C1_Control of Parallel Connected Inverters

8/10/2019 C1_Control of Parallel Connected Inverters...

1/8

136

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29 NO. 1 JANUARYIFEBRUAKY 1993

Control of Parallel Connected Inverters

in Standalone ac Supply Systems

Mukul

C.

Chandorkar ,

Student Member IEEE

Deepakra j

M.

Divan, Member

IEEE

a nd R a mba bu Ada pa , Senior Member

IEEE

Abstract-A scheme for controlling parallel-connected invert-

ers in a standalone ac supply system is presented in this paper.

This scheme is suitable for control of inverters in distributed

source environments such as in isolated ac systems, large and

distributed uninterruptible power supply (UPS) systems, photo-

voltaic systems connected to ac grids, and low-voltage dc power

transmission meshes. A key featur e of the control scheme is that

it uses feedback of only those variables that can be measured

locally at the inverte r and does not need comm unication of control

signals between the inverters. This is essential for the operation

of large ac systems, where distances between inverters make

comm unication imprac tical. It is also important in high-reliability

UPS systems where system operation can be maintained in the

face of a communication breakdown. Real and reactive power

sharing between inverters can be achieved by controlling two

independent quantities-the power angle, and the fundamental

inverter voltage magn itude. Simulation results obtained with the

control scheme are also presented.

I. INTRODUCTION

S

DC

TO

AC pow er converters feeding power to ac sup-

A

ly systems become more numerous, the issues relating

to their control need to be addressed in greater detail. Inverters

connecting dc power supplies to ac systems occur in numerous

applications. Photovoltaic power plants and battery storage

installations are examples of such applications. In either case,

the inverter interfaces could be connected to a common ac

system. Distributed uninterruptible power supply (UPS) sys-

tems feeding power to a common ac system are also possible

examples. In addition, over the past several years, there has

been considerable interest in applying inverter technology to

low voltage dc (LVDC) meshed power transmission systems.

The feasibility from the control viewpoint

of

an LVDC mesh

has been demonstrated in

[l]

The transmission system could

typically consist of inverters connected at several points on

the LVDC mesh, providing power to ac systems that could

be interconnected as well. Multiple inverters connected to a

common ac system essentially operate in parallel and need to

be controlled in a manner that ensures stable operation and

prevents inverter overloads. Although inverter topologies used

Paper IPCSD 92-16, approved by the Industrial Power Converter Committee

of the IEEE Industry Applications Society for presentation at the 1991 Industry

Applications Society Annual Meeting, Dearborn, MI, September 28-October

4.

This

work was supported by

NSF

grant 8 818 339 and EPRI Agreement

RP7911-12. Manuscript released for publication April 25, 1992.

M. C. Chandorkar and D. M. Divan are with the Department of Electrical

and Computer Engineering, University of Wisconsin, Madison, WI 53706.

R. Adapa is with the Electric Power Research Institute, Palo Alto, CA

94303.

IEEE

Log

Number 9204199.

Jnvener

""f

Fig. 1. Inverter connected to stiff ac system.

for power transmission have traditionally been current sourced,

in recent years, voltage source inverters (VSI) have been

increasingly used for high-power applications like electric

traction and mill drives, photovoltaic power systems, and

battery storage systems. Control schemes for VSI's in power

system environments have formed the topic of recent work

[2]. Further, with inverter topologies like the neutral-point

clamped (NPC) inverter

[3],

it is possible to achieve substan-

tial harmonic reduction at reasonably low PWM switching

frequencies.

A standalone ac system may be described as one in which

the entire ac power is delivered to the system through inverters.

In a standalone ac system, there are no synchronous alternators

present in the system that would provide a reference for the

system frequency and voltage. All inverters in the system need

to be o perated to provide a stable frequency and voltage in the

presence of arbitrarily varying loads. This paper first develops

a control method for an inverter feeding real and reactive

power into a stiff ac system with a defined voltage, as shown

in Fig.

1.

