1. UNIT-II POWER FLOW ANALYSIS

2. Power (or) Load Flow Analysis
Importance of load flow analysis
Bus classification
Load flow equation in complex & polar variable form
Load flow methods (or) solution for load flow problems

3. Importance of load flow analysis
Load flow analysis is the backbone of PSA.
It is required for Planning, Operation, Economic Scheduling & Exchange of power b/w utilities . Expansion of system & also in design stage.
Steady-state analysis, of an interconnected PS during normal operating conditions.

4. Contd…
Purpose of LFA
Compute steady-state voltage & voltage angle b/w all buses in n/w.
Real & Reactive power flow in every Tr. line and transformers under the assumption of known values of generation & load.

9. Pi +j Qi = (PGi - PDi) + j (QGi -QDi)
Load Bus (or) PQ Bus
Bus where only load is connected & no generator exists in this load bus .i.e.,(PG & QG =0)
Real power demand (PD) & Reactive power demand (QD) are drawn for supply.
PD , QD are known values.
|V| , δ are unknown quantities.
In Power balance eqn ,
PD , QD → Negative Quantities
PG , QG Positive Quantities
Pi +j Qi = (PGi - PDi) + j (QGi -QDi)

10. Generator bus (or) Voltage control Bus (or) PV Bus
Bus Voltage magnitude can be controlled in this bus.
At each bus where alternators are connected, MW generation can be controlled by adjusting the prime mover.
Real power (PG) & Voltage Magnitude (|V|) is known quantities.
Phase angle (δ) & Reactive power (QD) to be find.
For good voltage profile , AVR can be used.

11. Slack Bus (or) Swing Bus (or) Reference Bus
In PS, load flows from the generator to load via Tr.Lines.
I2R loss occurs due to losses in Tr. Line Conductors
Power balance relations:
PL, QL are power losses in Tr. n/w
PGi, QGi Generators Power, PDi, QDi Demand Power
Known values are |V|, δ
Unknown values are P & Q
N N
PL = Σ PGi - Σ PDi
i= i=1
N N
QL = Σ QGi - Σ QDi
i= i=1

12. Solution for Load flow problems
Gauss- Seidel Load Flow Method
Newton- Raphson Load Flow Method
Fast-Decouple Load Flow Method
In above mentioned load flow methods, voltage solution is assume & the iteration process can be proceeded until the reach of convergence.

13. Gauss-Seidel Algorithm
Form Y bus matrix
Assume, Vk = Vk(spec)∟0⁰ at all generator buses.
Assume , Vk = 1 ∟0⁰ = 1+j0 at all load buses.
Iteration count setting (iter=1)
Let bus number i=1
If ‘i’ refer to generator bus go to step no.7,or else go to step 8
a. if ‘i’ refers to the slack bus go to step 9, or else go to step 7(b).
7. b. Compute Qi using, N
Qi cal =- Im [ Σ Vi* Yij Vj ]
j=1
QGi= Qi cal QLi

14. Contd…
Check for Q limit violation. If Qi(min) < QGi < Qi(max), then Qi(spec) = Qical If Qi(min) < QGi, then Qi(spec) = Qi(min) - QLi If Qi(max) < QGi, then Qi(spec) = Qi(max) - QLi If Q limit is violated , then treat this bus as P-Q bus till convergence is obtained 8. Compute Vi using the equation, j-1 n Vinew = 1 Pi(spec)-Qi(spec) – Σ Yij Vjnew - Σ Yij Viold Yij Viold * i=1 i=j+1 9. If ‘i’ is less than number of buses, increment i by 1 and go to step 6.

15. Contd…
10. Compare two successive iteration values for Vi If Vinew - Viold < tolerance , go to step Update new voltages as Vinew = Viold + α (Vinew - Viold) Viold = Vinew 12. Compute relevant quantities N Slack bus power, S1= Pi – j Qi = V*I = Vi* Σ Yij Vj j=1 Line flow, Sij = Pij + Qij = Vi [ Vi* - Vj*] Yij series* + |Vi|2 Yij* PLoss = Pij + P ji Q Loss = Qij + Qji 13. Stop the execution.

