Ref 2

IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS

Damping H. A. PETERSON,

VOL.

PAS-85,

N O.

Power Swings in AC and DC System

of

P. C. KRAUSE, JR.,

FELLOW, IEEE, AND

Abstract-In an earlier paper, the authors presented a method of simulating a transmission system including ac and dc lines in parallel, and established the validity of the simulation. In this paper the method, which utilizes a direct and quadrature axis representation, is used to study with the aid of an analog computer the electromechanical oscillations in a system consisting of one machine tied to an infinite bus through two parallel transmission lines, one of which is ac and the other dc. Results make it clear that with proper dynamic control of power flow in the dc line, a substantial degree of damping of transient power swings may be achieved.

INTRODUCTION FROM EARLIER STUDIES it became apparent that with appropriate control, a dc link could be made to respond more quickly to demands for power flow than could an ac line. In those studies digital methods as well as an analog computer were used, depending upon the particular problem under study. Disturbances such as 3phase faults, sudden load changes, and sudden changes in dc reference current setting were investigated. An important paper by Dr. Uhlmann [1] presented equations and the basic analysis for a simplified parallel ac and dc transmission system. This analysis made it clear that with proper feedback control of power in the dc line, damping of electromechanical oscillations can be effectively achieved. This paper extends the previous studies reported. A 1machine and infinite bus, ac-dc system is studied in detail. A variety of disturbances are imposed on the system and the dynamic responses of the system are obtained with several different feedback control transfer functions. Results obtained point up the unique ability of a dc link to provide damping of electromechanical oscillations under certain conditions.

DECEMBER) 1966

12

a

Parallel

SENIOR MEMBER, IEEE

PAPt H, APO

X

Pdc +

APdc

Fig. 1. Simplified, 1-machine, infinite bus ac-dc system.

His analysis is based upon assumptions which are valid when small changes in system power are considered. While an analysis of this type has limitations, it permits one to readily establish equations which are invaluable in predicting the performance of an actual system. Although the purpose of this paper is to demonstrate the effects of these proposed methods of control by means of an analog computer study, it is advantageous to consider an analysis, similar to that given in Uhlmann [1 ] before presenting the results of this study. A simplified 1-machine, infinite bus ac-dc system is shown in Fig. 1. For this analysis it will be assumed that the bus voltages, E1 and E2, are constants and the ac line may be represented by a series reactance X. For small changes in the phase angle of the bus voltages, the change in ac power transmitted may be expressed Aw APac t = E1E2 cos 60 (1)

x

P

where

S0-initial angle between bus voltages Ao-change in speed of the synchronous machine p-the operator d/dt.

BASIC ANALYTICAL CONSIDERATIONS Methods of stabilizing an ac system by utilizing a Changes in rotor speed due to a small change in acceleratparallel dc link are proposed in a recent publication [1]. ing power may be written In this interesting and important paper, Dr. Uhlmann APa = 2HpAw (2) considers an idealized 2-machine system with parallel ac and dc links to establish and evaluate several methods of where H is inertia constant of the machine. control which may be used to improve system stability. The dc power may be controlled by either a current or a power regulator. Incorporated with this control is a Paper 31 TP 66-100, recommended and approved by the Trans- signal dependent upon the change in speed of the machine. mission and Distribution Committee of the IEEE Power Group for presentation at the IEEE Winter Power Meeting, New York, Thus, variation from a constant dc power will be deterN. Y., January 30-February 4, 1966. Manuscript submitted No- mined by a function of A/o, that is vember made available for 1, 1965; printing November 24, 1965. The authors are with the Department of Electrical Engineering, University of Wisconsin, Madison, Wis.

1231

APdc = f(ACO).

(3)

1232

IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS

DECEMBER

Assuming a small change in system power AlP the change If, for example, K1 is made large so that in accelerating power can be expressed EE2 APa = AP - APac' - APdc. K1X cos 50 << 1 (4) Substituting (1), (2), and (3) into (4) yields APdc - AP APac t 0. AlP = 2HpAw + f(Ac) + E1E2 cos X

0A_oP

I

(5)

Also, with this type of control, the deviation in the phase The following relationships are readily established from angle between the bus voltages may be limited during a the previous equations. break in the ac link (EjE2/X = 0) providing the dc system is capable of sustaining the necessary overload. AP& Pf (pAw) (6) The phase angle between the bus voltages will return D(p) AlP to its value prior to a system disturbance with

EX12 APl = D(p)X cos 0o Aco

APac t

(7)

where D(p)

=

E1E2 2Hp2Aw + pf(Ao\) + E- cos

x

o

Aw.