This forms the basis of a control method suitable for

standalone operation. The inverter is a VSI with gate turn-off

(GTO) thyristor switches, operating from a dc power source,

and feeding into the ac system through a filter inductor. In

a standalone system, a filter capacitor is needed to suppress

the voltage harmonics of the inverter. The requirements for

controlling such an interface are described in the next section.

Later sections describe the development of an effective control

scheme to meet these requirements and present simulation

results obtained from the study of a power distribution system

with parallel-connected inverters.

11.

REQUIREMENTS

OF THE CONTROL SYSTEM

The control of inverters used to supply power to an ac

system in a distributed environment should be based on

information that is available locally at the inverter. In typical

power systems, large distances between inverters may make

communication of information between inverters impractical.

Comm unication of information may be used to enhance system

0093-9994/93 03.00

0

993 IEEE


2/8

CHANDORKAR er

al.:

CONTROL OF PARALLEL-CONNECTED INVERTERS

137

I

3 I 2

P=X L

sin6

w Lf

Q =*

=cos6

w

Lf w Lf

Fig. 2.

Real and

reactive power

flows.

performance but must not be cr itical for system opera tion. This

essentially implies that inverter control should be based on

terminal quantities.

It is well known that stable operation of a power system

needs good control of the real power flow P and the reactive

power flow Q. The

P

and Q flows in an ac system are

decoupled to a good extent [4].

P

depends predominantly on

the power angle, and

Q

depends predominantly on the voltage

magnitude. This is illustrated in Fig. 2.It is essential to have

good control of the pow er angle and the voltag e level by means

of the inverter. Control of frequency dynamically controls

the power angle and, thus, the real power flow. To avoid

overloading the inverters , it is im portant to ensure that cha nges

in load are taken up by the inverters in a predetermined manner

without communication. This is achieved in conventional

power systems with m ultiple generators by introducing a droop

in the frequency of each generator with the real power P

delivered by the generator [4]. This permits each generator to

take up changes in total load in a manner determined by its

frequency droop cha racteristics and es sentially utilizes the sys-

tem frequency as a comm unication link between the gene rator

control systems. In this paper, the sam e philosophy

is

used to

ensure reasonable distribution of total power betwee n parallel-

connected inverters in a standalone ac system. Similarly, a

droop in the voltage with reactive power is used to ensure

reactive power sharing.

An important aspect of the control methodology developed

here is that it is highly modular in nature. Thus, the basic

control scheme can be very easily adapted to mee t variations in

the configuration of the power system, as show n in Sections 111

and IV. This modularity is achieved by choosing the controlled

quantities of the slow, outer control loops to meet the d ictates

of the power system configuration while maintaining the same

fast, inner inverter control structure. The controller for an

inverter connected to a stiff ac system, which is detailed

in Section 111, is easily modified for the control of parallel-

connected inverters feeding a standalone ac system, which is

detailed in Section IV.

111. CONTROL OF SINGLE INVERTER

FEEDINGNTO A STIFF SYSTEM

The power schematic of Fig. 1shows a single inverter

connected to a stiff ac system through a filter inductor.

The inverter is assumed to be a six-pulse GTO VSI. This

section details the control of the inverter based on feedback

of quantities measured locally at the inverter. The real and

reactive power fed into the ac system are the two va riables that

are controlled by the inverter. Given set points for the real and

V

d

1 :

nverter

Voltage

Vwtor

0:e I

For Choice

of

Inverter

Voltage Vector

(a)

1 2 3 4

(b)

Fig.

3.

(a) Inverter output voltage vectors; (b) inverter switch positions.

reactive power

P

and

Q*,

the real and reactive power P and

Q fed by the inv erter into the ac system c an be c ontrolled by

a me thod that controls the time integral of the inverter output

voltage space vector. This concept has previously been applied

extensively to ac motor drives

[ 5 ] , [6].

The entire control

of

the inverter is performed in th e stationary d-q reference frame

and is essentially vector control. The transformation from the

physical a-b-c reference frame to the stationary d-q-n reference

frame is described by the following equations [7].

