Dynamic Voltage Restorer Utilizing a Matrix Converter and Flywheel Energy Storage

Bingsen Wang General Electric Global Research Center

One Research Circle, K1-3C30 Niskayuna, NY 12309 wang@research.ge.com

Giri Venkataramanan Dept. of Electrical and Computer Engineering

University of Wisconsin – Madison Madison, WI 53706 giri@engr.wisc.edu

Abstract— A new series power conditioning system using a

matrix converter with flywheel energy storage is proposed to cope with voltage sag problem. Previous studies have highlighted the importance of providing adequate energy storage in order to compensate for deep voltage sags of long durations in weak systems. With the choice of flywheel as a preferred energy storage device, the proposed solution utilizes a single ac/ac power converter for the grid interface as opposed to a more conventional ac/dc/ac converter, leading to higher power density and increased system reliability. The paper develops the dynamic model for the complete system including the matrix converter in dual synchronous reference frames coupled to the flywheel-machine and the grid, respectively. The dynamic model is used to design a vector control system that seamless integrates functions of compensating load voltage and managing energy storage during voltage sag and idling modes. The numerical simulation results and experimental results from a laboratory-scale hardware prototype are presented to verify system performance.

Keywords-dynamic voltage restorer, flywheel energy storage, indirect matrix converter, vector control, voltage sag

I. INTRODUCTION As the reliability and availability of the power system

continue to improve, power interruptions have become rare events in power distribution systems. However, voltage sags arising from faults on parallel feeders are still a major power quality concern in terms of the severity of the incurred economic losses to sensitive loads. Due to the typical radial structure, the distribution system is inherently vulnerable to weather conditions, falling tree branches or animal contacts, and insulation failures or human activity [1]. At the distribution level, the voltage sags occur when a short circuit fault takes place on a parallel feeder. In addition, the sag depth depends on the distance from the fault location and impedance profile of the system [2]. While power interruptions do occur when the protection devices operate on the faulted branch, they do so at a smaller frequency compared with the occurrence of voltage sags (number of parallel branches vs. the faulted branch). Both the “Canadian Power Quality Survey” over 550 customers sites conducted by Canadian Electrical Associate (CEA) in 1991 [3] and the “Distribution System Power Quality Survey” carried on 222 utility distribution feeders by EPRI between 1993 and 1995 [4] have shown that voltage sags are the most common power quality events.

To cope with the voltage sag problem, a series compensation device, commonly called dynamic voltage restorer (DVR) has been applied as a definitive solution due to the advantages of the series compensation over the shunt compensation in terms of required power rating for typical voltage stiff systems [5]. All of the DVR topologies discussed in the literature have a dc link, where the energy storage, typically capacitors, is connected. Although energy storage can be minimal [13], the compensation capability in that case will fully depend on the load power factor [5]. If there is a separate energy storage device, a dc-dc converter is generally required to regulate the dc bus, between the dc link and the energy storage. If the energy storage is in ac form, the line interface inverter and the energy storage management converter can be integrated to an ac/ac converter, which leads to the proposed scheme in this paper.

With the herein proposed topology, elimination of the dc link stage leads to reduced maintenance and improved power density. The PM machine driven flywheel is chosen to be the energy storage based on the overall balance among the power density, efficiency, cost and environmental friendliness. The topology of the system is developed based on the functional requirements and is particularly tailored to the series compensation application. This paper is organized as follows. The power architecture is proposed in Section II followed by the modeling and controller design presented in Section III and Section IV, respectively. The predicted system performance is verified by detailed numerical simulation In Section V. The selected experimental results are presented in Section VI. Summary in Section VII concludes this paper.

II. SYSTEM ARCHITECTURE The system architecture is developed based on the operational requirements. At the system level, three requirements have been identified: 1. Bidirectional power flow is required to maintain and

recover the stored energy and mitigate voltage sags. 2. A wide range of power factor is desired at the converter

output connected to the grid through filter in order to guarantee the system to function properly regardless of the nature of the load.

0197-2618/07/$25.00 © 2007 IEEE 208

3. The converter should operate in buck mode from the energy storage to the grid since the voltage injection level may be very low while the machine terminal voltage is much higher due to the fully charged flywheel.

These three requirements are represented in Fig. 1, where only the key components of the system are explicitly shown.

Pow

er

Buc

k

No p.f. limit

Fig. 1 System level requirements for DVR with ac/ac converter.