(8)

f(Aco)

=

KoAco + Ki-+ p

p2

This characteristic is evident from the steady-state evaluation of (6) and (7) which yields, APdc = AP and

Apact

=

0.

Since these methods of control will be referenced quite Once f(Aw) has been defined, the previous equations may frequently in this paper, it is convenient to establish the be employed to predict the transient and steady-state following notation: performance of this simplified ac-dc system when subjected to small changes in system power. In this paper, Type A f(Awo) = KoAw, the results of a computer study will be presented rather than a hand analysis of these equations, however, several Type B f(Aw) = KoAo + K1important characteristics may be readily observed. p It is apparent from (6)-(8) that system damping may be achieved by making f(Aw) directly proporType C f(Aco) = KoAw+ K-+K K2p p2 tional to Aco. Moreover, f(Aco) can be selected so as to determine the steady-state operation after a change in Although other methods of control are possible, these power has occurred. These features are of importance three basic controls incorporate interesting features and shall be discussed briefly. If f(Aco) = KoAco, steady- which warrant investigation. state evaluation of (6) and (7) yields APd, = 0 and APact = AP. The change in system power is accepted by the ac AC-DC POWER SYSTEM STUDIED system. More important, however, is the fact that with = f(Acw) KoAw, system damping may be controlled by In an earlier paper, a method of representing an ac-dc adjusting Ko. Thus, a change in power might be accepted system in a direct and quadrature axis was presented [2]. by altering the ac transmitted power in a critically The method of simulation as well as results of an analog damped manner. Since the incorporation of a signal computer study of a 1-machine infinite bus system with directly proportional to the change in rotor speed pro- parallel ac and dc links are set forth. The ac-dc system used motes system damping, it seems logical to include this in the investigation reported here is identical to system signal as a part of any proposed f(Aco). described in the previous paper. Although the method Steady-state operation is influenced if of simulation will not be repeated, it seems appropriate to include a brief description of the ac-dc system. f(Aw) = KoAco + K1-. A 1-line diagram of the parallel ac-dc power system p which was simulated on the analog computer is shown in In this case, steady-state evaluation of (6) and (7) yields Fig. 2. In this system, a 4000 Mva equivalent machine is connected synchronously to an infinite bus by 500 miles of 1 APdC 500 kV-ac transmission line (50 percent compensated) and Ap E1E2 asynchronously by 500 miles of 500 kV-dc transmission + K1X ° line. A capacitor bank which delivers 18.85 Mvar and a 2000 Mva resistive load (unity power-factor load) are 1 APac_ connected to the generator bus. With the generator operatl K1X AP + at rated power input (4000 Mva) the system consumes ing E1E2 cos 80 50 percent of the generated power in the vicinity of the It is apparent that the value of K1 determines the steady- generator with approximately 50 percent of the power state mode of operation after a change in system power. transmitted to the infinite bus.

1966

override (ecR and eci*, respectively) are developed from the difference between a reference current (independent of w;~~~~~~~~~~~~~~~~~~I;l ~ changes in rotor speed) and the dc line current [2], [3]. 50% SERIES In this study, the method of developing the control signals COMPENSATION ecR and ecl* differs in that the reference current is the 230 KV sum of a set reference and f(Aco). In particular, -

500 MILES

I

500-KV AC LINE

18.85 MVAR

'1H3e 230 KV

4000 MVA

&-.

