Energy and Power Engineering, 2013, 5, 517-521
doi:10.4236/epe.2013.54B099 Published Online July 2013 (http://www.scirp.org/journal/epe)
Stability Analysis on Power System with Large
Power Source
Huabo Shi1, Xiaoyan Zhou2
1Sichuan Electric Power Research Institute China
2Sichuan University China
Received February, 2013
ABSTRACT
In this paper, the stability problems of power systems with large power source are analyzed with viewpoint of energy
balance. The phenomena are studied when the energy delivery are “blocked” by faults that occur on some key transmis-
sion lines of a large power source within a power system, on the transmission lines between the interconnected power
systems, or on some key buses. The cases are based on a practi c a l power system and its interconnected systems.
Keywords: Power System with Large Power Source; Stability Analysis; Energy Balance
1. Introduction
The load consumption is continuing growing along with
the economy development. The power system construc-
tion has been actively developed. The distribution of
power supply is uneven and the varying load demand
will inevitably lead to the high capacity power delivery.
However, the contradiction between the relative weak
grid structure and the high capacity power delivery has
become increasingly prominent.
Reference [1, 2] analyze and solve the problem of
power delivery and trade from the point of view of power
market. Reference [3, 4] makes a comparison of the ac-
cess manners of the power systems with massive output
energy. Reference [4] stud ies the solution s of the security
and stability con trol system. There are few papers study-
ing the stability of power system when fault occurs on
transmission lines with high capacity power sending.
Wide area interconnection of power systems is the de-
velopment trend, the faults on some delivery transmis-
sion lines or on some key buses will lead to the power
surplus of the sending system and the power shortage of
the receiving system. It will cause a great impact on the
security and the stability of the sending system and even
its interconnected systems.
In this paper, we focus on the power system stability
problems caused by fault occurs on transmission lines of
a practical power grid with high capacity power delivery.
2. Stability Analysis on the Power System
The power system with the high capacity po wer delivery
can be simplified to the model shown in Figure 1. It
shows that the energy is delivering through two trans-
mission lines to the receiving power system from the
large power base. The sending system is simplified as a
generator G1 and the receiving system is simplified as a
generator G2.
Suppose the prime mover output remains constant
during the transient, the generator’s equations of motion
is shown in Equation (1)
20
2(
me
j
dPP
T dt
 
) (1)
where 2
j
TH

.
Equation (1) multiplied d
dt

by both sides at the
same time to get Equation (2).
20
2()
me
j
dd d
PP
dt Tdt dt



 (2)
Namely
2
0()
me
dd d
PP
dt dtHdt






 (3)
Integrating Equation (3) on both sides to get Equation
(4)
2
0()
me
dPPd
dt H
 




 (4)
when the generator is in the steady state, d
dt

＝ 0. Its
value will change as the system is disturbed. For stable

H. B. SHI, X. Y. ZHOU
518
systems, the value of d
dt

will finally reaches 0 after the
disturbance.
0
0()
m
me
PPd 0
H





 (5)
where, δm is the maximum power angle of the generator,
and δ0 is the initial power angle. The rotor will accelerate
and kinetic energy will accumulate when δ changes from
δ0 to δ1. The energy accumulated is
1
0
1() me
EPP


d


 (6)
The rotor will decelerate and lose energy when δ
changes from δ1 to δm. The loss of energy is
1
2()
m
me
EPP


d


 (7)
If there is a certain distance between the fault position
and the sending generators G1, assuming the fault occurs
in the point F in Figure 1. The power sending will be
affected after relay cutting the line L2 to isolate the fault
and the sending system will be at the state of power sur-
plus. The e P

 curves of before, during and after the
fault are shown in the Figure 2[ 5, 6].
When the power system is in the steady state, me PP