The system architecture shown in Fig. 2 fulfils the three requirements listed above. In this configuration, the matrix converter is connected to the voltage stiff source formed by the filter capacitor on the machine side, while the converter is connected to the current stiff source formed by the inductor of the LC filter that interfaces the converter with the grid. If the voltage across the capacitor of the LC filter is treated as voltage source, then the configuration including the inductor of the LC filter, matrix converter, filter capacitor across the machine terminals and the machine indicated by the dotted box is the so-called boost configuration.

The matrix converter in Fig. 2 is realized using a particular configuration of the indirect matrix converter (IMC) illustrated in Fig. 3. The necessary bidirectional power flow capability is realized by keeping dc link voltage vpn positive while allowing the dc link current ip to be either positive or negative. The difficulty associated with commutation between any two four-quadrant switches in the current source bridge or CSB (connected to the machine) is eased by the zero dc link current created by the voltage source bridge or VSB (connected to the grid interface). To keep the dc link voltage positive, the displacement angle on the ac side of the CSB must be limited to (-π/6, π/6), which can be readily handled by the control algorithm given the choice of PM machine in the application under study. Furthermore, there are no operational limitations on the power factor of VSB.

III. DYNAMIC MODELING

A. State Space Averaged Model of the Matrix Converter In order to model the system in Fig. 2, a suitable model for

the matrix converter is developed. A state space averaged model of the IMC is a convenient description that is compatible with the rest of the ac system. For the topology in Fig. 3, a detailed description of the carrier-based modulation process has been published in previous work [14]. The averaged dc link

current ip and dc link voltage vp are related to the stiff currents iu, iv, iw and the stiff voltage va, vb, vc by the following expressions.

( )12p u u v v w w

pn a a b b c c

i m i m i m i

v m v m v m v

= + +

= + +

(1)

where ma, mb, mc and mu, mv, mw are modulation functions for the three phase-legs of the CSB and the VSB, respectively.

Grid Supply Load

Filter

Matrix Converter

InjectionTransformer

M/G

Filter

Flywheel

A B C

a b c

Boos

t Dire

ctio

n

Fig. 2 Proposed architecture of the DVR system.

ava +-

bvb +-

cvc +-

iu

iv

iw

ip

vpn

-

+

u

v

w

Fig. 3 Realization of the matrix converter with bidirectional dc link current and unidirectional dc link voltage.

By reciprocity, the averaged input current and output voltage (referred to output neutral) may be expressed as

209

a a p

b b p

c c p

i m i

i m i

i m i

=

=

=

; 2

2

2

u pnu

v pnv

w pnw

m vv

m vv

m vv

=

=

=

(2)

It is convenient to transform these variables represented in the a,b,c and u,v,w phase coordinates into a synchronously rotating phasor coordinates. First, the three-phase variables on the VSB side are transformed to the dq reference frame as follows. The space vectors of the modulation functions and the currents on the VSB side (output side) are defined as.

( )

( )

2

2

23

23

o

o

j to u v w

j to u v w

m m m m e

i i i i e

ω

ω

α α

α α

−

−

= + +

= + +

(3)

where ωo is the output fundamental frequency (VSB side). 23

je

π

α = The dot product of these two complex vectors is

( )wwvvuuoo imimimim ++=•32 (4)

In a similar manner, the space vectors of the modulation function and the voltage on the CSB side (input side) are defined as

( )

( )

2

2

23

23

i

i

j ti a b c

j ti a b c

m m m m e

v v v v e

ω

ω

α α

α α

−

−

= + +

= + +

(5)

where ωi is the fundamental frequency associated with the quantities on the CSB side.

With assumption of 0a b cv v v+ + = , the dot product of the modulation space vector and the voltage space vector of the CSB is determined to be

( )ccbbaaii imimimvm ++=•32 (6)

The averaged dc link current and voltage can be expressed in terms of space vectors by substituting (4) and (6) into (1).

iipn

oop

vmv

imi

•=

•=

23

43

(7)

The synthesized input current space vector and output voltage space vector are

( )

( )iioo

ooii

vmmv

immi

•=

•=

43

43

(8)

Due to the absence of passive components in the matrix converter, the input and output are related by the algebraic equations (8). This is in stark contrast to the ac/dc/ac converter case where dynamic equations are involved between the input and output variables due to the presence of dc link capacitor. Equations (8) can be pictorially represented by the equivalent circuit in .