L-3

2000 MVA UNITY pf

ecR

.05

53.0

=

.315

.026

'13 H

.315

.026

1.165 l.0

12

0.605

.108

sum

Fig. 3. System constant

.0926

.0926

on

~~~\\ ~~~7.74 I

T 4.25

.108

pu

INFINITE BUS

/

sum

1000-Mva base 230-kV bus voltage.

The system parameters, referred to a 1000 Mva power base with 230 kV as the base line-to-line voltage, are given in Fig. 3. The transformer connections and the converters are arranged so that with 1.0 per unit bus voltage, the noload rectifier output voltage is 1.65 per unit referred to the ac system. The machine is equipped with a voltage regulator which is adjusted to regulate 1.1 per unit generator bus voltage. The per-unit parameters of the machine are as follows:

ra Xia

armature resistance armature leakage reactance

rfd field resistance Xlf d field leakage reactance rkd direct-axis damper winding resistance Xlkd direct-axis damper winding leakage reactance rkq quadrature-axis damper winding resistance Xlkq quadrature-axis damper winding leakage reactance Xad direct-axis magnetizing reactance Xaq quadrature-axis magnetizing reactance H inertia constant

KR (I,

-

IR)

where

KR-gain of rectifier controller Kr-gain of inverter controller JR-rectifier current II-inverter current

.05

pu

=

ecI* = K1(kIr - I)

Fig. 2. A 1-line diagram of system simulated on analog computer.

1.1

1233

KRAUSE: DAMPING OF POWER SWINGS

PETERSON AND

Machine Base, 4000 Mva

System Base, 1000 Mva

0.005 0.1 0.00055 0. 1 0.02

0.00124 0.025 0.0001375 0.025 0.005

0.1

0.025

0.04

0.01

0.2 1.0 0.7

0.05 0.25 0.175

3 seconds 12 seconds

The 6-phase rectifier is equipped with a constant current control and is connected to the generator bus. A constant extinction angle control with a current override is incorporated in the inverter controller. In the computer studies presented in previous papers, the control signals of the rectifier and the inverter current

k-a constant less than unity (0.9 in this study) Ir- IrO + f(Aw) Iho-constant or set reference current.

RESULTS OF COMPUTER STUDY In this section the methods of control proposed in Uhlmann [1 and considered briefly in the opening section are investigated using an analog computer simulation of a 1-machine, infinite bus ac-dc system. In order to compare the action of these controls, relatively small changes in system power are considered about a common operating point. With one exception, which will be discussed, the initial condition of operation was that wherein the input torque to the generator was set at 4.0 per unit (4000 Mva); the reference current of the dc system set so that approximately 1.0 per unit, dc power was transmitted from the generator bus, and the resistiv-e load at the generator bus adjusted to consume 2.0 per unit power (1.1 per unit generator bus voltage). For this condition, the ac power transmitted from the generator bus is approximately 1.0 per unit. Small changes in system power were incurred by programming step changes in the generator input torque and generator bus loading (step changes in the resistance of the unity power factor load). In each case the following variables are recorded; Ei-exciter voltage, Vqy-qR-axis bus voltage, VR'-rectifier voltage, IR-rectifier current, Pac,-ac power transmitted from generator bus, Pd0-rectifier power, Ta-accelerating torque, and 6-power angle, that is, the angle between the quadrature axis of the machine and the quadrature axis of the infinite bus.

Performance of an AC-DC System during Changes in System Power-Stabilization Control not Incorporated The computer tracings given in Figs. 4 and 5 demonstrate the performance of the ac-dc system during system disturbances with f(Aco) = 0. In particular, Fig. 4 shows the system response due to input torque disturbance; Fig. 5 shows the system response due to step changes in the power consumed by the resistive load connected to the generator bus. With the initial condition of operation as stated above, the generator input torque (Fig. 4) was stepped from 4.0 to 4.25 per unit. The power angle

1234

IEEE TRANSACTIONS ON POWER APPARATUS AND

DECEMBER

SYSTEMS

2.0 EXCITER

1.0

VOLTAGE

BUS VOLTAGE

(qR-Gaxi)

Vq R

q 0

VR

1.0l

|

SEC.

RECTIFIER VOLTAGE

RECTIFIER CURRENT .0

AC POWER-TRANSMITTED

2D

DC POWER-RECTIFIER Pdc

ACCELERATING

TORQUE

5

1--INPUT TOGRUE INCREASES

TO

la-INPUT TORQUE 4.25 PU

DECREASED

-INPUT

TO

3.75 PU

TORGUE

INCREASED

TG

4.0 PU

POWER ANGLE

Fig. 4. The ac-dc system response to step changes in generator input torque; no stabilizing control. 2.0

Ex

BUS VOLTAGE (qR-oxis ) V

RR

VIn

|

RECTIFIER

CURRENT

AC POWER-TRANSMITTED

DC POWER

RECTIFIER

1.0t

Pd

c

To5 0.5

ACCELERATING

TORQUE

6

:

