Power Flow Analysis

In Gauss Seidel method, the computations appear to be serial. Further, each component of new iteration depends upon all previously computed components. Updates cannot be done simultaneously. In addition to this, new iteration depends on the order in which equations are examined. If this ordering is changed, the components of new iteration (and not just their order) also change. These limitations persuade engineers and researchers to go for Newton Raphson method.

Advantages 

• Gauss Seidel method is easy to program. 
• Each iteration is relatively fast (computational order is proportional to number of branches and number of buses in the system).  
• Acquires less memory space than NR method.

Disadvantages

• Tends to converge relatively slowly, although this can be improved with acceleration.
• Has tendency to miss solutions, particularly on large systems.
• Tends to diverge on cases with negative branch reactance (common with compensated lines).  
• Need to program using complex numbers.

In high voltage transmission systems, the voltage angles between adjacent buses are relatively small. In addition, X/R ratio is high. These two properties result in a strong coupling between real power and voltage angle and between reactive power and voltage magnitude. In contrary, the coupling between real power and voltage magnitude, as well as reactive power and voltage angle, is weak. Considering adjacent buses, real power flows from the bus with a higher voltage angle to the bus with a lower voltage angle. Similarly, reactive power flows from the bus with a higher voltage magnitude to the bus with a lower voltage magnitude.

Fast-decoupled power flow technique includes two steps: 

• decoupling real and reactive power calculations.
• obtaining of the Jacobian matrix elements directly from the Y-bus.

As the size of matrix becomes very large for a big bus system so for faster and less memory allocation, we prefer decoupled load flow where we take P independent of V and Q Independent of δ, and thus those Jacobian elements are taken as zero.

Advantages 

• The convergence is faster than other methods.
• The memory requirement is very less than the other methods like as Newton Raphson method, Gauss-Seidel method, etc.
• This method is less complicated than other methods, therefore it is more easy method to calculate the power flow.
• The number of iteration and size of equation used is less.

Disadvantages

• Take more iterations though time needs for each iteration is less than NR method
• The accuracy of the fast-decoupled load flow is mainly dependent on three factors:
  • System size and structure;
  • Convergence tolerances; and
  • Level of system Loading

Particularly in large systems with heavy loading the relatively small error in the state variables may cause larger errors in real and reactive power flow, but these errors are small in comparison with the line ratings. The accuracy of the solution is a controllable parameter and it can be improved by using a smaller convergence tolerance.

Comparison of the Load Flow Methods 

Load Flow Method	Speed	Accuracy	Solution Robustness
Gauss-Seidel	Very Slow	Approximate	Robust
Newton Raphson	Slow	Accurate	Robust
Fast Decoupled	Fast	Accurate	Less Robust

Industry Application of Power Flow Methods

Commercial power systems are complicated. It is not possible to analyze power flow through hand calculations. Physical models of power systems were analyzed through network analyzers in laboratories between 1929 and early 1960. Afterwards, invention of digital computers replaced the analog methods with numerical methods. Initially, linear methods were proposed to analyze power flow analysis. Among these, Cramer's method, Gauss elimination and LU factorization are notable. However, these methods cannot handle complex, nonlinear and big power systems. Therefore, iterative techniques i.e., Gauss Seidel method, Newton Raphson method are developed to solve complex power systems.

There are a number of very high-quality commercial power flow programs on the market today, some of which include those developed by the Electric Power Research Institute (EPRI), Power Technologies Incorporated (PTI), Operation Technology, Inc., and EDSA. Most of today's commercial software packages are menu-driven from a Windows environment. Few of the commonly used software are discussed briefly as below:

• ETAP software is used for simulation because of its extension of real time intelligent power management systems for monitoring, controlling, automating and optimizing power systems. It is a high impact software used for power flow analysis is generation, transmission and distribution systems of electric power engineering.

• PowerWorld Simulator is a software package designed to simulate high voltage power systems up to 100,000 buses. PowerWorld uses the Newton-Raphson iteration method, which provides an efficient and accurate solution. It also computes the Jacobian (Admittance Matrix), so that the one-line diagram characteristics can be ported to other analysis programs.

• CYME is a software which main objective is to analyze the steady-state performance of the power system under various operating conditions. It is the basic analysis tool for the planning, design and operation of any electrical power systems, be they distribution, industrial or transmission networks. The Power Flow module utilizes state-of-the-art sparse matrix/vector methods and multiple solution algorithms.