voltage sags and remain in service, drives and their motor loads must be included and modeled properly. The dynamic model of the VFD-motor system including the VFD, motor and the control system investigated in this paper is dedicated for such conditions.

The power of loads is the function of bus voltage and frequency [3]. Dai summarized that power system load model could be described as a set of mathematical equations describing relationship between the real & reactive power and the voltage & frequency at a given bus in the system. The static model involves algebraic equations, while the dynamic model involves differential equations [4].

Various load models for general loads in power systems were discussed in [5] including the polynomial load model, which is a static load model and referred as the ZIP model because it consists of the sum of constant impedance (Z), constant current (I), and constant power (P) terms. Polynomials of voltage deviation from rated (ll V) are sometimes used [5]. The frequency-dependent load model for a static load model is also discussed in [5]. However, it is warned in [3] that static models for dynamic load components should be used cautiously. Representation of loads by exponential models with exponent values less than 1 or by polynomial model in a dynamic simulation is questionable [3]. On the other hand, dynamic load models for general loads represented by transfer functions considering voltage and frequency dependence were investigated in [4, 6, 7, 8].

IEEE Task Force on Load Representation for Dynamic Performance recommended that a VFD was effectively constant power load if it is able to ride through voltage sags without tripping [5]. However, as indicated in [3] using a constant power load to represent a complex non-linear component like a VFD is questionable, a more accurate

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dynamic modeling method for this important type of loads in industrial facilities is required for power systems dynamic studies.

In this paper, a generic dynamic modeling technique for VFD-motor systems able to ride through power system disturbances is proposed in Section 11. To illustrate the proposed technique, a dynamic model for a low voltage 6-pulse PWM-controlled VSI and diode front-end type drive and an induction motor system with the voltage per Hz control is established in Section III. In Section IV, the developed dynamic model is verified through a case study by

comparing dynamic responses of the developed dynamic model with that of the detailed switching model. A VFD trip characteristic curve is proposed in Section V to consider the condition when the VFD is tripped out of lines due to large voltage sags. This curve provides criteria whether a VFD­motor system should be considered tripping and excluded in a power systems dynamic study.

11. A GENERIC VFD-MoTOR SYSTEM MODELING TECHNTQUE

A VFD-motor system usually consists of three main building blocks: 1) the VFD, 2) the motor, and 3) the control system. The type of VFDs could be voltage source inverter with diode rectifier, the current source inverter with silicon controlled rectifier (SCR) front end, or both rectifier and inverter using PWM controlIed IGBT switching etc. The motor could be induction motors, synchronous motors, or permanent magnetic synchronous motors. Each type of motors can be represented by a set of differential equations. The control system varies from one type to another. For example, there are three major control methods for induction motors: 1) voltage per Hz control, 2) field-oriented control, and 3) direct torque control.

A generic dynamic modeling technique for VFD-motor systems is proposed as folIows, which can be applied to any type of VFD-motor systems (Fig. l):

1) Find differential equations for the VFD, the motor and the control system,

2) Combine all equations together to establish the relationship among them, and

3) Linearize the combined differential equations to obtain dynamic model of the VFD­motor system.

The proposed dynamic load modeling method is based on linearization of differential equations, so the developed VFD­motor system model is suitable for small signal stability studies. On the other hand, VFDs will trip out of lines during large system disturbances, which will be discussed in detailed later in this paper, therefore, the proposed method will serve well for the VFD-motor system modeling for power system dynamic studies.

By applying the proposed technique, the dynamic model of a VFD-motor system can be established (Fig. 2). Both voltage and frequency dependence are included in the developed dynamic model.

Input variables for the dynamic model are the rms voltage per phase (E) and the frequency (fg) of the power source, and output variables are active power (P) and reactive power (Q) at the VFD AC input side connected to the power grid. The developed dynamic model is in the format that can be readily used in the computer simulation tools for power systems dynamic studies.

