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CONTINGENCY ANALYSIS 
Technical Seminar Report On 
“CONTINGENCY ANALYSIS” 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
under the guidance of 
Mr. Debasis Jena 
submitted by 
SIGMA DASH EE200198046
CONTINGENCY ANALYSIS 
INTRODUCTION 
 Simulator that evaluates, provides and prioritizes the impacts 
on an electric power system 
 AC power flow method is expensive, computationally and time 
taking. 
 DC power flow equations and bus voltage equations 
 Deterministic contingency analysis 
 The algo in CA uses network parameters to model, calculate 
& simulate the effects of removing equipment from the power 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
system.
CONTINGENCY ANALYSIS 
DC POWER FLOW METHOD 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
N-1 in number, only the real power flow , all line resistances are 
neglected 
ö 
æ 
* 
i 
P Real V Y V i 2,........ 
N 
i ij j 
d q d 
V e Y e V e 
i ij j 
ö çè 
÷ø 
Real 
= æ 
ö 
÷ ÷ø 
ç çè æ 
= 
= ÷ ÷ø 
ç çè 
= 
å 
å 
å 
+ - 
- 
i 
j( ) 
i j 
i 
Real ij 
j i 
V V Y e 
ij 
j 
j 
i 
j 
ij 
j 
j 
q d d 
Line resistance is neglected so 
Y ij= Gij + jBij = jBij
CONTINGENCY ANALYSIS 
i i j ij i j P =åV V B d -d 
sin( ) 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
i 
must be sufficiently small i j d -d 
å å 
= =+ 
Ultimately, P = K d + K d + 
K 
d 
i ij j ii i ij j N 
j i 
1 
i-1 
j 1 
or in matrix form P = Kd 
If P has to be constant, K & d will change from base values 
This provides the changes in the bus voltage angles 
Dd = - (K0)-1 DKds
CONTINGENCY ANALYSIS 
To study single contingencies, we use 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
D Kpp= Kpq 
DKqq = Kpq 
D Kpq = - Kpq 
D K qp= - Kqp 
Substituting these we get the matrix as 
= - (K0)-1 (d psDK p+ d psDKq Dd ) pq 
Changes in line flows due to the loss of line pq given are 
obtained by substituting the appropriate elements of Ddpq
CONTINGENCY ANALYSIS 
Z MATRIX METHOD 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
Methods include inverting Y bus matrix and injecting a 
fictitious current into the bus 
Converting the MVA loads to impedance loads using 
Zload i = 
2 
* 
i 
V 
i 
S 
Injecting a unit current, into the bus p which has to be removed 
ù 
ú ú ú ú ú ú 
û 
é 
ê ê ê ê ê ê 
V 
. 
. 
V 
ë 
1 
N 
. 
= 
ù 
ú ú ú ú ú ú 
û 
é 
ê ê ê ê ê ê 
ë 
1P 
Z 
NP 
. 
. 
. 
Z
CONTINGENCY ANALYSIS 
Ipq can be calculated using the equation 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
V V 
p q 
line pq 
pq Z 
I 
- 
= 
An adjustment parameter, d, has to be used 
S 
pq 
I 
pq 
I 
d 
D= 
Due to the injection lp = d, the new current in other elements 
d Z Z 
( - ) 
ip jp 
Z 
line ij 
I = pq 
where ij is not equal to mn
CONTINGENCY ANALYSIS 
The sought-after current flow changes due to removing line pq are 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
ij ij ij D I = I~ - I for all ij 
Calculating the current flow pattern in the modified network, 
in which line pq has been removed, requires only that we inject 
current I p=d, as before, into the modified network. 
ù 
ú ú ú ú ú ú 
û 
é 
ê ê ê ê ê ê 
ë 
= 
ù 
ú ú ú ú ú ú 
û 
é 
ê ê ê ê ê ê 
ë 
N 
~ ~ . . . ~ 
Z Z Z 
11 12 1 
. 
. 
. 
N N NN 
~ 
V 
i 
. 
. 
. 
N 
Z Z Z 
V 
~ ~ . . . ~ 
~ 
1 2 
ù 
ú ú ú ú ú ú 
û 
0 
é 
ê ê ê ê ê ê 
. 
d 
0 
ë 
. 
= 
ù 
ú ú ú ú ú ú 
û 
é 
ê ê ê ê ê ê 
ë 
d 
d 
p 
~ 
1 
. 
. 
Np 
Z 
~ 
Z 
. 
The voltages are
CONTINGENCY ANALYSIS 
POST CONTINGENCY EQUILLIBRIUM 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
Methods to compute the equilibrium condition immediately 
following a disturbance to an electric power system 
 Analysis by Integration 
 Analysis by Simultaneous 
Iteration 
 Analysis by partitioned iteration
CONTINGENCY ANALYSIS 
CONCLUSION 
 Methods for evaluating both isolated and interconnected areas 
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
 Used as an online decision support tool 
 Faster approximate methods for locating potential trouble spots
Technical Seminar Presentation 2004 Presented by – SIGMA DASH 
CONTINGENCY ANALYSIS 
THANK YOU !

