39318107-Voltage-Stability.ppt

Voltage Stability
เสถียรภาพของแรงดันไฟฟ
้ า
( Definition and Concept )
by
Mr.Ong-art
sadmai
Mr.Danai
Thongthawat

Introduction to
The power system stability problem
• Basic concept and definitions
– Rotor angle stability
– Voltage stability and Voltage collapse
– Mid-term and Long-term stability

The following are some
examples
• New York power pool disturbances of
September 22,1970
• Florida system disturbance of December 28,1982
• French system disturbances of December 19,1978
and January 12,1987
• Etc.
• Reference *
– Prabha kundur ,”Power system Stability and
Control”

Basic concept & Definitions
Power system stability may be broadly
defined as the property of a power system
that enables it to remain in a state of
operating equilibrium under normal
operating conditions after being subjected
to a disturbance.
Instability in a power system. This aspect
of stability influenced by the dynamics of
generator rotor angles and power angle
relationships.

Voltage stability and voltage
collapse
Voltage stability is the ability of a power
system to maintain steady acceptable
voltage at all buses in the system under
normal operating conditions and after
being subjected to a disturbance. A
system enters a state of voltage
instability when. ….
– Disturbance
– Load demand
– Uncontrollable drop in Voltage

The main factor causing instability is inability of the
power system to meet the demand for Reactive
power.
The heart of the problem is usually the voltage drop
that occurs when Active power and Reactive power
flow through inductive reactance associated with the
transmission network.
A criterion for voltage stability is that, At a given
operating condition for every bus in the system, The
bus voltage magnitude increases as the reactive
power injection at the same bus increaseed.
collapse

Conditions for Voltage unstable
– The bus magnitude voltage decrease
when reactive power injection at the
same bus increased. In the other words,
An V-Q sensitivity is show indicates is
positive voltage stable and difference
way.
– Progressive drop in bus voltage can also
be associated with Rotor angles going
out of Step.
collapse

 Voltage instability may occur in several
different ways. In its simple from it can
be illustrated by considering the two
terminal network of figure below.
Figure 1 A simple radial system for illustration of
Voltage stability phenomenon
Constant voltage

 The expression for Current I in figure1 is
LD LN
E
I
Z Z


When I and E are phasors
2 2
( cos cos ) ( sin sin )
s
LN LD LD LN
E
I
Z Z Z Z
   

  
…… (1)
…… (2)

Figure 2 Receiving voltage current and power
as a function of load demand For The system
in figure1

From figure2
 Power transmitted is maximum when
the voltage drop in the line is equal in
magnitude to Vr, that is when
 As ZLD is decreased gradually, I increase
and Vr decrease, Initially, at high value
of ZLD the increase in I dominates over
the decrease in Vr and hence Pr
increase rapidly with decrease in ZLD
( / ) 1
LN LD
Z Z 

From the view point of Voltage stability
 The relationship between PR and VR is of interest. This
shown in figure3 for the system under consideration
when the load power factor is equal to 0.95 lag
1 LD
R LD S
LN
Z
V Z I E
F Z
 
2
cos cos
S
LD
R R
LN
E
Z
P V I
F Z
 
 
   
 
…… (3)
…… (4)

Figure3 Vr-Pr characteristics of the system of
figure1 with difference load-power factor

For purposes analysis It is useful to classify voltage
stability in the following subclasses
Large disturbance voltage stability
Small disturbance voltage stability
Voltage stability

Large disturbance voltage stability
 Large disturbance voltage stability is concerned with
a system’s ability to control voltages following large
disturbances such as a system faults , loss of
generation, or circuit contingencies. This ability is
determined by the system load characteristics and
the interaction of both continuous and discrete
controls and protections
 Determination of LDVS is requies the examination of
non-linear dynamic performance of the system over a
period of time.
 Study period of interest may extend from a few
second to tens a minutes and then long-term
dynamic simulations is required.

