INERTIAL, GOVERNOR, AND AGC ECONOMIC DISPATCH LOAD FLOW SIMULATIONS OF LOSS OF GENERATION CONTINGENCIES

IEEE Transactions on Power Apparatus and Systems, Vol. PAS-104, No. 11, November 1985
3020
INERTIAL, GOVERNOR, AND AGC/ECONOMIC DISPATCH LOAD FLOW
SIMULATIONS OF LOSS OF GENERATION CONTINGENCIES
by
R. Schlueter, Senior Member
M. Lotfalian
Michigan State University
University of Evansville
East Lansing, Michigan
Evansville, Indiana
P. Rusche
D. Idizior
Consumers Power Company
Jackson, Michigan
A. Yazdankhah
L. Shu
S. Tedeschi
Michigan State University
East Lansing, Michigan
The transient phenomena associated with the loss
of generation contingency is described i n this paper.
The propagation of the disturbance, the time instant
at which the inertial load flow captures a snapshot of
the transient, and the time instant at which the
governor load flow captures a snapshot of the
transient is described. A method of determining the
subset of generators that participate in governor load
flow is described based on this discussion of the
propagation and evolution of the transient phenomena
associated with loss of generation contingencies.
Finally, the application of inertial and governor load
flow in planning is discussed. A description of the
inertial and governor load flow program, developed for
EPRI and residing in the EPRI Software Center, is
described.
Comparisons of the inertial load flow and governor load flow bus angles with a snapshot of the
angles at t = .25 seconds and t = 10 seconds from EPRI
Mid Term Stability simulation is presented for different contigencies on a 49 bus test system. The
results not only indicate that the inertial and governor load flows are accurate but also that the inertial
and governor load flow capture shapshots of the Mid
Term Stability simulation at particular instants.
Introduction
The simulation of the transients for loss of
generation contingencies can be performed using Transient/Mid Term [1] or Long Term Simulation [2]
packages. The load flow simulation of loss of generation contingencies usually assigns the mismatch caused
by the loss of generation contingency to a swing bus.
Programs exist. that allow the mismatch to be split
among all or some subset of the generators, according
to participation factors. The participation factors
could be proportional to inertia, generation capacity,
AGC participation factors, or economic dispatch participation factors.
The transients accompanying loss of generation
contingencies are described in classical papers and
books [3,4,5]. Although load flow programs have been
written that allow inertial or governor distributior
A paper recommended and approved
85 WM 055-9
by the IEEE Power System Engineering Committee of
the IEEE Power Engineering Society for presentation
at the IEEE/PES 1985 Winter Meeting, Niew York, New
York, February 3
1985. Manuscript submitted
made available for printing
-
August 30, 1984;
December 12, 1984.
3,
of the mismatch, use of such programs in planning only
appears in regional planning documents that are not
open literature. Moreover, there has never been any
effort to determine whether the inertial load flow
(inertial distribution of mismatch) captures a snapshot of the actual transient/mid term simulation of
that contingency. Moreover, there never has been an
effort to model the effect of governor deadband on the
governor load flow (governor distribution of mismatch). Thus, there is confusion as to the similarity
and differences between the inertial and governor load
flow.
2.1 Formulation Qf
InertiaS
Load Flo Problems
1C1QpratQr
o
Oego
Load Flo Formulation
Load flow solutions provide bus voltage angles
and power flows in the transmission system for specified generation and load conditions.
To study the affect of generation response to a
loss of generation or load contingency for inertial,
governor, and AGC/operator distribution, the real
electrical power to be delivered into the network for
each distribution must be specified, and load flow
equations must then be solved for unknown, wanted
variables.
The load flow equations can be written as:
PGj(K)
PDi
QGi QDi=
=
i
jEAi
jcAi
Qij
~~~~~~~~(1)
jrAi
*sincij + ViVjYijsin (6i-6j-otij)
= V?Y
Qi;
ij
= .
Vi(Y
- 1/2
VwVhYerCeS (:
j
Bij)
-
j)
where:
=
set of buses connected to bus i
PDi+jQDi
=
canplex power load at bus i
PG(K)+jQGi
=
complex power from generation at
Ai
bus i
ij= (900
- the impedance angle of
line ij)
Bi 1= the total charging susceptance
of the line connecting buses i
and j
0018-9510/85/1100-3020$01.00© 1985 IEEE
a
3021
QGiMin < QGi < QGiMax for
rGi(2)
regulated buses
QGi= reactive power generated by
generator i
These AC load flow equations can be solved given PDi +
jQD at load buses, Vi and 6 at the swing bus, and
PGtK) and Vi at generator buses. The variables
caiculated by solving the load flow equations are V
and 6i at load buses, losses at swing bus, and QG( an3
6. at generator buses. The load flow is calcu?ated
under the constraint:
Gi QGiMax
QGiMin K
Sj
presented.
