Download Improvement of Voltage Stability by the Advanced High Side Voltage

Improvement of Voltage Stability by the Advanced
High Side Voltage Control Regulator
Hitomi Kitamura, Masaru Shimomura (Member)
John Paserba (Member)
Mitsubishi Electric Corporation
Kobe, Japan
Mitsubishi Electric Power Products, Inc.
Warrendale, Pennsylvania, USA
Abstract: An advanced High Side Voltage Control (HSVC)
regulator that can improve power system voltage stability by adding
supplemental control to conventional generator excitation system
control has been developed. This paper describes the principles,
characteristics, and advantages of applying advanced HSVC in
comparison with a conventional automatic voltage regulator (AVR)
or a static var compensator. When applying the advanced HSVC,
a high side voltage of a step-up transformer can be controlled to a
set value and maintained to a higher value than with conventional
excitation systems. This advanced HSVC is realized without any
feedback signal from the high voltage side of a step-up transformer
(i.e., no high-side voltage measurement required). Stable parallel
operation among adjacent generators is also possible. In addition,
with an adequate phase compensating function added to the
advanced HSVC, oscillatory stability can also be improved.
II.
PRINCIPLE & CHARACTERISTICS of HSVC
The configuration of the advanced HSVC is shown in
Figure 1. The basic principle of the advanced HSVC on a
simple power system, shown in Figure 2, is as follows.
n : Ratio of the step-up transformer
Xt: Reactance of the step-up transformer (pu)
Xe: Reactance of the power system (pu)
Xdr: Voltage Droop rate (pu)
VH
Tap
position
HSVC Control Block
S.Tr
＋
f (Vg,Q,Xt,Xe,Xdr,Iq0,n) ＋
−
Keywords:
Secondary Voltage Control, Automatic Voltage
Regulator (AVR), Static Var Compensator, Line Drop Compensator
(LDC), Excitation System, Voltage Stability, Oscillatory Stability.
I.
INTRODUCTION
Voltage instability of power systems is becoming a more
serious problem with the ever-increasing utilization and
higher loading of existing transmission systems. Various
countermeasures, i.e., synchronous condensers, shunt
capacitors, static var compensators, etc., have been
increasingly utilized.
Other effective alternatives, such as the line drop
compensator (LDC) that compensates the voltage drop by a
reactive current, or the power system voltage regulator
(PSVR) that uses a high side voltage as a feedback signal [1],
have also been applied as control methods of the high side
voltage of a step-up transformer (S.Tr) via a generator
excitation system.
The advanced High Side Voltage Control (HSVC)
regulator that controls the high side voltage of a step-up
transformer has been developed with no requirement for any
direct feedback signal (i.e., measurement) from the high
voltage side of a step-up transformer. Though the control
principle of the advanced HSVC is similar to that of the LDC,
the advanced HSVC is superior to the traditional methods
with respect to control performance, reliability, and economy,
as described in this paper.
VHref
AVR Control
Block
EXC
G
Figure 1.
Construction of HSVC control system
Vg
G
＋
Iq
Figure 2.
S.Tr
VH
Xe
Vs
Xt
~
Simple power system
1) Basic Function
With a target setting value of the high side voltage
(VHref), the generator terminal voltage (Vg), i.e., the low
side voltage, is controlled to be:
Vg=VHref + (Xt - Xdr) Iq
(1)
Where, Iq = Q / Vg. On this condition, the resultant high
side voltage (VH) becomes,
VH= VHref - Xdr Iq
This characteristic can be expressed as shown in Figure 3.
(2)
4) Compensation Function of the Droop Rate
Corresponding to the Variation of the Tap Position of
the Step-Up Transformer
VH
Slope: - Xdr
VHref
0
Figure 3.
Iq
Characteristics of HSVC
In words, for a target of VHref, the VH can be controlled
to only drop for part of Xdr. This Xdr is necessary for
stable parallel operation among multiple generators.