In these equations, the quantity generically denotes a

physical quantity, such as a voltage or a current. In the absence

of a neutral c onnection, the quantity f n is of no interest. For

a six-pulse VSI, the inverter output voltage space vector can

take any of seven positions in the plane specified by the d-q

coordinates. These are shown in Fig.

3

as the vectors

0-6.

The time integral of the inverter output voltage space vector

is called the inverter flux vector for short. The flux vector

does not have the same significance as in motor applications.

Rather, it is a fictitious quantity related to the volt-seconds in

the filter inductor. The

d

and

q

axis components of the inverter


3/8

138

IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL.

29

NO. 1, JANUARY/FEBRUARY 1993

P I

Regulator

P' & Q*

:

Set Points for Real & Reactive Power

L o w

Pass

Filter

Fig. 4.

Inverter

control scheme-stiff ac system.

flux vector are defined as

t

d u

=

d d r (4)

--CO

t

,U

= / ( 5 )

CO

The magnitude of & is

The angle of

5

ith respect to the y axis is

6 = tan- 7 )

The d and

y

axis components of the ac system voltage flux

vector 5 ts magnitude, and angle are defined in a similar

manner. The angle between

(8)

and6 s defined as

6 = 6 Se.

Control of the flux vector has been shown

to

have good

dynamic and steady-state performance [ 5 ] , 6]. It also provides

a convenient means to define the power a ngle since the inverter

voltage vector switches position in the

d - y

plane, whereas

there is no discontinuity in the inverter flux vector. It is useful

to develop the power transfer relationships in terms of the

flux vectors. The basic real power transfer relationship for the

system of Fig. 1 in the d-q reference frame is

(9)

3

2

P

= - eq i ,

+ e d i d ) .

In (9), e , and e d are the q- and d-axis components, respec-

tively, of the ac system voltage vector

E .

n addition, i, and i d

are the components of the current vector

7.

When i , and

i d

are

expressed in terms of the fluxes, the equation is expressed as

Taking into account the spatial relationships between the

two flux vectors and assuming the ac system voltage to be

sinusoidal, (10) can be expressed as

w , , sin

6.

= -

3

2L.f

In this expression, and are the magnitudes of the ac

system and the inverter flux vectors, respectively, and 6

is

the

spatial angle between the two flux vectors.

w

is the frequency

of rotation of the two flux vectors. The expression for reactive

power transfer for Fig. 1can be derived in a similar manner.

This is

(12)

w

Q = - U , C O S

-

/ 5 3 .

2 L.f

Equations (11) and (12) indicate that P can be controlled

by controlling

S

which can be defined as the power angle,

and Q can be controlled by controlling &,. The cross coupling

between the control of

P

and

Q

is also apparent from these

equations.

The control system for the inverter is given in Fig. 4.The

two variables that are controlled directly by the inverter are

is controlled to have a specified

magnitude and a specified position relative to the ac system

flux vector6.his control forms the innermost control loop

and is very fast. It is noted that both the inverter and the

and

6.

The vector


4/8

CHANDORKAR

t al :

CONTROL OF PARALLEL-CONNECTED INVERTERS

139

TABLE

CHOICE

F

SWITCHINGVECTOR

Sector

No.

(Location

of z)

I

I I m r v v v 1

Increase

2 3 4 5 6 1

Decrease &

3

4 5 6 1 2

(The zero vector

is

chosen to decrease

4,

ac system voltage space vectors ,are obtained by me asuring

instantaneous voltage values that are available locally. The se t

points for the controller are

P

and

Q*,

and the set points for

the innermost control loop

:

and

6

are derived from these.

The a ctual values of P and Q calculated from the feedback are

compared with the se t values. The error drives a proportional-

integral (P-I) regulator, which generates the set points and

6

for the innermost control loop. The control of the inve rter

to generate the specified

,

and 6 is detailed in the next

subsection.