 Small disturbance voltage stability is concerned
with the system’ ability to control voltages
following small perturbations such as incremental
changes in system load.
 Characteristic of load
 Continuation controls
 Discrete control at a given constant of time.
 The basic processes contributing to small-disturbance
voltage instability are essentially of a steady state
nature. Therefore, Static analysis can be effectively use
to determine stability margins.
Small disturbance voltage stability

 A distinction between angle stability
and voltage stability is important for
understanding of underlying causes of
the problems in order to develope
appropriate design and operating
procedure.
 A more detailed of discussion of
voltage stability, including analytical
techniques and method to preventing
voltage collapse is present continuation.

Voltage stability Analysis
 The analysis of voltage stability for
given system state involves the
examination of two aspect
 Proximity to voltage instability
 Mechanism of voltage stability : How
and why does instability occur? What
are the voltage weak area? What
measures are most effective in
improving voltage stability ?

(1) Dynamic Analysis
( Voltage stability analysis )
 The general structure of the system model for
voltage stability analysis is similar to that for
transient stability analysis. The overall system
equations, Comprising a set of first order difference
equations.
 a Set of algebraic equations
 When x is state vector of the system
 V is bus voltage , I is current injection vector , YN is
network node admittance matrix
.
( , )
x f x V

 
, N
I x V Y V


 It can be solved in time domain by using any of the
numerical integration methods such as
 Euler methods
 Modified Euler methods
 Runge-Kutta methods
 Implicit Integration methods [reference Phaba kundu
‘Power system ’]
 Network power flow analysis
 Newton Raphson-methods and Gouss-seidel methods
etc.
(1) Dynamic Analysis

 V-Q sensitivity analysis is linearized form
(1) Static Analysis
V
V V
JP JP
P
JQ JQ
Q
 


   
 
   
  

    
R
Q J V
  
1
R
V J Q

  
…… (5)
…… (6)
…… (7)

 Example 1 for 500kV 322 km. line system
consider write the equations of the power
flow from the sending end to the receiving
end in the following form
(1) Static Analysis
( , )
P f V


( , )
Q g V



39318107-Voltage-Stability.ppt

(1) Static Analysis
With a shunt capacitor connected at the receiving end of the
line, The self admittance is
Y22=2.142-j(22.897-BC)
(i) With P=5000MW and a 450 MVar shunt Capacitor
2 0.981
V  0
39.1
  
Since Bc=4.5 pu.
Y22=2.142-j(22.897-BC)=2.142-j18.397

 With this new value of Y22, The reduce Q-V
Jacobian matrix ,Calculated by Using equation is
 JR = 5.348 indicating that is Voltage stable
 (ii) With P= 1900 MW and 900MVAr shunt
Capacitor
 Since Bc=9.5 pu.
 JR = -13.683 indicating that is Voltage unstable
(1) Static Analysis V-Q sensitive analysis (
Voltage stability analysis )
2 0.995
V 
0
52.97
  

The continuation power flow analysis
(Voltage stability analysis)
 The jacobian matrix becomes singular at the
voltage stability limit. The continuation
power flow analysis uses and iterative
process involving predictor and corrector
steps as predicted in figure below
1. Know initial value solution A, A
tangent Predictor is used to
estimate solution B from a Specified
pattern of load increase.
2. The corrector step then determines
the exact Solution C using a
conventional power flow analysis
With the system load to be fixed.

 Mathematical formulation the basic
equations are similar to those of a standard
power flow analysis except that increase in
load is added as a parameter.
( , , ) 0
F V
  
Where
 Is load parameter 
V K
Is the vector of bus voltage angle
Is the vector representing percent
Load change at each bus
Is the vector of bus
Voltage magnitude

 Solution step the power flow equation for
the system
 Load vector
 Iteration 1 (Predictor step)
K

1
0
K
 

 
  
 
1
0
0
0
0
0
1
k k k
d
d Jk Jk K
dV dV Jk Jk K
d e e e
d



 

 
     
   
 
       
 
 
   
 
 
     
 

0
0
1
d
dV
d


   
   

   
   

   
Predictor value
Corrector step
( , , ) 0
F V
  
0
predicted
k k
X X
 
* Computational methods for electric power system

39318107-Voltage-Stability.ppt

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