The value of PGi(J) i = 1, 2, ...., N for the
inertial load flow assumes that the acceleration of
every generator is constant dwi/dt = dw0/dt, and thus:
dwo
Pmi =Mi dt
=
N
d)0
dt
z
i=l
(PMi.L
(2a)
FGi(O))
L
-
(2b)
N
Mi
where:
PGi(0)
=
real electrical power delivered to the
network before loss of generation by
er'eerator i
PMi =PG(0) - APM = mechanical power sent to
the generator after loss of generation APMi
A
PMi
=
rGi(0)O
i = k
i t k where k is the lost
generator
PGi(l)
real electrical power delivered into the
network by generator i after loss of generation for inertial distribution of mismatch power
The va l ue PGi(2) i = 1, 2,.., M for the
governor load flow assumes that the governor action is
complete and that frequency is constant everywhere
Aw=Aw0 so that:
PGi (2)
where:
=
N
E
= frequency response characteristic of
generator i
Y
4M
FGi(3) = Pi
where:
MP
<
The inertial, governor , and AGC/operator load
flows differ based on the generator injection PGi(K)
for inertial (K = 1), governor (K = 2), and AGC/economic dispatch (K = 3) distributions described below.
The formulas for calculating the injections PGi(K) for
all generators for inertial (K 1), governor (K =
2), and AGC/economic dispatch (K - 3) distributions
of loss of generation or load mismatch are now
where:
the real electrical power delivered into the
network by generator i when governor frequency regulation is complete
For the final distribution of power by the
AGC/economic dispatch PGi(K) for (K = 3) satisfies:
at PV buses where voltage is held to specified levels.
PGi(l)
=
PMi -6iAwo
(3a)
(PMi- j(0))
i=l N
o -w-
M = number of generators on regulation.
(3b)
=
=
1
(4b)
(PM, - PGi(O))
i =1
number of generators participating in AGC/economic
AElk =
MP
MP
£y
i=
(4a)
dispatch.
PGi(3)
yi
= real power delivered to the network
by
generator i after economic dispatch or AGC
action is complete
=
KAC/economic dispatch participation factor
The load flow equations (1) are solved for bus voltage
angles and power flow across the lines, given the
values of PGi(K) from (2), (3), and (4) for the inertial, governor, and AGC/economic dispatch load flows,
respectively.
The inertial, governor, or AX/economic dispatch
load flows are solved using Consumers Power Company
Multiple Contingency Fast Decoupled Load Flow. The
package can handle systems with 750 generators, 5500
lines, and 3000 buses. It requires a solved base case
from a Philadelphia Electric Load flow. It is extremely fast and can solve an 800 bus AC load flow in
approximately 1 second. It can determine either AC
decoupled or DC load flow solutions. The mismatch for
loss of generation contingencies can be distributed to
all or a subset of buses by reading the appropriate
distribution factors. The inertial or AGC/economic
dispatch load flows for a set of contingencies can
thus be solved by directly calling this program with
the appropriate inertias (M.) as participation factors
for inertial load flow or gi) participation factors
for AGC/economic dispatch load flow and specifying the
set of contingencies to be solved. The governor load
flow is performed for a set of contingencies by use of
a main program that calls this Multiple Contingency
Fast Decoupled Load Flow to solve the inertial load
flow for each of the contingencies. This program then
analyzes the inertial load flow results for each contingency to determine a set of participating generators that would respond under governor load flow for
each contingency. The governor load flow for each
separate contingency is then simulated by calling the
Multiple Contingency Fast Decoupled Load Flow for that
contingency and setting the participation factors as
the MW capacities (C.) for generators that will participate in governor load flow for that contingency.
Participation factors for generators that do not participate in governor load flow for that contingency
are set to be zero. This program thus can permit
governor load flow simulation of a set of contingencies and is automated so that the user need not perform several separate calls to obtain governor load
flows for a single loss of generation or a set of.loss
of generation contingencies.
2.2
QMr.Wk Low El
M1ling
The inertial load f low is run in some large
interregional transmission performance studies. The
3022
inertia constants for every generator in the interconnection must be specified to run this load flow. She
AGC/economic dispatch load flow is sometimes run to
study whether the redistribution of power for loss of
generation contingencies in the particular utility of
concern will cause thermal overload problems in the
transmission system for that utility. The AGC participation or economic dispatch participation factors
for the generators in that utility must be specified.
The inertial load flow represents a snapshot of
the transient when all generators experience identical
decelerations due to the synchronizing action of the
network-thO pu 1lls a ll the-generators toward a mean
deceleration. The governor frequency regulation is
initiated approximately six seconds after the loss of
generation in order that the mismatch caused by the
loss of generation contingency be eliminated. The
subset of the generators on regulation that participate in supplying this mismatch power is unclear due
to governor deadband. Thus, the power flows caused by
governor load flow will be distinctly different than
inertial load flow where AUJ generators in the interconnection respond. The AGC/economic dispatch load
flow, which redistributes the mismatch from the subset
of generators in the governor load flow to a preselected set of generators in the utility according to
known participation factors, is again quite different
from either the inertial or governor load flow. A
method for determining the subset of the generators on
regulation that participate in governor load f low is
now derived.