LOAD |_-RESISTIVE DECREASED TO 1.75 PU

s

t\

0

LOAD INCREASED TO

-RESISTIVE

225 PU

a-RESISTIVE LOAD

DECREASED TO 2.0 PU

POWER ANGLE _

Fig. 5. The ac-dc system response to step changes loading; no stabilizing control.

in

generator bus

1966

PETERSON AND KRAUSE:

oscillates about the new operating point illustrating the small amount of damping present in this ac-dc system. After establishing steady-state operation at this increased power angle, the input torque was stepped from 4.25 to 3.75 per unit. When the system had again established steady-state operation, the input torque was stepped from 3.75 per unit to the original value of 4.0 per unit. This switching sequence was used for all studies wherein the system response to generator input torque disturbances was investigated. The effects of load switching at the generator bus are illustrated in Fig. 5. From the initial operating condition the resistance was changed so that the power consumed by the unity power factor load decreased from 2.0 to 1.75 per unit (1.1 per unit bus voltage). After steady-state operation was re-established, the resistive load was switched from 1.75 to 2.25 per unit followed by a step change in bus loading from 2.25 per unit to the original 2.0 per unit. The input torque was maintained at 4.0 per unit throughout this study. This same sequence of load switching was used for all studies involving load switching at the generator bus. Performance of an A C-DC System during Changes in System Power-Stabilization Control Incorporated The computer tracings given in Figs. 6-11, demonstrate the performance of the ac-dc system with Types A, B, and C controls incorporated. More specifically, Figs. 6 and 7 illustrate the performance of the ac-dc system during changes in system power with a Type A control; Figs. 8 and 9-Type B, and Figs. 10 and 11-Type C. In each case, the initial operating condition was that described previously. System response to changes in the generator input torque are shown in Figs. 6, 8, and 10. The system performance during load switching at the generator bus are given in Figs. 7, 9, and 11. In order to illustrate the complete characteristics of these controls it would be necessary to consider variations in all of the control parameters (Ko, K1, and K2). For example, the characteristics of a Type C control and the influence of each control parameter could be obtained only after an extensive study wherein independent variations of Ko, K1, and K2 are considered. This type of a study is important but seems impractical at this time. In the studies shown in Figs. 6-11, satisfactory system response during changes in system power was obtained by adjusting Ko for the Type A control. With Ko maintained at this value, K1 was adjusted to give acceptable system response for the Type B control. Similarly, Ko and K1 were fixed and K2 adjusted to obtain satisfactory system response with the Type C control. A comparison of Figs. 6 and 7 with Figs. 4 and 5, respectively, reveals the system damping which is possible by incorporating a Type A control. The value of Ko which yields this near critically damped response of the power angle was found to be 0.75. Variations about the new operating point, after a system disturbance, is determined primarily by the characteristics of the voltage regulator.

DAMPING OF POWER SWINGS

1235

The action of a Type B control is shown in Figs. 8 and 9. In this case, Ko was held at 0.75, and K1 was adjusted so as to minimize the change in power angle as well as the overshoot in the dc power as the dc system accepts the larger part of change in system power. The value of K1 used in Figs. 8 and 9 was 0.66. Figures 10 and 11 show the system response with a Type C control incorporated. Ko, K1, and K2 were set at 0.75, 0.66, and 0.19, respectively. The value of K2 was selected so that the power angle returned to its original value in a relatively small time interval with satisfactory control of the dc power maintained. The computer recordings shown in Figs. 12 and 13 demonstrate system response with controls which have not been considered previously. The tracings shown in Fig. 12 illustrate the system response during input torque disturbances with a control incorporated wherein KD = K2 = 0 and K1 = 0.66. Since Ko = 0, the system is quite oscillatory. The sustained oscillations after the initial step change in generator input torque is attributed to the large value K1 which at this increased dc power level (small delay angle) causes alternate control of the current in the dc system by the rectifier and the inverter. At the reduced dc power level, the rectifier is able to maintain control and system oscillations are damped out after several seconds. Thus, K1 adds some damping to the system. This feature is further illustrated in Fig. 13 wherein Ko = 0.75 and K1 = 0. It was found that the system was unstable with K2 set at the value used in Figs. 10 and 11. In order to obtain the system response to input torque disturbance shown in Fig. 13, it was necessary to reduce K2 to 3 X 10-4. With this low value of K2, it required a longer time interval for the ac system to return to its original power angle than in Figs. 10 and 11 where K1 = 0.66 and K2 = 0.19.

