Comparison between PID and PSS effects on transient stability
F. JURADO, A. CANO, M. ORTEGA
Department of Electrical Engineering
University of Jaén
EUP Alfonso X, s/n. 23700. Linares (Jaén)
SPAIN
Abstract:- Transient stability is the ability of the power system to maintain synchronism when subjected to a
severe transient disturbance. We examine the transient behavior of the generator by considering a torque
perturbation about the operating point. The function of a PID controller is to add damping to the generator
rotor oscillations. The power system stabilizer (PSS) uses auxiliary stabilizing signals to improve power
system dynamic performance.
Key-words:- AVR, exciter, damping.
1 Introduction
For a simplified intuitive description of transient
stability, a power system may be regarded as a set
of synchronous machines and of loads
interconnected through the transmission network.
Under normal operating condition, all the system
machines run at the synchronous speed. If a large
disturbance occurs the machines start swinging
with respect to each other, their motion being
governed by differential equations. Transient
stability of the generator is dependent on several
factors.
The generation excitation system maintains
generator voltage and controls the reactive power
flow. The sources of reactive power are
generators, capacitors, and reactors. The primary
means of generator reactive power control is the
generator excitation control using automatic
voltage regulator (AVR). The role of an AVR is
to hold the terminal voltage magnitude of a
synchronous generator at a specified level.
In this paper, we examine the modeling issues
arising from the use of the transient model for the
generator in conjunction with a static network
representation. The function of a PID controller is
to add damping to the generator rotor oscillations
and improve the dynamic response as well as to
reduce or eliminate the steady-state error in AVR
loop.
The power system stabilizer (PSS) uses
auxiliary stabilizing signals to control the
excitation system so as to improve power system
dynamic performance. Commonly used input
signal to the PSS is shaft speed.
2 Transient stability
Transient stability is the ability of the power
system to maintain synchronism when subjected
to a severe transient disturbance such as a fault on
transmission facilities, loss of generation, a
sudden increase in the mechanical power input, or
loss of a large load [1,2]. The system response to
such disturbances involves large excursions of
generator rotor angles, power flows, bus voltages,
and other system variables. Stability is influenced
by the non-linear characteristic of the power
systems. If the resulting angular separation
between the machines in the system remains
within certain bounds, the system maintains
synchronism. Loss of synchronism because of
transient stability, if it occurs, will usually be
evident within 2 to 3 seconds of the initial
disturbance.
To study the stability of a generator connected
to a very large or “infinite” system, the system
may be modeled as an infinite bus, i.e., a constant
voltage source with fixed frequency. This
generator-line-infinite bus model is useful for
initial stability studies of generation stations, and
it is usually used to illustrate several of the
stability issues described above when applied to
power systems.
Fig.2. Stable and unstable equilibrium points
Fig.1. Generator-Infinite Bus Angle Stability
The model depicted above is typically used to
study this stability problem; all losses are
neglected. The transmission system connecting
the generator to the system is represented by an
equivalent reactance XT . The generator is
assumed to be a round rotor machine (saliency is
usually neglected for this type of analysis), and is
represented using the transient model, i.e., a
constant voltage source E’ behind transient
reactance X’d.
The AVR is not considered, and the governor
is assumed to deliver a fixed mechanical power
to supply the demand of the system (infinite bus),
i.e., Pm = P. Based on these models, the following
set of equations may be used to study the stability
of this system:
dδ
=ω
dt
dω
1
(P − Pe − Dω )
=
dt M
E 'V∞
Pe =
sinδ
X
(1)
where X = Xd’ +XT , and E’ is computed based on
the initial reactive power demand Q of the system
(power flow problem).The quantity Jω is called
the inertia constant and is denoted by M. It is
related to kinetic energy of the rotating masses,
Wk.
Wk =
1 2 1
Jω = Mω
2
2
(2)
We now define the important quantity known as
the H constant or per unit inertia constant.
H=
Wk
SB
(3)
where SB is machine rating in MVA. The value of
H ranges from 1 to 10 seconds, depending on the
size and type of machine. We get,
2 H d 2δ
= P( pu ) − Pe ( pu )
ω dt 2
(4)
where P(pu) and Pe(pu) are the per unit mechanical
power and electrical power, respectively.
As long as there is a difference in angular
velocity between the rotor and the resultant
rotating air gap field, induction motor action will
taken place between them, and a torque will be set
up on the rotor tending to minimize the difference
between the two angular velocities. This is called
the damping torque. The damping power is
approximately proportional to the speed
deviation.
Pd = D
dδ
dt
(5)
The damping coefficient D may be determined
either from design data or by test. Additional
damping torques are caused by the speed/torque
characteristic of the prime mover and the load
dynamic.
The equilibrium points (δo,0) are given by
Pe=P, i.e., the crossing points of the sinusoid Pe
with P. This yields several equilibrium points,
one s.e.p. (dP/dδ > 0) and two u.e.p.s (dP/dδ < 0).
If a severe transient disturbance is applied to the
system, the state variables (δ,ω) move away from
the equilibrium point (δo,0).
3 Factors affecting transient stability
From the above discussions we can conclude that
transient stability of the generator is dependent on
the following [3]:
• How heavily the generator is loaded.