After inertial distribution of mismatch power,
each generator is controlled- by its governor. A loss
of generation contingency causes frequency deviation.
Governor frequency regulation on each generator in the
interconnection work together to arrest the change in
frequency. This frequency regulation begins approximately six seconds after the disturbance occurs. When
the governor frequency regulation is complete, frequency is constant at a deviation Aw 0 above nominal
system frequency throughout the interconnection. Tlhe
deviation of power at each generator from the governor
model shown in Figure 1 is:
C.
Pi(3) W=M1i
Apik(3
iw=i
Awi = Si Awo
(5)
where
Awi =
radians/sec for all the generators
w
Ci
OR
frequency response characteristic of
i= -
generator i
Ci =w capacity
R = system
of generator i
regulation coefficient (R
= .05)
nominal systen frequency in radians/second
The total mismatch *PMk is the sum of all the power
w
=
changes.
equal to
AP
and from (5) and (6):
SiAEMk
APik (3) =
i
i=l
sa is approximately equal to MW capacity of generator
(b divided by system regulation coefficient (R). The
other factors involved in governor response are generator and turbine dampinq and load dependence on
frequency,
M
-E i
i=1
AFMk
=w iX -
This model of governor action that linearly relates generation change to frequency deviation is
idealized. The governor deadband causes a generator
to be insensitive to frequency deviation less than
.036 Hz; if the frequency deviation sensed by a generator is greater than .036 Hz, the generator may
still not respond to governor command if the unit is
operating at a valve set point or if the generator is
not under governor frequency regulation.
The effects of governor deadband and valve set
points have the effect of reducing the frequency response characteristics Si of generators electrically
distant from the point of mismatch (bus k). The
effects of the loss of generation on both the frequency and deceleration of generators electrically close
to bus k are larger than at generators distant to bus
k, as the effects of disturbance ripple out and ultimately achieve an inertial distribution. The large
short transient initial frequency deviations close to
disturbed bus k will overcome governor deadband and
valve set point nonlinearities, making the generator's
actual change in generation equal to 1.2% Ci. The
generators far from the disturbance do not feel the
large initial frequency transient but rather a slow
exponential drop in frequency by .036 Hz. If the
frequency transient does not exceed .036 Hz at a
generator, that generator's governor deadband of 0.036
Hz prevents that governor from responding at all to
the loss of generation at bus k. Thus, generators
which experience a frequency transient above the nom.inal system frequency drop of A = .036 x 2 7 = 0.226
rad/sec experience a percentage change of generation
equal to
A PMi
i=l
~i
(6)
1
C. _= (- )
Awo
p. u. Hz
deadband
Governor model of a generator.
Figure 1.
Since the Awi of all the generators are
Awo, one obtains:
=
i
'wo
i
U
x-2)
=
( .05
1-) (-036
60 x 21
=
1.2% Ci
=
= .012
k
(7)
or a
APMi
change in generation. The generators electrically
distant from the generator bus, that do not experience
3023
a frequency transient above .036 Hz, do not experience
any change in generation and thus do not participate
in governor regulation along with units not under
governor frequency regulation.
The frequency transient will always exceed .036
Hz at some buses in the. system no matter how small the
loss of generation is since otherwise no other generator's governor will be able to detect the mismatch and
this mismatch will continue to reduce system frequency
as well as the local frequency near the bus at which
the generation loss occurred. The larger the loss of
generation is, the larger the local frequency
transient is above .036 Hz. The frequency transient
is not as large at buses further from the bus with the
loss of generation induced mismatch because local
generator governors have begun to pick up 1.2% of
their megawatt nameplate capacity (Ci) and reduced the
effective mismatch seen by generators further electrically from the disturbed bus k. The peak of the
frequency transient occurs later and later as the
frequency transient propagates from the disturbed bus
and generators that have experienced the transient
begin to produce their 1.2% C. contribution. This has
been observed on both simulation and measurements for
actual loss of generation contingencies.
It is clear.that in order to model the governor
response with deadband for the governor load flow one
must determine the group of generator ieIk that respond to the loss of generation APM for the generator
at bus k. The megawatt capacity of these generators
CIk must satisfy from (7).