2) Reactive Current Compensation Function
To equal the VH with VHref at the specified reactive
current (Iq0), a supplemental control can be adopted by using
Iq0. The VH at large reactive current can be kept to a
higher value by this function. The Vg is controlled to be:
Vg = VHref + Xt Iq - Xdr (Iq-Iq0)
(3)
and the VH becomes,
VH = VHref - Xdr (Iq - Iq0)
(4)
This characteristics can be expressed as shown in Figure 4.
VH
Slope : - Xdr
VHref0
0
Figure 4.
Iq0
Iq
Characteristics of reactive current compensation
function
3) Reactive Current Compensation Function by Xe
This function is used to follow Iq0 automatically
corresponding to the variation of the VHref.
For an original setting value VHref0 and an external
reactance Xe, a change of the reactive current ( ∆ Iq0) by a
new setting value VHref is approximately given as (5).
∆ Iq0 = (VHref - VHref0)/Xe
(5)
Therefore, this function can be realized by adding (5) to
Iq0 of (3) and (4).
When the Vg is controlled by the advanced HSVC, the Vg
may be generally maintained higher than its rated voltage in
order to keep the VH to a constant value. On the other hand,
the continuous allowable Vg is generally up to 5% of the
rated voltage. If the Vg is near this maximum voltage in a
steady state condition, the improving effect of the voltage
stability by the advanced HSVC is reduced by this limitation.
Therefore, in the case of a step-up transformer with LTC, the
cooperative control between the advanced HSVC and the tap
position control can increase the ability of the advanced
HSVC by way of keeping the Vg to around the rated voltage
in steady state condition. The following division of roles
between the advanced HSVC and the tap position control is a
suitable solution to improve the voltage stability.
Control
HSVC
Tap control
Function
Controls VH to VHref
Controls Vg to approximately the rated
voltage
However, the droop rate changes according to the
variation of the voltage ratio and the reactance of step-up
transformer (Xt) by controlling the tap position. As a result,
the parallel operation among adjacent generators may become
difficult due to an unbalance of reactive power on each
generator, which is caused by discrepancy of tap position of
each step-up transformer. For preventing this condition, the
compensation function that keeps the droop rate constant
corresponding to the tap position can be added to the HSVC.
In the case that both a change of the voltage ratio and the
reactance by a change of the tap position is the same value (n),
the basic control function is changed from (1) to (6).
Vg = VHref /n + (Xt - Xdr/n) Iq
(6)
The resultant VH becomes the same as (2).
As mentioned above, although this characteristic is the
same as with the application of LDC, the advanced HSVC has
the following superior features.
• The VHref can be directly set to a desired value from
local and/or remote location.
Accordingly, the
cooperating control of the power system voltage among
multiple generators and/or substations is possible.
• A feedback signal (i.e. measurement) of a high side
voltage is not required.
• The following optional functions can be added to the
HSVC:
Reactive current compensation function
Reactive current compensation function by Xe
Compensation function of the droop rate
corresponding to the variation of the tap position of
the step-up transformer.
- A phase compensation function can be added to
further improve stability by modifying the response
characteristics of the HSVC control loop.
- The oscillatory stability of a power system can be
improved by adding an adequate phase compensation
function.
The performance of the HSVC described in the equations
above was verified by simulation analysis of a step-change of
the VHref from 1.0pu to 1.01pu on a simple power system.
These results are shown in Figure 5 and Figure 6.
Figure 5 shows each resultant characteristic that is plotted
according to the simulation results before and after a stepchange. Where each line shows the theoretical characteristic.
The case A shows the droop characteristics of HSVC that
is represented by (2). In this figure, theoretical and
simulated results are obtained for variations in VHref and Xdr.
These resultant points can be shown to fit each theoretical
line very well.