( )ii vmm •043( )ooi imm •

43

oiiv

Fig. 4 Averaged model of IMC in synchronous reference frame

B. Model of the Complete System The state equations for the ac quantities in the system can

be formulated in synchronous reference frame (SRF) in the complex vector domain [15]. In the proposed SRF formulations, the q-axis is aligned with the positive real axis and the d-axis is aligned with the negative imaginary axis. Since the frequency on the grid side is typically different from the machine side, two SRFs are used. On the grid side, the SRF rotates at the grid frequency ωo with the q-axis aligned with the voltage vector at PCC. On the machine side, the SRF rotates at the rotor frequency ωr with q-axis aligned with machine back-emf vector.

The complete system may be represented in the form of a single-line equivalent circuit. The matrix converter is represented by the compact vector model as shown in Fig. 5. The state equations of the system can be consequently expressed using complex space vectors [15]. It can be observed that the states on the grid interface side (iLf, vinj) are coupled with the state variables of machine (ipm, vpm) through the modulation index mi and mo. The system can also be represented by the complex state block diagram as shown in Fig. 6. The block diagram is divided to two subsystems, the grid side LC filter and the flywheel, SPM machine and filter capacitor across machine terminals. These two subsystems are coupled to each other through the matrix converter. For the overall system, there are two manipulated control inputs, mi and mo, and two uncontrollable inputs (that may be considered as disturbances): system load current iload and flux linkage created by the permanent magnets λpm. Two outputs of the system are vinj, the target injection voltage to compensate voltage sags/swells, and ωrm, the mechanical speed of the machine/flywheel.

( )

( )

( ) ( )

rmmLpmpmrm

m

injfoloadLfinj

f

LffofinjpmioLf

f

pmpmrLfoipmpm

pm

pmpmrpmpmpmrmpm

pm

BTipdt

dJ

vCjiidtvd

C

iLjRvvmmdtid

L

vCjimmidtvd

C

iLjRvpdtid

L

ωλω

ω

ω

ω

ωλω

−−×=

−−=

+−−•=

−•−=

+−−=

23

43

43

(9)

where p Number of pole pairs.

λpm Flux linkage of the PM machine

210

ipm Stator current space vector vpm Stator terminal voltage space vector iLf Filter inductor current space vector vinj Injected voltage space vector mi Modulation index space vector for the

bridge connected to the machine mo Modulation index space vector for the

bridge connected to the grid interface Jm Momentum of inertia of the flywheel Bm Damping coefficient Rpm Stator resistance of the SPM machine Lpm Stator inductance of the SPM machine TL Load torque, TL = 0 ωrm Mechanical speed of the machine/flywheel

+

-vs

- +

vinj +-

Cf

+-vpm

Cpm

+- E

vo

ii

Ls Lload Rload

Lf

Lpm

iLf

iload

ipm

Converter

Rpm

+-Te ωrmJm

Bm

+- TL

vpcc

Machine

Flywheel

Fig. 5 A single-line equivalent circuit of the proposed system.

IV. CONTROLLER DESIGN There are two control objectives: to control the injected

voltage to the system and to regulate the speed of the flywheel during idling. Under the voltage sag (or swell) condition, the speed of the flywheel is allowed to vary to supply (or absorb) the required active power. During the startup and idling operating mode, the flywheel speed is regulated so that enough ‘spinning’ energy storage is ready for the voltage sag compensation. A control structure to realize these two objectives is illustrated in Fig. 7.

The injection voltage controller in the inner-loop takes the injection voltage reference as the input and outputs the modulation function vectors for the matrix converter. The key function of this controller is to force the injected voltage vector vinj track the reference vector v*

inj. The injection reference generator takes the reference of the load voltage amplitude |v*

load| as input and generates the injection voltage reference v*

inj. Under idling conditions, the speed of the flywheel is regulated. Under voltage sag (or swell) conditions, speed

regulation of the flywheel is deferred if the active power needs to be drawn from (or supplied to) the flywheel.

-

-

jωrCpm Rpm+jωrLpm

--

+

+

ipm

+

-

+-

--

Rf +jωoLf jωoCf

iLf

Cpm

1

vinj

vo

iload

vpm

43

ii

mi

mo

Lpm

1

Cf

1Lf

1s1

43

s1

s1

s1

Dot productof two vectors

Product of vector andscalar

Flywheel, SPM Machine and Filter Capacitor

Grid Interface LC Filter

MatrixConverter

Bm

-+

ωrm

Jm

1s1

23p

Magnitude of crossproduct of two vectors

λpm

Epm p

vload

vpcc

+

+

Fig. 6 Complex vector state block diagram of the overall plant.