A. Control of and

6

The control of 4, and 6 forms the first level of control

and directly controls the inverter switching. The choice of

the inverter switching vector is made on the basis of the

deviations of ,, and 6 from the set values

:

and 6

and the position of the inverter flux vector in the

d-q

plane

give n by 6,. If the devia tion of 6 from 6 is more than

a specified limit, a zero switching vector is chosen. If this

deviation is less than a specified limit or if

,

deviates from

by more than a specified amount, a switching vector that

increases 6 and changes in the correct direction is chosen.

This is essentially accomplished by hysteresis comparators for

the set values and then using a look-up table to choose the

correct inverter output voltage vector. The c onsiderations for

developing the look-up table are de alt with in [ 5 ] .The choice

of

inverter switching vector is dictated by the value of

6,.

The d-q plane is divided into six sectors for 6 as shown in

Fig. 3(a), which also shows the inverter switching vectors.

The inverter switch positions for the vectors are show n in Fig.

3(b). The value of 6, determ ines the cho ice of two possible

inverter switching vectors apart from the zero vector. One

vector increases the magnitude

,,

and the other decreases

it, whereas both tend to increase 6,. Thus, to decreas e 6 the

zero switching vector is chosen. To correct the value of ,,,

one of the two active switching vectors is chosen, depending

on the sign of the correction required. Table I gives the ch oice

of active vectors for given positions of the inverter flux vector,

which is specifie d by 6,. In this man ner, and 6 are tightly

controlled to lie within specified hysteresis bands by means

of inverter switching. The tip of the inverter flux vector is

guided along

an

almost circular path. Control of and

6

in this manner results in a PWM voltage waveform at the

inverter output.

.ii

3 3

N

10

c

-

L I U 6 00

-2.011 2 00

6

00 In

h v VS

Fig.

5.

Inverter

flux

vector.

I

1.694

1l.727

1l.760 1'.794 1l.827

s

1'.860

T

*10-1

Fig.

6.

Inverter voltage and current waveforms.

the power system of Fig. 1are presented in Figs.

5-7.

The dc

bus voltage is taken to be 10 kV, and the line-to-line voltage

of the ac system is taken to be 3.3 kV rms. The inductor L

is 17 mH. Fig. 5gives the plot of the locus of the inverter

flux vector6.he locus is seen to be close to a circle since

the magnitude , is very tightly controlled. Fig. 6 shows the

inverter line-to-line voltage ? and the inverter line current u

for

P*

=

1

MW and Q* =

500

kvar.Fig.7shows the response

of the inverter

to

step changes in Q* and P*, uccessive ly. It

is noted that there is a disturbance in P when Q* is changed

and a disturba nce in

Q

when P* is changed. In eac h case, the

P-I regulators modify the set values of

6

and

4,:

to main

the P and the Q at the set values. In addition, the tight contro

of

P

and

Q

within limits is apparent from Fig.

7.

I v . CONTROL

OF INVERTERS

IN A

STANDALONE

SYSTEM

B. Simulation Results

The control of a single inverter feeding a stiff ac system

based only on instantaneous measurement of terminal quanti-imulation results of the c ontrol scheme of Fig. 4applied to


5/8

140

IEEE TRANSACTIONS ON INDUSTRY A PPLICATIONS,

VOL.

29, NO. 1, JANUARYFEBRUARY 1993

I I I I

I

o l

I

I

0 .02 0.06 0.11 0.15 0 .20 S 0 . 2 5

T

Fig.

7.

Inverter real and reactive power.

Fig. 8. Standalone ac system.

ties now forms the basis of the control scheme for multiple

inverters in standalone system environments. The essential

difference in the control scheme is that in the standalone

system, there is no ac side voltage available for reference. The

inverters themselves produce the ac system voltage, which is

fed back to control the inverters. There is thus a possibility

of contro lling the voltage and the frequency of the ac system

by inverter control. Fig.

8

shows two inverters feeding into

a standalone ac system. The inverters are interfaced to the ac

system through

LC

filters. The two inverters are connected by

a tie line, and each inverter has a local load. The dc power

source represents a 10-kV dc power transmission mesh. The

nominal voltage on the ac system is

3.6

kV rms line to line, and

the nominal frequency is 60 Hz.

Each inverter is a six-pulse

VSI made up of GTO switches.