Performance of AC-DC System during a Break in the AC Line-Type C Control If the dc system is capable of accepting the ac transmitted power without failure, Type B and C controls will limit the power angle between the mnachine and the infinite bus when the ac power flow is disrupted. In the case of a Type B control, a deviation from the original power angle will occur in the steady-state, however, with a Type C control the power angle will return to its original value. The computer recording shown in Fig. 14 illustrates the system performance and the action of a Type C control (Ko = 0.75, K1 = 0.66, and K2 = 0.19) during a loss of transmitted ac power. In this study the input torque was fixed at 3.5 per unit with an initial transmitted ac power of approximately 0.5 per unit. The loss of ac transmitted power was simulated by suddenly de-energizing the ac line. The action of Type C control causes the power angle to return to its original value after a transient deviation of approximately eight degrees. The ac line was re-energized in approximately nine seconds after' the break. The electrical transients of the ac line decay relatively fast and the system readily established its initial mode of operation.

1236

IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS

DECEMBER

2.0r 2.0

I1.

1.0.

EXCITER VOLTAGE

EXCITER vOLTAGE

BUS VOLTAGE (qR-GtIS)

BUS VOLTAGE qIR-Gols)

L

L.r I

I

Vq R

Vq;-J

SEC.

-.O

1.0 SEC.

VKIF

O

1

RECTIFIER VOLTAGE 2.0

2s 'N

Pt

IR

RECTIFIER CURRENT

2

AC

RECTIFIER CURRENT

t{

1.0 2.0 r

POWER-TRANSMITTED

PtS

AC POWER-TRANSMITTED

L

'LF

20

2.0

DC POWER- RECTIFI ER

DC POWER-RECTIFIER

Pdc 1.0 0

05

ACCELERATING

-0.!

0.5

TORQUE I-INPUT TORQUE

I-INPUT TOROUE

DECREASED TO 3.75 PU

INCREASED TO 4.25 PU

L

TORQUE

ACCELERATING

-INPUT TORQUE INCREASED T0 4.25 PU

|.-INPUT TORQUE

INCREASED TO 4.0 PU 6

6

Fig. 6. The ac-dc system response to step changes in generator input torque-Type A control; Ko = 0.75.

|-INPUT TORQUE

DECREASED TO 3.7SPU

-INPUT TORQUE

INCREASED TO 4.0PU

4- r POWER ANGLEL P0W

Fig. 8. The ac-dc system response to step changes in generator input torque-Type B control; Ko = 0.75, K1 = 0.66. 2.0

2.0

E

E0 EXCITER

1.0

VOLTAGE

BUS VOLTAGE

I

EUCITER

BUS VOLTAGE q R-aXISI)

(qp-oxis) -I

F 1.0 SEC. V

RECTIFIER VOLTAGE

VR. OA

L

o

-|f 1.0 SEC.

'4 *CL1

V R

VOLTAGE

O.

RECTIFIER VOLTAGE

0:1

2.o[

2.0r

RECT IF ER CURRENT

IR

RECTIFIER CURRENT

,.0

oL

L.

2.0

2.0 cc

-

r-

AC POWER-TRANSMITTED

pt

.0E

AC POWER-TRANSMITTED b

Pt 2.01

Pdc

2.0

DC POWER -RECTI F IER

DC POWER-RECTIFIER

Pd.,<

o

0.5r T,, 0O -Q.5

ACCELERATING TOROUE LOAD I-RESISTIVE DECREASED TO 1.7S PU

LOAD I|-RESISTIVE INCREASED TO 2.25 PU

I-RESISTIVE LOAD2.0 DECREASED TO

6 POWE R

LOAD

|-RESISTIVE

LOAD INCREASED TO 2.25 PU

-RESISTIVE

DECREASED

LOAD

TO

2.0

PU

I POWER ANGLE

A N GLE

Fig. 7. The ac-dc system response to step changes in generator bus loading-Type A control; Ko = 0.75.

|-RESISTIVE

TORQUE

DECREASED TO 1.75 PU

PU

0

6 6

ACCELERATING

Fig. 9.

The ac-dc system response to step changes in generator bus loading-Type B control; Ko = 0.75, K1 = 0.66.

1966

2.0

E

2.0

o.0|

E,

EXCI TER

.

i

EX0O

- 1.0

2.0

L vqR'it v|

I

R

0~

.OI

~~

BUS VOLTAGE (qR-axsl)

I 0 -4

-

'

1.0 SEC.

RECTIFIER VOLTAGE

0.8

2.0.

RECTIFIER CURRENT

RECTIFIER CURRENT

L_ 2.0 .

2.01

ptQC

ECITER VOLTAGE

SEC.

RECTIFIER VOLTAGE

0.8[

IR

VOLTAGEI

BUS VOLTAGE (qR-OxiS)

Vq0

'B

1237

PETERSON AND KRAUSE: DAMPING OF POWER SWINGS

_

1.0

P1

AC POWER-TRANSMITTED

L

1:0

DC

2.0

2.0.

POWER-RECTIFIER

Pd. 1.0,

Pdc t_

-f

L

p 0.5

Ta

PUT

T.

TORQUE I-INPUT DECREASED TO 3.75 PU

TORQUE

INCREASED TO 4.25 PU

go*f 40 D

r..

ACCELERATING TORQUE

0.5

TORQUE

ACCELERATING

o -0.5,

-_

DC POWER -RECTIFIER

0

-INPUT TOROUE

INCREASED TO 4,0 PU

...

-40

POWER ANGLE o

L

-|INPUT TORQUE DECREASED TO 3.75 PU

IRPUT TORQUE

INCREASED TO 4.0 PU

PO,

9U

Fig. 10. The ac-dc system response to step changes in generator input torque-Type C control; Ko 0.75, K1 = 0.66, K2 0.19. =

|_N PUT TORQUE INCREASED TO 4.25 PU

601ol