Injection ReferenceGenerator

vload*

Injection VoltageController

vinj*

mi

MatrixConverter

AC InterfaceLC Filter

PM machineFlywheel

vinj

+

+ vload

vpcc

ωrm

iload

mo

Plant

Fig. 7 Block diagram of overall control structure.

A. Injection Voltage Controller (the Inner Controller) One of the control objectives for the inner controller is to

regulate the injected voltage vector vinj by manipulating the converter output voltage vector vo. However, the manipulated inputs of the system are mi and mo, which are coupled to the states that affect the output voltage. The modulation inputs mi and mo may be algebraically decoupled in favor of an alternative control input vo

* and θii* using feedback of the state

vpm as follows:

*

*

43

*

ii

ii

ji

jpm

oo

em

ev

vm

θ

θ

=

•=

(10)

211

The algebraic decoupling process is also illustrated in the block diagram in Fig. 8.

vo

vpm

43

ii

43

MatrixConverter

mo

mi43

÷×

*vo

iLfInput

Decoupling

ejθii*

Fig. 8 Input decoupling for injection control.

In terms of these new control inputs, the converter output voltage and input current vectors are related to the system variables as:

*

*

*

*

ii

ii

j

pmj

Lfoi

oo

eve

ivi

vv

θθ •

•=

=

(11)

Substituting (10) into (9) results in a system described by (12) with vo

* being the new manipulated input.

( )

( ) ( )

( )

*

*

* *

* *cos sin

32

f

f

f

ii

injL load injf o f

Lo inj Lf f o f

q q d dpm o Lf o Lf j

pm pmpm r pmq dpm ii pm ii

pmpm pm pmpm r pm r pm

rmpm pmm L m rm

d vC i i j C v

dtd i

L v v R j L idt

v i v idvC i e j C v

dt v v

diL j v R j L i

dtd

J p i T Bdt

θ

ω

ω

ωθ θ

ω λ ω

ω λ ω

= − −

= − − +

+= − −

−

= − − +

= × − −

(12)

Clearly, the system described in (12) features various nonlinearities. In order to examine its behavior in terms of stability and design suitable controllers, it may be linearized around a desired steady state operating point. The linearized system, in its scalar form (where the real and imaginary components of the complex vectors are separated) may be described in the form of

dx Ax Budt

= + (13)

where x is the vector of state variables given by

f f

Tq d q d q d q dinj inj L L pm pm pm pm rx v v i i v v i i ω =

.

The A matrix is determined by computing the Jacobin of at the operating point of interest. The A matrix is block-triangular, given by

11

21 22

0AA

A A =

(14)

where

11

10 0

10 0

1 0

10

of

of

fo

f f

fo

f f

C

CA R

L LR

L L

ω

ω

ω

ω

− = −− − −−

;

( ) ( )( )

( ) ( )( )

* * 2 *

2* *

* * 2 *

2* *

22

2

cos 10

cos sin

sin 10cos sin

10

10

30 0 0

2

f f

f f

q q d do L o L ii d

r pmq dpmpm pm ii pm ii

q q d do L o L ii q

r pmq dpmpm pm ii pm ii

pm pm dr pm

pm pm pm

pm qr pm

pm pm

pm m

m m

V I V IV

CC V V

V I V IV

CC V V

A RI

L L LR

IL L

p BJ J

ω

ω

λω

ω

λ

+ Θ − − Θ − Θ

+ Θ

Θ − Θ

= −−− −

−−

−

Since the A matrix is a block-triangular matrix, its determinant may be factored into the following form [16]:

( ) ( ) ( )11 22det det detA A A= (15) where det(•) denotes the determinant of a matrix. Due to this factorial decomposition, the eigenvalues of A are the union of the eigenvalues of A11 and the eigenvalues of A22. Therefore, the design of a stable controller with desirable dynamic performance of the states and inputs corresponding to the partitioned sub-matrix A11 may be attempted independently, so long as the resulting partitioned sub-matrix A22 is verified to represent a stable subsystem as well. The controller design is based on the reduced-order plant model (LC filter), and the stability of the overall system is ensured by subsequently examining the eigenvalues of A22.