Fig. 9 shows the block diagram of the control of inverters

in a standalone system.

As

in the sing le inverter case, the two

variables that are directly controlled are

and

6

for each

inverter. Middle control loops are then used to control the

magnitude and angular frequency of the ac system voltage

frequency of are obtained from the outermost loop, which

implements specified droop characteristics for the frequency

with

P

and magnitude with Q , as mentio ned in Section 11. The

entire control

is,

thus, a three-level structure. The innermost

control level controls and 6 and is the same as that

described in the previous section. The second level controls

the ac side frequency and the voltage at each inverter and

provides set points

6

and for the innermost level. The

third level computes the set points for frequency and voltage

for each inverter. The two outer control levels are described

below.

A . Control of Frequency and Voltage

The frequency co ntroller determines the setpoint

6

that

is

needed to attain the specified frequency. The structure of the

frequency controller is given in Fig.

10.

The frequency setting

w* is integrated to obtain a reference for the position 6:c of

the ac system voltage vector across the filter capacitor. This

is compared with the actual position Sa of

E .

The error is

used to drive a P-I regulator, which produces the setpoint

a which is given to the innermost control loop described

previously. This scheme achieves a very tight control

of

the

output frequency since the regulator attempts to control the

output voltage vector angle at every instant.

The voltage controller determines the setpoint that is

needed to attain the specified ac system voltage magnitude.

The voltage controller needs to take care of the filter dynamics

to determine the exact value of

:

The structu re of the voltage

controller is given in Fig.

11.

The controller command input

is

E*,

which is the specified value of the magnitude of

F .

The con troller consists of a com mand feedforward term and a

voltage magnitude feedback term. The command feedforward

term is given by

The command feedforward gives the value of needed to

achieve the specified E* with an unloaded filter and is intended

to speed up the voltage control loop. The voltage magnitude

feedback term is used to generate an error signal that actuates

a P-I controller. The resultant value of is used as a setpoint

for the innermost control loop described previously.

The ac system frequency

w

is computed six times

in

one

cycle. For this purpose, six axes are defined in the d-q plane.

The time taken by the vector

E

to cross from one axis to

the next consecutive axis is used to compute the frequency.

For parallel operation of multiple inverter units, the setpoints

w* and E* need to be chosen to ensure the correct

P

and

Q

sharing between the inverters in response to arbitrary load

changes. This has to be done without communication of the

setpoints between the two inverter systems. The next subsec-

tion describes the outermost control loop, which determines the

setpoints

w*

and

E*

for each inverter system independently

without any signal communication. This is done on the basis

vector

E .

The set points fo r the magnitude and angular

of the real and reac tive power loading of the inverter systems.


6/8

CHANDORKAR et al.: CONTROL OF PARALLEL-CONNECTED INVERTERS

141

Outer

hop:

Droop

Characteristics

Middle

Loop:

E and Innerbop:

vv

nd Sp

- 1

-- --- --T--

_--

_--

---

I - - - --- --- --

E

I

vv*

I

Droops

I

W V

Inverter nverter I

SYStelll E

Flux

Vector

o a n d ,

Vector

AC System I

Voltage J

Feedback

'

PandQ

E*=f(Q)

Voltage

Vector

Control Calc.

,

1

I

AC System

Voltage

Inverter

Voltage

Feedback

Feedback

E

V

Control

+Inverter

Switches

Fig. 9.

Inverter control scheme-standalone ac system.

*

0

sx I

From Filter

Output

Fig.10.

Frequency contro ller for standalone system.

Regulator

From Filter

Fig. 11 .

Voltage controller for standalone system.

B.

Computing

w*

and

E* for

Parallel Operation

The outermost loop determines the setpoints for w* and

E*

to

ensure correct real and reactive powe r sharing between

the parallel connected inverters. This action is similar to that

used in conventional power systems to ensure the corre ct load

sharing between generators feeding to a common ac system

[4]. or the frequency set point, a droop is defined for the P -

w characteristic of each inverter. The frequency set point is

thus made to dec rease with increasing real power supplied by

the inverter. The P-U* droop characteristic can be described

(13)

by

w t =

W O m,(Po; P,) = g, (P) .