1.2% C
E z
iEIk
=1.2% Ci = AMpm
k
(8)
The 5ystem frequency change is
APMk
Aw
°
i
=
APMk
- =4
=
'Ik
i
SIk (woR
k
=
.i
(0.O5)wo (.012)
-
.0006 wo= .0006 (60
=
(.036)2ar
=
x
2T1
Hz
The generators i EIk are t.he generators that exlargest frequency deviations.
he generators with the argest frequency changes wi 1 have
the largest ang.le change from the time instant at
which the disturbance at bus k occurs unti al1 generator buses are at their own peak frequency deviation. The peak frequency deviations at each bus occurs at a different time but al l occur shortly after
al l buses experience the same acceleration and the
snapshot of the transient is approximated by the inertial load flow. The change in generator bus angles
6 H(i k)
-
6
0(i)
(11)
from smallest to largest should rank those generators
with the largest frequency deviations sincP bus k wi l l
have the largest, frequency and angle change. The set
i£ Ik is obtained by adding up only the capacities of
units that have governor frequency regulation as one
goes down this ranking table until
1.2%
E
Cj > APMk
iEIk
(12)
Units that do not have governor frequency regulations
and thus do not,- participate in governor frequ'ency
regulation are neglected in this summing of capacities
in the ranking table. This procedure has been implemented in FORTRAN to analyze an output file from an
inertial load flow produced by the-Consumers Power
Company Multiple Contingency Fast Decoupled Load Flow
in order to determine the set i cIk of generators that
participate in governor load f low for a loss of generation contingency at bus k. The set Ik is then used
to set governor response characteristics 6 to zero at
generators
¢Ik
in the governor load flow.
.226 radians/sec
perience the
=
[A6H(isk) - AdH(k,k)]
Ci
or
Ad H(i k)
is a measure of the magnitude of the frequency deviations at each bus i at the time instant when the
inertial load flow captures a snapshot of the
transient. Since the ranking of the magnitude of the
frequency deviations at the time instant when the
inertial load flow approximates the transient should
be identical to the r-anking of the peak frequency
deviations that occur at some short interval later, Ad
H(i,k) can be used to rank the generators with the
largest frequency deviations and thus determine the
subset of generators iF Ik that participate in governor. The ranking of
Generators ijel that have governors frequency regulation wi l l clearly have governor response characteristics
icIk
fo= .36
for loss of generation at bus k
i
i
Rub
H(i,k) = inertial load flow bus angle at generator i
(10)
where
6 0(i)= bus ang l e at generator i at the predisturbance base case condition
It shoulI'd be noted that if a uti 1 ity loses its
tie lines, a loss, of generation contingency can exceed
1.2% of the capacity of the uti l ity and then al l
generators in the uti l ity wi l1l partici pate in the
governor response.
The above dePrivation and justificatibn of the
method for determining the, generators that participate
in governor load flow when governor deadband is considered is an important contributtion because it allows
both characterization and simulation of the transient
without actual time step integration of the nonlinear
differential equations out to ?0 seconds.
2.3 Aipplication of Inertial and Governor Load Flows
The long distance power transfers, as experienced
in the. -PA [7] systeml or planned from Canada and the
Midwest to replace oil generation in the Niortheast,
utilize certain transmiiission corridors and bring
loading much closer to their thernmal overload limits.
A loss of oeneration contingency in the area receiving
the transfer causes large inadvertent transfers over
the same corri(ors providing the larqe planned
transfers. These inadvertent transfers are due to
inertial or governor distribution of the nmismatch from
3024
the loss of generation contingency and can be concentrated on just one corridor. The planned transfers
can be distributed among several corridors by establishing the proper operating practice for each of the
utilities in the interconnection where the transfers
are planned. The inadvertent transfers cannot be
distributed among the various corridor options but are
dictated solely by the inertial or qovernor responses
of generation in the interconnection and thus can be
concentrated in just one or a relative few corridors.
shown in Figure 2. The 49 bus test system was chosen
since it was used and tested to validate the Mlid Term
Stability Program, and the governor models for mid
term stability studies were available for this system.
Generator data, governor models, and base case load
flow data used in this study are available through the
EPRI Mid Term Stabi 1 ity Package [1] and, therefore,
are not reproduced here.
ALFA 4=16
ALSA 1=15
ALCA
ALFA 17
T7
Thermal overload can cause loss of equipment life
and sagging of lines that can lead to faults and other
contingencies that ultimately can cause cascading
outages and islanding.
,
_
AL.FA 2
Almost every major blackout and islanding problem
can be associated with interconnection wide power
flows. This problem is in great part associated with
inertial and governor generation response.
The load flow methods developed in this section
al low direct assessment of stability and security
problems due to generation response to loss of generation contingencies. The development of load flow
models leads to a better understanding of the different power transfers associated with inertial and
governor load flow time scales. The effects of these
power flows on transmission qrids were also an objective.