VFO Molor Lin.arlz� Obtau. diffaential diffaential thcwhole dynamic equations "'IuatiollS comhin.d moddof

Ir 11 :::; syst= F wo·

diff<=nlial motor

[ 1 equatlo,", system

Control sys lern equatiollS '-

Fig. I A generic dynamic modeling technique for VFD-Motor systems

Power E, f VFD-motor system Grid P, Q dynamic model

Fig. 2 Dynamic model for VFD-Motor systems

III. THE PWM CONTROLLED VSI AND DIODE FRONT-END TYPE VFD AND INDUCTION MOTOR SYSTEM MODEL

The low voltage 6-pulse PWM controlled VSI and diode front-end type drives (Fig. 3) are most commonly used in various industrial facilities supplying power to induction motors. One of the control methods for this type of VFD­induction motor system is the voltage per Hz control. To illustrate the proposed modeling technique, a dynamic model for this type VFD-motor system is developed. The voltage per Hz control scheme provided in Matlab/Sirnulirlk (Fig. 4) is adopted in the dynamic model development in this study [10].

A. Differential Equations for VFDs

The differential equations for this type of VFDs can be written in Equations (1 )-(19). The effect of the commutation inductance Ic in front of the VFD is inc1uded [11].

(1)

(2)

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. . C ded

I, =Id - dc --dt

. 2J3 . [ . ( 5Jr) . ( 5Jr )] 1 =--1 sm u-- -sm -- + qgcom Jr d 6 6

3J2E 3J2E ( )(COSU-I)+ ( )(I-COS2U) Jrlc 2;ifg 4Jdc 2;ifg

Vds = 0

P1M = % (Vd)dS + Vq)dJ

�nverler = P IM

where,

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11 )

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

P and Q - active and reactive power at the input of the VFD in front of the commutation inductor, lc - the commutation inductor, E - the rms value of the power source voltage per phase, fg - the power supply frequency at the input of the VFD. Vd - the DC link voltage after rectifier ed - the DC link voltage before inverter id - the DC link current after rectifier

i, - the DC link current entering inverter V diode - the diode on-state voltage

(a) Rectifier and OC link

..

(b) Inverter

Fig. 3 Configuration of a PWM controlled VSI and diode front-end type low voltage 6-pulse VFO [11]

N · � �t - t

ry . pcctl �ign � (\lel'On

hllcgrnl. LIIUllcd comPCI' .. �I;\)n VoilUSc gorn Illlcgrulor Hm iler 1Hz. ralio limltcr

dir

I :� � ((l lip

b- +ill'· .}-.''"Y" fTlvolts: Proportional Frequency

N' , guin limilcr � � I L._._.i First-order

low-pass ITIter

Three-phase generator aIJ vector

F.�r�,(,� Iv:'1 -rJ:: '" �' dir ! I L-.!VS",-------",------, �� :- .. '-Vdc! ! low-pass B ' I bus filter us l >.-!----fuJ ' •• __ •• 1

'----

Ramp

req" -,

Fig. 4 The detailed voltage per Hz controller Schematics provided in Matlab/Simulink [10]

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Cde - the capacitance of DC link capacitor rde - the resistance of DC link Lde - the inductance of DC link reactor Vqg - the q-axis power source voltage Vdg - the d-axis power source voltage iqg - the q-axis ac current at VFD input iqgeom - the q-axis ac current at VFD input during commutation period iqgcond - the q-axis ac current at VFD input during conduction period idg - the d-axis ac current at VFD input

idgeom - the d-axis ac current at VFD input during commutation period idgcond - the d-axis ac current at VFD input during conduction period u - the commutation angle vqs - the q-axis voltage at inverter output Vds - the d-axis voltage at inverter output d - duty cycle PIM - the active power at motor terminal (assuming there is only a short cable between the drive and the induction motor) Pinveter - the active power at output of the drive

B. Differential Equations for lnduction Motors

The differential equations for induction motors are given as follows [12, 29] :