In this expression, =

1

for inverter

1,

and

=

2 for

inverter

2

(Fig. 8). WO is the nominal operating frequency of

the ac system and is taken to be 377 rads

(60

Hz).

Po,

is the

power rating of the ith inve rter, and P, is its actual loading.

The slope of the droop characteristic is

m,

and is numerically

negative. The values of m; for different inverters determine

the relative power sharing between the inverters. In typical

systems, the P-w* characteristics are stiff, and the frequency

change from no load to full load is extremely small. If the

slopes

m,

for different inverters are chosen such that

mlPo2

=

maPo2

= ... =

mnPon

(14)

then for a total power

P ,

the load distribution between the

inverters satisfies the relationships

mlP1 = mzP2

=

...

=

m n P n

(15)

By choosing the slopes according to

(14),

it can be ensured

that load changes are taken up by the inverters in proportion

to their power ratings. The power-sharing mechanism can

be best understood by considering the two-inverter system

shown in Fig. 8. An increase in power drawn by the load

near Inverter 2 results in increased power from both inverters.

If the magnitude of m 2 is larger than that of m l ,

w;

would

tend to drop lower than w: . Hence, the vector

Fz

would lag

the vector

E l ,

and the power flow in the tieline from Inverter

1

to Inverter 2 would increase. Thus, Inverter

1

would take

up a larger proportion of the load. It is possible to define

a composite power-frequency curve for all the inverters in

the system. The composite load curve is likewise defined.

At the steady-state operating point on the composite load-

frequency curve, the total power delivered by the inverters

matches the power consum ed by the loads. Depending on the

stiffness of the com posite power-frequency curve, the steady-

state system frequency will change on changing loads. The

frequency may then be restored to its nominal value by a

slower outer loop. To restore the frequency, the value of Po;,

(13) has to be modified for the inverters. This is equivalen t to

shifting the power-frequency curve v ertically. The restoration

of the frequency may be done in a slow, coordinated manner

by a master controller, using a slow communication channel

between the inverters.

In a similar manner, the setpoints E,* for the ac system

voltages at the inverter systems ca n be determined from

drooping reactive power-voltage characteristics

(Q-E)

for


7/8

142

IEEE

TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 29, NO.

1

JANUARYIFEBRUARY 1993

the inverters. This droop ensures the desired reactive power

sharing between the inverter systems and is described by

Ef = Eo - n;(Qoi - Q;)

=

f ; (P ) .

(17)

In (17), EO s the nominal voltage on the ac system , Q o; s

the nominal reactive power supplied by the ith inverter, and

n;

is the slope of the droop characteristic.

The control system described above has been applied to the

standalone system of Fig. 8. The results of simulation studies

are presented below.

C. Simulation Results

systems are cha racterized by the following parameters:

For the simulation studies, the droops of the two inverter

Pol = 0.75 MW

Po = 0.6 MW

ml =

-1.4 x (radls)/W

mz = -1.75

x (radls)/W

Qol

=

0.2 Mvar

n1 = -1.0 x 10-4

V/VX

Qo2 = 0.1

M V U

n

=

- 2 .0 x V/var.

The nominal voltage is

3.6

kV rms line to line, and the

nominal frequency is

60

Hz. The filter components for the

two inverter systems are identical as are the initial load

components. The component values

are

typical for a low-

power ac system. With reference to Fig. 8, the component

values are

Fig. 12 shows the response of the inverters when the

resistance RE^ (Fig. 8) is decreased suddenly to half its value.

Fig. 12shows the real and reactive powers supplied by the two

inverter systems to the load. The figure shows that Inverter 1

carries a larger share of the real power since it has a stiffer

slope. Fig. 13shows the line-to-line voltage across the filter

capacitor of Inverter

1.