Lack of understanding of different power mismatch
distributions in present planning methods, in some
cases, caused improper use of the inertial load flow
that was deve 1 oped af ter the 1965 b l ackout when records of the power flow experienced did not agree with
ex i st i ng load f 1 ow ana l ys i s. The present planning
methods have been considering the power flows due to
qeneration response to loss of generation to be almost
equal for inertial and governor distribution of mismatch power. Moreover, some conventional load flow
programs are not able to address the stability and
security problemns associated with inertial load flow
and governor load flow. Miany present load flow
techniqujes distribute the mismatch power to a large
swing generator. This is not wJhat happens in a real
power system, and the accuracy of this approximation
to inertial or governor distribution wi 11 depend
heavi ly on the representation of the system and the
choice of the swing buis.
The recently developed Mid Term stability Package
[1] could be used to assess the stability for loss of
generation contingencies, but this package cannot
handle very large data bases required to analyze liarge
interconnected networks associated with long distance
power transfers where al l the generators must have
governor turbine representation. Th'us, even if it is
upgraded, it would be very computational ly expensive
to run for the simulation time interval needed ( >20
seconds) to analyze governor response distribution.
Thus, the lhWid Term Stability program can be used to
determine inertial response to l oss of generation
contingencies for large data bases but can at present
only confirm governor response on smal 1 system data
bases and then only at considerable computational
cost.
3.
Application of the Inertial and Governor Load Flow
on a 49 Bus Test System
To demonstrate the performance of the inertial
and the governor load flow methods developed in
Section 2, loss of generation contingencies were siviulated] using the inertial and governor load flow programis on the 49 bus Electric Power Research Institute
(EPRI) test system. A schematic of this system is
ALFA
°ALFA
_If
10
Zl
1=3
Z-2ETA I=40
0
0
RH
ALIA
;llD_
_ _
_
2
ZETA
0
_T12
RHO-
ZETA
.9
10TA 3=11
10 4 =10
BETA. I
.=20
IAA
I Q -1;~~~~~~~~~~~
Figure 2. 49 bus system transmission grid.
The inertial and the governor load flow results
will be compared with the M id Term Stability Program's
results of the samne contingencies to verify the inertial and the governor load flows. The accuracy of the
Mid Term Stability Program in the simulation of loss
of generation contingencies out to the 10-20 seconds
allows evaluation of the accuracy of the inertial and
governor load flow simulation methods.
Early results uncovered a steady state st.ability
problem on the 49 bus test system. For the purpose of
this research, this steady state stability problern had
no effects on the results of the simulation in the
time frame (.25 seconds) of inertial load flow and has
little effect in the time frame (10 seconds - 10
minutes) of governor load flow if the magnituide of the
loss of generation is large (>600 MW'') and thus dwarfs
the effects of the ste-ady state oscillation.
3.1
Inertial Load Flow
The EPRI Mid Term Stabi 1 ity Program was used to
simulate the angle and frequency excursions for a 790
MiW loss of generation contincency at Zeta 3.
The plot of frequency deviations for all generagiven in Figure 3 The frequency deviations
tors is
3025
have approximately the same rate of change at t = 0.25
seconds just before generators in the Zeta system
begin to oscillate against one another. Thus, the
time instant t = .25 seconds is the instant at which
the "snapshot" of the transient stabil ity simulation
should resemble the quasi steady state condition given
by the inertial load flow. The angle change from the
base case load flow was determined at t = .25 seconds
on the midterm transient stability simulation results
such as shown in Figure 4 and tabulated in Table 1.
The changes in bus angle for the inertial load flow
from those in the base case load flow were also tabulated in Table 1. The angle change within each of the
stiffly connected groups Alpha (1,4,28,31), Alpha
(27,29), Alpha (24-26), Alpha (9-13), Rho (3-4), Zeta
(1-4), and (Gama 1, Beta 1, Zeta 5) are nearly the
same in both the inertial load flow and midterm stability simulation. These stiffly interconnected groups
were determined [51 utilizing a coherency measure that
can detect stiffly connected groups and the weak
transmission boundary that connects such groups. The
angle change from any generator in the reference group
Beta 1, Gama 1, Zeta 5, to any generator in any of the
other stiffly interconnected groups differs by 1.60
from comparing the inertial load flow and midterm
stability simulations. The angle changes for generators within these groups or between groups other than
the reference group are in excellent agreement by
comparing the inertial load flow and midterm stability
simulation results. The 1.60 error in the angle between generators in the reference group and any other
generator not in that group in the inertial load flow
may be due in part to the fact that al l mismatch is
distributed inertially in the midterm stability simulat ion but only the loss of generation is distributed
in the inertial load flow.
Q
8
H
o
40
cv
o 8
6
c)
I4
¢i
a
2.0
Figure
U)
Bus
4.10
3.0
Tine
Figure
3.
in
Govern'or
Load
The governor
Table
Generator
frecuency
deviation
for
of
3.3
5
Seconds
790
generation at
11W.loss
Zeta
3.
Flow
load
flow
calculated
neglecting
generation
is greater than 1.2% of the generation capacity with
governor regulation
capabilities.