~~~~~~~~~~~~~~~~~~~POWER ANGLEL

Fig. 12. The ac-dc system response to step changes in put torque; Ko K2 0, K1 0.66. =

=

=

generator in-

=

2.0r

EX 1.

EXCITER VOLTAGE

1.0

EXCITER VOLTAGE

BUS VOLTAGE (qR-RXIl)

v* '-.0

-~~~~~~U 1.0 SEC.

VR6}

20.02.0 1

_9 L3L16

VOLAG

R.

-.O SEC.

1.6 RECTIFIER

VOLTAGE

RECTIFIER CURRENT

VR:0.

RECTIFIER VOLTAGE

0B 2.0

RECTIFlIER

CURRENT

IRI. 2.0

AC POWER -TRANSMITTED

pt

L DC

2.0

P.t

WT AC POWER-TRANSIUITTED

..O.

POWER-RECTIFIER

0

.0 0.5S

To

2

ACCELERATING

ACCELERATING

05

TORQUE

TORQUE

To o59

l s-RESISTIVE

DECREASEOD

LOUD TO I7T

RESIP5UT

*-RESISTIVE

I V NECLOAgt A

INCREASED

LOAD

-

25 TO 2025P

RESISTIVE

D PUDECREASES -RE S

TO

LOAD TO

20P-INPTTRU S T |VS

A2.0

6

40 POWER

INCREASED TO

OER

=

=

=

NPTTOQE-INPUT

DECREASED

TORQUE

INCREASED TO 4.0 PU

TO 3.75 PU

p

ANGLE

Fig. 11. The ac-de system response to step changes in generator bus loading-Type control; Ko 0.75, K1 0.66, K2 0.19.

4.25 PU

Fig. 13.

ANGLE

The ac-dc system response to step changes in generator input torque; Ko = 0.75, K1 = 0, K2 3 X 10-4. =

1238

1EEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS

REFERENCES

2.0

E,

I.G0

EXCITER VOLTAGE

BUS VOLTAGE IqR-xisl) 1.0

VqR

F-t0

VA-

0.8

SEC.

RECTIFIER YOLTAGE

oL2.0

RECTIFIER CURRENT

Is

0

2.0

AC POWER-TRANSMITTED

p t

0

2.0

DC POWER-RECTIFIER

1.0 0

ACCELERATING

T

. -0.5

DECEMBER

LINE I-ACDEENERGIZED

TORQUE

-AC

LINE

REENERGIZED

so,-. 401

POWER ANGLE

Fig. 14. Performance of ac-dc system during break in ac line-Type C control; Ko = 0.75, K1 = 0.66, K2 = 0.19.

SUMMARY AND CONCLUSION A relatively simple case of a single machine tied to an infinite bus through parallel ac-dc lines has been studied in detail and typical results presented in this paper. These results make it clear that the electromechanical oscillations following a major disturbance are influenced markedly by the presence of the dc line. Furthermore, with proper attention to the transfer function properties of the feedback loop in the dc line, substantial beneficial damping of power swings is achievable. It is not the intention to draw far-reaching conclusions relative to the effects of dc lines in composite ac-dc systems at this time. Such conclusions must await results, and evaluation thereof, of far more comprehensive studies than these reported in this paper. It is hoped, however, that results of studies of simplified systems in rigorous detail as in this case will continue since it is believed that a useful purpose is served in setting forth the basic differences between the ac and dc line dynamic power transmitting properties. A knowledge of these properties, once grasped, can aid in establishing confidence as analysis is extended to more complex systems, each of which must, in the final analysis, be studied as a separate problem. ACKNOWLEDGMENT This study was performed on the analog computer at Allis-Chalmers Manufacturing Co., Milwaukee, Wis. The authors wish to thank Mr. A. E. Kilgour of Allis-Chalmers for his help in preparing this paper for publication.