The plot for the reactive powers in

Fig. 12 shows oscillations. These oscillations are the result of

filter interactions and occur in the absence of active damping

of the loop formed by the two filter capacitors and the tie-line

inductance. These oscillations are not uncommon in power

systems and can be damped by the inverters, given sufficient

inverter bandwidth. One effective means of damping these

oscillations is the introduction of a series active filter

[8]

between the capa citor and the ac system bus. As mentioned in

[8],

this method presents a low resistance to the fundamental

and a high resistance to harmonics, thus effectively limiting

the harmonic current injection into the ac system. The series

active filter inverter is not expected to handle real pow er and

can have a reasonably low rating.

U.

24 0.28 U.32 U . 3 6 U .4U

T

3 I I I I I J

O.ZI1

11.24

0.28 0 . 3 2

0 . 3 6 s U . 4 0

Inverter real and reactive power (standalone system).

T

Fig. 12.

L

U.2U

U. 24 0 .28 0 . 32

0.36 S

0 .40

T

Fig.

13.

Voltage across Inverter 1 filter capacitor.

V.

CONCLUSIONS

This paper has described a method to effectively control

inverters in a standalone ac supply system without any form of

signal communication. The control m ethodology has a highly

modular structure. This feature enables easy modification of

the controls to meet the requirements of different ac system

structures. The simulation results presented indicate that the

scheme effectively achieves the goals of power sharing in

the presence of arbitrarily changing loads. Active damping in

the loop formed by the filter capacitors and the tieline would

enhance the performance further. The scheme described in this

paper uses

P-I

regulators to determine

the

set points for 6


8/8

CHANDORKAR

ef

al.:

CONTROL

OF

PARALLEL-CONNECTED INVERTERS

143

and

:.

However, the dynamic performance of the system can

be substantially improved if an observer structure is used to

determine the frequency . The position

of

the ac system voltage

vector can be determined very accurately at any time. This

information can be used to set up a frequency observer, the

output of which would be an estimated frequency. The time

integral of the estimated frequency can be compared with the

actual position of the voltage vector, and the estimated fre-

quency can be modified accordingly. Feedback

of

the observer

states results in a system w ith very good dynam ic response and

disturbance rejection properties.

In summary, this paper has

discussed control system requirements for inverters inter-

faced to an ac system, with emp hasis on a standalone ac

system

developed a modular control scheme that meets these

requirements without control signal communication be-

tween parallel-connected inverters

presented simulations for the control scheme as applied

to an inverter connected to a strong ac system and to two

inverters connected in parallel to a stan dalone ac system

briefly discussed the issue of filter interaction in the c ase

of

parallel-connected inverters and suggested a method

for minimizing these interactions.

REFERENCES

[ ]

B.

K. Johnson, R. H. Lasseter, and R. Adapa, Power control applica-

tions on a superconducting LVdc mesh, IEEE Trans. Power Delivery

vol. 6, no. 3, pp. 1282-1288, July 1991.

[2] L.

Angquist and

L.

Lindberg, Inner phase angle control of voltage

source converter in high power applications, in IEEE

PESC

Con

Rec.

[3]

A. Nabae, I. Takahashi, and H. Akagi, A neutral-point-clamped PWM

inverter, IEEE Trans. Industry Applicaitons vol. IA-17, pp. 518-523,

Sept./Oct. 1981.

[4]

A.

R.

Bergen,

Power System Analysis.

Englewood Cliffs, NJ: Prentice-

Hall, 1986.

[5]

I.

Takahashi and T. Noguchi, A new quick-response and high-efficiency

control strategy of an induction motor,

IEEE Trans. Industry Applica-

tions

vol. IA-22, pp. 820-827, Sept./Oct. 1986.

[6]

M.

Depenbrock, Direct self-control (DSC) of inverter-fed induction

machine,

IEEE Trans. Power Electron.

vol. 3, pp. 420-429, Oct 1988.

[7]

T. A. Lipo, Analysis of synchronous machines, course notes, Univ.

of Wisconsin-Madison, 1990.

[8]

S

Bhattacharya,

D.

M. Divan, and B. Banerjee, Synchronous frame

harmonic isolator using active series filter, in Proc. 4th Euro.