,
0

 . The operating point moves from a to b when
fault occurs,

don’t change suddenly because of the
rotor inertia. It means that the loss of load of G1 will lead
to the mechanical power becoming greater than the elec-
tromagnetic power for the sending system. With the ac-
cumulation of the kinetic energy, the fault line will be cut
when δ changes to δ1, operation point moves from c to d,
now the electromagnetic power is greater than the me-
chanical power, rotor decelerates and rotor angle contin-
ues to increase until the kinetic energy accumulated dur-
ing the fault is fully depleted by the receiving system. It
means that the loss of power supply will lead to the me-
chanical power becoming smaller than the electromag-
netic power for the receiving system. The rotor deceler-
ates and rotor kinetic energy continues to decrease until it
reaches the energy balance between the receiving and
sending systems. If the accumulated kinetic energy of the
sending system can’t be fully dissipated and the loss en-
ergy of the receiving system can't be supplied, it will at
last lead to the disconnection of the receiving system
while at most the collapse of the whole system.
tr
X
1
E 1
X
1
2
X
2G
2
2
X
F
1
L
2
L
Figure 1. The power system with large-scale output power.
The power with the concentrated load model is shown
in Figure 3[5]. In the model, the power goes through the
series impedance to supply the load, which represents
large power base goes through transmission lines to sup-
ply the load area.
The power supplied to the load is
cos
RR
PVI


(8)
2
(cos cos)(sinsin)
S
LNLDLN LD
E
I
ZZ ZZ




The system P-V character is shown in Figure 4.

e
P
faultBefore
faultAfter
faultDuring
m
P
a
b
c
d e
1
A
2
A
0

1

m

Figure 2. Pe-δ curve when fault occurs.
 
LN
Z
R
V
S
E
 
LD
Z
I
Figure 3. Power source with concentrated load model.
vol ta g eCritical
SR
EV /
max
/PP
R
0.1
0.1
6.0
0
Figure 4. System power-voltage character.

H. B. SHI, X. Y. ZHOU 519
When a bus failure occurs within the receiving system,
the voltage of the system will drop, and the reactive
compensation power generated by the ca-
pacitor will decrease as the voltage drops, so the voltage
of system can't be effectively enhanced. The load power
will decrease with the voltage drop, as is shown in Fig-
ure 4. The more the voltage drop is, the more the load
loss is. As the load decreases, the power surplus phe-
nomenon appears within the system. The preceding
analysis shows, If a failure in the system causes the volt-
age drops substantially, it will inevitably lead to the over
accumulation of the kinetic energy of the generator and
the destruction of system stability.
2
QBU
3. Case Study
Although the analysis abov e is for the simple system, the
stability mechanism is the same for the large complex
power system.
The practical interconnected power system is shown in
the Figure 5. System 1 stands for a large power base,
whose load is not heavy relatively. System 1 is connected
to the system 3 through four- loop EHV AC lines, to sys-
tem 2 with a DC transmission line, and to system 4 with
two DC transmission lines. In addition, system 3 con-
nects with system 5 through a UHV line.
The power transmitted by No.1, No.4, No.5 DC trans-
mission lines are 3000 MW, 7200 MW and 6400 MW
respectively. The total power transmitted by No.2 and
No.3 AC transmission lines is 4000 MW. The power
transmitted form system 5 to the system 3 is 5000 MW.
The structure of the system 1 is shown in the Figure 6.
Five hydropower bases (base 1-base 5) sends large
amount of power to the system 1 to meet the load and the
remaining power is transmitted to the external system
through AC-DC hybrid tr ansmission channel as shown in
Figure 5.
The mechanism of power transfer blocking and reme-
dies will be analyzed in the Figure 5 belo w.
Figure 5. The practical power system and its interconnec-
tion systems.
Figure 6. Power bases of system1.
3.1. The Blocking of Transmission Channels of
the Base of System 1
There are 8 generators in the base 5; a total of 4800MW
active power is transmitted by four-loop transmission
lines. When N-2 failure occurs within these transmission
lines, the relay will remove the failure side of the line
0.09s after the fault and remove the other side of the
same line as well as the other parallel line 0.01 s later.
Because of the loss of two lines, large amount of power
can’t be transmitted outside, which will lead to the con-
tinuous accumulation of the generator kinetic energy and
the transient energy will be spread to the external system.
Because of the loss of two lines, a large amount of power
can’t be transmitted outside, which lead to the continuous
accumulation of the generator kinetic energy. The tran-
sient energy will be spread to the external system. The
system 3 is in the state of a large amount of power short-
fall and in order to maintain the energy balance of system
3 a great quantity of power of system 5 will be forced to
flow to the system 3. The voltage across line 6 continues
to drop and eventually system 3 and system 5 will be
disconnected when the low voltage disconnecting limit is
reached.
System 3 will not be able to meet the load demand,
which causes the continuous loss of power of the gen-
erators. The contradiction of energy imbalance among
systems will eventually lead to significantly oscillation of
all the generators in the grid and the out-of-step with the
main grid. To ensure the system 3 and system 5 not to
disconnect, it is obliged to limit the power flow of line 6
to 4000 MW an d cut 1800 MW power of b ase5 after the
failure.
The power curve of the key line after the fault of the
transmission channel of hydropower base 5 is shown in
Figure 7.
3.2. The Blocking of Transmission Lines of the
External Connected Systems and System 1
When N-2 failure occurs in the AC line 3 as shown in