[1] E. Uhlmann, "Stabilisation of an A. C. link by a parallel D. C. link," Direct Current, pp. 89-94, August 1964. [21 H. A. Peterson and P. C. Krause, Jr., "A direct- and quadrature-axis representation of a parallel AC and DC power system," IEEE Trans. on Power Apparatus and Systems, vol. PAS-85, pp. 210-225, March 1966. [3] H. A. Peterson, P. C. Krause, Jr., J. F. Luini, and C. H. Thomas, "An analog computer study of a parallel AC and DC power system," IEEE Trans. on Power Apparatus and Systems, vol. PAS-85, pp. 191-209, March 1966. [4] H. A. Peterson, D. K. Reitan, and A. G. Phadke, "Parallel operation of AC and DC power transmission," 1964 IEEE Internat'l Cony. Rec., vol. 12, pt. 3, pp. 84-89. [5] M. Riaz, "Analogue computer representations of synchronous generators in voltage-regulation studies," Trans. AIEE (Power Apparatus and Systems), vol. 75, pp. 1178-1184, December 1956. [6] P. C. Krause, "Simulation techniques for unbalanced electrical machinery," Ph.D. dissertation, University of Kansas, Lawrence, 1961. [7] R. H. Park, "Two-reaction theory of synchronous machines-generalized method of analysis; Part I," Trans. AIEE, vol. 48, pp. 716-727, July 1929. [8] C. Concordia, Synchronous Machines. New York:Wiley, 1951. [9] R. A. Hedin, "The dynamic behavior of a synchronous generator with a rectifier load," M. S. thesis, University of Wisconsin, Madison, 1964. [10] C. Adamson and N. G. Hingorani, High Voltage Direct Current Power Transmission. London: Garraway, Ltd., 1960. [11] C. Concordia and L. K. Kirchmayer, "Tie-line power and frequency control of electric power systems," AIEE Trans. (Power Apparatus and Systems), vol. 72, pp. 562-572, June 1953. [12] ,"Tie-line power and frequency control of electric power systems-Part II," AIEE Trans. (Power Apparatus and Systems), vol. 73, pp. 133-146, April 1954. [13] E. Uhlmann, "The representation of an H. V. D. C. link in a network analyser," CIGRE, vol. III, paper 404, 1960.

Discussion Edward W. Kimbark (Bonneville Power Administration, Portland, Ore.): Oscillations in a power system of the type considered in the paper can be divided into two types: large and small. The large oscillations are caused by big disturbances, such as severe short circuits. The main danger is that the disturbance may be nonoscillatory, that is, that synchronism may be lost. Clearly, an analysis based on linearization of the sinusoidal power-angle curve is not valid for such large disturbances. The small oscillations can be started by little disturbances. If they decay, there is no serious problem. The danger is that because of net negative damping they may grow into large oscillations. Linear analysis can show whether small oscillations will grow into big enough ones to be nuisances. Negative damping can be caused by lags in governors, in excitation control systems, or by too low a ratio of reactance to resistance in ac transmission lines. Unless the negative damping is offset by positive damping, either that inherent in the system or that added artificially, the oscillations will grow. There are several possible methods of introducing artificial positive damping. One was discussed in the paper, namely, the modulation of the power on a parallel de line. It seems that this method is very effective if the de line is available. However, artificial damping may be needed in power systems having no dc line or in those having one which is out of service for maintenance or repair. Another method is to modulate the power input of one or more prime movers driving ac generators. This is accomplished by periodically varying the throttle opening of a steam turbine or the gates of a waterhweel. The control signal may be derived from power flow on the ac tieline or from frequency (speed) deviation. This method is in

Manuscript received February 14, 1966.

IEEE TRANSACTIONS ON POWER APPARATUS AND SYSTEMS

VOL.