R . \TI dTds vds = slds -ws T qs + --

dOJ, = � (T - T )

dt 2H e m

where, Rs - Stator resistance

dt

Ls - Total stator inductance, and Ls = Lls + Lm

(20)

(21)

(22)

(23)

(24)

(25)

(26)

(27)

(28)

(29)

Lls - Stator leakage inductance Lm - Magnetizing inductance vqs, iqs - q-axis stator voltage and current Vds, ids - d-axis stator voltage and current 'I' qs, 'I' ds - stator q and d axis fluxes 'I' q" 'I' dJ - rotor q and d axis fluxes ffir - Electric angular velocity of the rotor ffis - Stator field angular velocity in electrical radis P - number of pole pairs Te - electromagnetic torque Tm - shaft mechanical torque

H - Combined rotor and load inertia constant

Assuming the stator transients can be negligible:

d'l'ds = 0 dt

d'l'qs - =0 dt

(30)

(31)

For induction motors, the rotor is shorted, and thus, we have

C. Equationsfor Voltage Per Hz Control

(32)

(33)

Based on the voltage per Hz controller provided in Matlab/Simulink (Fig. 4), the simplified block diagram for the voltage per Hz control scheme used for the formula derivation in this study is shown in Fig. 5. The equations for the voltage per Hz control are listed as folIows:

Where Kpm - proportional gain of the speed controller Kim - integral gain of the speed controller

D. Dynamic Model for the VFD-Motor System

(35)

(36)

By combining Equations (1 )-(36) and conducting linearization for the whole set of differential equations of the overall system, a dynamic model for the PWM controlled VSI and diode front-end type VFD and induction motor system using the voltage per Hz control is obtained and expressed by Equations (37) and (38).

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P = Po + GplllE + GPlllE2 + (Gp1 + Gp4llE)llfg

Q = Qo + GQ11lE +GQzllEz + (GQ3 +GQ41lE}llfg

(37) coefficients, Gp" Gpb Gp3, Gp4, GQ" GQ2, GQ3, and GQ4, of the dynamic model are expressed by 7th order transfer

(38) functions.

This model includes both voltage and frequency dependence for the real and reactive power, and the

N N D d

Fig. 5 Block diagram of the voltage per Hz control scheme used for the formula derivation for low voltage 6-pulse VSI based drives

The AC current at the input side of the VFD can be determined by Equations (39) and (40). Both voltage and frequency dependence are also considered. The coefficients, G1qg" G1qgb Gld�l' and G1dgb in the AC current calculations are expressed by i order transfer functions.

iqg =iqgo + G1qg11'1E+ G1qg2tJ.!g idg = idgo + G1dglllE + Gldg2tJ.fg

(39)

(40)

All coefficients appear in the dynamic model and AC currents calculation can be determined by Equations (41)­(54).

(G�IS7 +G�ZS6 +G�3S5 +G�ß4 +J l G�5S3 + G�6SZ + G�7S + G�8

(GP21S7 + GPZ2S6 + GP2lS' + GP24S4 +J GP2,Sl + GPZ6SZ + GP27S + GP28

(G�IS7 +G�2S6 +G�lS' +G�4S4 +J

G�,Sl + G�6S2 + G�7S + G�8

(41 )

(42)

(43)

(GP41S7 + GP42S6 + G�lS' + GP44S4 +J

GP4,Sl + GP46SZ + GP47S + GP48

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(44)

(45)

(46)

(47)

(48)

(49)

(50)

2013-PSEC-270 Page 6 of 11

( G'dg21S7 + G'dg22S6 + G'dg23S5 + G'dg24S4 +

J l Gldg2SS3 + G'dg26S2

+ G'dg27S + G'dg28

(51)

(52)

(53)

(54)