The frequency
changes from the base c'ase have approximately reached
quasi-steady state condition afte'r t
10 seconds and
governor
deadband
since
t-he
was
790
MW
loss
obf
=
thus the angle changes from base case at t =10
seconds, tabulated in Table 2, should represent the
quasi-steady state condition predicted by the governor
load flow. The change from base case angles for the
governor load flow is also given in Table 2.
5.0
6.0
EPRI Midterm
Stability Program
at t=.25 seconds
Governor
Load Flow
Alpha 1
Zeta
.0
.o
Angle Changes from Base Case
Beta
Gama
Rho
~4-
3.0
Time in Seconds
4. Generator angle deviation
for 790 MWJ loss of generation at Zeta 3.
1.6482
3.2520
4
1.6524
3.2700
9
2.3074
3.7820
10
2.3084
3.7820
11
2.3889
3 .8740
12
2.2414
3.8000
13
2.0864
3.5580
24
1.5249
2.6990
25
1.5247
2.6980
26
1.5249
2.6990
27
2.1101
3.7032
28
1.6597
3.1680
29
2.2781
3.8740
31
1.6217
3.1140
35
2.4231
4.5910
1
.3203
.1870
1
.3203
.1880
3
2.2027
4.0050
4
2.4337
3.9540
1
-4.6787
-3.5320
3
-17.0998
-16.1420
4
-7.7194
-6.4020
5
0.0000
0.0000
1. Generator bus angle changes from
inertial load flow and EPRI midterm stability simulation at the
inertial time frame.
Comparison of the angle changes predicted by this
governor load flow and the midterm stability simulation model indicates that the governor load flow predicts a consistent 90 smal'ler angle change at all
buses other than in the stiffly interconnected group
Beta 1, Gama 1 Zeta 5, containing the reference. The
angle changes within Alpha (27,29), Alpha (24-26),
Al-pha (9-13), Rho (3,4), Zeta (1-4) are nearly identical in both governor load flow and the midterm stability simulation. The angle changes between generators
in each group and from group to group are in excel lent
agreement reflecting the accuracy of the governor load
flow. The only real error in the governor load flow
is not predicting the angle difference between generators is any of these groups and the reference group
3026
Beta 1, Gama 1, and Zeta 5 which is due possibly to
the fact that all mismatch is distributed by governor
control in the midterm stability simulation but only
the loss of generation is distributed in the governor
load flow.
The governor load flow and the midterm stability
simu lation both used linear governor models without
deadband because the 790 MW contingency was greater
than 1.2% of the generation capacity of generation
with governor controls. Thus, al 1 generators wil l
participate and wil l participate proportional to their
governor gain
M
=1
The midterm stability governor model used for the
49 bus example system did not uti l ize the long term
Thus, no ef
governor models that inc'lude deadband.
fort was made to simulate loss of generation contingencies with generation losses of less than 1.2% of
generation capacity where governor deadband would
modify the participation of generators in governor
load flow. The use of the governor deadband in the
governor load flow is illustrated in the results for
governor load flow on the Nanticoke post mortem in a
subsequent paper.
-
of the transient trajectory determined by the inertial
load flow. A description of the computer package
developed for the EPRI Software Center to simulate the
inertial and governor load flow is given. The application of the inertial and governor load flow in
operation and planning are also discussed.
The comparison of the inertial and governor load
on the 49 bus test system with simulation of the
same contingency on the EPRI Mid Term Stability Program. The testing is performed on this example system
because (1) the EPRI package is the only one accurate
enough to validate the accuracy of the inertial and
governor load flow and verify its ability to capture
snapshot of the transient trajectory associated with
the time simulation and (2) because the EPRI package
was validated on this test system. A comparison of
the inertial and governor load flow with simulation
and measurements of the line power flows and frequency
for a post mortem of a large 2000 MW loss. of generation contingency was also made. These extensive results conf irm the accuracy of the inertial and
The results for this post mortem
governor load flows.
will be presented in a subsequent paper.
flow
Referencs
1.
2.
3.
Angle Changes from Base Case
Stability Program
at t=10 seconds
Bus
Governor
Load Flow
Alpha 1
4
9
10
11
12
13
24
25
26
27
28
29
31
35
Beta 1
Gama 1
3
Rho
4
Rho
Zeta 1
Zeta 3
Zeta 4
Table 2.
28.5731
28.5769
28.7341
28.4984
27.8775
24.4408
24.4393
24.4408
26.3057
25.6085
26.6745
25.4991
29.3026
- .0531
- .0529
28.5341
29.2463
3.0343
-11.2391
-
.4263
16.3780
16.3760
16.3780
0.0000
0.0000
20.8370
20.5670
.3710
-13.0190
- 2.595
Generator bus angle changes from the
governor load flow and the mid-term
Co=Jusilons
A description of the transient phenomena associated.with loss of generation contingencies is
presented in order to develop the equations that
describe the inertial, governor, and AGC/economic dispatch load flows. A method for determining the subset
of generators that experience peak frequency excursions above .036 hz and thus participate in governor
load flow is presented. The procedure does not require time step integration of the system differential
equations but only proper modeling of the transient
propagation and proper interpretation of the snapshot
Power,
erfo
rm
Elecri
stems, McGraw-Hill, New York, 1950 (MIT
MA,, 1967).
in Electrical Power
Sstems Design, Chapman and Hall, London, 1966.
