Gauss-Seidel Load Flow Analysis: A Power System Lab Exercise, Study notes of Power Distribution and Utilization

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2018/2019

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Power System Analysis and Design Lab
Lab 5
26
Name: _______________________ ID: ____________________ Date: ____/____/_______
Experiment # 5:
Load Flow Analysis by Gauss-Seidel Method
(CLO 4, PLO 1,5)
Objective:
โ€ข To develop a computer program to solve the set of nonlinear load flow equations using
Gauss-Seidal load flow iterative algorithm.
โ€ข To understand the basic aspects of steady state analysis of power systems that are required
for effective planning and operation of power systems.
โ€ข To understand the formulation of load flow model in complex form and a simple method
of solving load flow problems of small sized system using Gauss-Seidal iterative algorithm.
Software Required: MATLAB
Theory:
Load flow analysis is the study conducted to determine the steady state operating condition of the
given system under given conditions. This analysis is performed on a symmetrical steady-state
operating condition of a power system under โ€˜normalโ€™ mode of operation and aims at obtaining
bus voltages and line/transformer flows for a given load condition. This information is essential
both for long term planning and next day operational planning.
In long term planning, load flow analysis helps in investigating the effectiveness of alternative
plans and choosing the โ€˜bestโ€™ plan for system expansion to meet the projected operating state. In
operational planning, it helps in choosing the โ€˜bestโ€™ unit commitment plan and generation
schedules to run the system efficiently for them next dayโ€™s load condition without violating the
bus voltage and line flow operating limits.
Many numerical algorithms have been developed and Gauss Seidel method is one of such
algorithms. The Gauss Seidal method is an iterative algorithm for solving a set of non- linear
algebraic equations. The relationship between network bus voltages and currents may be
represented by either loop equations or node equations. Node equations are normally preferred
because the number of independent node equation is smaller than the number of independent loop
equations.
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Name: _______________________ ID: ____________________ Date: ____/____/_______

Experiment # 5 :

Load Flow Analysis by Gauss-Seidel Method

(CLO 4 , PLO 1,5)

Objective:

  • To develop a computer program to solve the set of nonlinear load flow equations using Gauss-Seidal load flow iterative algorithm.
  • To understand the basic aspects of steady state analysis of power systems that are required for effective planning and operation of power systems.
  • To understand the formulation of load flow model in complex form and a simple method of solving load flow problems of small sized system using Gauss-Seidal iterative algorithm. Software Required: MATLAB Theory: Load flow analysis is the study conducted to determine the steady state operating condition of the given system under given conditions. This analysis is performed on a symmetrical steady-state operating condition of a power system under โ€˜normalโ€™ mode of operation and aims at obtaining bus voltages and line/transformer flows for a given load condition. This information is essential both for long term planning and next day operational planning. In long term planning, load flow analysis helps in investigating the effectiveness of alternative plans and choosing the โ€˜bestโ€™ plan for system expansion to meet the projected operating state. In operational planning, it helps in choosing the โ€˜bestโ€™ unit commitment plan and generation schedules to run the system efficiently for them next dayโ€™s load condition without violating the bus voltage and line flow operating limits. Many numerical algorithms have been developed and Gauss Seidel method is one of such algorithms. The Gauss Seidal method is an iterative algorithm for solving a set of non- linear algebraic equations. The relationship between network bus voltages and currents may be represented by either loop equations or node equations. Node equations are normally preferred because the number of independent node equation is smaller than the number of independent loop equations.

Problem Formulation: The performance equation of the power system may be written of [I bus] = [Y bus] [V bus] (1) Selecting one of the buses as the reference bus, we get (n-1) simultaneous equations. The bus loading equations can be written as Ii = Pi-jQi / Vi* (i=1,2, 3โ€ฆโ€ฆโ€ฆ. n) (2) Where, Pi=Re [โˆ‘ ๐‘› ๐‘˜= 1 Vi โˆ— Yik Vk] (3) Qi= - Im [โˆ‘ ๐‘› ๐‘˜= 1 Vi โˆ— Yik Vk] (4) The bus voltage can be written as ๐‘‰๐‘–= 1.0/๐‘Œ๐‘–๐‘– [Ii โˆ’ โˆ‘ ๐‘› ๐‘—= 1 ๐‘Œ๐‘–๐‘— ๐‘‰๐‘–๐‘œ] jโ‰ i (i=1, 2โ€ฆโ€ฆโ€ฆโ€ฆn) & i โ‰  slack bus Substituting Ii in the expression for Vi, we get ๐‘‰๐‘–new= 1.0/๐‘Œ๐‘–๐‘– [Pi โˆ’ JQi ๐‘‰๐‘–๐‘œ^ โˆ—^

โˆ’ โˆ‘^ ๐‘› ๐‘—= 1 ๐‘Œ๐‘–๐‘— ๐‘‰๐‘–๐‘œ]

We get ๐‘‰๐‘–new=1/๐‘Œ๐‘–๐‘– [Pi โˆ’ JQi ๐‘‰๐‘–๐‘œ^ โˆ—^

โˆ’ โˆ‘ ๐‘› ๐‘—= 1 ๐‘Œ๐‘–๐‘—๐‘‰๐‘—๐‘›^ โˆ’โˆ‘ ๐‘› ๐‘—=๐‘–+ 1 ๐‘Œ๐‘–๐‘—๐‘‰๐‘–๐‘œ]

The above equation is the required formula. This equation can be solved for voltages in interactive manner. During each iteration, we compute all the bus voltage and check for convergence is carried out by comparison with the voltages obtained at the end of previous iteration. After the solutions is obtained. The stack bus real and reactive powers, the reactive power generation at other generator buses and line flows can be calculated.

Flowchart: START Read

  1. Primitive Y matrix
  2. Bus incidence matrix A
  3. Slack bus voltages
  4. Real and reactive bus powers Pi& Qi
  5. Voltage magnitudes and their limits Form Y bus Make initial assumptions Compute the parameters A i (^) for i=m+1,โ€ฆ,n and B ik (^) for i=1,2,โ€ฆ,n; k=1,2,โ€ฆ,n Set i teration count r= Set bus count i=2 and V max= Test for type of bus Q (^) i(r+1)^ > Qi, max Q^ i (r+1) (^) < Q i,min Compute Q (^) i(r+1) Q (^) i (r+1)^ = Q (^) i,max Q^ i (r+1) (^) = Q i,min Compute A^ i (r+1) Compute A (^) i Compute V (^) i (r+1) Compute ฮด i (r+1) (^) and V (^) i (r+1)^ = |Vi s|/ฮดi (r+1)

Lab Task: The figure 1.1 shows the single line diagram of a simple 3 buses power system with generator at bus 1. The magnitude at bus 1 is adjusted to 1.05pu. The scheduled loads at buses 2 and 3 are marked on the diagram. Line impedance are marked in pu. The base value is 100kVA. The line charging susceptances are neglected. Determine the phasor values of the voltage at the load buses 2 and 3.

Replace Vi

r

by Vi

(r+1)

and

advance bus counti = i+

Is i<=n Is V (^) max <=

Advance iteration

count, r = r+

Compute slack bus power ๐‘ƒ 1 + ๐‘—๐‘„ 1 and all line flows

B

A

Figure 2. Figure 1.

2. What are the advantages and disadvantages of Gauss Seidal method?

Conclusion:

Instructorโ€™s Signature Marks Obtained