load flow analysis
CHAPTER 3
LOAD FLOW ANALYSIS
[CONTENTS: Review of solution of equations, direct and iterative methods, classification of buses, importance of slack bus and YBUS based analysis, constraints involved, load flow equations, GS method: algorithms for finding the unknowns, concept of acceleration of convergence, NR method- algorithms for finding the unknowns, tap changing transformers, Fast decoupled load flow, illustrative examples]
REVIEW OF NUMERICAL SOLUTION OF EQUATIONS
The numerical analysis involving the solution of algebraic simultaneous equations forms the basis for solution of the performance equations in computer aided electrical power system analyses, such as during linear graph analysis, load flow analysis
(nonlinear equations), transient stability studies (differential equations), etc. Hence, it is necessary to review the general forms of the various solution methods with respect to all forms of equations, as under:
1. Solution Linear equations:
* Direct methods:
- Cramer’s (Determinant) Method,
- Gauss Elimination Method (only for smaller systems),
- LU Factorization (more preferred method), etc.
* Iterative methods:
- Gauss Method
- Gauss-Siedel Method (for diagonally dominant systems)
2. Solution of Nonlinear equations:
Iterative methods only:
- Gauss-Siedel Method (for smaller systems)
- Newton-Raphson Method (if corrections for variables are small)
3. Solution of differential equations:
Iterative methods only:
- Euler and Modified Euler method,
- RK IV-order method,
- Milne’s predictor-corrector method, etc.
It is to be observed that the nonlinear and differential equations can be solved only by the iterative methods. The iterative methods are characterized by the various performance features as under:
Selection of initial solution/ estimates
Determination of fresh/ new estimates during each iteration
Selection of number of iterations as per tolerance limit
Time per iteration and
LOAD FLOW ANALYSIS
[CONTENTS: Review of solution of equations, direct and iterative methods, classification of buses, importance of slack bus and YBUS based analysis, constraints involved, load flow equations, GS method: algorithms for finding the unknowns, concept of acceleration of convergence, NR method- algorithms for finding the unknowns, tap changing transformers, Fast decoupled load flow, illustrative examples]
REVIEW OF NUMERICAL SOLUTION OF EQUATIONS
The numerical analysis involving the solution of algebraic simultaneous equations forms the basis for solution of the performance equations in computer aided electrical power system analyses, such as during linear graph analysis, load flow analysis
(nonlinear equations), transient stability studies (differential equations), etc. Hence, it is necessary to review the general forms of the various solution methods with respect to all forms of equations, as under:
1. Solution Linear equations:
* Direct methods:
- Cramer’s (Determinant) Method,
- Gauss Elimination Method (only for smaller systems),
- LU Factorization (more preferred method), etc.
* Iterative methods:
- Gauss Method
- Gauss-Siedel Method (for diagonally dominant systems)
2. Solution of Nonlinear equations:
Iterative methods only:
- Gauss-Siedel Method (for smaller systems)
- Newton-Raphson Method (if corrections for variables are small)
3. Solution of differential equations:
Iterative methods only:
- Euler and Modified Euler method,
- RK IV-order method,
- Milne’s predictor-corrector method, etc.
It is to be observed that the nonlinear and differential equations can be solved only by the iterative methods. The iterative methods are characterized by the various performance features as under:
Selection of initial solution/ estimates
Determination of fresh/ new estimates during each iteration
Selection of number of iterations as per tolerance limit
Time per iteration and