4.
R.A. Hore, Advancl Studi
5.
A.S. Debs, A.R. Bentson, "Security Assessment of
Power Systems#," presented at the Engineering
Foundation Conference on Systems Engineering for
Power, New England College, Henniker, NH, August
17-22, 1975.
6.
R.A. Schlueter, et al., "Method of Analysis of
Generation's Governor Response and System
Security," Report to EPRI under RP 1999-1,
January, 1984.
7.
C.W. Taylor, F.R. Nassief, T.L. Cresap,
"Northwest Power Pool Transient Stability and
Load Shedding Control for Generation Load
Imbalances," IEEE Transactions on Power Apparatus
and Systems, PAS-100, July, 1981, pp. 3486-3495.
14.2930
16.5190
18.0120
16.3230
-16.8460
R. Rudenberg, Transient
Press, Cambridge,
19.2800
19.2800
19.2940
19.1880
18.6410
stability simulation at the governor
time frame.
4.9
"Long-Term Power System Dynamics, Phase II,"
Final Report of EPRI Research Project 764-1,
October, 1976.
Governor
790 mw Loss
Load Case z/z
EPRI Midterm
"Mid-term Simulation of Electric Power Systems,"
Ontario Report on EPRI Project 745, June, 1979.
This research has been supported by
the Electric
Power Research Institute under RP-1999-1. The program
manager was Jim Mitsche. The research support is
gratefully acknowledged.
3027
Discussion
C. W. Taylor (Bonneville Power Administration, Portland, OR): The
authors' paper is thought-provoking and stimulates a number of questions and comments. In addition to the authors' references, Chapter 3
of a well known recent textbook includes a good discussion of the distribution of power impacts [1]. Following a power impact such as generation
loss, power is distributed first according to synchronizing power coefficients (electrical closeness to disturbance), then by relative inertia values,
then by governor action, and finally by AGC. There are considerable
overlaps among these processes. For instance, a utility losing a generator
has 10 minutes to cover the loss and restore system frequency. During
this time generators and loads throughout the interconnection can respond to the frequency and voltage deviations.
It should be emphasized that generation loss is a frequently occurring
disturbance. In the western North American interconnection between
December 1978 and March 1984, there were about 100 frequency excursions due to loss of 800 MW or more of generation. About 23 events
involved 1350-2450 MW generation loss. Most of these disturbances did
not cause problems. With increased transmission utilization in the future,
however, loss of generation may become more important as regards transient and voltage stability, and thermal overload.
I was surprised that t = 0.25 seconds was chosen as the time for the
inertial power flow snapshot. This would be well before synchronizing
swings are damped. A typical situation is shown on Fig. 3.8 of Ref. [1].
I was also surprised that a 0.036 Hz (0.06%) deadband or backlash
width was chosen. The 0.06% deadband is based on old standards; deadbands on modern governors are much smaller. Hydro governors, for instance, have vibrating motors for dither modulation to reduce effective
deadband. Ref. [2] provides further discussion
One measure of effective deadband width is system frequency fluctuations during normal operations (closure of Ref. [3]). These are generally 0.01 Hz or less. The RMS value for system frequency deviaiton in
the western North American interconnection is about 0.008 Hz [2]. Could
the authors substantiate the 0.036 Hz deadband?
The authors assume that the entire deadband width must be overcome
for governor response. It is more likely that deadband positions would
be randomly distributed and that most units in the interconnection would
participate in frequency control. Exceptions would be units with valves
wide open, units with governors blocked in raise direction, and units with
unusually wide deadbands with unfavorable position within deadband.
In the future, a significant proportion of generation could be from small
dispersed generation without speed governors (overspeed control only).
One way to represent deadband effects would be to assume larger
regulation values for smaller frequency excursion. The area frequency
regulation (ft = 1/R + D) noted during relatively large real system frequency excursions is 9 to 160o rather than the nominal value of near 5%.
For the governor power flow, however, the actual value does not matter as long as each area has roughly the same proportion of active
With some modification, I believe the authors' program could be used
for voltage stability. The post-disturbance power flow would distribute
the lost generation by some combination of governor, load (both voltage
and frequency), and AGC response. The distribution would depend on
the time after the disturbance, power plant response speed to AGC commands, etc.
A simple and conservative approach would be the governor power flow
with constant power loads. Assuming relatively slow AGC, this could
represent post-disturbance conditions about 30-60 seconds after the power
impact. Power flow convergence difficulties would indicate potential instability (usually voltage instability). Results could be compared with
stability program results at the end of the simulation (say 10 seconds).