The structure of the system is well documented in literature, suggesting a complex state feedback controller as illustrated in Fig. 9 [17]. The controller employs a classic inner current loop/outer voltage loop structure. The inner current regulator with a proportional regulator Kip is designed to yield necessary bandwidth of the inner current loop. In this design, the bandwidth of the inner loop is chosen to be 500 Hz. The outer voltage regulator is a classical PI regulator Kvp + Kvi/s, which generates the current command for the inner current loop. Kvp and Kvi are chosen to shape the loop gain of the outer loop, yielding zero steady state error and acceptable bandwidth, while maintaining adequate stability margin. In addition to the inner current loop gain and the outer voltage loop PI coefficients, the regulator also incorporates complex state feedback terms that are used to compensate for the coupling that is present between the d and q axis quantities. They introduce correction terms that compensate for the voltage across the transformer series impedance by measuring the transformer current and for the current through the filter capacitor by measuring the injected capacitor voltage. A virtual resistance Rv is added in parallel with the capacitor Cf, which can make the controller less sensitive to the accuracy of the parameter estimation and improve the controller robustness. The according PI regulator zero should be designed to match the pole formed by Rv and Cf.

212

Lf

1s1

Rf +jωoLf

Cf

1s1

- -+ +

-vovinj

iload

iLf

jωoCf

-1

Rf +jωoLf^ ^

Kip++--

Kvp-

sKvi

v*inj

Grid Interface Filter - Reduced-Order Plant Model

+

-

+

+ +

-jωoCf^

Rv

1

+

Fig. 9 Block diagram of the voltage controller with complex state feedback in SRF.

B. Injection Voltage Reference Generator During a voltage sag, the voltage reference v*

inj is set to be in phase with the voltage at PCC vpcc, which can be measured. This choice maximizes the compensation voltage range possible at a given flywheel speed. On the other hand, to regulate the flywheel speed during idling mode, it is desired to keep the load voltage undisturbed, or at least the amplitude of the load voltage should be kept at the desired level. By utilizing the reactive nature of the loads, which is typical in the distribution systems, real power may be drawn from the system while the load voltage v*

load being kept equal the voltage at PCC vpcc as shown in Fig. 10. The amount power drawn from the system is determined by the q-axis component of injected voltage vq*

inj. This injection voltage reference for the idling mode is obviously different from the injection voltage reference for sag compensation mode as expressed. The injected voltage references under two different operating modes are actually seamlessly merged together by exploiting the fact that the bandwidth requirement for speed regulation is much slower than the voltage sag compensation mode. A complete block diagram of the injection voltage generator is illustrated in Fig. 11.

vload

vpccδ

Locus of load voltage and vpcc

vinj

Injected voltagereal component

Load current

φload

Fig. 10 Phasor diagram of the injection voltage reference vector during the idling mode

+-

ωrm*

ωrm

Ksp

Ksi

s

+

+

vinj1q*

q*inj

*load

vδ φ-acos +cosφ

v

=

d* q*inj inj

π δv v tan φ -2+ =

vinj1d*

|vload*|

cosφ-jsinφ

|vpcc|

vinj2*

+-j +

vinj*

+

+

+

-

vinj1*

Voltage Sag Compensation FF

Energy Restoration FB

Fig. 11 Block diagram of the injection reference generator.

C. Converter and Machine Interactions As mentioned before, the stability of the overall system can be examined separately on the partitioned subsystems formed by the grid interface LC filter (represented by A11) and the subsystem consisting of the machine filter capacitor and the machine/flywheel set (represented by A22). The stability of A11 subsystem has been guaranteed by the proper controller design. . The stability of the A22 subsystem will be examined by the eigenvalues.

It is desired to orient the converter input current in phase with the machine back emf for maximum available voltage on the grid side, and the q axis of the SRF is aligned with machine back emf. With these choices, the phase angle of the machine input current is Θ*

ii = 0, which result in the A22 matrix from (14) being the following format.

( )* *

2

22

2

1 0

10 0

1 0

10

30 0 02

f f

q q d do L o L d

r pmqpmpm pm

qr pm

pm

pm pm dr pm

pm pm pm

pm qr pm

pm pm

pm m

m m

V I V IV

CC V

VC

RA IL L L

RI

L L

p BJ J

ω

ω

λω

ω

λ

+− −

− −= − − −− −

(16)

Detailed numerical studies over a range of parameters indicate the large positive element in (1,1) potentially leads to the eigenvalues in the left half plane. The conditions for stability under typical range of design parameters have been studied empirically and are presented in the form of an impedance matching criterion described further.