use and has proven satisfactory. An entire session of this meeting is devoted to it [1]-[4]. A third method [5],[6] is to inject an auxiliary signal into the generator voltage regulators in addition to the usual ac terminal voltages. The auxiliary signal may be almost any quantity which varies during the oscillation to be damped. One such signal is the rate of change of terminal voltage. A fourth method is to vary periodically the transfer impedance of the ac transmission link, for example, by switching a series capacitor bank alternately in and out of the circuit. The transmission system

should be strengthened (by insertion of the capacitors) while the machines at the two ends are swinging apart and weakened (by removal of the capacitors) while they are swinging together. The principal practical obstacle to the application of this method is the lack of a high-voltage switch suitable for continual operation. The same general method is effective for defense against large disturbances such as the complete loss of the dc line in the system considered in the paper as a result of a permanent 2-pole fault [7]. Damping of large disturbances can be controlled so as to be "dead-beat" [8]. If artificial positive damping is required, it should be applied redundantly as to methods or locations, so that if one generator or line having such provision be out of service the remaining ones will still provide adequate damping. One bipolar dc line, controlled as suggested in the paper, would be adequate except in the rare event of loss of both poles. Two dc lines or one dc line plus one of the other methods would be better. REFERENCES [1] F. R. Schleif, G. E. Martin, and R. R. Angell, "Damping of system oscillations with a hydrogenerating unit," IEEE Trans. on Power Apparatus and Systems, to be published.

PAS-85,

DECEMBEBR, 1966

NO. 12

[2] F. R. Schleif and J. H. White, "Damping for the NorthwestSouthwest tieline oscillations-An analog study," this issue, page 1239. [3] E. A. Gissel, T. B. Hardy, and E. F. Timme, "Performance of the Northwest-Southwest intertie," presented at the 1966 IEEE Winter Power Meeting, New York, N. Y., January 30February 4. [4] J. S. Hooper, G. E. Adams, and J. C. Conder, "Damping of system oscillations with steam electric generating units," presented at the IEEE Power Meeting. [51 P. Althammer, "Questions of stability of E.H.V. transmission systems," Brown Boveri Rev., vol. 51, no. 1/2, pp. 10-20, January February 1964; esp. p. 15. [6] H. M. Ellis, A. L. Blythe, J. E. Hardy, and J. W. Skooglund, "Dynamic stability of the Peace River transmission system," IEEE Trans. on Power Apparatus and Systems, pp. 586-600, June 1965. [7] E. W. Kimbark, "Improvement of system stability by switched series capacitors," IEEE Trans. on Power Apparatus and Systems, vol. PAS-85, pp. 180-188, February 1966. [8] 0. J. M. Smith, "Optimal transient removal in a power system," IEEE Trans. on Power Apparatus and Systems, vol. PAS-84, pp. 361-74, May 1965.

H. A. Peterson and P. C. Krause, Jr.: The authors appreciate the comments of Dr. Kimbark, who has effectively summarized the methods of providing damping of power swings in large systems. We concur in his concluding remarks that if artificial positive damping is required, it should be applied redundantly so that at all times such damping requirements can be satisfied.

Manuscript received March 7, 1966.

Damping for the Northwest Southwest Oscillations-An Analog Study -

F. R. SCHLEIF,

SENIOR MEMBER, IEEE, AND

Abstract-Oscillations which developed on the initial transmission tie between the Northwest and Southwest systems brought about trip-outs and threatened to limit its usefulness. The analog study described reveals much about the nature of the oscillations and shows some unusual relief measures to be possible. While sources of the negative damping were indicated to be such that correcting them directly might be impracticable, means of offsetting them with stabilizing effort developed by special control of fast responding generation are proposed. The required stabilizing effort is indicated to be within the capability of a large nonreheat steam unit. This amount is startlingly small for influencing such large systems.

Paper 31 TP 66-13, recommended and approved by the Power System Engineering Committee of the IEEE Power Group for presentation at the IEEE Winter Power Meeting, New York, N. Y., January 30-February 4, 1966. Manuscript submitted September 22, 1965; made available for printing November 9, 1965. F. R. Schleif is with the Electric Power Branch, Division of Research, Office of Chief Engineer, Bureau of Reclamation, Denver, Colo. J. H. White is with Sargent and Lundy, Engineers, Chicago, Ill.

J. H. WHITE, MEMBER,

Tieline

IEEE

INTRODUCTION I NTERCONNECTED power systems of the Northwest, predominantly hydro, and interconnected power systems of the Southwest, predominantly steam, were initially linked together in October 1964 through a transmission tie of modest relative capacity. Although the initial tie comprised of one 230-kV transmission line and soon augmented by another longer 230-kV line is of respectable

capacity considered alone, the total tie capacity was small compared to the 30 000- to 40 000-MW total for the systems it interconnected (Fig. 1). Soon after the first closure of this tie at Glen Canyon Powerplant, Arizona, a natural frequency of load swing at about 6 c/min was observed on the tie. This tie operated satisfactorily for a time, but trip-outs developed due to rather wide 3-c/min oscillations of the Northwest system frequency.

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