H. B. SHI, X. Y. ZHOU
520
Figure 5, due to the normal operational state of DC line
1,4,5 is either constant power or constant current, the loss
of line 1 or 2 will lead to a large quantity of power flow-
ing to the line 1 or 2. Because of the thermal stability
limit or the limit of transient stability of the line 1 or 2,
the power flow can’t be completely transferred to the
external system. The phenomena of power surplus will
occur within the generators in system 1, along with the
kinetic energy accumulation of the system 1, and finally
lead to the disconnection of line 6. Only in the way of
limiting the power flow of line 6 to 3000 MW, limiting
the power flow of system 1 under 3000 MW, emergency
DC power support to transfer part of power flow during
the failure, or removing some generators of system 1, can
the energy accumulated in system 1 be dissipated during
the failure and the system be stable.
curves and bus voltage curves of some generators after
failure of a bus of the system 1 are shown in Figure 9(a)
and Figure 9(b) respectively.
05 10 15 20
-80
-60
-40
-20
0
20
40
60
80
P(p.u.)
line3 no control
line3 with c ontrol
line6 with con trolline6 no control
The power curve of the critical lines after the failure of
line 3 is shown in Figure 8. Figure 7. The power curve of the key line after the fault of
the transmission line.
3.3. The Power Transmission Blocking Due to
the Failure of Internal Bus of System 1
05 10 15 20
-80
-60
-40
-20
0
20
40
60
80
t(s)
P(p.u.)
line6 with control
line2 no control
line6 no control
line2 with cont rol
The failure of some buses of system 1 will lead to a rela-
tively large range of short-term voltage drop. The kinetic
energy of generators will increase during the fault, by
this time, because of the wide range of voltage drop of
the system, if the load is constant impedance; the bus
voltage which drops significantly, its load is bound to
decrease. If the load is constant power characteristics,
such load will hinder the voltage recovery after the fail-
ure which will lead to the affect of power recovery of the
associated constant impedance load. At this time, the
generator is in the state of kinetic energy surplus, the
ability of energy consumption of the load will also be
reduced, under the effect of the contradiction; the power
grid dynamic behavior will be towards the direction of
instability. When the unbalanced energy reaches a certain
threshold, the system will lose stability. The power angle Figure 8. The power curve of the critical lines after the fail-
ure of line 3.
05 10 15 20
20
30
40
50
60
70
80
90
100
t(s)
deta(deg)
05 10 15 2
0
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
t(s)
V(p.u)
(a) Angle curve (b) Voltage curve
Figure 9. Power angle and voltage curve after the fault of system1.

H. B. SHI, X. Y. ZHOU 521
As can be seen from Figure 9, the power angles of
generators oscillate obviously after the fault, the transient
kinetic energy accumulated is relatively large and the
voltage drop of certain bus is relatively obvious. Al-
though the system is still stable during this failure, the
energy balance will be severely affected from the analy-
sis of section 2. If the kinetic energy of the generator
excessively accumulated, excessive voltage drop will
lead to the excessive load drop and the loss stability of
the system.
4. Conclusions
In this paper, the stability of power system with massive
energy output is analyzed with viewpoint of energy bal-
ance. The stability of the power system after the blocking
of the output hydropower transmission lines of the inner
system and the external transmission lines is studied
based on the practical power system and its intercon-
nected systems. The study found that power blocking and
the restriction of power transmitted by the power system
with massive output energy are mainly due to the stabil-
ity issue of the power system with massive energy output
and the operation mode of its connected power systems.
To guarantee the stability of the interconnected system，
the “stopgap strategy” is to limit the power flow and
strengthen the security control, while the fundamental
strategy is to strengthen the grid structure and construc-
tion of the power transmission lines.
5. Acknowledgements
This paper is sponsored by Sichuan electric power cor-
poration, China on project (12H0959).
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