Case &Condition
Xdr=0.01
[2] [1]
0.1
VHref=1.0
0.2
0.3
Iq（pu）
[3]
0.4
5
4
5
6
1
[2]
1
2
3
time(s)
6
0.3
[3]
Iq(pu)
VH（pu）
VHref’=1.01
VHref=1.0
[2]
Iq0=0.0
0
0.1
Iq0=0.2
0.2
0.3
Iq（pu）
0.2
0.1
0
0.4
0.5
[2]
0
1.015
1
2
3
time(s)
4
5
6
(c) Generator Reactive Current
[4]
1.01
VH(pu)
4
(b) Generator Terminal Voltage
VHref’=1.01
Figure 6.
[2]
1.005
VHref=1.0
1
III.
[2],[4]
Iq0=0.0
0
0.1
Iq0'=0.2
0.2
0.3
Iq(pu)
0.4
Initial Condition : P1=0.9pu, Q1=0.04pu, VHref=1pu
Step : ∆ VHref=0.01pu,
Figure 5.
0.5
[2]
1
0.995
3
time(s)
0.4
1.01
0.995
2
1.01
0.99
0
1.015
1.005
[2]
1
1.02
Xdr=0.01
0.995
0
1
(a) High Side Voltage
Vg(pu)
VH（pu）
[2]
1.005
1
C. Study of effects of
Iqo compensation
function by Xe
Common Condition
Xdr=0.01pu
Iq0=0.0pu
Parameter :
compensation function
[2] off
[4] on(Xe=0.05pu)
[1]
1.01
1.03
VHref’=1.01
1.01
1.02
0.99
0
1.015
B. Study of effects of
Iqo function
Common Condition
Xdr=0.01 pu
Parameter : Iq0(pu)
[2] Iq0=0.0
[3] Iq0=0.2
1.03
Characteristics
A. Study of effect of the
droop rate Xdr
Common Condition
Iq0=0.0pu
Parameter : Xdr(pu)
[1] Xdr=0.0
[2] Xdr=0.01
The case B shows the characteristic of Iq0 function that is
represented by (3). In this figure, theoretical and simulated
results are obtained for variations in VHref and Iq0. In the
case of Iq=Iq0, the VH is the nearer value to the VHref.
Therefore, if the Iq0 is set to the actual value on the normal
operation condition, the VH can be controlled to the VHref.
The case C shows the characteristic of the Iq0
compensation function by Xe. In this figure, theoretical and
simulated results are obtained for variations in VHref and
without or with this function. These results show that the
VH is controlled near the value of VHref both before and
after the change of VHref, according to the theory.
Figure 6 shows the response characteristics of the
advanced HSVC in the case of [2]. The VH reaches the
VHref at about 1.5 sec. and is also controlled smoothly and
stably.
VH(pu)
-
100MVA base
Verification result of HSVC function
0.5
Response characteristics of the HSVC
IMPROVEMENT of VOLTAGE STABILITY
The improving effect on the voltage stability of a power
system by the advanced HSVC was estimated by P-V
characteristics [2, 3]. Figure 7 shows a model of a simple
power system. The resultant P-V characteristics by applying
a static var compensator and the advanced HSVC are
respectively shown as Figures 8(a) and 8(b).
IV.
Vg
Vr
VH
S.Tr
Pr+jQr
G
Xt=0.1pu
Xe=0.3pu
Static Var
Compensator
(1000MVA base)
Figure 7.
IMPROVING EFFECTS OF OSCILLATORY
STABILITY
Simple model of a single machine and one load
The improving effect on oscillatory stability by the
advanced HSVC can be treated via the extended
DeMello/Concordia model [4] shown in Figure 9.
Parameters K7 and K8 can be respectively calculated by (7)
and (8). The simplified model can be expressed as shown in
Figure 10.