Po, Qo, Eo, fgo are steady-state values for the real power and reactive power, voltage per phase, frequency at a specific bus at AC input side of the VFD connecting to the power grid. Gpll-GpIS, ... , GQ41-GQ4S' and Glqgll-GlqgIS, ... , Gldg2l-Gldg2S, Pbl-PbS are characteristic parameters in the form of real constant numbers for a given system. S is the Laplace transform variable. For a given VFD-motor system, the denominators of the transfer functions for all coefficients (Gph GP2, Gp3, Gp4, GQh GQ2, GQ3, GQ4, G1qgh G1qg2, G1dgh and G1dg2) are the same and determined by Pb1-PbS'

The similar form for voltage dependence of the active power and reactive power dynamics by a transfer function is summarized in [8] as folIows:

M(S) = bnSn +··· +b,S +bo i1V (S) Lo anSn +··· +aIS +ao Vo

(55)

Therefore, the transfer function format representing dynamic load models has been weil accepted.

The developed dynamic model of the PWM controlled VSI VFD-induction motor system in the format of Equations (37) and (38) is based on differential equations of the overall system including the VFD, the motor and their control system. Therefore, this model should be able to capture major dynamic characteristics of the VFD-motor system and accurately determine its contribution to the power grid during disturbances. To verify the accuracy of the dynamic model, a case study is conducted in next section.

IV. VERIFICATION OF THE DEVELOPED DYNAMIC MODEL

To verify the developed dynamic model for the low voltage 6-pulse PWM-controlled VSI and diode front-end type drive and induction motor system using the voltage per Hz control, a sampie VFD-induction motor system is used as a case study. The parameters of the sampie system can be found in Table I.

The detailed switching model and the proposed dynamic model for the sampie system are created using these parameters and simulated by Matlab/Simulink. The detailed switching model utilizing the library component, "Space Vector PWM VSI induction motor drive", readily available in Matlab/Sirnulink. This library component consists of a low voltage 6-pulse VFD with a diode rectifier and a PWM controlled VSI, an induction motor, and the voltage per Hz controller. Its PWM control method is the space vector PWM. The dynamic model is created based on Equations (37) and (38).

Table I Parameters of electrical components in the VFD motor system -

Induction Motor Converter. inverter, DC parameters. Parameters PI speed controller Nominal Power - 2238 VA Diode forward voltage = 1.3 V Nominal voltage = 220 V (rms) DC bus capacitor C = 3400e-6 F Nominal frequency = 60 Hz DC bus resistance rdc = 0 Ohms Rs = 0.435 ohms DC bus inductance Ldc = 0 H Is = 0.002 H Output frequency = 50Hz R,= 0.816 ohms PT speed controller Proportional gain Ir = 0.002 H Kpm=9 Lm = 69.3Ie-3 H PI speed controller Integral gain Inertia J = 0.089 Kg* m2 Kim= 10 Nominal speed 1705 rpm Power Source Pole pairs P = 2 Rated voltage 230V (rms) Load torque TL = 11 NM Rated frequency 60Hz Target speed n, = 1700 rpm Commutation inductance Ic = 10mH

A. Voltage Depedence of the Model

The voltage dependence verification of the developed dynamic model is conducted. The power source frequency remains constant. The detailed switching model for the sampie system is shown in Fig. 6.

A three phase fault is applied near the power source in front of the commutation inductance lc of the VFD in the detailed switching model. The fault is applied at l.4s and cleared at 1.65s. The total simulation time is 2 seconds. The applied three phase fault will result in a 90% voltage sag and 80% voltage sag at the fault location in the detailed model to represent real life events.

The resultant 90% and 80% voltage sags from the detailed switching model are applied directly to the developed dynamic model. The dynamic responses of the detailed switching model are then compared with that obtained from the developed dynamic model for the model verification purpose.

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Dynamic responses of the detailed switching and proposed dynamic models at the fault location for 90% and 80% voltage sags are shown in Figs. 7 and 8, respectively. It is

found that there are good agreements between the two models. Therefore, it is verified that the voltage dependence of the developed dynamic model is accurate.