17. Disadvantage of Gauss Seidel Method i. Not suitable for larger systems
Advantage of Gauss Seidel Method i. Calculation are simple. ii. Programming task is lesser. iii. Used for small size system.
Disadvantage of Gauss Seidel Method
i. Not suitable for larger systems
ii. Required more no.of. iterations to reach convergence.
iii. Convergence time increases with size of the system.

18. Newton-Raphson Algorithm
Form Y-bus matrix
Assume flat start for starting voltage solution
δi⁰ = 0, for i=1,2,…N for all buses except slack bus
|Vi⁰| = 1.0, for i=M+1,M+2,….N (for all PQ bus.
|Vi| = |Vi| (Spec) , for all PV buses and Slack bus.
3. For load bus, calculate Pi cal and Qi cal
4. For PV buses, check Q-limit violation .
If Qi(min) < Qi cal < Qi(max), the bus acts as P-V bus.
If Qi cal > Qi(max), Qi(spec)=Qi(min)
If Qi cal < Qi(min), Qi(spec) = Qi(min), the P-V bus will act as P-Q bus.
5. Compute mismatch vector using,
∆ Pi = Pi(spec) – Pi cal
∆Qi = Qi(spec) - Qi cal

19. Contd….
6. Compute ∆ Pi(max) = max |∆ Pi|, i=1,2,…N(except Slack bus) ∆Qi (max) = max |∆Qi|, i=M+1….N 7. Compute Jacobian matrix using, ∂Pi |V| . ∂Pi ∂δ ∂|V| J = ∂Qi |V| . ∂Qi ∂δ ∂|V| 8. Obtain static correction vector using ∆ δ ∆ P = [J]-1 ∆ V ∆Q |V|

20. Contnd….
9. Update state vector using, V new = V old + ∆V = V old + [ ∆ V / |V old | ] = V old + [1+ {∆ V / |V old | }] δ = δ old +∆δ 10. This procedure is continued until, |∆ Pi | < ε and |∆Qi | < ε, otherwise go to step 3.

22. Advantage of Newton – Raphson Method i. suitable for large size system
Advantage of Newton – Raphson Method i. suitable for large size system. ii. It is faster, reliable &the results are accurate. iii. No.of. Iteration are less to reach convergence & also iterations are independent of the no.of.buses.
Disadvantage of Newton – Raphson Method
i. Programming logic is complex than GS Method
ii. Required more memory.
iii. No.of.calculation per iteration are higher than GS method

23. For the system show in fig
For the system show in fig. determine the voltage at the end of first iteration by Gauss Seidel method and also find the slack bus power, line flow and transmission loss. Assume base MVA as 100.

24. 1. What is Power System Analysis & write the components of power system? 2. Explain the requirements of planning the operation of a power system. 3. What is single line diagram & draw a simple diagram? 4. What are the advantages of per unit computation? 5. A generator rated at 30 MVA, 11 KV has a reactance of 20%. Calculate its per unit reactance for a base of 50 MVA and10KV. 6. What are the functions of power system analysis? 7. Define per unit analysis of any electrical network. 8. Write the equation for per unit impedance if change of base occurs. 9. What is Y- bus matrix & write its applications? 10. How loads are represented in reactance & impedance diagram? 11. What are the information that are obtained from a power flow study?

25. 12. Explain bus classification in power flow analysis with their known and unknown quantities?
13. Define Voltage control bus.
14. What do you mean by flat voltage start?
15. Distinguish between Gauss Seidel and Newton Raphson methods.
16. What is the need for load flow study?
17. What are the methods mainly used for solution of load flow study?
18. Write the quantities that are associated with each bus in a system.
19. What is the need for swing (or) slack bus?
20. Write is the advantage and disadvantage of Newton Raphson Method.
21. What is P-Q bus in power flow analysis?
22. What are the application of Z-Bus?
23.Write an equation for per unit impedance .