K7 =
1.1
− X d′ ido + Vqo
X q i qo + Vdo
Vb sin δ o −
X d′ + X e
Xq + Xe
(7)
Vb cos δ o
1
V(pu)
0.9
K8 =
0.8
0.7
0.6
0.5
800
1000
1200
P(MW)
(a) P-V curve (static
1400
basic case
150Mvar
300Mvar
1600
+
-
-
ω0
1
Ms
K5
s
D
var compensator)
basic case
K8
-
0.8
+ +
K4
HSVC
+
(*1)
K3
0.7
+
Excitation system
0.6
1400
-
+
∆etref
(*1) with phase conpensation function
1200
P(MW)
+
K7
1
1+Td’ s
0.9
1000
+
K6
Xdr=0.025pu
Xdr=0.01pu
1
V(pu)
K1
∆Tm
+
(8)
X d′ + X e
K2
1.1
0.5
800
X e i do + Vqo
1600
Figure 9.
Extended DeMello/Concordia model
(b) P-V curve (HSVC)
K1
Figure 8.
P-V characteristics
-
∆ Tm +
For the static var compensator, the allowable sending end
power increases according to larger capacities of installed
static var compensator, but the “nose” voltage tends to go up.
On the other hand, for the advanced HSVC, the allowable
sending end power increases according to a decrease in the
droop rate and the nose voltage tend to go down. In other
words, the advanced HSVC can also improve the system
voltage characteristics by way of both pushing out the “nose”
of the curve and not getting near the normal operating voltage
of the power system. Moreover, since the advanced HSVC
can be installed on all generators, including already installed
facilities, the existing capability of power plants can
effectively be put to practical use for voltage stability.
Therefore, the advanced HSVC is also superior on economy.
+
-
-
1
Ms
ω0
s
D
+
+
Figure 10.
K1AVR + DAVR
K1HSVC + DHSVC
Simplified model
K1AVR and DAVR are the factors of the synchronizing
torque and the damping torque by the excitation system,
respectively. Similarly, K1HSVC and DHSVC are the
factors of the synchronizing torque and the damping torque
by the HSVC, respectively.
Accordingly, if a phase
compensation function is added such that DHSVC becomes
positive, then this means that damping, D, is added and thus
the oscillatory stability of the power system can be improved.
Figure 11 shows the simulation result in the case of a threephase fault on the high voltage side of step-up transformer
with the advanced HSVC equipped with a suitable phase
compensation function.
Where, in both cases of AVR and
HSVC, a conventional PSS is not applied. This result shows
a good mitigating effect of power system oscillations.
1.4
0.7
0.6
1.2
0.6
1.2
This compensating signal (Vcc) is:
Vcc = Xc Iq
(9)
Because of this reason, the advanced method that reduces
the cross current by the deviation signal between generators is
adopted. This compensating signal (Vac) for G1 is shown in
(10).
Vac = Kc (Iq2 - Iq1)
(10)
0.5
QG(pu)
0.8
0.6
0.4
0.4
0.2
0.0
0
0
1
0
1
AVR
HSVC
2
3
4 5 6
Time(s)
2
3
4
5
Generator Reactive Power(pu)
0.4
0.8
Generator Power(pu)
PG(pu)
1
0.3
0.2
0.1
0.0
0
-0.1
-0.2
-0.2
6
Time(s)
(a) Generator Power
1.4
1.2
1.2
VH(pu)
0.8
0.6
0.4
0.4
0.2
0.0
0
3
4
5
6
Time(s)
1
0
1
AVR
HSVC
2
3
4 5 6
Time(s)
2
3
4
5
0.8
0.8
Vg
0.6
0.4
0.2
6
0.0
0
Time(s)
0
0
1
1
AVR
HSVC
2 3
4 5 6
Time(s)
2
3
Time(s)
4
5
Vg
6
0
Suppressing effect of power oscillation
The performances for two cases of the parallel operation
of two generators G1/G2 and four generators G1/G4 on the
power system shown in Figure 12 were studied.
P2,Q2 G2
P3,Q3 G3
P4,Q4 G4
Figure 12.