Differences would be largely due to the load modeling and generation
reactive capability assumptions.
An interesting application in the western interconnection involves loss
of a major ac or dc line followed by generator tripping (300-3000 MW)
to maintain stability. AGC may be shut off because of tie line loss.
Voltage stability or thermal overload (particularly series capacitor
overload) is of interest. Do the authors' envision use of the program for
voltage stability evaluation?
In summary, the post-disturbance power flow for generation loss is
an attractive idea. It is much simpler and faster than mid-term or longterm dynamic simulation. A significant difficulty with dynamic simulation is the lack of data bases for boilers, tap changing equipment, etc.
REFERENCES
[1] P. M. Anderson and A. A. Fouad, Power System Control and
Stability, Iowa State University Press, Ames Iowa, 1977.
[2] C. W. Taylor, K. Y. Lee, and D. P. Dave, "Automatic Generation Control with Governor Deadband Effects," IEEE Trans. on
PowerApp. and Syst., vol. PAS-98, pp. 2030-2036, Nov./Dec. 1979.
[3] C. Concordia, L. K. Kirchmayer, and E. A. Szymanski, "Effect
of Speed-Governor Deadband on Tie-Line Power and Frequency
Control Performance," AIEE Trans. on Power App. and Syst.,
vol. 75, pp. 429-435, Aug. 1957.
Manuscript received March 1, 1985
governors.
My opinion is thus that inertial and governor power flows should produce roughly similar results. By the time synchronizing swings have
damped, however, the transition from inertialplus synchronizing swings
to governor power flow is largely complete.
For the problem described in the authors' Ref. [7], we considered use
of an inertial power flow to develop arming criteria for controls for high
speed tripping of up to 3000 MW of industrial load. However, it was
difficult to relate inertial power flow results to the highly nonlinear transient stability problem. The transient stability representation is of very
high dynamic order and one would not expect the static power flow to
be an adequate approximation.
In the authors' study, was the system stressed enough so that the 790
MW loss threatened transient stability? If not, what would be the purpose of the inertial power flow? Have the authors compared stability
and inertial power flow results when the generation loss threatens transient stability? I disagree with the authors' conclusion that inertial power
flow can replace transient stability evaluation by numerical integration.
In Section 3.1 the distribution of power flow among corridors is stated
to be due solely to the inertial or governor responses. Of course the relative
impedance values of the corridors and other network considerations will
partly determine corridor power flow. Regarding frequency sensitive
loads, was damping applied at the generator or were the load injections
modified?
What assumptions were made for the voltage sensitivity of loads for
each of the three types of power flows? What assumptions were made
for transformer tap changing and other voltage controlled devices? For
the PV busses was short-time overload capability represented in the
values assumed?
Qmax
M. Lotfalian and R. Schlueter: The authors thank the discusser for his
interest and comments. With reference to the questions posed by Mr.
Taylor:
(a) The time t = 0.25 seconds is when all the generators experience the
same decelerations. The inertial load flow results agreed with the
transient stability simulation results at t = 0.25 seconds. This time
will vary with system size. The intertial time frame was 3-6 seconds
based on a transient stability simulation of a 1980 MW loss of
generation on the Nanticoke postmortem.
(b) The standard 0.036Hz(0.06%) deadband width was selected based
on the assumption that the generating units in the particular system
under consideration had this deadband. The frequency
measurements at six different sites at various distances from the
Nanticoke station clearly showed a 0.036Hz quasi steady state change
in frequency after the initial large frequency transient associated
with the inertial response. Although a 0.036Hz deadband was appropriate for the system modeled for the Nanticoke postmortem,
a different level of deadband could be utilized.
(c) The assumption that the entire deadband width must be overcome
depends on whether loads are increasing, decreasing, or relatively
constant. If loads are decreasing through the system, then the
assumption that the entire deadband width must be overcome would
be valid. A smaller effective deadband width could be assumed if
the system load level was not decreasing.
(d) The governor and inertial load flow on the Nanticoke postmortem
accurately reflected the measurements of power flow on lines and
3028
on utility transmission boundaries. The governor and inertial load
flows were not identical. However if governor deadband was assumed smaller (0.036 Hz) and governor regulation was assumed to be
larger than 5O70, then more generating units would participate in
governor load flow. Whether the governor load flow would approximate the inertial load flow under the assumptions would depend
on whether the inertial constant for all units in each area in the
system is proportional to the sum of the governor constants of all
units in each area.
(e) The loads were considered as constant powers. The program is able
to simulate the effect of tap changing transformers if desired.
(f) In the study of 49 bus system, the 790 MW loss of generation stressed
the system enough to threaten transient stability.
(g) We agree with Mr. Taylor that the program can be used for voltage
stability considering voltage and frequency sensitive load modeling.
Manuscript received April 1, 1985