• The generator output during the fault. This
depends on the fault location and type.
• The fault-clearing time.
• The post-fault transmission system reactance.
• The generator reactance. A lower reactance
increases peak power and reduces initial rotor
angle.
• The generator inertia. The higher the inertia,
the slower the rate of change in angle. This
reduces the kinetic energy gained during fault;
i.e., area Aa is reduced.
• The generator internal voltage magnitude E’.
This depends on the field excitation.
• The infinite bus voltage magnitude V∞ .
One of the most common controllers available
commercially is the proportional-integralderivative controller (PID) [5,6,7]. The PID
controller is used to improve the dynamic
response as well as to reduce or eliminate the
steady-state error. The derivative controller adds a
finite zero to the open-loop plant transfer function
and improves the transient response. The integral
controller adds a pole at origin and increases the
system type by one and reduces the steady-state
error due to a step function to zero.
The function of a PID controller is to add
damping to the generator rotor oscillations and
improve the dynamic response as well as to
reduce or eliminate the steady-state error in AVR
loop.
As explained in [3], a PSS can be viewed as
an additional block of a generator excitation
control or AVR, added to improve the overall
power system dynamic performance, especially to
control power/frequency oscillations. Thus, the
PSS uses auxiliary stabilizing signals such as
shaft speed, terminal frequency and/or power to
change the input signal to the AVR. This is a very
effective method of enhancing small-signal
stability performance on a power network.
4 Excitation systems
The generation excitation system maintains
generator voltage and controls the reactive power
flow. The generator reactive powers are
controlled by field excitation. The primary means
of generator reactive power control is the
generator excitation control using automatic
voltage regulator (AVR). The role of an AVR is
to hold the terminal voltage magnitude of a
synchronous generator at a specified level.
Fig.4. A typical block diagram of a PSS
Fig.3. AVR system with PID controller
Fig.3. AVR system with PID controller
There are three basic blocks in a PSS, as
illustrated in the typical block diagram of Fig. 4,
namely, the Gain block, the Washout block and
the Phase-compensation block [8,9,10].
The Phase-compensation block provides the
appropriate
phase-lead
characteristic
to
compensate for the phase lag between the exciter
input and the generator electrical (air-gap) torque;
in practice, two or more first-order blocks may be
used to achieve the desired phase compensation.
The Washout block serves as a high-pass filter,
where the time constant T3 is high enough to
allow the signal associated with oscillations in
rotor speed to pass unchanged; without the
Washout block, the steady state changes would
modify the terminal voltages. Finally, the
stabilizer Gain block determines the amount of
damping introduced by the PSS. In the current
paper, a PSS with two Phase-Lead/Lags, a
Washout block and a Gain block is used for
controlling [4].
|Vt|
0.7
0.6
0
5
10
15
Time in sec
1500
delta
1000
500
0
8
9
10
11
12
Time in sec
13
14
15
Fig. 7. Plots for generator with PID, Si=1+0j,
Tp =0.1
1.1
1
|Vt|
In this paper, we examine using MATLABTM the
transient behavior of the generator by considering
a torque perturbation about the operating point.
The generator-line-infinite bus model is used and
the values of delivered complex power Si and
torque perturbation about operating point Tp are
subject to change in p.u. The characteristics of
generator are: 18 kV 830MW. A PID and a PSS
are added in the AVR system .
1
0.9
0.8
0.9
0.8
0.7
0.6
0
5
10
15
10
15
Time in sec
1.4
1.3
delta
5 Results
1.1
1.2
1.1
1
0
5
Time in sec
Fig. 8. Plots
Si=1+0j,Tp=0.1
1.1
|Vt|
1
for
generator
with
PSS,
0.9
0.8
0.7
0.6
1.1
0
5
10
15
1
|Vt|
Time in sec
1.5
0.9
0.8
delta
0.7
0.6
1
0
5
10
15
10
15
Time in sec
1.5
0.5
0
5
10
15
delta
Time in sec
Fig. 5. Plots for generator with PID, Si=0.8+0.6j,
Tp =0.1
0.5
0
5
Time in sec
Fig. 9. Plots for generator with PID, Si=0.8+0.6j,
Tp =0.2
1.1
1
|Vt|
1
0.9
0.8
0.7
0.6
0
5
10
1.1
15
Tim e i n s e c
|Vt|
1
0.8
0.9
0.8
0.75
0.7
delta
0.7
0.6
0
0.65
5
10
15
10
15
Time in sec
0.6
0.9
0.55
0
5
10
0.8
15
delta
Tim e i n s e c
0.7
0.6
0.5
0
Fig. 6. Plots for
Si=0.8+0.6j,Tp=0.1
generator
with
PSS,
5
Time in sec
Fig. 10. Plots for generator
Si=0.8+0.6j,Tp=0.2
with PSS,
6 Conclusion
Methods of improving transient stability try to
achieve reduction of the influence of the
accelerating torque through control of excitation
system. The results show a satisfactory transient
response, however settling time is lower with PSS
and damping is higher with PID. Power system is
unstable with PID for delivered complex power Si
with unity power factor.
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