Iq2
Iq3
Iq1
Iq2
Iq
Cross current Ic
Vg
Vg
Voltage of G1
Vg=
Vgref
Kc : larger
Vgref
Vg
Cross current Ic
(a) Advanced method
Figure 13.
Voltage of G1
Vcc
Voltage of G2
Voltage of G2
0
Iq1
0
Iq
100MVA base
PERFORMANCE ON PARALLEL OPERATION
P1,Q1 G1
Vgref
(d) High Side Voltage
Condition : xt=0.05pu, Xe=0.2pu,
Figure 11.
Vg
Vg=Vgref
0.4
(c) Generator Terminal Voltage
V.
AVR
HSVC
2
3
4
5 6
Time(s)
2
1
0.8
High Side Voltage(pu)
Generator Terminal Voltage(pu)
1
1
By increasing the suppression gain of cross current Kc,
the cross current can be reduced and the deviation between
generators becomes smaller. Accordingly, the Vg is not
influenced by the reactive current of each generator and is
kept to constant. These characteristics of the conventional
method and the advanced method are compared in Figure 13.
1.2
1
0
0
0
(b) Generator Reactive Power
1.4
1.2
Vg(pu)
0.4
0.2
0
Cross current Ic
(b) Conventional method
Characteristics of cross current suppression
function
IqT1
Vg1
S.Tr
VH
Xe
Vs
Xt
Xs
~
Vg2
Iq4
IqT2
LOAD
(PL)
(100MVA base)
Four machines model for studying the parallel
operation
For this study, the advanced cross current suppression
function is added to suppress the reactive cross current
between the generators directly connected on the low voltage
side of the step-up transformer. Here, it is between G1 and
G2 and between G3 and G4. The conventional cross current
compensating function that uses a load current of each
generator may have a negative impact on voltage stability,
because Vg would decrease as reactive power increases.
Figure 14 and Figure 15 show respectively the simulation
results for the step response (=0.01PU) of VHref on the
parallel operation of two generators and four generators.
The results on two generators operation is as follows and
mainly verifies the characteristics of the advanced cross
current suppression function.
(a) The VH follows against a step of the VHref within
several seconds and is smoothly controlled without
fluctuation. The resultant VH fits the theoretical value.
(b) Even if the Vg detected by each AVR is different, the
VH can be stably controlled according to the VHref.
(c) In spite of a discrepancy of each AVR gain, the VH can
be controlled according to the VHref except for a slower
response of Iq2 by the lower AVR gain.
(d) In spite of a discrepancy of each AVR response
characteristic, the VH can be controlled to the VHref
except for a slower response and increasing an
overshoot of the G2.
(e) In spite of a discrepancy of operation mode, the VH can
be stably controlled. As the Xc becomes large, a
deviation of Iq becomes small.
(f) Even if the step signal to G2 AVR is delayed, the VH
can be stably controlled according to the VHref.
The results on four generators operation is also as follows
and mainly verifies the characteristics between generator
groups, G1/G2 and G3/G4.
(a) The VH follows against a step of the VHref within
several seconds and is smoothly controlled without
fluctuation. The resultant VH fits the theoretical value.
(b) Even if the Vg detected by each AVR is different, the
VH can be stably controlled according to the VHref
except for a discrepancy of Iq and Vg between the
groups.
(c) In spite of a discrepancy of each AVR gain, the VH can
be controlled according to the VHref except for a slower
response of Iq3/Iq4 by the lower AVR gain.
(d) In spite of a discrepancy of each AVR response
characteristic, the VH can be controlled to the VHref
except for a slower response and increasing the
overshoot of G3/G4.
(e) In spite of a discrepancy of operation mode, the VH can
be stably controlled. As the Xdr becomes large, a
deviation of Iq becomes small.
(f) Even if the step signal to G3/G4 AVR is delayed, the
VH can be stably controlled according to the VHref.
VI.
CONCLUSIONS
The performance of the various functions of advanced
HSVC based on a simple power system were introduced.
