Nov 21, 1978  basic principle of the method is that the dc link is operated in order to maintain constant active power flow in the ac tie lines and constant ...
416
IEEE Transactions
Power Apparatus and Systems, Vol.PAS98, No.2 March/April 1979 DAMPING OF POWER SWINGS IN AC TIE LINES USING A PARALLEL DC LINK OPERATING AT CONSTANT REACTIVE POWER CONTROL on
G.D.Galanos
N. A. Vovos
Power Systems Laboratory School of Engineering Patras Greece. University of Patras ,
Abstract damping of power
This swings
paper presents a in the ac lines
method for the interconnecting
utilising the fast electronic power flow control characteristics of a parallel dc link. The basic principle of the method is that the dc link is operated in order to maintain constant active power flow in the ac tie lines and constant reactive power consumption at the converter terminals. The proposed control strategy was tested using dynamic simulation techniques and the results obtained show that ,under certain condithe contribution of a parallel dc link to the tions stability the ac system can be significant. two power systems
,
,
INTRODUCTION Most of the existing dc transmission schemes have been decided for purely technical and economic reasons and fall into one three main groups: 1. Transmission of energy over long distances from remote sources of generation to the load centers ,or to strong points of an ac transmission system. In these cases dc transmission is the only technical solution. 2. Interconnection of systems where a long cable circuit is essential and where it is not only technically preferable but economically more attractive to use dc transmission. 3. Coupling between systems of different frequency, or bulk transfer without increase in shortcircuit duty and to defer the need for higher on the switchgear network voltages. The electronic control of power flow in a dc link however offers the possibility of another application , thus to interlace dc transmission with closely interconas yet nected ac systems and to use the advantages in controlled load flow and stabilargely unexploited lity improvement (1),(2),(3),(4). mainly analog computer simuFrom earlier studies it became apparent that, with appropriate conlations trol,the stability of the acdc system could be improved for various cases of fault conditions and other disturbances (5),(6). The systems considered, consisted of a machine connected to an infinite bus via an acdc transmission network (7),(8),(9),(10),(11). The possibility of improving the stability of a consisting of two control areas interconpower system by nected via ac tie lines and a parallel dc link suitable converter control strategy is investigated in the following sections. The important feature of the reactive proposed firing control method is that the power consumption at the converter terminals remains ,
affected by the power swings in the dc line. The damping of electromechanical oscillations can be effectively achieved by a method (6) using dc power feedback control. The proposed converter control scheme combines this method and the requirement for constant reactive power consumption by the converter plant. The interconnected acdc system is represented by dynamic simulation and the control method is tested for various disturbances. The same tests are carried out for the case of replacing the dc link by an equivalent ac line. From the comparison of these results it is shown that the proposed control method is effective in achieving fast and stable transient response of the system in the presence of large disturbances.
at the converter busses is not
LIST OF PRINCIPAL SYMBOLS
f(i
Vdi Li id
a
R
The index i takes the values areas 1 and 2 respectively.
,
,
1
or
2
for
the
control
DESCRIPTION OF THE SYSTEM STUDIED
,
,
The rms line voltage at bus i Phase angle of the voltage at bus t Angular velocity of the area i Frequency of the area i Direct voltage at the converter i Leakage inductance of transformer i Direct current Angle of delay Angle of advance dc line resistance
Vi 8i
A power system consisting of two control areas interconnected via two ac tie lines and a dc interconnection is shown in fig. 1. All the generators in each control area are assumed to constitute a coherent group.
,
,
practically constant
over a
wide
range
of
real
power
flows in the link ,and thus the magnitude of the voltage
Fig. A paper reccarended and approved by F 78 2347. Power System Engineering Comnittee of the the :EEE Power Engineering Society for presentation at the IEEE PES Winter Meeting, New York, NY, January 29 February 3, 1978. Manuscript submitted September 6 1977; made available for printing November 28, 1977.
1.