Power source

160

150

140

> 130 ",' > 120

110

100

90

80

1.2

o

1 -1

-2

Measuring real power and reactive power ------------------------------------

" �, ,

, : � I-'---T------' ICCmn'I.l.IIOI�'I01 I �I-___ '� ____ � : CommoIal ftli.<Dnw � : I � 1-'--7----' ,com'It .... Jia, NUD _ �.,-r

Commutarion in du ctance �

Stmor CUffEflI

OCllJsv<mgl

Fig. 6 The detailed model simulation circuit using Matlab/Simulink (the power source frequency fg is constant)

� I

1.4

-Va detailed, V

1.6

Time, 5

I

•

(a) Voltage Sag

1.8

-- P dynamic, kW ----. p detailed, kW

/\ f\ -1 V

1.4 1.6 1.8

Time, 5

(b) Real Power P

-- Qdynamic, kvar ----- Qdetailed, kvar 35

'" 25 .;:: b �. '"

1.5 � 0 0. J\

J \ '" .2: 05 'g '" 0

11 M

er:

-Q5 1 . 4. .fi . lß. ·1

-15

Time, 5

(c) Reactive Power Q

Fig. 7 Dynamic responses of the detailed model and the proposed dynamic model for a 90% voltage sag (the power source frequency fg is constant)

160

1 50

140

> 130 rn > 120

110

100

90

80

I

1.2 1.4

-Va detailed, V

1.6

Time, 5

(a) Voltage Sag

1.8

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'" > -'" .: QJ 3 o C>­QJ > tl '" QJ

o -1

-2 1

a: 0 1

·1

-2

2

-- P dynamic, kW ----- P detailed, kW

11 n \ �

1 r ,H

, . , �

Time,s

(b) Real Power P

--Qdynamic, kvar ----. Qdetailed, kvar

� 1\

- Jt U'

1.4 1.6 1.8

Time, 5

(c) Reactive Power Q

Fig. 8 Dynamic responses of the detailed model and the proposed dynamic model for an 80% voltage sag (the power source frequency fg is constant)

B. Frequency Depedence of the Model

The proposed dynamic model of the VFD-motor system is further verified for the frequency dependence. The parameters used in the simulation model for both detailed switching model and the proposed dynamic models are the same as those shown in Table I except the following slight loading change of the induction motor: Load torque TL= 12 NM, Target speed nr = 1705 rpm.

The disturbance of the system in this case is a step change of the power source frequency from the steady-state 60Hz to 52Hz (86.67% frequency drop) at the power source. The frequency variation is applied at l.4s and c1eared at 1.65s. The total simulation time is 2 seconds. It is interesting to notice that when the power source frequency is changed, a small voltage variation in the detailed switching model occurs. The resultant frequency and voltage variations are applied directly to the developed dynamic model for the model verification purpose.

The dynamic responses of the detailed switching model and the proposed dynamic model at the drive AC input (in front of the commutation inductance) in this case are shown in Fig. 9. It is found that there are good agreements between the two models. Therefore, the frequency dependence of the developed dynamic model is verified to be accurate.

> ro >

� QJ 3 0 C>-

ro QJ '"

� �

L-QJ

3 0 C>-QJ .2: 1il QJ '"

-fg detailed, Hz 65

"

\ I \ J

60

55

50

45

40

35

30

1.2 1.4 1.6 1.8

TimeIs

(a) Frequency Sag

-Va detailed, V 140

138

136

134

132

1 30

128

126

124

122

120

1.2 1.4 1.6 1.8

Time, 5

(b) Voltage variation during the frequency sag

35

25

1.5

05 0

1.2

1.8 1.6 1.4 1.2

1

0.8 0.6 0.4

0.2 0

1.2

-- P dynamic, kW ----- P detailed, kW

1.4 1.6

Time, 5

v

(c) Real Power P

1.8

--Qdynamic, kvar ----. Qdetailed, kvar

-

1.4 1.6 Time, S

v

(d) Reactive Power Q

1.8

Fig. 9 Dynamic responses of the detailed model and the proposed dynamic model when the power source frequency fg has a step sag

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Based on the model verification, it is concluded that the proposed dynamic model is able to capture major dynamic characteristics of the VFD-motor system and accurately determine its contribution to the power grid during system disturbances. Therefore, it is an adequate model for VFD­motor systems suitable for power systems dynamic studies.