The simulation results were in agreement in every respect
according to theoretical expectation and it was confirmed that
the advanced HSVC could be put to practical use.
For future development steps, the following studies will
be continued to further improve the functions and benefits of
the advanced HSVC.
• Analysis and brush-up of the improving effects of the
voltage stability and the oscillatory stability on the multimachines model.
• Study of the control method and the improving effects
for a transient stability by the advanced HSVC.
VII.
REFERENCE
[1] T. Michigami, N. Onizuka, S. Kitamura, “Development of
Advanced Generator Excitation Control Regulator
(PSVR) for Improving Voltage Stability of a Bulk
Power Transmission System,” The Institute of Electrical
Engineers of Japan, Vol. 110-B, No. 11, November
1990, pp. 887-894
[2] C. Taylor, Power System Voltage Stability, McGraw-Hill,
Inc., 1994.
[3] P. Kundur, Power System Stability and Control, McGrawHill, Inc., 1994, pp. 216-220.
[4] F. P. De Mello and C. Concordia, “Concepts of
Synchronous Machine Stability as Affected by
Excitation Control,” IEEE Transactions on Power
Apparatus and Systems, Vol. PAS-88, Apr. 1969, pp.
316-329.
VIII.
BIOGRAPHIES
Hitomi Kitamura received a M.S. degree in Electrical
Engineering from Kansai University in 1998. Since 1998, she
has been with the Mitsubishi Electric Corporation in Kobe,
Japan, and is working for the design and the development of
excitation system and the analysis of power system stability.
Masaru Shimomura received a B.S. degree in Electrical
Engineering from Kyusyu University in 1970. Since 1970, he
has been with the Mitsubishi Electric Corporation in Kobe,
Japan, and has been mainly developing the excitation control
system. His present main activity is management of electrical
engineering for control system of power plant.
John Paserba earned his BEE (87) from Gannon University,
Erie, PA., and his ME (88) from RPI, Troy, NY. Mr.
Paserba worked in GE’s Power Systems Energy Consulting
Department for over 10 years before joining Mitsubishi
Electric Power Products Inc. (MEPPI) in 1998. He is the
Chairman for the IEEE PES Power System Stability
Subcommittee and was the Chairman of CIGRE Task Force
38.01.07 on Control of Power System Oscillations. He is
also a member of the Editorial Board for the IEEE PES
Transactions on Power Systems.
0.3
0.5
1.03
1.02
0.3
1.01
0.1
0.05
0
1
2
3
4
time(s)
Iq1,Iq2
5
6
Vg(pu), VH(pu)
0.15
0.2
Iq(pu)
Iｑ(pu)
Vg(pu), VH(pu)
0.2
0
0.1
0
1
0.99
0
-0.1
Vg1
VH
1
2
3
4
time(s)
5
-0.2
0
6
1
2
3
4
time(s)
0.5
1.02
0.4
0.3
Iq(pu)
Vg(pu), VH(pu)
1.01
0.1
0.05
Iq1
Iq2
0
1
2
3
4
time(s)
5
6
0.2
0.1
0
1
0.99
0
1
2
3
4
time(s)
5
Vg1
VH
-0.1
-0.2 0
6
1
Iq1,Iq2
2
3
4
time(s)
[G1-Vg : G2-Vg=0.995 : 1.005]
(b)Discrepancy of AVR feedback voltage
0.2
1.01
0.1
0.05
Iq1
Iq2
0
1
2
3
4
time(s)
5
6
0.1
0
1
0.99
0
Vg1
VH
1
2
3
4
time(s)
5
6
-0.1
-0.2
0
1
2
0.1
0.05
Iq1
Iq2
1.01
0.2
0.1
0
1
2
3
4
time(s)
5
6
0
1
2
3
4
time(s)
Vg1
VH
5
6
-0.1
-0.2
0
Vg(pu), VH(pu)
0.15
0.1
0.05
0
1
Iq1 [1]
Iq1 [2]
Iq2 [1]
Iq2 [2]
2
3
4
5
time(s)
1.03
0.5
1.02
0.4
0.3
0.1
1
0
1
2
3
time(s)
Vg1 [1],[2]
VH [1],[2]
4
5
6
0
-0.1
-0.2
0
0.4
0.15
0.3
1.01
0.2
0.1
0.1
0.05
Iq1
Iq2
0
1
2
3
4
time(s)
5
6
Iq(pu)
1.02
Vg(pu), VH(pu)
0.2
Iq(pu)
Iq1,Iq2 [1]
Iq3,Iq4 [1]
Iq1,Iq2 [2]
Iq3,Iq4 [2]
1
2
3
4
5
6
time(s)
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0
0.5
1.03
0.25
0
1
0.99
0
1
2
3
4
time(s)
Vg1
VH
5
6
[Timing for change of VHref for G2 is 0.1s later than for G1.]