For operating points when the flywheel is supplying power, i.e. * * 0

f f

q q d do L o LV I V I+ > , A22 has been found to have all its

eigenvalues on the left half plane if 1

c nm

Z QY

> (17)

where Ym defined as 2** 2)( qpm

dLf

do

qLf

qom VIVIVY +≡ is the

incremental admittance looking forward into the matrix converter. Characteristic impedance Zc and quality factor Qn are given by

pmpmc CLZ = and Qn = Zc / Rpm. Furthermore,

213

when the flywheel is absorbing power, i.e. * * 0f f

q q d do L o LV I V I+ < ,

the (1,1) element of A22 is negative and the eigenvalues of A22 are on the left half plane. In addition to the eigenvalue analysis, extensive time-domain simulations have been conducted to validate of the stability condition.

V. NUMERICAL VERIFICATION The time-domain performance of the whole system is

verified in detailed numerical simulation using a SimuLink model. Selected waveforms during the voltage sag and swell period and plotted in the abc reference frame as shown in Fig. 12(a) and Fig. 12(b). It can be observed that the injected voltage after sag/swell decrease slowly, but the load voltage is still equal to the voltage at the PCC. This demonstrates the effectiveness of the phase angle control in the control algorithm.

1.95 2 2.05 2.1 2.15 2.2 2.25 2.3 2.35

−200

0

200

v pcc (

V)

1.95 2 2.05 2.1 2.15 2.2 2.25 2.3 2.35−100

0

100

v inj (

V)

1.95 2 2.05 2.1 2.15 2.2 2.25 2.3 2.35−200

0

200

v load

(V

)

t (s) (a)

5.95 6 6.05 6.1 6.15 6.2 6.25 6.3 6.35

−200

0

200

v pcc (

V)

5.95 6 6.05 6.1 6.15 6.2 6.25 6.3 6.35−100

0

100

v inj (

V)

5.95 6 6.05 6.1 6.15 6.2 6.25 6.3 6.35−200

0

200

v load

(V

)

t (s) (b)

Fig. 12 Simulated results: load volage response to (a) voltage sag; (b) voltage swell; from top to bottom traces are source voltage, injection voltage,

load voltage

VI. EXPERIMENTAL RESULTS The hardware validation of the proposed system are being

conduced and on laboratory scale prototype, as shown in by the photograph in Fig. 13. The power supply 345-ASX, with the rating of 4.5 kVA, is capable of generating three-phase balanced voltage sags that emulate the voltage sag events in at PCC. The energy storage used in the experiment is realized by a SPM machine coupled to the rotor of an induction machine. During the final experimental test, the induction machine is not energized and only the rotor is utilized to increase the total moment of inertia of the system. . The 4-pole SPM is rated at 3.7 kW at rated speed of 1500 rpm. Although the rated speed of

the SPM is below typical speed of flywheels, it is adequate to validate the power conditioning concept and the control algorithm with this setup. The control algorithm presented in has been implemented with the floating-point DSP TMS320C31. The sag correction performance of the system is illustrated by the load voltage response to the voltage sag from the source in Fig. 14.

Fig. 13 A photograph of the experimental setup.

Fig. 14 Three-phase voltages at PCC with 60% voltage sag (0.6 pu left) lasting for 0.2 second and three-phase voltages measured at the load (bottom

three traces).

214

VII. CONCLUSIONS This paper has presented a DVR system employing matrix

converter and flywheel energy storage. The overall proposed system is modeled in two SRFs that are synchronized with the grid and the machine back emf, respectively. The resulting system model is challenging for controller design due to the time-varying modulation and nonlinearity caused by the matrix converter coupling. To overcome the control design challenge, a non-linear input decoupling strategy is put forth which allows application of classical servo-control design methodology to the reduced-order subsystem, namely the grid interface LC filter. The non-linear time-varying input decoupling approach may be employed as very useful methodology in dealing with power conversion systems with ac/ac power converters.

For the proposed system, a stability criterion is identified and empirically validated through the eigenvalue analysis and time-domain simulations. With the stability criterion, the overall system stability is guaranteed by properly sizing component parameters on the machine side. Consequently, the stability criterion assures the validity of the controller design around the subsystem. Furthermore, the stability criterion has extended the impedance matching criteria commonly utilized in dc/dc converter systems to the field of ac/ac systems.

The overall system encompassing the voltage injection controller and the plant is simulated via detailed Simulink model and tested with laboratory-scale prototype system. The time domain waveforms from both simulation and experiment demonstrate the acceptable dynamic response of the injected voltage.

ACKNOWLEDGMENT The authors would like to acknowledge support from the

Wisconsin Electric Machine and Power Electronics Consortium (WEMPEC) at the University of Wisconsin-Madison. The work made use of ERC shared facilities supported by the National Science Foundation (NSF) under AWARD EEC-9731677.

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