Such dynamic model expressed by 7th order transfer functions can be inserted into commercially available computer simulation tools for power systems dynamic studies.

V. VFD TRIP CHARATERISTIC CURVE

The dynamic model of a VFD-motor system is proposed for the case that a drive is able to ride through voltage sags during the system disturbance, wh ich is extensively discussed in previous sections. However, when voltage sags are large and exceed the thresholds of the drive protection, the drive will trip out of lines, in this case, the VFD-motor system should be excluded from power systems dynamic studies.

In order to provide a comprehensive VFD-motor system modeling technique, a VFD trip characteristic curve and a simple screening procedure are proposed in this paper serving as criteria wh ether drives should be considered tripping or not. This trip curve is developed based on literature review for the drives protection and control, field survey regarding VFDs tripping status during disturbances, and also based on drive manufacturer specifications [17-28].

The sensitivity of VFDs to voltage sags is usua11y expressed as a voltage tolerance characteristic curve, in terms of one pair of voltage sag magnitude/duration values. These two values are denoted as the thresholds. If the voltage sag lasts longer than the specific duration threshold and/or with its magnitude deeper than the specific magnitude threshold, the VFD will malfunctionltrip. In other words, the area below and on the right from the curve represents that voltage sags will cause malfunction/tripping of the VFD, while the area above and on the left from the curve represent that voltage sags will not cause the VFD tripping [1, 2].

Based on the published results of equipment testing, the voltage magnitude threshold may vary between 59% and 71 % for VFDs, whereas corresponding duration threshold varies between 15ms to 175ms. The probabilistic trip counts may vary over a wide range, from 68 trips per year using a low sensitivity threshold to 152 trips per year using a high sensitivity threshold [17].

The under-voltage trip settings for the Siemens's Mediwn Voltage Drive, Robicon Perfect Harmony, will trip on voltage sags with duration of 100ms (6 cycles) or more and having a voltage drop of more than 30%, which is below 70% of rated voltage [18].

As the requirements to the equipment responding to voltage sags/dips, IEC 61000 (parts 6-1 and 6-2) specifies that a11 equipment must ride-through a voltage dip of a

residual voltage of 70% for 10 ms, and must not be damaged for a voltage dip of a residual voltage of 40% for 100 ms [19]. CIGRE/CIRED/UIE Joint Working Group proposed immunity classes against voltage dips for balanced voltage dips (type III). The equipment will remain in service: 1) When the voltage dip is above 70% between 10 ms and 200 ms (1/2 cycle to 12 cycles), and 2) When the voltage dip is above 80% between 200 ms (12 cycles) to 3000 ms [20]. VFDs as electrical equipment should also follow such guidelines.

Voltage sag measurements in two industrial facilities for 17 months were conducted in [21], which was able to link voltage sags to the tripping of VFDs. The two facilities for measurements were fed by 115 kV utility transmission lines. Even faults in 230 kV or 400 kV lines were feit by the utility entrance substation as voltage sags. The field records of voltage sags and subsequent VFD tripping status indicates that voltage sags with duration of 12 cycles or more and having a voltage drop of more than 20% will trip out a VFD [21].

Since most fault duration is between lOms and 3000ms, a conservative VFD trip characteristic curve is proposed for this fault duration as shown in Fig. 10. Based on this curve, voltage sags above 70% between 10 ms and 200 ms (12 cycles), and above 80% from 200 ms (12 cycles) to 3000 ms will not cause VFD tripping. In Fig. 10, a voltage sag marked as a "*,, above the proposed curve will not cause the VFD tripping, while a voltage sag marked as a "#" below the proposed curve will cause the VFD tripping.