(f)Discrepancy of timing for change of VHref
Figure 14.
VH
5
6
1
2
Vg1
Vg2
3
4
time(s)
VH
5
6
Vg1
Vg2
1
2
3
4
time(s)
VH
5
6
1
Vg1[1]
Vg2[1]
VH [1]
2
3
4
time(s)
Vg1[2]
Vg2[2]
VH [2]
5
6
[G1/2:HSVC,G3/4:AVR Xdr(pu) : [1] Xdr=0.01 [2] Xdr=0.025]
(e)Discrepancy of operation mode
[G1:HSVC, G2:AVR Xc(pu):[1] Xc=0.1 [2] Xc=1.0]
(e)Discrepancy of operation mode
0.3
6
0.2
1.01
0.99
6
0
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0
Vg(pu), VH(pu)
Iq(pu)
0.2
1
Iq1,Iq2
Iq3,Iq4
2
3
4
5
time(s)
Iq(pu)
0.3
0.25
2
[G1/2- ω c:G3/4- ω c= 1 : 0.5 ω c:cross over frequency]
(d)Discrepancy of AVR response characteristics
[G1- ω c : G2- ω c= 1 : 0.5( ω c:cross over frequency)]
(d)Discrepancy of AVR response characteristics
0
Iq3,Iq4
5
6
0
1
0.99
1
Vg1
Vg2
3
4
time(s)
Vg(pu), VH(pu)
0.3
Iq(pu)
1.02
Vｇ(pu), VH(pu)
Iｑ(pu)
0.15
0
Iq1,Iq2
3
4
time(s)
0.4
0.2
0
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0.5
1.03
0.3
Vg1,Vg2
VH
5
6
[G1/2-K:G3/4-K = 1 : 0.5]
(c)Discrepancy of AVR gain
[G1-K : G2-K = 1 : 0.5]
(c)Discrepancy of AVR gain
0.25
3
4
time(s)
Vg(pu), VH(pu)
0.15
0.3
Iq(pu)
Vg(pu), VH(pu)
Iｑ(pu)
0.5
1.02
0.2
0
Iq3,Iq4
5
6
0.4
0.25
2
[G1/2-Vg:G3/4-Vg=0.995 : 1.005]
(b)Discrepancy of AVR feedback voltage
1.03
0.3
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0
Vg(pu), VH(pu)
Iq(pu)
0.2
1
Vg(pu), VH(pu)
1.03
0.25
0.15
Iq1-Iq4
5
6
(a)Basic case
(a)Basic case
0.3
0
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0
0.4
0.25
Performance for two generators operation
-0.1
-0.2
0
1
Iq1,Iq2
Iq3,Iq4
2
3
4
5
6
time(s)
1.05
1.04
1.03
1.02
1.01
1
0.99
0.98
0.97
0
Vg1
Vg2
1
2
3
4
time(s)
VH
5
[Timing for change of VHref for G3/4 is 0.1s later than for G1/2.]
(f)Discrepancy of timing for change of VHref
Figure 15.
Performance for four generators operation
6