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Contingency analysis

  • 1. CONTINGENCY ANALYSIS Technical Seminar Report On “CONTINGENCY ANALYSIS” Technical Seminar Presentation 2004 Presented by – SIGMA DASH under the guidance of Mr. Debasis Jena submitted by SIGMA DASH EE200198046
  • 2. CONTINGENCY ANALYSIS INTRODUCTION  Simulator that evaluates, provides and prioritizes the impacts on an electric power system  AC power flow method is expensive, computationally and time taking.  DC power flow equations and bus voltage equations  Deterministic contingency analysis  The algo in CA uses network parameters to model, calculate & simulate the effects of removing equipment from the power Technical Seminar Presentation 2004 Presented by – SIGMA DASH system.
  • 3. CONTINGENCY ANALYSIS DC POWER FLOW METHOD Technical Seminar Presentation 2004 Presented by – SIGMA DASH N-1 in number, only the real power flow , all line resistances are neglected ö æ * i P Real V Y V i 2,........ N i ij j d q d V e Y e V e i ij j ö çè ÷ø Real = æ ö ÷ ÷ø ç çè æ = = ÷ ÷ø ç çè = å å å + - - i j( ) i j i Real ij j i V V Y e ij j j i j ij j j q d d Line resistance is neglected so Y ij= Gij + jBij = jBij
  • 4. CONTINGENCY ANALYSIS i i j ij i j P =åV V B d -d sin( ) Technical Seminar Presentation 2004 Presented by – SIGMA DASH i must be sufficiently small i j d -d å å = =+ Ultimately, P = K d + K d + K d i ij j ii i ij j N j i 1 i-1 j 1 or in matrix form P = Kd If P has to be constant, K & d will change from base values This provides the changes in the bus voltage angles Dd = - (K0)-1 DKds
  • 5. CONTINGENCY ANALYSIS To study single contingencies, we use Technical Seminar Presentation 2004 Presented by – SIGMA DASH D Kpp= Kpq DKqq = Kpq D Kpq = - Kpq D K qp= - Kqp Substituting these we get the matrix as = - (K0)-1 (d psDK p+ d psDKq Dd ) pq Changes in line flows due to the loss of line pq given are obtained by substituting the appropriate elements of Ddpq
  • 6. CONTINGENCY ANALYSIS Z MATRIX METHOD Technical Seminar Presentation 2004 Presented by – SIGMA DASH Methods include inverting Y bus matrix and injecting a fictitious current into the bus Converting the MVA loads to impedance loads using Zload i = 2 * i V i S Injecting a unit current, into the bus p which has to be removed ù ú ú ú ú ú ú û é ê ê ê ê ê ê V . . V ë 1 N . = ù ú ú ú ú ú ú û é ê ê ê ê ê ê ë 1P Z NP . . . Z
  • 7. CONTINGENCY ANALYSIS Ipq can be calculated using the equation Technical Seminar Presentation 2004 Presented by – SIGMA DASH V V p q line pq pq Z I - = An adjustment parameter, d, has to be used S pq I pq I d D= Due to the injection lp = d, the new current in other elements d Z Z ( - ) ip jp Z line ij I = pq where ij is not equal to mn
  • 8. CONTINGENCY ANALYSIS The sought-after current flow changes due to removing line pq are Technical Seminar Presentation 2004 Presented by – SIGMA DASH ij ij ij D I = I~ - I for all ij Calculating the current flow pattern in the modified network, in which line pq has been removed, requires only that we inject current I p=d, as before, into the modified network. ù ú ú ú ú ú ú û é ê ê ê ê ê ê ë = ù ú ú ú ú ú ú û é ê ê ê ê ê ê ë N ~ ~ . . . ~ Z Z Z 11 12 1 . . . N N NN ~ V i . . . N Z Z Z V ~ ~ . . . ~ ~ 1 2 ù ú ú ú ú ú ú û 0 é ê ê ê ê ê ê . d 0 ë . = ù ú ú ú ú ú ú û é ê ê ê ê ê ê ë d d p ~ 1 . . Np Z ~ Z . The voltages are
  • 9. CONTINGENCY ANALYSIS POST CONTINGENCY EQUILLIBRIUM Technical Seminar Presentation 2004 Presented by – SIGMA DASH Methods to compute the equilibrium condition immediately following a disturbance to an electric power system  Analysis by Integration  Analysis by Simultaneous Iteration  Analysis by partitioned iteration
  • 10. CONTINGENCY ANALYSIS CONCLUSION  Methods for evaluating both isolated and interconnected areas Technical Seminar Presentation 2004 Presented by – SIGMA DASH  Used as an online decision support tool  Faster approximate methods for locating potential trouble spots
  • 11. Technical Seminar Presentation 2004 Presented by – SIGMA DASH CONTINGENCY ANALYSIS THANK YOU !

Editor's Notes

  1. The algo in CA uses network parameters to model, calculate & simulate effeeffects of removing equipment from the power system
  2. or in matrix form if P has to be constant, K &  will change from base values
  3. Substituting these we get the matrix as
  4. Z MATRIX METHOD
  5. where ij is not equal to mn
  6. The voltages are
  7. faster approximate methods for locating potential trouble spots
  8. THA