12 0

100

u

! o .. 0 :1 �

z

0

0

0

0

..,

J I I I 1 *Vl fU will nOi trip

1 1 1 I 11 1

= ""D_ ,, '� � I � I I I I

'00 l00u )00 o Dur".I •• (mI)

Fig. 10 VFD trip characteristic curve

A simple screening procedure is proposed to determine wh ether a VFD will trip under a given system disturbance as fo11ows:

1) Conduct a three-phase short-circuit study on the study system if the outage event of interest involves a short-circuit fault, which will yield a voltage sag magnitude at the VFD location. In the short circuit

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study, the VFDs can be omitted since they have little contributions to the fault current.

2) Check the relay setting involved in clearing the fault. This setting will provide the voltage sag duration value for the outage event.

3) The resulting magnitude and duration values for voltage sags are then compared with the VFD trip characteristic curve. If the point is below the curve, the VFD will trip and they shall not be modeled in power systems dynamic studies. If the point is above the trip curve, a VFD-motor system dynamic model proposed in Equations (37) and (38) are needed for dynamic simulation.

VI. CONCLUSIONS

A comprehensive VFD-motor modeling technique is proposed considering either the VFD trips out of lines or remains in service during system disturbances for power systems dynamic studies.

For the case that a VFD is able to ride through voltage sags and remains in service, the dynamic model of VFD­motor systems can be developed using the generic modeling technique proposed in this paper. To illustrate this technique, the dynamic model for a commonly used low voltage 6-pulse PWM-controlled VSI and diode front-end type drive and induction motor system with voltage per Hz control is developed. The developed model includes both voltage and frequency dependence and its coefficients are expressed as ih order transfer functions. The accuracy of the dynamic model is verified by the detailed switching model. Such dynamic model can be inserted into commercially available computer simulation tools for power systems dynamic studies.

For the case that a VFD will trip due to large voltage sags, the VFD-motor system should not be included in power systems dynamic studies. A VFD trip characteristic curve is proposed to evaluate wh ether the drive will trip or not based on the magnitude and duration of voltage sags.

A simple screening procedure is proposed for the power system dynamic study involving VFDs. This procedure provides instructions on how to use the VFD trip characteristic curve, and wh ether a dynamic model of VFD­motor system shall be developed and inserted into the simulation tool or simply take the VFD out of line due to tripping for the outage event.

In the past decades, the proper dynamic models of VFD­motor systems are not available for power systems dynamic studies although needed by utility companies. The comprehensive VFD-motor modeling technique proposed in this paper will serve as a milestone for accurately modeling this important type of loads in power systems dynamic studies.

VII. REFERENCES

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VIII. BIOGRAPHIES

Xiaodong Liang (SM'09, M'06) was born in Lingyuan, China. She received the B.Eng. and M.Eng. degrees from Shenyang Polytechnic University, Shenyang, China in 1992 and 1995, respectively, and the M.Sc. degree from the University of Saskatchewan, Saskatoon, Canada in 2004, all in Electrical Engineering. She is perusing the Ph.D. degree in Electrical Engineering at the University of Alberta, Edmonton, Canada. Her research interests

include power systems dynamies, power quality, and electric machines. From 1995 to 1999, she served as a lecturer at the department of

Electrical Engineering, Northeastern University, Shenyang, China. In October 2001 she joined Schlumberger in Edmonton, Canada where she is currently a Principal Power Systems Engineer.

Ms. Liang is a registered professional engineer in the Province of Alberta, Canada.

Wilsun Xu (M'90-SM'95-F'05) received the Ph.D. degree from the University of British Columbia, Vancouver, BC, Canada, in 1989. He was an Engineer with BC Hydro, Burnaby, BC, Canada from 1990 to 1996. Currently, he is a Professor and a NSERC/iCORE Industrial Research Chair at the University of Alberta, Edmonton, AB, Canada. His research interests are power quality and power system modeling.

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