The system studied Converter stations: sixpulse configuration Ac system frequency: 50 Hz
In the event of a change of the area loads by APDii the area changes its generation by APGi due to the action of the turbine controllers. The net power surplus APDi is compensated by: in the area APGi
00189510/79/03000416$00. 75 (

1979 IEEE
417
The change of the kinetic energy of the area at the rate dWkin,i/dt The change of the load, due to the variation of the frequency, equal to Di = DPDi/Df puMW/Hz The variation of the export of power via the tie lines APtie,i , thus:
1.
2. 3.
APGiAPDi
dt (Afi)+DiAfi+zAPtie,i
=
(1)
where Hi is the per unit inertia constant and fo the nominal frequency. The equation (1) can be written as follows:
dt Afi
p tiDe,t i dt
=
where T
=
2H.
foDi
and
I i Tpi Kpi~ Tf ~~~~
1K
(2)
1
K. Pi
Di
Assuming that the magnitudes of the bus voltages V1jl and 1V21 remain constant, a reasonable assumption since the converters operate on constant reactive power control, the variation of power transmitted by the ac tie lines is: d
dt
pV IV21 2nt Xi
ptie,i
cos
(8142) (AflAf2)
The block diagram of each control area, reheating turbines is shown in fig. 2.
assuming
The differential equations (2) to (6) describe the ac part of the system. The characteristics of the power system under study were taken as follows:
Control area 1
Control area 2
H1 =5.00 sec R1 =2.40 Hz/pu MW D1 =0.01 pu MW/Hz
H2 =7.00 sec R2 =1.80 Hz/pu MW D2 =0.015 pu MW/Hz
TG1=0.08 sec TT1=O.3 sec
TG2=0.09 TT2=0.04 K2 =0.3
K1 =0.227 Tp1=20 sec/pu MW Kp1=1O° Hz/pu MW
sec sec
TP2=18.67 sec/pu
MW
Kp2=66.67 Hz/pu MW
DYNAMIC SIMULATION
OF THE DC LINK
The differential equations describing the dc link are automatically assembled using tensor techniques (12) (13), (14) to deal with the time varying topology of the network caused by the switching action of the converter va 1 ves.
(3) no
L
R
id(1)
R
VC

L id(2)
C
Vd2
Vd 1
Fig. 3. The dc link
The generalized loop impedance matrix (14), of the system shown in fig. 3 is assembled as follows:
rtie, i
APTi (s)=APGi (s)
Z(1)
0
0
0
0
B1
0 B2
Fig. 2. The block diagram of area i From the block diagram the differential equations of the system are obtained as follows: d dt
dt Yi dt
=
ci
KiAfi (P
=
Gi
where:TGi TTi
TTi
is is Tpi is Ki the
(Z) =
0
Z(2)
0
+ 0
(4) RI
Af iyi)
Gi )
(5) Al
A2
A3
0
0
0
C1
C2
0
0
(7)
(6)
the time constant of the governor the time constant of the turbine the time constant of the power system gain of integrator of the frequency error.
where (Z(1)) and (Z(2)) are the matrices of the converters 1 and 2 respectively,(Al),(A2) and (A3) are calculated from the state equations of the system and (B1), (B2),(Cl),(C2) are calculated from the equations of the
418 dc voltages.The tensor (Cn) that relates the independent currents to the loop currents is generated as follows:
START I Read c i rcu i t data
0
0
T=O
T=T+H
(Cn)
=
0
Cn (2)
0
0
0
1
(8)
Yes
Change the load
The loop impedance matrix for the state becomes (14)
particular conduction
(Zn) = (Cn)t(Z)(Cn) = (Rn)+(pLn)
KuttaMerson numerical intergration procedure
(9)
Using the CRPC method calculate ctfl
and the differential equations of the link are:
(Pln)
=
(Ln) 11(Vn)

(Rn)(In)}
(10)
The dynamic model, of the system under consideration, was implemented by a digital computer program the flow chart of which is shown in fig. 4.