Con5

Power Electron. Applications

(Florence, Italy), 1991, vol.

3,

pp. 30-35.

1991, pp. 293-298.

Mukul

C. Chandorkar

(S90) received

the

B.Tech.

degree in electrical engineering from the Indian

Institute of Technology, Bombay, India, in 1 984 and

the

M.

Tech. degree in electrical engineering from

the Indian Institute of Technology, Madras, India, in

1987. Since 1989, he has

been

working on the Ph.

D. program in Electrical and Computer Engineering

at the University of Wisconsin, Madison

From 1984 to 1986, he was with Larsen and

Toubro Limited, Bombay, India, working

on

the

engineering of cement and chemical plants. He

Deepakraj

M.

Divan

(M83) received the B. Tech


Institute of Technology, Kanpur, India, in 1975. He

also received the M.Sc and Ph.D degrees in elec-

trical engineering from the University

of

Calgary,

Canada.

He has worked for two years as a Development

Engineer with Philips India Ltd. After finishing

his

Masters program in 1979, he started his own con-

cem in Pune, India, providing product development

and manufacturing services in the power electronics

and instrumentation areas. In 1983, he joined the Depa&ent of Electrical

Engineering at the University of Alberta as an Assistant Professor. Since 1985,

he has been with the Department of Electrical and Computer Engineering at

the University of Wisconsin, Madison, where he is presently an Associate

Professor. He is also an Associate Director of the Wisconsin E lectric Machines

and Power Electronics Consortium (WEMPEC). His primary areas of interest

are in power electronic converter circuits and control techniques. He has over

30 papers in the area as well as many patents. He is also a consultant for

various industrial concems.

Dr.

Divan was a recepient of the Killam Scholarship while in the Ph.D

program and has won various prize papers including the IEEE-US Best Paper

Award for 1988-89, first prize paper for the Industrial Drives and Static Power

Converter Committee in 1989, third prize paper in the Power Semiconductor

Committee and the 1983 third prize paper award of the Static Power Converter

Committee of the IEEE Industry Applications Society. He has been the

Program Chairman for the 1988 and 1989 Static Power Converter Committee

of the IEEE-IAS, Program Chairman for PESC 91, and a Treasurer for PESC

89. He is also a Chairman of the Education Com mittee in the IEEE Pow er

Electronics Society.

Rambabu Adapa

(S81-M786-SM90) was bom

in Andhra Pradesh, India, on Sept. 2, 1956. He

received the B.S. degree in electrical engineering

from Jawaharlal Nehru Technological University,

Kakinada, India, in 1979. He received the

M.S.


Institute of Technology, Kanpur, India, in 1981.

He

received the Ph.D. degree in electrical engineering

from the University of Waterloo, Canada, in 1986.

He joined the Power System Planning and Oper-

ations urogram of the Electrical Svstems Division

of the Electric Power Research I n & & (EPRI), Palo Ako, CA, in June

1989. Prior to joining EPRI, he was Staff Engineer in the Systems Engi-

neering department of McGraw-Edison Power Systems, Franksville,

WI.

At

McGraw-Edison, he was involved in several digital and analog

studies,

which

included transient, harmonic, and insulation coordination studies performed

for electric utilities. At EPRI, he manages the Electro-Magnetic Transients

Program (EMTP) development and maintenance project, commercialization

of the Harmonic Analysis Software

(HARMFLO)

endeavor, and several

other EPRUNSF-funded projects.

His

interests include EMTP, power system

planning and operations, HVDC transmission, harmonics, and expert systems.

Dr. Adapa is a Senior Member of the IEEE Power Engineering Society,

a member of the DC Transmission subcommittee of the Transmission and

Distribution Committee, a member of CIGRE and of the local IEEE Santa

Clara chapter. He is a Registered Professional Engineer in the State of

Wisconsin.

worked as a design engineer in the power electronics industry in India

during 1988-1989. His primary technical interests are in power electronics

applications to electric machines and to power systems.

Documents

C1_Control of Parallel Connected Inverters