The analysis of a power system, consisting of two control areas interconnected by an acdc transmission network, was carried out (6) under the following assumptions: The transmission system is lossless. The loads are independent from the frequency, the system damping is zero and the powerfrequency controllers are neglected. Under these assumptions it was proved theoretically that damping of the power swings in the tie lines is achieved using the following control procedure:
tv+1
APdc
tv+ aAf+bJ &fdt+cf/ff(dt)2 tv tv
(1
)
where:
=
K[a
dt W1+bW,+ 2 cW2(tv+1tv)]
K =
xl x2
Wl
V+1
W2tPtiee
tie,2 tie,1 V+1
Pv1
1+Ptie,2 tie, 1
Yes
Form
is the estimatio
[VnI,
7
[Rn],
[Ln], [Ln]1
KuttaMerson numerical
intergration procedure
No
Calculate all branch currents Estimate turning off thyristor and time of extinction
Thyristor extinction control  is there any extinction
Yes
Calculate all
No
thyristor voltages
t or store resto
iT=T+H
No
Thyristor ignition
im
controll
(12)
O (xl +x2) IV 1 V21Io(5182)
tie,1
Construct tensor [Cn]
Estim
where tV and tw+1 are two successive control instants. The first term of the right hand side influences the transient behavior of the system and has no effect on the steady state. The second term influences the steady state according to the value of the coefficient b which in fact determines how the dc and ac lines share the extra load in the steady state. Finally the third term forces the dc line to carry all the extra load so that when the steady state is reached the phase angles of the bus voltages return to their innitial values. The control equation (11) using equation (3) can be written as follows:
APdc
Change the
state vector
accu
THE CONTROL STRATEGY
=
No
isTT
tie,2
tie,2
This equation is suitable for real time control since APdc is obtained by measuring the power flow in the ac tie lines at discrete control instants.
 es rEst imate turn ing on thyr istor and ignition time
sChange the
state
vector
Fig.4. The flow chart of the dynamic simulation program
419
CONSTANT REACTIVE POWER CONTROL
All the existing dc transmission schemes are operated with constant(minimum) extinction angle control at the inverter in order to minimize reactive power consumption and dc power flow control at the rectifier side. This type of control is suitable for the applications classified in groups 1,2 and 3 in the introduction of this paper. For the proposed application however the link must be operated in a way permitting the fast increase or degrease of dc power flow in either direction with the minimum effect on the state of the ac system, defined by the magnitudes and angles of the voltages of the area busses 1V1, 6l1 62. The requirement for constant 61 and 62 is taken care by the third term of the right hand side of equation (11). In order to keep the bus voltages constant the reactive power consumption by the converter terminals must be independent from the dc power flow in the link. Thus the converters must be operated at constant reactive power control. The converter firing angles in the steady state are expected to be larger than in the case of conventional control systems in order to permit fast of change of dc power in either direction in the event ac system disturbances. The constant reactive power control strategy is derived from the following steady state analysis. The dc power is given by:
IV21,
(x 1 COsx2COs1)
pdc
(R+yj+Y2)2
where:
x1 = 372"
El
X
3w1Lj
Yi =
[(R+y2)x1cossa+Y1x2cosr3)]
Y2
1n
(13)
3 4 E2
3_2L2 T1
and hence the variation of dc power as a function of the initial values of the firing angles and neglecting higher order terms is given by:
APdc
1
2IPisinh+P2sinR43]
(14)
(R+yl+y2)2
where: P1 =
P2
=
2(R+y2)xl2cosQ+(R+y2y1)xlx2cosD
2ylx22cosf+(R+y2yl)xlx2cosa
The apparent power of the rectifier at the time
Sv= Xldv
xi[x1cxl[ 1
tv is:
(15)
=
The apparent power at the time instant tv+l is:
[x xcs(a+&i)x2cos(
v+1
V+1
[
+1A3)
R+y1 +Y2J
(16)
neglecting higher order terms we obtain: 5V+1~v sV _ sV+1 
2sincL&axlx2sinMfg
XilSi aaX X25 i R+y1+y2
(17)
For constant reactive power control: 2
=
(Sv) 2_ (pv) 2
=
(Sv+l) 2_ (pV+l) 2
(18)
Where Qc is the reactive power setting of the rectifier. It must be clarified that reactive power is a quantity defined only in the steady state. The requirement therefore is to maintain constant reactive power consum
ption by the converters during steady state operation. Substituting in equation (18) and neglecting higher order terms we obtain: x s X
X Adc l
i nsinao+x2 si nDAO
From the solution of the equations obtain for the rectifier: M
(19)
(R+y2) xl cosa+yl x2cosO)(14)
[(clcosa+c2cos) (c3cosa+c4cos,)c5]
(19)
and APd
we
(20)
si na [c8cosf+c9cosa] and for the inverter:
[(c6cOsa+c4cOs)(clcosa+c2cos Ap)c7]
sinD[c8cosD+cqcosa]
c
(21)
where cl to cg are constants depending on xl,x2,yl,y2,R. The proposed control procedure is based on the numerical calculation of the next firing instants from the present values of the firing angles and the estimated variation of dc power, according to:
vl
= a
v+
=
+La
= f (aV
e,APdc)
e+A3 f(Ov,ef&,APdc) =
(22) (23)
The firing angle corrections A]L and AD can be calculated independently at the dc link terminals provided that the desired dc power variation APdc is available at both busses. The estimation of APdc according to equation (12) theoretically must be different at the two busses due to the losses of the ac tie lines. In practice however the difference is expected to be so small that for practical purposes the firing angle corrections can be calculated independently at each terminal according to equations (20) and (21). A communication channel is necessary in order to synchronize the two terminals of the system if the accumulated errors over a time interval exceeds a tolerable limit. Finally it must be noted that with the proposed control method the reactive power consumption at the rectifier is expected to be constant. At the inverter terminal however, the reactive power is expected to vary with the dc power within very narrow limits due to the losses of the dc line. From the dynamic simulation results it can be clearly seen that for all practical purposes the reactive power is maintained constant at both terminals using the proposed converter control strategy. DYNAMIC SIMULATION RESULTS The proposed control method was applied to the power system under study operating at the following conditions:
Generation of area 1 PG1 = 1152 MW PDl = 1000 MW Load of area 1 Generation of area 2 PG2 = 1363 MW Load of area 2 PD2 = 1500 MW Voltage phase angle 8182 = 36 deg Power transmitted by tie l ine 1 Ptie,1= 74 MW Power transmitted by tie lI ne 2 Ptie,2= 78 MW Power transmitted by the dc l ink Pdc = 78 MW The power system is subjected to step variations of the area loads and its transient behavior is recorded. The load change occurs at the time instant t = 100 ms. Each test is carried out for the following cases:
420 a. The control areas are interconnected via the ac tie lines 1 and 2 and therefore the system is controlled only by the turbine power frequency control lers. b. The control areas are interconnected via the ac tie line 1 and the dc link operated under the proposed constant reactive power control scheme. For the first test a step change of the loads is applied as follows: APD1 = 140 MW
APD2
The transient behavior of the following figures:
system
is
50 MW
=
shown
in the
1300 200
u)
E 1100
U
IC
80
900
o 70
120
170
220 t ime
)
270 ms
4C
(L2
120
L
go0
l111llllllXl lulX
lfl 1ill1
lllu lllI
OLl
60
30F
70
120
170
220
time
I
270
) msecs
power at the rectifier, the reactiat the inverter and the variation of the firing angles during the control process.
Fig. 6. The reactive ve power
Fig. 5. The dc current of the link, the dc voltage the dc power at the rectifier side.
and
The quantities associated with the dc link were plotted for a time period of 300 msecs in order to allow detailed recording of the various waveshapes. The quantities generaassociated with the power system such as power tion voltage phase angles and frequency are plotted for The smoothing a time period of the order of 8 secs. inductances were taken equal to 0.1 Henry as a worst case study. With larger inductances, as in most practical cases, the dc waveshapes are expected to be smoother.
421
In the case studied, the switching of load is such that the control causes the reduction of power transmitted by the dc link. It can be clearly seen that in the controlled case the power swing on the ac line is completely damped, the phase angles of the bus voltages remain constant, the frequency dip is considerably reduced and the two areas are swinging coherently. Finally it can be observed that the reactive power remains constant at the dc terminals. For the second test a step change of the area loads is applied as follows:
1550 F . ~
7
1350
a%.7
/
~
b
~

CX